A world-class program incorporating the highly effective Readiness-Engagement-Mastery model of instructional design
Enhanced support for effective implementation of Readiness-Engagement-Mastery pedagogy
Digital PR1ME Mathematics Teaching Hub for additional teaching resources and online professional development
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Chapter
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TM Mathematics is a world-class program that works for every student and teacher. It incorporates:
• the teaching and learning best practices from the global top performers in international studies such as Trends in International Mathematics and Science Study (TIMSS) and Programme for International Student Assessment (PISA): Singapore, Hong Kong and Republic of South Korea, and
• Singapore’s Mathematics Curriculum Framework in which mathematical problem solving is the central focus.
Turn to the pages listed below to understand how TM Mathematics:
• supports lear ning to mastery of all students with a pedagogical framework and instructional design based on proven teaching and learning practices,
• integrates assessment for learning so that every child can succeed, and
• offers a comprehensive, accessible suite of teaching and learning resources for flexibility in planning and instruction, and lear ning.
Supports learning to mastery of all students because it incorporates a pedagogical framework and instructional design based on proven teaching and learning practices of global top-performing education systems.
The central focus of the TM Mathematics Framework is problem solving. Learning progressions ensure focus and coherence in content using an instructional design that incorporates the Readiness-Engagement-Mastery model.
Learning experiences based on the Readiness-Engagement-Mastery instructional model
Learning mathematics via problem solving
Development and communication of mathematical thinking and reasoning
Learning mathematics by doing mathematics
Focused and coherent curriculum based on learning progression principles
Integrates assessment for learning to enable every child to succeed.
Offers a comprehensive, accessible suite of teaching and learning resources for flexibility in planning, instruction and lear ning.
The instructional design of each chapter comprises learning experiences that consistently involve three phases of learning: Readiness, Engagement, and Mastery so that teaching and learning mathematics is effective, measurable and diagnostic.
Because mathematical knowledge is cumulative in nature, a student’s readiness to learn new concepts or skills is vital to learning success.
Let’s Remember systematically assesses students’ grasp of the required prior knowledge and provides an accurate evaluation of their readiness to learn new concepts or skills.
The objective and chapter reference for each task are listed so that teachers can easily reteach the relevant concepts from previous chapters or grades.
Let's Remember
Recall:
1. Converting time from the 12-hour clock notation to the 24-hour clock notation (CB4 Chapter 15)
2. Converting time from the 24-hour clock notation to the 12-hour clock notation (CB4 Chapter 15)
Explore encourages mathematical curiosity and a positive learning attitude by getting students to recall the requisite prior knowledge, set learning goals and track their learning as they progress through the unit.
3. Finding the duration of a time interval given time in 24-hour clock notation (CB4 Chapter 15)
EXPLORE
Have students read the word problem on CB p. 278. Discuss with students the following questions:
•Do you have friends or family living in other parts of the world?
•Do they live in a different time zone ? What is the time difference from where you are living?
•Have you tried to communicate with them before? What was the mode of communication? How was your experience like?
Have students form groups to complete the tasks in columns 1 and 2 of the table. Let students know that they do not have to solve the word problem. Ask the groups to present their work.
Tell students that they will come back to this word problem later in the chapter.
Questions are provided for teachers to conduct a class discussion about the task. Students work in groups to recall what they know, discuss what they want to learn and keep track of what they have learned.
This is the main phase of learning for which TM Mathematics principally incorporates three pedagogical approaches to engage students in learning new concepts and skills.
Both concept lessons and formative assessment are centered on the proven activity-based Concrete-Pictorial-Abstract (CPA) approach.
CPA in formative assessment provides feedback to teachers on the level of understanding of students.
CPA in concept lessons consistently and systematically develops deep conceptual understanding in all students.
Concept lessons progress from teacher demonstration and shared demonstration to guided practice, culminating in independent practice and problem solving.
In Let’s Learn, teachers introduce, explain and demonstrate new concepts and skills. They draw connections, pose questions, emphasize key concepts and model thinking.
Students engage in activities to explore and learn mathematical concepts and skills, individually or in groups. They could use manipulatives or other resources to construct meanings and understandings. From concrete manipulatives and experiences, students are guided to uncover abstract mathematical concepts.
Let’s Do is an opportunity for students to work collaboratively on guided practice tasks.
Students work on Let’s Practice tasks individually in class. Teachers assign Exercises in the Practice Book as independent practice for homework.
This approach is about learning through guided enquiry. Instead of giving the answers, teachers lead students to explore, investigate and find answers on their own. Students learn to focus on specific questions and ideas, and are engaged in communicating, explaining and reflecting on their answers. They also lear n to pose questions, process information and data, and seek appropriate methods and solutions.
Purposeful questions provided in the Teacher’s Guide help teachers to encourage students to explain and reflect on their thinking.
The three approaches detailed above are not mutually exclusive and are used concurrently in different parts of a lesson. For example, the lesson could start with an activity, followed by teacher-led enquiry and end with direct instruction.
There are multiple opportunities in each lesson for students to consolidate and deepen their learning.
1.
Practice helps students achieve mastery in mathematics. Let’s Practice in the Coursebook, Exercises in the Practice Book and Digital Practices incorporate systematic variation in the item sets for students to achieve proficiency and flexibility. These exercises provide opportunities for students to strengthen their understanding of concepts at the pictorial and abstract levels and to solve problems at these levels.
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2.
There are a range of activities, from simple recall of facts to application of concepts, for students to deepen their understanding.
Think About It and Math Journal provide opportunities for students to reflect on what they have lear ned, and in doing so, consolidate and deepen their learning.
Assessment after each chapter and quarterly Reviews provide summative assessment for consolidation of learning throughout the year.
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2.
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Summative assessments help the teacher measure
Mind Stretcher, Create Your Own, Mission Possible and Mathematical Modeling immerse students in problem solving tasks at various levels of difficulty.
Students
Every lesson is designed to develop deep conceptual
Evidenced through its sustained performance on international benchmarking assessments, Singapore’s Mathematics Curriculum Framework (shown in the diagram below) enumerates the critical, inter-related elements of an effective mathematics program and identifies mathematical problem solving as central to mathematics learning.
• Beliefs
• Interest
• Appreciation
• Confidence
• Perseverance
• Numerical calculation
• Algebraic manipulation
• Spatial visualization
• Data analysis
• Measurement
• Use of mathematical tools
• Estimation
• Monitoring of one's own thinking
• Self-regulation of learning
Source: www.moe.gov.sg
• Numerical
• Algebraic
• Geometric
• Statistical
• Probabilistic
• Analytical
• Reasoning, communication, and connections
• Applications and modelling
• Thinking skills and heuristics
TM Mathematics incorporates this framework in its instructional design and develops mathematical problem-solving ability through five-inter-related components: Concepts, Skills, Processes, Metacognition and Attitudes.
In , problem solving is not only a goal of learning mathematics, it is also a tool of learning.
81 – 45 = 36
The number is 36 more than 10.
10 + 36 = 46
At the beginning of each chapter, Explore provides the opportunity to engage prior knowledge in problem solving, leading to independent thinking and greater ownership of learning.
3.
Throughout the chapter, students revisit the problem and persevere in solving it.
Mathematical problems are used as contexts for introducing concepts and to develop deep conceptual understanding.
Concepts are introduced in Let’s Learn in each unit via problems that the students solve using the Concrete-Pictorial-Abstract approach. Teachers lead students to investigate, explore and find answers on their own. Students are thus guided to uncover abstract mathematical concepts and ideas.
Developing a problem-solving mindset –students can extrapolate from what they know and apply their knowledge of mathematics in a range of situations, including new and unfamiliar ones.
Students learn to solve problems by applying concepts, skills and processes learned to various problem situations both familiar and non-routine. Each chapter ends with a problem-solving lesson.
Word problems help students recognize the role that mathematics plays in the world by applying the concepts and skills they have learned within a context.
Word problems assess students’ ability to apply the knowledge learned.
Mind stretchers are specially crafted problems that require students to apply concepts and skills to unusual or complex problem situations and solve the problems using heuristics and higher order thinking skills. Students learn how to select, innovate and compare their strategies.
Teachers will guide students through the worked out examples in the coursebooks. Additional mind stretchers are provided in the Teaching Hub for students to try out such questions on their own.
Create Your Own is a proven problem-posing and problem-solving activity in which students are encouraged to explore, share failures and successes, and question one another In doing so, they become more confident in posing problems and persist with challenging problems.
Students work in pairs or groups to create a word problem, exchange the problem with others, solve the problem and present their work to the class. Students have to explain how they come up with the word problem before presenting the solution.
Building on the mathematics concepts and skills learned, Mission Possible tasks introduce students to computational thinking, an important foundational skill in STEM education.
Prompts are provided in the teacher’s guide for teachers to guide students through the stages of computational thinking (decomposition, pattern recognition, abstraction and algorithms) to solve the problem.
Decomposition
Students break down the problem into smaller and simpler problems.
Pattern recognition
Students analyze the information and look for a pattern.
Abstraction
Students focus on information that will help them solve the problem and ignore the irrelevant details.
Algorithms
Students provide a step-by-step solution for the problem.
MISSION POSSIBLE
Have students complete the task on CB p. 329 independently. Point out to students that the bot is facing the line of symmetry. Go through the task using the prompts given below.
1. Decomposition
Ask: How can we break down the problem into smaller and simpler problems? (Answer varies. Sample: Identify the squares that need to be shaded to complete the figure. Draw a continuous path through the shaded squares. Write down each step to get from the first square to the last square.)
2. Pattern Recognition Ask: What if the bot is not facing the line of symmetry? Will the first step still require the bot to move forward? (No) What will the first step for the bot be in this case? (To make a turn) When can the first step for the bot to go forward be? (When the bot is in a shaded square and facing the line of symmetry) When will the first step require the bot to make a turn? (When the bot is not facing the line of symmetry)
3. Abstraction Ask: What information will help you solve the problem? (Which grid squares are shaded to form the symmetric figure, where the line of symmetry is, where the bot is, the direction the bot is facing, the restriction that the bot should not return to any grid squares previously colored, the words to use, the steps given, the labels on the grid)
4. Algorithms Have a student describe the steps he/she used to solve the problem and present the solution. Guide students to generalize the steps needed for the bot to complete a symmetric figure when: a) the bot is in a shaded square facing the line of symmetry. b) the bot is in a shaded square not facing the line of symmetry.
Mathematical Modeling is a way of connecting mathematics with real-world problems. Students represent a real-world problem using mathematics and formulate a model which may describe, explain or predict the real-world problem. The formulated model is thereafter used to obtain a solution to the real-world problem.
Phase 1: Discuss Introduce the real-world problem to the students.
Phase 2: Manipulate Students create a suitable mathematical model or framework for the given problem. They may decide on the variables involved, make sense of data and define terms.
Phase 3: Experiment and Verify Students construct the model. This usually involves the use of concrete materials or pictorial representations.
Phase 4: Present Students present their model with supporting findings and observations.
Phase 5: Reflect Students examines the limitations of the model and extends it to other similar real-world situations.
School Camp
Your school is planning a 3 days 2 nights school camp for all the grade 4 students. The camp site is 235 kilometers away from the school. Everyone will be going to the camp site by rental bus, van or both bus and van.
Work in groups to plan the number of buses and/or vans needed to fit all the people who will be going to the camp site with the least cost.
1. What are some questions you need to ask to complete the task?
Present your findings in a suitable format
a) How many vehicles do you need? b) How much will it cost to rent these vehicles?
TM Mathematics explicitly teaches students to use various thinking skills and heuristics to solve mathematical problems. Thinking skills are skills that can be used in a thinking process, such as classifying, comparing, sequencing, analyzing parts and wholes, and spatial visualization. Heuristics are problem-solving strategies.
TM Mathematics teaches the following heuristics:
Use a representation
Make a calculated guess
Walk through the process
Change the problem
• Draw a picture
• Make a list
• Choose an operation
• Guess and check
• Look for a pattern
• Make a supposition
• Use logical reasoning
• Act it out
• Work backwards
• Restate the problem in another way
• Solve part of the problem
This problem is solved using the guess and check strategy. This strategy provides a starting point for solving problems. Students should modify their subsequent guesses based on the results of the earlier guesses instead of making random guesses.
4.2 Mind stretcher
Let's Learn
The bar model method, a key problem-solving strategy in TM Mathematics, helps students understand and draw representations of a problem using mathematical concepts to solve the problem.
In arithmetic word problems, the bar model method helps students visualize the situations involved so that they are able to construct relevant number sentences. In this way, it helps students gain a deeper understanding of the operations they may use to solve problems.
CREATE YOUR OWN
Bottle A contains 75 grams of salt.
Bottle B contains 15 grams more salt than bottle A.
a) What is the mass of salt in bottle B?
b) If Mrs. Chen uses 8 grams of salt from bottle B, what is the mass of salt left in bottle B?
Read the problem. Change the masses in the word problem. How did you decide what masses to use?
Next, solve the word problem. Show your work clearly. What did you learn?
The model method lays the foundation for learning formal algebra because it enables students to understand on a conceptual level what occurs when using complex for mulas and abstract representations. Using the model method to solve algebraic word problems helps students derive algebraic expressions, construct algebraic equations and simplify algebraic equations.
3.3 Mind stretcher
Let's Learn Let's Learn
Let the mass of Brian be x
Brian and his father have a total mass of 90 kilograms. Brian’s father is 50 kilograms heavier than Brian. What is Brian’s mass? I can draw a
x + y = 90
y = 50 + x
x + y = 90
x + 50 + x = 90
2x + 50 = 90
2x = 40
x = 20
1 Plan what to do.
the
2
Let the mass of Brian’s father be y
model to compare their masses. What is the total mass of Brian and his father? Who is heavier? How many kilograms heavier? What do I have to find? Understand the problem.
Brian’s mass is 20 kilograms.
Step-by-step guidance in the lesson plans as well as complete worked solutions assist the teachers in teaching students how to solve mathematical problems using the bar model method with confidence.
Develops a growth mindset in every student –the understanding that each effort is instrumental to growth and to be resilient and persevere when initial efforts fail.
A unique 5-step Understand-Plan-Answer-Check-PlusTM (UPAC+TM) problem-solving process that ensures students’ problem-solving efforts are consistently scaffolded and students develop critical and creative thinking skills to not only solve the problem but also to consider alternatives that may be viable.
The “+” in the UPAC+TM problem-solving process, unique to TM Mathematics, is designed to develop “the top skills and skill groups which employers see as rising in prominence … include groups such as analytical thinking and innovation, complex critical thinking and analysis as well as problem-solving” (The Future of Jobs Report 2020, World Economic Forum). It is a crucial step that develops flexible problem solvers who can evaluate information, reason and make sound judgments about the solutions they have crafted, after considering possible alter native solutions. This is critical for solving real world problems.
1 2 3 4 5
U Understand the problem.
• Can you describe the problem in your own words?
• What information is given?
• What do you need to find?
• Is there information that is missing or not needed?
P Plan what to do.
• What can you do to solve the problem?
• Which strategies/heuristics can you use?
Work out the A Answer.
• Solve the problem using your plan in Step 2.
• If you cannot solve the problem, make another plan.
• Show your work clearly.
• Write the answer statement.
C Check if your answer is correct.
• Read the question again. Did you answer the question?
• Does your answer make sense?
• Is your answer correct?
• How can you check if your answer is correct?
• If your answer is not correct, go back to Step 1.
+ Plus
• Is there another way to solve this problem?
• Compare the methods.
• Which is the better method? Why?
• If your answer is not correct, go back to Step 1.
Being able to reason is essential in making mathematics meaningful for all students.
Students are provided with opportunities to consolidate and deepen their learning through tasks that allow them to discuss their solutions, to think aloud and reflect on what they are doing, to keep track of how things are going and make changes when necessary, and in doing so, develop independent thinking in problem solving and the application of mathematics.
In Think About It, purposeful questions based on common conceptual misunderstandings or procedural mistakes are posed. Using question prompts as scaffolding, students think about the question, communicate their reasoning and justify their conclusions. Using the graphic organizers in Think About It, teachers act as facilitators to guide students to the correct conclusion, strengthen students’ mathematical knowledge and provide opportunities for students to communicate their reasoning and justify their conclusions.
As students get into the habit of discussing the question, anxieties about mathematical communication are eased, their mathematical knowledge is strengthened and metacognitive skills are honed. Teachers get an insight into students’ understanding and thought processes by observing the discussions.
This question highlights a conceptual misconception about comparison of fractions. Students often compare fractions without realizing that the wholes must be the same for the comparison to be valid.
This question shows a procedural mistake about subtraction of whole numbers. It is common for students to mix up the addition and subtraction algorithms.
Thinking mathematically is developed as a conscious habit.
Math Journal tasks are designed for students to use the prompts to reflect, express and clarify their mathematical thinking, and to allow teachers to observe students’ growth and development in mathematical thinking and reasoning.
There are concept-based and process-based journaling tasks in TM Mathematics Teaching Hub.
Concept-based
Process-based
Let's Practice
Task 1 requires students to count by threes to find the total number of objects and complete the multiplication sentences. Task 2 requires students to count by threes to complete the patterns.
Students learn through guided enquiry, a process during which instead of giving the answers, teachers lead students to explore, investigate and find answers on their own by posing purposeful questions provided in the Teacher’s Guide. Purposeful questions are used to gather information, probe thinking, make the mathematics visible and encourage reflection and justification. Posing purposeful questions helps to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.
1.2 Using dot cards
Let's Learn
Objectives:
• Observe the commutative and distributive properties of multiplication
• Relate two multiplication facts using ‘3 more’ or ‘3 less’
1.2 Using dot cards Let's
• Build up the multiplication table of 3 and commit the multiplication facts to memory
Materials:
• Dot Card F (BM10.1): 1 copy per group, 1 enlarged copy for demonstration
• Dot Card G (BM10.2): 1 copy per group, 1 enlarged copy for demonstration
•Counters
Resources:
• CB: pp. 195–197
• PB: p. 127
(a) Stage: Concrete Experience Draw 6 circles on the board and stick 3 counters in each circle.
Ask: How many counters are there in each group? (3) How many groups are there? (6)
Say: We have 6 groups of 3 counters.
Stage: Pictorial Representation
Say: We can use a dot card to help us find the total number of counters. Have students work in groups. Distribute counters and a copy of Dot Card F (BM10.1) to each group. Stick an enlarged copy of Dot Card F (BM10.1) on the board. Put counters on the three circles in the first row of the dot card.
Say: There is 1 row of counters. There are 3 counters in 1 row. have shown 1 group of 3.
Ask: How do we show 6 groups of 3 on the dot card? (Put counters on 6 rows of the dot card.)
Demonstrate how the counters are to be placed on the dot card to show 6 groups of 3.
The activity-based Concrete-Pictorial-Abstract (CPA ) approach is a key instructional strategy advocated in the Singapore approach to mathematics learning. In TM Mathematics, the CPA approach is embedded in the learning experiences:
Concept Development
(Objective: Developing deep conceptual understanding): Let’s Learn
Formative Assessment
(Objective: Evaluating levels of understanding): Let’s Do
Summative Assessment
(Objective: Evaluating conceptual mastery and procedural fluency): Let’s Practice, Practice Book Exercises, Digital Practice
Each Let’s Learn segment provides a hands on, teacher-facilitated experience of concepts through the CPA stages.
Concrete
Students use manipulatives or other resources to solve a problem. Through these activities they explore and learn mathematical concepts and skills, individually or in groups, to construct meanings and understandings.
Pictorial
Pictorial representation of the objects used to model the problem in the Concrete stage enables students to see the connections between mathematical ideas and the concrete objects they handled.
Abstract
Once conceptual understanding is developed, students learn to represent the concept using numbers and mathematical symbols.
Throughout the activity, the teacher observes what the students say and do and provides feedback to students.
The CPA approach to mathematics instruction and learning enables students to make and demonstrate mathematical connections, making mathematical understanding deep and long-lasting.
Within each concept lesson, Let’s Do provides vital feedback to the teacher to understand the level of conceptual understanding of each student and to make appropriate instructional decisions for students.
The tasks in Let’s Do are systematically varied so that as students move from one task to the next, the teacher is able to gauge their level of understanding of the concept and if they can progress to independent work.
Task 1(a) requires students to add like fractions within 1 whole with pictorial aid. Task 1(b) is an extension of Task 1(a). It requires students to simplify the answer after adding the fractions.
Let’s Practice, Practice Book Exercises and Digital Practice help students to transition their understanding of concepts from pictorial to abstract levels.
Practices start with pictorial tasks, moving on to abstract tasks with pictorial aids and finally solely abstract tasks to help students make the transition from pictorial to abstract levels.
Coherent framework, spiral curriculum.
Singapore’s Mathematics Curriculum Framework in which mathematical problem solving is the central focus is at the center of the curriculum design of TM Mathematics. The framework stresses conceptual understanding, skills proficiency and mathematical processes and duly emphasizes metacognition and attitudes. It also reflects the 21st century competencies.
Mathematics is hierarchical in nature. TM Mathematics has a focused and coherent content framework and developmental continuum in which higher concepts and skills are built upon the more foundational ones. This spiral approach in the building up of content across the levels is expressed as four Learning Progression Principles that are a composite of the successful practices and lear ning standards of the top performing nations, and, are unique to TM Mathematics.
INESS Metacognition Processes Concepts Skills Attitudes
1 3 MASTERY ENGAGEMENT
2
The
careful spiral sequence of successively more complex ways of reasoning about mathematical concepts – the learning progressions within – make the curriculum at the same time, rigorous and effective for all learners.
Learning
Progression Principle 1:
Deep focus on fewer topics builds a strong foundation.
The early learning of mathematics is deeply focused on the major work of each grade— developing concepts underlying arithmetic, the skills of arithmetic computation and the ability to apply arithmetic. This is done to help students gain strong foundation, including a solid understanding of concepts, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the classroom.
Across
Learning Progression Principle 2:
Topics within strands are sequenced to support in-depth and efficient development of mathematics content. New learning is built on prior knowledge. This makes learning efficient, while revisiting concepts and skills at a higher level of difficulty ensures in-depth understanding.
Example
Strand: Numbers and Operations
Grade 1
Topic: Numbers 0 to 10
Development of number sense
• counting
• reading and writing numbers
• comparing numbers
• by matching • by counting
Topic: Number Bonds
Number bonds (part-part-whole relationship):
• 3 and 2 make 5.
• 4 and 1 make 5.
Topic: Addition
Addition (part-part-whole):
• 3 + 2 = 5 part part whole
Topic: Subtraction
Subtraction (part-part-whole):
• 5 – 3 = 2 whole part part
Topic: Numbers to 20
• counting and comparing
• ordering
Topic: Addition and Subtraction
• Addition within 20
• Subtraction within 20
• Students first learn to count, read and write numbers and to compare numbers.
• The concept of number bonds, that the whole is made up of smaller parts, builds on students’ knowledge of counting and comparing.
• The part-part-whole relationship between numbers forms the foundation for understanding addition and subtraction, and the relationship between these operations.
• Counting and comparing are revisited at a higher level of difficulty and are extended to ordering.
• Addition and subtraction are revisited and the concept of regrouping is introduced.
Learning Progression Principle 3:
Sequencing of learning objectives within a topic across grades is based on a mathematically logical progression.
Learning objectives within a topic are sequenced across grades according to a mathematically logical progression.
Example
Strand: Numbers and Operations
Topic: Fractions
Grade 1:
• Halves and quarters
Grade 2:
• Halves, thirds and quarters
• Naming fractions with denominator up to 12
Grade 3:
• Comparison of fractions
• Equivalent fractions
• Addition and subtraction of like and related fractions within 1 whole
Grade 4:
• Mixed numbers and improper fractions
• Fraction and division
• Addition and subtraction of like and related fractions greater than 1 whole
• Multiplication of a fraction and a whole number
Grade 5:
• Addition and subtraction of unlike fractions
• In grades 1 and 2, conceptual understanding of fractions is developed. Students lear n to recognize and name fractions.
• In grade 3, students learn to compare fractions. Equivalent fractions are introduced to help students add and subtract fractions.
• In grades 4 and 5, mixed numbers and improper fractions are introduced. The complexity of operations is also expanded to cover fractional numbers greater than one whole as well as multiplication and division.
Learning Progression Principle 4: Purposeful sequencing of learning objectives across strands deepens links and strengthens conceptual understanding.
The ordering of content for one topic is frequently aligned to reinforce the content of another topic across strands.
Example
Grade 1
Strand: Numbers and Operations
Chapter 16
Topic: Fractions
Learning objective: Recognize and name one half of a whole which is divided into 2 equal halves.
Strand: Measurement
Chapter 18
Topic: Time
Learning objective: Tell time to the half hour
Chapter 16
• Fractions are introduced prior to the lesson on telling time to the half hour so that students will be able to make the connection between the visual representation of halves in fractions and the representation of the half hour on a clock face.
• As students lear n to tell time to the half hour, the concept of halves, learned in a prior chapter, is reinforced.
Chapter 18
TM Mathematics covers all the curriculum standards and topics in the curricula of Singapore, Hong Kong and Republic of South Korea. It also completely covers the Cambridge Primary Mathematics curriculum. Additional topics are also available in the Teaching Hub for alignment to different education systems.
TM Mathematics enables every child to succeed by integrating formative and summative assessment with instruction for effective teaching and independent learning.
When instruction is informed by insights from assessment, students are more engaged and take greater ownership of their learning.
Dividing by
Formative assessment is a vital part of the ongoing, interactive process by which teachers gather immediate insight about students’ learning to inform and support their teaching.
5.1 Dividing by
Let's Do at each step of concept development are formative and diagnostic assessments. They assess the student’s learning and level of conceptual understanding to provide timely feedback to teachers.
Let's Practice Let's
Let’s Do enables teachers to immediately assess students’ understanding of the concepts just taught and identify remediation needs.
Task 1 assesses students’ understanding of division by 5 at the pictorial and abstract levels.
Task 2 assesses students’ understanding of division by 5 at the abstract level.
Purposeful Practice tasks in print and digital formats complement and extend learning. They encourage students to develop deep conceptual understanding and confidence to work independently. Practice tasks also serve as for mative and diagnostic assessment providing essential information to students and teachers on learning progress.
5.1 Dividing by
Let's Do Let's
1.
Recap provides a pictorial and abstract representation of the concrete activity carried out in
2.
1.
Tasks
are ordered by level of difficulty and are systematically varied to gradually deepen the student’s conceptual understanding.
Easy to assign and with instant access, Digital Practice includes hints to support students and provides immediate feedback to teachers on students’ learning.
Students
Summative assessments enable teachers to assess student learning at the end of each chapter and beyond.
Reviews provide summative assessment and enable consolidation of concepts and skills learned across various topics.
There are four reviews per year to consolidate learning across several chapters.
Digital Assessment provides topical, cumulative and progress monitoring assessments for evaluating fluency, proficiency and for benchmarking throughout the year.
There is an assessment at the end of every chapter to consolidate learning for the chapter.
There is an assessment at the end of each quarter of the year to test the topics taught to date.
There are assessments in the middle and end of the year. These assessments can be administered as benchmark tests.
Auto-generated reports for Digital Practice and Assessment make data easily accessible and actionable to support every teacher’s instructional goals. Teachers can review high level reports at class level or dive into the details of each student, chapter, topic, concept and practice or assessment item.
Meaningful actionable insights help teachers easily find learning gaps and gains.
Reports for Practice provide timely formative and diagnostic data on student learning that teachers can act on immediately to adjust instructional practices in an effort to address and maximize individual students’ learning.
Class List by Practice Report shows student performance on each practice.
Teachers can tell at a glance how well students in a class have performed on a practice and determine if remediation is required.
Class List by Learning Objective Report shows student performance against the learning objectives of each practice.
Before proceeding to the next lesson, teachers can review this report to identify the learning objectives that students have difficulty with, reteach these lear ning objectives or pay special attention to the struggling students in class. Doing so will ensure that the next lesson is off to a good start and increase the chances of students keeping up with the lesson.
Reports for Assessments provide in-depth mastery analysis in an easy to access and view format.
Class List by Assessment Report shows student performance on each assessment.
Actionable, real-time reports accessible on the teacher’s dashboard help to monitor student progress and make timely instructional decisions.
This report informs teachers on how well students have learned each chapter.
Class List by Learning Objective Report shows student performance against a topic or learning objective by aggregating the results for it across multiple assessments.
This report helps teachers to identify the strengths and weaknesses of the class as well as individual students and take intervention actions as needed.
All class reports can be drilled down to the individual student level.
All reports in Digital Practice and Assessment can be printed for reporting by school administrators.
A comprehensive range of resources for grades 1 to 6 supports teaching, learning, practice and assessment in a blended, print or digital environment to provide flexibility in planning and instruction, and lear ning.
Serves as a guide for carefully constructed, teacher-facilitated learning experiences for students. This core component provides the content and instruction for all stages of the learning process—readiness, engagement and mastery of concepts and skills.
Correlates to the coursebooks and contains exercises and reviews for independent practice and for mative and summative assessments.
Online opportunities for students to consolidate learning and demonstrate understanding.
Coursebook in online format with embedded videos to ensure that learning never stops.
Comprehensive lesson plans support instruction for each lesson in the Coursebooks.
This one-stop teacher’s resource center provides access to lesson notes, demonstration videos and Coursebook pages for on-screen projection.
A digital component that enables teachers to assign Practice and Assessment tasks to students and provides teachers with meaningful insight into students’ learning through varied, real-time reports.
Video tutorials and related quizzes in this online resource provide anytime, anywhere professional learning to educators.
These posters come with a poster guide to help teachers focus on basic mathematical concepts in class and enhance learning for students.
Every mathematics teacher is a master teacher.
TM Mathematics provides extensive support at point of use to support teacher development along with student lear ning, making teaching mathematics a breeze.
A comprehensive Teacher’s Guide, available in print and digital formats, provides complete program support including:
• developmental continuum,
• Scheme of Work,
• detailed notes for each lesson in the Coursebook,
• answers for practice tasks in the Coursebook and Practice Book, and
• reproducibles for class activities.
This one-stop teacher’s resource center provides resources for planning and teaching. It contains
• all the content from the Coursebook and Practice Book,
• all lesson notes from the Teacher’s Guide,
• lesson demonstration videos embedded at point of use,
• extra lessons addressing learning objectives for regional curricula and
• jour nal tasks.
The Teaching Hub functions as a teacher resource for front-of-class facilitation during lessons. Controlled display of answers in the Coursebook and Practice Book assists teachers in carrying out formative assessment during lessons.
Teachers can view the demonstration video to see and hear a lesson before teaching the lesson to students. The video can even be played during the lesson to help explain the mathematical concept to students.
Teachers can attach content they have created to the Coursebook pages to customize lessons.
Additional lessons and other resources not available in the print Coursebook and Practice Book are downloadable so that teachers can print them for students.
TM Professional Learning Now! provides on-demand professional development for teachers to learn mathematics pedagogy anytime, anywhere — in the convenience and comfort of their home or in-between lessons, or just before teaching a topic. Each learning video is intentionally kept to approximately 5 minutes so that teachers will be able to quickly and effectively learn the pedagogy behind the concept to be taught. With a short quiz of 4 or 5 questions and a performance report, professional development is relevant and effective for teachers at any stage in their teaching career. Teachers can also re-watch learning videos to reinforce their pedagogical content knowledge anytime, anywhere.
TM Mathematics Teacher’s Guides are designed to help teachers implement the program easily and effectively.
The Developmental Continuum provides an overview of prior, current and future learning objectives. Strands are color-coded to help teachers identify the connected topics within a strand.
Numbers and Operations
Measurement
Geometry
Data Analysis Algebra
The objectives of each lesson are listed in the Scheme of Work to help teachers establish mathematics goals during lesson planning.
The suggested duration for each lesson is 1 hour. Teachers can adjust the duration based on the school calendar and the pace of individual classes.
Unit 2: Addition and Subtraction Without Regrouping
2.1 Adding a 1-digit number to a 2-digit number
Let's Learn Let's Learn
Objectives:
•Add a 1-digit number and a 2-digit number without regrouping using the ‘counting on’ method, number bonds and place value
•Check the answer to an addition by using a different strategy
Materials:
•2 bundles of 10 straws and 4 loose straws
•Base ten blocks
Resources:
•CB: pp. 27–29
•PB: pp. 23–24
Stage: Concrete Experience
Write: Add 21 and 3. Show students two bundles of 10 straws, and 1 loose straw. Highlight to them that each bundle has 10 straws.
Ask: How many straws are there here? (21)
Add another 3 loose straws to the 21 straws.
Ask: How many straws are there now? (24)
Say: When we add 3 straws to 21 straws, we get 24 straws.
(a) Stages: Pictorial and Abstract Representations
Draw a number line with intervals of 1 from 21 to 26 as shown in (a) on CB p. 27 on the board.
Say: We can add by counting on using a number line.
Have students add 21 and 3 by counting on
3 ones from 21. (21, 22, 23, 24) As students count on, draw arrows on the number line as shown on the page.
Ask: Where do we stop? (24)
Say: We stop at 24. When adding a number to 21, we start from 21 and count on because we add. We count on 3 ones because we are adding 3.
Write: 21 + 3 = 24
(b) Stage: Abstract Representation Say: Another way to add is by using number bonds. Show students that 21 can be written as 20 and 1 using number bonds. Write: 21 + 3 = 20 1 Say: First, add the ones. Ask: What do we get when we add 1 and 3? (4) Say: Now, add the tens to the result. We add 20 to 4. Elicit the
Detailed lesson plans explain the pedagogy and methodology for teaching each concept, equipping teachers to teach lessons with confidence.
For each task in Let’s Remember, the objective of the task and the chapter reference to where the skill was taught earlier are listed for teachers to reteach the relevant concepts. Chapter 2: Addition and Subtraction
Explore gets students to recall prior knowledge, set learning goals and track their learning as they progress through the chapter. Questions are provided in the Teacher’s Guide to aid class discussion about the context of the task.
Have
Have students form groups to complete the tasks in columns 1 and 2 of the table. Let students know that they do not have to solve the word problem. Ask the groups to present their work.
Tell students that they will come back to this word problem later in the chapter.
Unit 1: Sum and Difference
1.1 Understanding the meanings of sum and difference
Let's Learn
Objectives:
•Associate the terms ‘sum’ and ‘difference’ with addition and subtraction respectively
•Use a part-whole bar model or a comparison bar model to represent an addition or subtraction problem
Materials:
•Connecting cubes in two colors
•Markers in two colors
Resources:
•CB: pp. 25–26
•PB: p. 22
Vocabulary:
Suggested instructional procedures are provided for the concrete, pictorial and abstract stages of learning.
Let's Do Let's
Task 1 requires students to associate the terms ‘sum’ and ‘difference’ with addition and subtraction respectively.
Task 2 requires
Let's Practice
Tasks 1 and 3 require students to associate the term ‘sum’ with addition.
Tasks 2 and 4 require students to associate the term ‘difference’ with subtraction.
•difference
•sum
(a)
Stage: Concrete Experience Have students work in pairs. Distribute connecting cubes in two colors, for example, red and blue, to each pair and have students follow each step of your demonstration. Join 3 red connecting cubes to show 3. Then, join 8 blue connecting cubes to show 8.
Ask: How many red cubes do you see? (3) How many blue cubes do you see? (8)
Join the bar of red cubes and the bar of blue cubes together.
Ask: How many cubes are there altogether? (11)
Stage: Pictorial Representation
Use two markers in different colors to draw a part-whole bar model with 3 equal units and 8 equal units to illustrate the numbers 3 and 8, as shown by the connecting cubes. Relate this model to the earlier connecting cubes activity. Erase the lines between the units in the bar model to create a simplified version of the model as shown on the right in (a) on CB p. 25.
Say: This is a bar model.
Point out that the length of each part of the model corresponds to the number of connecting cubes of each color.
Say: The two parts form a whole. This model shows the total or the sum of 3 and 8. The sum of two numbers is the total of the two numbers.
We found earlier that the total of 3 cubes and 8 cubes is 11 cubes, so the sum of 3 and 8 is 11.
Separate the bar of connecting cubes into its two parts, 3 and 8, again. Place the bar of 3 cubes above the bar of 8 cubes and left align the bars.
Say: Notice that the total number of cubes has not changed. Let us represent the sum of 3 and 8 in another model.
Draw the comparison bar model as shown in the thought bubble in (a) on the page.
Conclude that we can represent the sum in two types of bar models.
Stage: Abstract Representation
Say: We want to find the sum of 3 and 8. The sum of 3 and 8 is the total of 3 and 8. We find the sum by adding the two numbers.
Write: 3 + 8 = 11
Say: The sum of 3 and 8 is 11.
(b) Stage: Concrete Experience
Have students continue to work in pairs and follow each step of your demonstration.
Reuse the two bars of connecting cubes formed in (a). Place the bar of 3 cubes above the bar of 8 cubes and left align the bars.
Ask: How many red cubes are there? (3) How many blue cubes are there? (8) Which bar is shorter, the bar of red cubes or the bar of blue cubes? (Red cubes) Which is less, 3 or 8? (3)
Say: Let us find out how many more blue cubes than red cubes there are by counting the number of cubes.
For each Let’s Do task, the objective is listed for teachers to reteach the relevant concepts. Answers are provided for all tasks.
For each task in the Practice Book Exercise, the objectives and skills assessed are identified in the Teaching Hub to enable teachers to check learning and address remediation needs. Answers are provided for all tasks.
Digital Practice provides immediate feedback to teachers on students’ learning so that teachers can provide early intervention if required. The items come with hints to promote independent learning for students.
1
2
David is checking his friend's answer to a subtraction.
Students
Have students work in groups to discuss the tasks. Ask the groups to present their answers.
Point out to students that 12 in the ones column represents 1 ten 2 ones and not 3 ones. David has mixed up addition and subtraction with regrouping in the vertical form. Conclude that David is not correct.
Reiterate that if there are not enough ones to subtract from, we need to first regroup the tens and ones before we subtract.
Make use of the examples presented by the groups to let students understand the importance and usefulness of knowing how to subtract numbers.
Think About It poses purposeful questions to facilitate meaningful mathematical discourse and promote reasoning and communication. Students work in groups to discuss the task and present and justify their answers to the class.
1. Understand
Have students read the word problem then articulate in their own words what information is given and what is unknown. Pose questions given in the Coursebook to direct students.
2. Plan
Have students plan how to solve the problem. Have them discuss the various strategies they have learned and choose one.
3. Answer
Have students solve the problem using the chosen strategy.
4. Check
Have students check their answer for accuracy or reasonableness.
5. + Plus
Explore other strategies identified in step 2. Compare the different strategies and discuss preferences.
Resources:
Have
1.
3.
what we have to find.
Ask: How can we find the number of cupcakes left? (Subtract the number of cupcakes given away from the number of cupcakes Emma buys.)
Write: 24 – 16 = Ask a student to work out the subtraction on the board.
Say: Emma has 8 cupcakes left.
For each Let’s Do task, the objective is listed for teachers to reteach the relevant concepts. Answers are provided for all tasks.
For each task in the Practice Book Exercise, the objectives and skills assessed are identified in the Teaching Hub to enable teachers to check learning and address remediation needs. Solutions are provided for all tasks.
Digital Practice provides immediate feedback to teachers on students’ learning so that teachers can provide early intervention if required. The items come with hints to promote independent learning for students.
Solve the word problems. Show your work clearly.
1. There are 82 sandwiches on a table.
25 are egg sandwiches, 34 are tuna sandwiches and the rest are chicken sandwiches.
a) How many egg and tuna sandwiches are there altogether?
b) How many chicken sandwiches are there?
2. Karen had 27 red apples.
She had 18 more green apples than red apples.
She used 29 green apples to make some juice.
a) How many green apples did she have at first?
b) How many green apples did she have left after making juice?
3. Vivian has 51 storybooks.
1, 3 To solve 1-step word problems involving addition with regrouping
2 To solve 1-step word problems involving subtraction with regrouping
4 To solve 1-step word problems involving subtraction with regrouping
Students are expected to solve 1-step word problems involving addition with regrouping. They can draw a partwhole bar model to help them solve each word problem.
Students are expected to solve a 1-step subtraction word problem involving a comparison situation by finding the smaller quantity given the larger quantity and the difference. They can draw a comparison bar model to help them solve the word problem.
She has 13 more storybooks than Kevin.
a) How many storybooks does Kevin have?
b) How many storybooks do they have altogether?
CREATE YOUR OWN
Nathan has 46 stamps.
He has 19 more stamps than Tim.
a) How many stamps does Tim have?
b) If Tim gives 8 stamps to Zoe, how many stamps will he have left?
Read the word problem. Replace ‘more’ with ‘fewer’. Next, solve the word problem. Show your work clearly. What did you learn?
To solve 1-step word problems involving addition with regrouping
To solve 1-step word problems involving subtraction with regrouping
Tasks 1 to 3 require students to solve 2-step word problems involving addition and subtraction.
CREATE YOUR OWN
Have students work in groups to create and solve the word problem. Have a few groups present their work.
Students are expected to replace ‘more’ with ‘fewer’ in the word problem. So, they have to add in the first part and subtract in the second part to solve the word problem.
Students are expected to solve a 1-step word problem involving subtraction with regrouping. They can draw a part-whole bar model to help them solve the word problem.
Students are expected to solve a 1-step addition word problem involving a comparison situation by finding the larger quantity given the smaller quantity and the difference. They can draw a comparison bar model to help them solve the word problem.
Students are expected to solve a 1-step subtraction word problem involving a comparison situation by finding the difference given the two quantities. They can draw a comparison bar model to help them solve the word problem.
4.2 Mind stretcher
Let's Learn Let's Learn
Objective:
•Solve a non-routine problem involving addition and subtraction using the strategy of working backwards
Resource:
•CB: pp. 62–63
Create Your Own tasks facilitate meaningful mathematical discourse and promote reasoning and problem solving. Students work in pairs or groups to discuss the task and present their work to the class.
Have students read the problem on CB p. 62.
1. Understand the problem.
Pose the questions in the
Write: Stage 3: + 20 = 81
Say: To find the missing number, we subtract 20 from 81.
Write: 81 – 20 =
Elicit the answer from students. (61)
Write ‘61’ in the third box in the diagram.
Write: Stage 2: – 5 = 61
Ask: How do we find the missing number? (Add 5 to 61.)
Write: 61 + 5 = Elicit the answer from students. (66)
Write ‘66’ in the second box in the diagram.
Write: Stage 1: + 20 = 66
Ask: How do we find the missing number?
(Subtract 20 from 66.)
Write: 66 – 20 = Elicit the answer from students. (46)
Write ‘46’ in the first box in the diagram.
Say: Julia starts with the number 46.
4. Check if your answer is correct.
Guide students to check their answer by starting with 46 and going through the three stages in the problem to see if they get 81 in the end.
5. + Plus Solve the problem in another way.
Have students try to solve the problem in a different way.
Have 1 or 2 students share their methods.
If students are unable to solve the problem in a different way, explain the method shown on CB p. 63.
Ask: Which method do you prefer? Why?
(Answers vary.)
EXPLORE
Have students go back to the word problem on
CB p. 24. Get them to write down in column 3 of the table what they have learned that will help them solve the problem, and then solve the problem. Have a student present his/her work to the class.
Mind Stretcher provides opportunities for students to apply concepts and skills learned to unusual or complex problem situations. Encourage students to solve the problem using different strategies.
Chapter 2: Addition and Subtraction Within 100 63
MISSION POSSIBLE
Chapter 2: Addition and Subtraction Within 100 64
Mission Possible tasks introduce students to computational thinking, an important foundational skill in STEM education. The Teacher’s Guide provides prompts to help teachers facilitate the class discussion.
Have students work in groups to complete the task on CB p. 329.
Go through the task using the prompts given below.
1. Decomposition Ask: How can we break down the problem into smaller and simpler problems? (Answer varies. Sample: Find out how much money Miguel has, find all the combinations of two presents Miguel can buy, find the total cost of each combination of presents, find the amount of money left after buying each combination)
2. Pattern Recognition Lead students to say that every time they find the total cost of the combination of presents, they have to check which of the total cost is closest to $78 and less than $78.
3. Abstraction Ask: What information will help you solve the problem? (The notes that Miguel has, the cost of the book, the costs of the presents, and he wants to use up as much of his money as possible)
4. Algorithms Guide students to draw a simple flow chart to show the steps used to solve the problem. Ask a group to write their solution on the board.
MATHEMATICAL MODELING
Duration: 5 h (5 one-hour sessions)
Mathematical Modeling tasks require students to apply mathematics to complex real-world problems. Prompts and rubrics are provided to assist teachers in conducting the lesson and assessing students’ performance.
Material:
•1 device with access to internet per group
•1 copy of Mathematical Modeling
Resource: •CB:
Task:
Digital Chapter Assessment enables consolidation of learning in every chapter. Auto-generated reports provide actionable data for teachers to carry out remediation or extension as required.
Math Journal tasks in the Teaching Hub allows teachers to gain insight into students’ thinking. Rubrics are provided to help teachers give feedback to students.
1To
2To
3
4To
6To
7To
Digital Quarterly and Half-Yearly Assessments provide opportunities for summative assessment at regular intervals throughout the year. Auto-generated reports help teachers to measure students’ learning.
Practice Book Reviews provide opportunities for summative assessment. They consolidate learning across several chapters. The last review in each grade assesses learning in the entire grade. For each task, the objectives assessed are identified in the Teaching Hub to enable teachers to check learning and address remediation needs.
TM Mathematics can be flexibly used in print, blended or digital formats based on the context to maximize teaching and learning.
Start of school year: Developmental Continuum
Start of chapter: Scheme of Work
Start of lesson: Lesson plan
Lesson demonstration video
Let’s Remember Explore
Teach concepts and skills:
Let’s Learn
Let’s Do Practice Book Exercise
Digital Practice Think About It
Teach problem solving: Let’s Learn (UPAC+™) Let’s Do Practice Book Exercise
Digital Practice
Create Your Own Mind stretcher
Mission Possible Mathematical Modeling
Digital Chapter Assessment
Math Journal
Practice Book Reviews
Digital Quarterly Assessment
Digital Half-Yearly Assessment
Available
Born and brought up in Mumbai, India, Dr. Aziz has lived in Singapore for more than 30 years now and is the proud grandma of three lovely girls. At Scholastic, she has oversight of Scholastic’s global education business and the research and development of all education products, technology and print.
She completed her doctoral research at the Leeds Metropolitan University and holds a bachelor’s degree in English Language and Literature from the Open University. She holds Graduate degrees in Business Administration and English Studies from the University of Strathclyde and the National University of Singapore, respectively. Inspired by her work in development of materials for teaching and learning, Duriya’s Master’s research was on the role of teacher feedback in materials development, and her doctoral research culminated in the presentation of a framework for development and evaluation of materials in meeting the objectives of stakeholders in education and their impact on teaching and learning.
Though an English language specialist by training, math education found her and Dr. Aziz has spent almost 20 years developing curriculum programs based on Singapore mathematics pedagogical principles and practices for more than 20 countries, in different languages, and worked with ministries, schools and teachers on the implementation of these programs. Dr Aziz’s primary interest is in the development and implementation of programs that incorporate global best practices while remaining culturally and contextually appropriate, to drive sustainable change at a systemic level including development of teacher competence, knowledge and independence.
Duriya has written several textbooks for learners of English and children’s picture books, as well as academic articles on English language teaching and materials development for education.
Kelly Lim holds a Masters in Mathematics Education from The Institute of Education, London, a degree in Mathematics from the National University of Singapore (B. Sc.) and a Post-Graduate Diploma from the National Institute of Education in Singapore (PGDE).
In her current role at Scholastic, she provides program implementation support and professional development to school leaders, educators and parents around the world wherever Scholastic’s acclaimed mathematics programs, particularly PR1ME Mathematics, are in use.
Kelly was the founding headmaster of the third campus of a Singapore international school in Thailand before joining Scholastic. Her stint in Thailand, which lasted for about a decade, was preceded by her time in Singapore, where she taught in government schools for a similar period.
Oscar holds a Master’s degree in Mathematics Education, a specialization on applied ICT in education from Universidad Pedagogica Nacional and a degree in Mathematics from Sergio Arboleda University in Colombia. Currently, he is working on his second Master in Educatronics.
He was a mathematics teacher for 12 years and was head of the mathematics department in a bilingual school, in which he was leading the PR1ME Mathematics program implementation. He has written articles and spoken at different events on Pedagogical Content Knowledge (PCK), B-Learning Flipped Classroom, Statistics teaching and Singapore mathematics.
Oscar was a Calculus and Statistics professor at Sergio Arboleda University in Colombia. Currently, he is the mathematics consultant at Scholastic, offering professional development and supporting the implementation of PR1ME Mathematics and ¡Matemáticas al Máximo! in Latin America, the Caribbean, Middle East, Africa and Europe.
Óscar Mauricio Gómez holds a Master’s degree in Mathematics Education from Francisco José de Caldas District University in Bogotá, Colombia. Óscar has been working in the educational field for the last 14 years as a math teacher in both schools and college classrooms. He worked as a curricular advisor for the Colombian Ministry of Education in the national curricular restructuring in 2016 and the program of Colombia Aprende.
Clara Guerrero’s professional experience combines over 10 years of classroom teaching at the primary level with over 20 years in the field of educational publishing. She has a Master’s degree in Education and a Bachelor’s degree in English Language Teaching.
As a reviewer, Clara focused on the linguistic and cultural aspects of PR1ME Mathematics. Given the fact that a considerable number of students and teachers using the program around the world are not native speakers of English, Clara ensured that the language and contexts used throughout the series were appropriate and did not hinder the lear ning of mathematical concepts.
Teachers can use the Developmental Continuum to understand the links between learning objectives within and across strands and grade levels. It provides a useful overview of prior, current and future learning objectives. Teachers will observe how new learning is built on prior learning across the grades and how each topic forms the foundation for future learning.
Grade 3
Whole Numbers / Place Value
Count within 1000.
Read and write a number within 1000—the numeral and the corresponding number word.
Use number notation and place values (hundreds, tens, ones).
Find the number which is ones, tens or hundreds more than or less than a given number within 1000.
Count on and backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000.
Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000.
Compare and order numbers within 1000.
Use ‘>’ and ‘<’ symbols to compare numbers.
Read and place numbers within 1000 on a number line.
Count within 10 000.
Read and write a number within 10 000—the numeral and the corresponding number word.
Use number notation and place values (thousands, hundreds, tens, ones).
Find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000.
*Identify patterns in a hundred chart.
Count on and backwards by ones, tens, hundreds or thousands within 10 000.
Describe, complete and create a number pattern by counting on or backwards by ones, tens, hundreds or thousands within 10 000.
*Describe and complete a number pattern by repeated addition or multiplication.
Compare and order numbers within 10 000.
Give a number between two 3-digit numbers. Use ‘>’ and ‘<’ symbols to compare numbers.
Round a 2-digit or 3-digit number to the nearest ten.
Read and place numbers within 10 000 on a number line.
Round a 3-digit number to the nearest hundred. Give a number between two 4-digit numbers.
Identify odd and even numbers.
Round a 3-digit or 4-digit number to the nearest ten.
Read and write a number within 1 000 000—the numeral and the corresponding number word.
Identify the values of digits in a 5-digit or 6-digit number.
Compare and order numbers within 1 000 000.
Round a whole number to the nearest ten, hundred or thousand.
Find all the factors of a whole number up to 100.
Find out if a 1-digit number is a factor of a given whole number.
Find the multiples of a whole number up to 10.
Relate factors and multiples.
Find out if a whole number is a multiple of a given whole number up to 10.
Identify multiples of 2, 5, 10, 25, 50 and 100 up to 1000.
Identify prime numbers and composite numbers.
Recognize prime numbers up to 20 and find all prime numbers less than 100.
Identify square numbers.
Whole Numbers / Place Value (continued)
Addition / Subtraction
Add and subtract within 1000.
Add three or four 3-digit numbers.
Check the answer to addition or subtraction.
Estimate sums and differences.
Check reasonableness of answers in addition or subtraction using estimation.
Use a part-whole bar model or a comparison bar model to represent an addition or subtraction situation.
Round a 3-digit or 4-digit number to the nearest hundred.
Round a 4-digit number to the nearest thousand.
Solve 1-step and 2-step word problems involving addition and subtraction.
Add and subtract within 10 000.
Estimate sums and differences.
Check reasonableness of answers in addition or subtraction using estimation.
Solve 1-step and 2-step word problems involving addition and subtraction.
Find pairs of multiples of 50 with a total of 1000 and write the addition and subtraction facts for each number pair.
Mentally add:
- two 2-digit numbers with regrouping
- a 2-digit, 3-digit or 4-digit number to a 3-digit or 4-digit number with regrouping
- three or four 1-digit or 2-digit numbers
- three 2-digit multiples of 10
Mentally subtract:
- a 2-digit number from another 2-digit number with regrouping
- a 2-digit, 3-digit or 4-digit number from a 3-digit or 4-digit number
*Identify triangular numbers.
*Extend spatial patterns formed from adding and subtracting a constant.
*Extend spatial patterns of square and triangular numbers.
*Identify cube numbers.
Estimate sums and differences.
Check reasonableness of answers in addition or subtraction.
Investigate and generalize the result of adding and subtracting odd and even numbers.
Do mixed operations involving addition and subtraction without parentheses.
Do mixed operations involving the four operations with or without parentheses.
Write simple expressions that record calculations with numbers.
Interpret numerical expressions without evaluation.
*Identify patterns in an addition chart.
Find pairs of multiples of 100 with a sum of 1000 and write the addition and subtraction facts for each number pair.
Solve multi-step word problems involving four operations of whole numbers.
Add two numbers up to 4 digits by counting on in thousands, hundreds, tens and ones.
Addition / Subtraction (continued) Find pairs of numbers with a sum of 100 and write the addition and subtraction facts for each number pair.
Find the missing part in an addition or subtraction sentence.
Use the ‘=’ sign to represent equality.
Mentally add:
- ones, tens or hundreds to a 2-digit or 3-digit number without regrouping
- a 1-digit number to a 2-digit or 3-digit number with regrouping
- tens to a 2-digit or 3-digit number with regrouping
- two 2-digit numbers without regrouping
Mentally subtract:
- ones or tens from a 2-digit number without regrouping
- ones, tens or hundreds from a 3-digit number without regrouping
- a 1-digit number from a 2-digit or 3-digit number with regrouping
- tens from a 3-digit number with regrouping
- a 2-digit number from another 2-digit number without regrouping
Multiplication / Division Recall multiplying numbers within the multiplication tables of 2, 3, 4, 5 and 10.
Recall dividing numbers using the multiplication tables of 2, 3, 4, 5 and 10.
Observe the commutative and distributive properties of multiplication.
Build up the multiplication tables of 6, 7, 8 and 9 and commit the multiplication facts to memory.
Multiply numbers within the multiplication tables of 6, 7, 8 and 9.
Divide numbers using the multiplication tables of 6, 7, 8 and 9.
Subtract a number up to 4 digits by counting backwards in thousands, hundreds, tens and ones.
Multiply ones, tens or hundreds by a 1-digit number.
Investigate and generalize the result of multiplying odd and even numbers.
Multiply a 3-digit whole number by a 1-digit number. Know and apply tests of divisibility by 2, 3, 4, 5, 10, 25 and 100.
Multiply three 1-digit numbers.
Apply the commutative and associative properties of multiplication in computation.
Multiply a whole number up to 3 digits by 10.
Divide hundreds or tens by a 1-digit number.
*Identify patterns in a multiplication chart. Divide a 3-digit whole number by a 1-digit number.
Multiply or divide a whole number by 10, 100 or 1000.
Multiply or divide a whole number by tens, hundreds or thousands.
Multiply pairs of multiples of 10 or multiples of 10 and 100.
Multiply a 4-digit whole number by a 1-digit whole number.
Multiply a 2-digit whole number by a 2-digit whole number.
Multiplication / Division (continued)
Multiply a number by 0 or 1.Divide a whole number up to 3 digits by 10.
Multiply ones or tens by a 1-digit number.
Multiply a 2-digit number by a 1-digit number.
Estimate products and quotients.
Check reasonableness of answers in multiplication or division using estimation.
Divide a number by 1.Solve up to 3-step word problems involving multiplication and division.
Divide ones or tens by a 1-digit number.
Associate the terms ‘quotient’ and ‘remainder’ with division.
Divide a 2-digit number by a 1-digit number.
Estimate products and quotients.
Check reasonableness of answers in multiplication or division using estimation.
Use a part-whole bar model or a comparison bar model to represent a multiplication or division situation.
Solve 1-step and 2-step word problems on multiplication and division.
Find doubles of 2-digit numbers mentally.
Find halves of even numbers up to 200 mentally.
Find doubles of 2-digit numbers mentally.
Divide a 4-digit whole number by a 1-digit whole number.
Divide a 2-digit whole number by a 2-digit whole number.
Estimate products and quotients.
Check reasonableness of answers in multiplication or division.
*Divide a 5-digit whole number by a 1-digit whole number.
Find doubles of multiples of 10 up to 1000 mentally. Do mixed operations involving multiplication and division without parentheses.
Find doubles of multiples of 100 up to 10 000 mentally. Do mixed operations involving the four operations with or without parentheses.
Find halves of whole numbers up to 200 mentally. Write simple expressions that record calculations with numbers.
Find halves of multiples of 20 up to 2000 mentally.
Interpret numerical expressions without evaluation.
Find halves of multiples of 200 up to 20 000 mentally. Solve multi-step word problems involving four operations of whole numbers.
Multiply tens or hundreds by a 1-digit number.
Multiply a 2-digit number close to a multiple of 10 by a 1-digit number.
Multiply a 1-digit or 2-digit number by 25 by multiplying by 100 and dividing by 4.
*Divide tens or hundreds by a 1-digit number.
Find doubles of whole numbers up to 100.
Find halves of whole numbers up to 200.
Fractions / Concepts
Fractions / Arithmetic Operations
Find the fraction that must be added to a given fraction to make a whole.
Compare and order fractions which have a common numerator or denominator.
Use 0, 1 2 and 1 as benchmark fractions.
Read fractions on a number line.
Compare and order fractions with different numerators and denominators.
Recognize and name equivalent fractions of a given fraction with denominator up to 12.
Find equivalent fractions of a given fraction using multiplication or division.
Express a fraction in its simplest form.
Write the sum of a whole number and a proper fraction as a mixed number.
Read and place mixed numbers on a number line.
Compare and order mixed numbers on a number line.
*Decompose a mixed number or a non-unit fraction into a sum of fractions with the same denominator.
*Interpret a non-unit fraction as a multiple of a unit fraction.
Write an improper fraction.
Distinguish among whole numbers, proper fractions, improper fractions and mixed numbers.
Write an improper fraction as a whole number or a mixed number.
Write a mixed number as an improper fraction.
Write a mixed number as another mixed number.
Associate a fraction with division.
Express a whole number as a fraction.
Add and subtract like and related fractions within 1 whole.
Solve 1-step word problems involving fractions.
Divide a whole number by another whole number and write the quotient as a mixed number.
Add two or three like or related fractions with a sum more than 1 whole.
Subtract one or two fractions from a whole number.
Describe and complete a number pattern involving addition and subtraction of fractions with the same denominator.
Use a fraction to represent a part of a set of objects.
Add and subtract unlike fractions.
Multiply fractions.
*Add and subtract mixed numbers.
*Multiply a whole number by a mixed number.
*Interpret multiplication as scaling.
Fractions / Arithmetic Operations (continued)
Decimals
Find the value of a fractional part of a quantity.
Multiply a fraction and a whole number.
Solve 1-step and 2-step word problems involving fractions.
*Multiply a fraction or mixed number by a mixed number.
*Divide a fraction by a whole number.
*Divide a whole number by a fraction.
*Convert a measurement of length, mass, volume of liquid or time from a larger unit of measure involving a proper fraction or a mixed number to a smaller unit.
*Convert a measurement of length, mass, volume of liquid or time from a larger unit of measure involving a mixed number to compound units.
*Express a measurement of length, mass, volume of liquid or time in the smaller unit as a fraction of a measurement in the larger unit.
Solve multi-step word problems involving fractions.
Read and write a decimal up to 2 decimal places.
Express a fraction or mixed number whose denominator is a factor of 100 as a decimal.
Interpret a decimal up to 2 decimal places in terms of tens, ones, tenths and hundredths.
Identify the values of digits in a decimal up to 2 decimal places.
Express a decimal up to 2 decimal places as a fraction or mixed number in its simplest form.
Write tenths or hundredths as a decimal.
Read and place decimals on a number line with intervals of 0.1 or 0.01.
Read and write a decimal with 3 decimal places.
Interpret a decimal with 3 decimal places in terms of tens, ones, tenths, hundredths and thousandths.
Identify the values of digits in a decimal with 3 decimal places.
Express a fraction or mixed number with a denominator of 1000 as a decimal.
Express a decimal with 3 decimal places as a fraction or mixed number in its simplest form.
Read decimals on a number line with intervals of 0.001.
Compare and order decimals up to 3 decimal places.
Decimals (continued)
Integers
Compare and order decimals up to 2 decimal places.
Find the number which is 0.1 or 0.01 more than or less than a given number.
Round a decimal to the nearest whole number or 1 decimal place.
Compare and order whole numbers, decimals and fractions.
Find the number which is 0.1, 0.01 or 0.001 more than or less than a given number.
Complete a number pattern with decimals involving addition and subtraction.
Round a decimal to 2 decimal places.
Add and subtract decimals up to 2 decimal places.
Multiply and divide decimals up to 2 decimal places by a 1-digit whole number.
Divide a whole number by a 1-digit whole number and give the quotient as a decimal.
Estimate sums, differences, products and quotients.
Check reasonableness of answers in addition, subtraction, multiplication or division.
Solve 1-step and 2-step word problems involving decimals.
Find pairs of decimals with 1 or 2 decimal places with a total of 1.
Find pairs of decimals with 1 decimal place with a total of 10.
Find doubles of decimals with 1 or 2 decimal places.
Find halves of decimals with 1 or 2 decimal places.
Interpret integers in everyday contexts.
Read integers on number lines.
Compare and order integers using number lines.
Describe and complete a number pattern involving positive and negative integers by counting on and backwards by ones, twos, threes, fours, fives or tens.
Rate
*Find the rate by expressing one quantity per unit of another quantity.
*Find a quantity using the given rate.
*Solve word problems involving rate.
Length
Measure the length of a line segment or a curve in centimeters.
Draw a line segment given its length in centimeters.
Measure lengths in meters and centimeters.
Understand that a kilometer is longer than a meter and a millimeter is shorter than a centimeter.
Measure and compare lengths in kilometers or millimeters.
Choose a suitable unit or tool of measure.
Solve 1-step and 2-step word problems on length.
*Measure and compare lengths to the nearest half or quarter inch.
Recall the units of measurements of length.
Know the meanings of the prefixes ‘kilo’, ‘centi’ and ‘milli’.
Know the relationship between units of length.
Measure the length of a line segment in centimeters or centimeters and millimeters.
Draw a line segment given its length in centimeters or centimeters and millimeters.
Convert a measurement of length from compound units to a smaller unit, and vice versa.
Compare and order measurements of length in compound units.
Add and subtract lengths in compound units.
*Measure lengths to the nearest half, quarter or eighth of an inch.
*Measure and compare lengths in feet and inches.
*Express feet and inches in inches, and vice versa.
*Add and subtract lengths in feet and inches.
*Measure and compare lengths in yards and feet.
*Express yards and feet in feet, and vice versa.
*Convert a measurement of length from a larger unit of measure involving a proper fraction or a mixed number to a smaller unit.
*Convert a measurement of length from a larger unit of measure involving a mixed number to compound units.
*Express a measurement of length in the smaller unit as a fraction of a measurement in the larger unit.
Length (continued)
Perimeter / Area
*Add and subtract lengths in yards and feet.
*Measure and compare lengths in miles.
*Choose a suitable unit of measure when measuring lengths and distances.
Solve 1-step and 2-step word problems on length.
Measure area in nonstandard units.
Find the area of a figure made up of unit squares and half squares.
Compare areas of figures made up of unit squares and half squares.
Visualize the sizes of 1 square centimeter and 1 square meter.
Find the area of a figure made up of 1-centimeter or 1-meter squares and half squares.
Compare areas of figures made up of 1-centimeter or 1-meter squares and half squares.
*Visualize the sizes of 1 square inch and 1 square foot.
*Find the area of a figure made up of 1-inch or 1-foot squares and half squares.
*Compare areas of figures made up of 1-inch or 1-foot squares and half squares.
Find the perimeter of a figure made up of 1-centimeter or 1-meter squares.
Measure the perimeter of a figure.
Compare areas and perimeters of figures made up of 1-centimeter or 1-meter squares.
Find the perimeter of a rectilinear figure given the lengths of all its sides.
Find the perimeter of a regular polygon given the length of one side.
*Find an unknown side length of a figure given its perimeter and the other side lengths.
Find the area and perimeter of a square given one side.
Find the area and perimeter of a rectangle given its length and width.
Draw a square and a rectangle and measure and calculate their perimeters.
Estimate the area of an irregular shape by counting squares.
Find one side of a rectangle given the other side and its area or perimeter.
Find one side of a square given its area or perimeter.
Solve word problems on areas of squares and rectangles.
Solve word problems on perimeters of polygons.
Volume and Capacity
Compare volume of liquid in two containers visually.
Mass / Weight
Measure and compare volume of liquid in two or more containers in liters.
Tell the difference between volume and capacity.
Measure and compare volumes and capacities in milliliters.
Measure volumes and capacities in liters and milliliters.
Choose a suitable unit or tool of measure.
Solve 1-step and 2-step word problems involving volume and capacity.
Recall the units of measurements of volume of liquid.
Know the relationship between liter and milliliter.
Know the meanings of the prefixes ‘kilo’, ‘centi’ and ‘milli’.
Compare readings on different scales.
Express liters and milliliters in milliliters, and vice versa.
Compare and order volumes in liters and milliliters.
Add and subtract volumes in liters and milliliters.
Solve 1-step and 2-step word problems on volume.
*Convert a measurement of volume of liquid from a larger unit of measure involving a proper fraction or a mixed number to a smaller unit.
*Convert a measurement of volume of liquid from a larger unit of measure involving a mixed number to compound units.
*Express a measurement of volume of liquid in the smaller unit as a fraction of a measurement in the larger unit.
*Find the volume of a solid made up of unit cubes in cubic units.
*Visualize a solid that is made up of unit cubes and state its volume in cubic units.
*Visualize the sizes of 1 cubic centimeter, 1 cubic meter, 1 cubic inch and 1 cubic foot.
*Find the volume of a solid made up of 1-centimeter, 1-meter, 1-inch or 1-foot cubes.
*Compare the volumes of solids made up of 1-centimeter, 1-meter, 1-inch or 1-foot cubes.
*Find the volume of a rectangular prism, given its length, width and height.
*Find the volume of a rectangular prism, given area of one face and one dimension.
*Find the volume of a solid figure composed of two rectangular prisms.
*Solve word problems involving volume of rectangular prisms.
Estimate, measure and compare masses of objects in kilograms or grams using weighing scales.
Recall the units of measurements of mass.
*Convert a measurement of mass from a larger unit of measure involving a proper fraction or a mixed number to a smaller unit.
Mass / Weight (continued)
Measure masses of objects in kilograms and grams.
Choose a suitable unit or tool of measure.
Solve 1-step and 2-step word problems on mass.
*Measure and compare weights in pounds or ounces.
*Solve 1-step and 2-step word problems on weight.
Know the relationship between kilogram and gram.
Know the meanings of the prefixes ‘kilo’, ‘centi’ and ‘milli’.
Compare readings on different scales.
Express kilograms and grams in grams, and vice versa.
Compare and order masses in kilograms and grams.
Add and subtract masses in kilograms and grams.
Solve 1-step and 2-step word problems on mass.
*Measure and compare weights in pounds and ounces.
*Express pounds and ounces in ounces, and vice versa.
*Add and subtract weights in pounds and ounces.
*Measure and compare weights in tons.
*Know the relationship between tons, pounds and ounces.
*Choose a suitable unit of measure when measuring weights.
*Solve 1-step and 2-step word problems on weight.
*Convert a measurement of mass from a larger unit of measure involving a mixed number to compound units.
*Express a measurement of mass in the smaller unit as a fraction of a measurement in the larger unit.
Time: Calendar
Time: Clock
Know the number of days in a month and in a year.
Read a calendar and calculate time intervals in days and weeks.
Tell time to the minute on analog and digital clocks.
Find the duration of a time interval in hours and minutes.
Express hours and minutes in minutes, and vice versa.
Tell time to the second.Calculate time intervals in months.
Find the duration of a time interval in seconds.
Measure duration of activities in seconds.
Calculate time intervals in years.
Calculate time intervals in years and months.
Time: Clock (continued)
Add and subtract durations in hours and minutes. Know the relationship between units of time.
Solve 1-step and 2-step word problems involving time.
Choose suitable units to measure time intervals.
Express minutes and seconds in seconds, and vice versa.
Express years and months in months, and vice versa.
Express weeks and days in days, and vice versa.
Tell time using the 24-hour clock notation.
Convert time between the 12-hour and 24-hour clock notations.
Compare times using digital and analog clocks.
Find the duration of a time interval given time in 24-hour clock notation.
Read and interpret timetables in 12-hour and 24-hour clock notations.
Use a timetable to solve problems.
Solve word problems on time.
*Convert a measurement of time from a larger unit of measure involving a proper fraction or a mixed number to a smaller unit.
*Convert a measurement of time from a larger unit of measure involving a mixed number to compound units.
*Express a measurement of time in the smaller unit as a fraction of a measurement in the larger unit.
Temperature
Money
*Read and measure temperatures in Celsius or Fahrenheit using thermometers.
Count and tell the amount of money in a group of notes and coins in dollars and cents.
Read and write an amount of money in decimal notation.
Change dollars and cents to cents, and vice versa.
Make up an amount of money using a group of coins and notes.
Compare two or three amounts of money in dollars and cents.
Express cents in dollars.
Money (continued) Make $1.
Give change for a purchase paid with $1.
Add and subtract money in dollars and cents up to $10.
Solve 1-step and 2-step word problems involving addition and subtraction of money.
Lines and Curves
2D Shapes Name, describe and draw 2D shapes: pentagon, hexagon, octagon and semicircle.
Find 2D shapes in the environment.
Sort 2D shapes by the number of sides, vertices and right angles.
*Make new 2D shapes by combining 2D shapes.
Identify open and closed figures.
Differentiate between polygons and non-polygons.
Name polygons according to the number of sides.
Identify regular and irregular polygons.
*Name 2D shapes that make up a new shape. Find examples of polygons in the environment and in art.
Complete a symmetric figure given half of the figure and the line of symmetry.
Make polygons on geoboards.
Identify perpendicular and parallel line segments.
Draw perpendicular and parallel line segments.
Recognize that the sum of angle measures in a triangle is 180º.
Identify and describe properties of triangles and classify as isosceles, equilateral or scalene.
Identify right triangles.
Find an unknown angle measure in a triangle.
Recognize reflective symmetry in regular polygons.
Count the number of lines of symmetry in regular polygons.
Draw polygons on dot grids.Make a symmetric pattern with two lines of symmetry.
Classify polygons using criteria such as the number of right angles, whether or not they are regular and their symmetrical properties.
Identify a symmetric polygon.
Count the number of lines of symmetry in polygons.
Recognize rotational symmetry in 2D shapes.
Identify the order of rotational symmetry in 2D shapes.
Identify where a polygon will be after a translation and give instructions for translating the shape.
2D Shapes (continued)
Draw lines of symmetry in polygons and patterns.
Find examples of symmetry in the environment and in art.
*Make a symmetric pattern with one line of symmetry.
Predict where a polygon will be after a reflection where the mirror line is parallel to one of the sides.
*Identify the unit shape in a tessellation.
*Determine if a given shape can tessellate.
*Draw a tessellation on dot paper.
*Make different tessellations with a unit shape.
*Make a tessellation with two unit shapes.
3D Shapes Understand that 3D shapes can be formed by nets. Identify and draw different types of prisms and pyramids.
Identify the nets of a cube.Identify the faces, edges and vertices of prisms and pyramids.
Find examples of prisms and pyramids in the environment and in art.
Understand that cross sections of a prism are of the same shape and size as the parallel faces of the prism.
Understand that cross sections of a pyramid are of the same shape as the base but of different sizes.
Classify prisms and pyramids according to the number and shape of faces, number of vertices and edges.
Identify the nets of prisms and pyramids.
Identify the prism or pyramid which can be formed by a net.
Make prisms and pyramids from nets.
Make nets of prisms and pyramids.
*Build a solid with unit cubes.
*Visualize a solid drawn on dot paper and state the number of unit cubes used to build the solid.
*Visualize and identify the new solid formed by changing the number of unit cubes of a solid drawn on dot paper.
Angles
Position and Movement
Identify, name and draw a point, a line, a line segment and a ray.
Name an angle using notations such as ∠ABC and ∠x.
Identify an angle. Recognize that the measure of a right angle is 90°.
Compare sizes of angles.Estimate and measure the size of an angle in degrees and classify the angle as acute, right or obtuse.
Identify angles on an object or in a shape.
Draw acute and obtuse angles using a protractor.
Recognize that the sum of the angle measures on a straight line is 180°.
Recognize that the sum of the angle measures at a point is 360°.
Recognize that vertically opposite angles have equal measures.
Find the unknown measures of angles involving angles on a straight line, angles at a point and vertically opposite angles.
Identify right angles. Relate turns to right angles.Recognize that the sum of angle measures in a triangle is 180º.
Tell whether a given angle is equal to, smaller than or bigger than a right angle and describe it as being right, acute or obtuse.
Identify right angles on an object or in a shape.
Find right angles in the environment.
Draw right angles using a set square.
Recognize that a right angle is a 1 4 -turn, 2 right angles is a 1 2 -turn, 3 right angles is a 3 4 -turn, and 4 right angles is a complete turn.
Recognize that a straight line is equivalent to two right angles.
Recognize that a right angle is a 1 4 -turn, 2 right angles is a 1 2 -turn, 3 right angles is a 3 4 -turn, and 4 right angles is a complete turn.
Find and describe the position of a box on a grid where the rows and columns are labeled.
Relate a 1 4 -turn to 90°, a 1 2 -turn to 180°, a 3 4 -turn to 270° and a complete turn to 360°.
Find an unknown angle measure in a triangle.
Relate turns to right angles.Read and plot coordinates in the 1st quadrant of the Cartesian plane.
Relate a 1 4 -turn to 90°, a 1 2 -turn to 180°, a 3 4 -turn to 270° and a complete turn to 360°.
*Plot corresponding terms from two patterns on a Cartesian plane.
Position and Movement (continued)
Give and follow directions to a place on a grid.
Tell direction using the 8-point compass.
Give and follow directions to a place on a grid.
Data Collection Collect and record data in a tally chart and a frequency table.
Read and interpret a tally chart and a frequency table.
Tables Collect and record data in a tally chart and a frequency table.
Read and interpret a tally chart and a frequency table.
Sort data in a Carroll diagram with 2 or 3 criteria.
Graphs Make, read and interpret a bar graph with a scale of 1 or greater.
*Make, read and interpret a line plot with a scale marked in whole numbers, halves or quarters.
Venn Diagrams Group objects in a Venn diagram using different criteria.
Sort data in a Venn diagram with 1 criterion and read the Venn diagram.
Collect and present data in a graph.
*Solve word problems involving the Cartesian plane.
Identify where a polygon will be after a translation and give instructions for translating the shape.
Predict where a polygon will be after a reflection where the mirror line is parallel to one of the sides.
Identify the data to collect to answer a set of related questions.
Collect and present data in an appropriate data display.
Draw conclusions from data and identify further questions to ask.
Collect and present data in a bar line chart.
Collect and present data in a graph.
Interpret a graph.
Compare the impact of representations where scales have different intervals.
*Make, read and interpret a line plot with a scale marked in whole numbers, halves, quarters or eighths.
Sort data in a Venn diagram with 2 or 3 criteria.
*Make, read and interpret a line plot.
Collect and present data in a bar line chart.
Consider the effect of changing the scale on the axis.
Read and interpret a bar line chart.
Complete, read and interpret a line graph.
Probability
*Identify events that will happen, will not happen or might happen.
Identify events as being ‘certain’ or ‘uncertain’ to happen.
Identify events as being ‘possible’ or ‘impossible’ to happen.
Identify events as being ‘likely’ or ‘unlikely’ to happen.
Patterns
Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000.
*Identify patterns in an addition chart.
Expressions
*Identify patterns in a multiplication chart.
*Identify patterns in a hundred chart.
Describe, complete and create a number pattern by counting on or backwards by ones, tens, hundreds or thousands within 10 000.
*Describe and complete a number pattern by repeated addition or multiplication.
Describe and complete a number pattern involving addition and subtraction of fractions with the same denominator.
Complete a number pattern with decimals involving addition and subtraction.
Describe and complete a number pattern involving positive and negative integers by counting on and backwards by ones, twos, threes, fours, fives or tens.
*Generate two number patterns from given rules and identify the relationships between corresponding terms.
Write simple expressions that record calculations with numbers.
Interpret numerical expressions without evaluation.
Equations
Find the missing part in an addition or subtraction sentence.
*Lessons are available in PR1ME Mathematics Teaching Hub.
Strand: Numbers and Operations
• CB: pp. 1–2
Objectives
• Count and write a number within 1000— the numeral and the corresponding number word
• Write a 3-digit number in hundreds, tens and ones
• Identify the position of each digit in a 3-digit number
• Find the number which is ones, tens or hundreds more than or less than a given number within 1000
• Complete number patterns by counting on or backwards
• Compare and order numbers within 1000
• Place numbers within 1000 on a number line
Let’s Remember
Unit 1: Thousands, Hundreds, Tens and Ones
• thousand
• CB: pp. 3–5
• PB: pp. 9–10
• Digital Practice
• 1 enlarged copy of Place V alue Cards (BM1.1)
• Base ten blocks
• Place value disks
• CB: pp. 5–7
• PB: p. 11
• Digital Practice
• 1 enlarged copy of Place V alue Cards (BM1.1)
• Count within 10 000
• Read and write a number within 10 000— the numeral and the corr esponding number word
1.1 Counting, reading and writing numbers
• Write a 4-digit number in thousands, hundreds, tens and ones
1.2 Identifying values of digits
• Identify the values of digits in a 4-digit number
Unit 2: Order of Numbers
• CB: pp. 8–9
• PB: p. 12
• Digital Practice
• CB: pp. 10–11
• PB: p. 13
• Digital Practice
• CB: pp. 12–13
• PB: p. 14
• Digital Practice
• CB: pp. 14–15
• PB: pp. 15–16
• Digital Practice
• CB: pp. 15–16
• PB: p. 17
• Digital Practice
• CB: pp. 16–17
• PB: p. 18
• Digital Practice
• CB: pp. 17–18
• PB: p. 19
• Digital Practice
• Counters
• Find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000
2.1 Finding more than and less than
• Count on and backwards by ones, tens, hundreds or thousands within 10 000
Number patterns
2.2
• Describe, complete and create a number pattern by counting on and backwards by ones, tens, hundreds or thousands within 10 000
• Compare and order numbers within 10 000
• Use ‘>’ and ‘<’ symbols to compare numbers within 10 000
2.3 Comparing and ordering numbers using place values
Unit 3: Rounding Numbers
• Read numbers within 10 000 on a number line
3.1 Reading number lines
• Place numbers within 10 000 on a number line
• Give a number between two 4-digit numbers
• Round a 3-digit or 4-digit number to the nearest ten
3.2 Rounding numbers to the nearest ten
• Round a 3-digit or 4-digit number to the nearest hundred
3.3 Rounding numbers to the nearest hundred
• Round a 4-digit number to the nearest thousand
3.4 Rounding numbers to the nearest thousand
Unit
• CB: pp. 19–20
• Solve a non-routine problem involving numbers to 10 000 using the strategy of looking for a pattern
Unit 4: Problem Solving 4.1 Mind stretcher
• term Digital Chapter Assessment — Available in PR1ME Mathematics Digital Practice and Assessment
The suggested duration for each lesson is 1 hour.
Let's
2. Count the hundreds, tens and ones. Then, write the missing numbers.
6. Arrange the numbers in order. Begin with the greatest. a) 182, 305, 310 b) 453, 437, 457
310, 305, 182 457, 453, 437
7. Mark 505 and 525 with crosses on the number line. 490500510520530540
The Summer Olympic Games are held every four years. The total number of medals won by United States, Germany and Russia from 1896 to 2016 are given below.
United States 2523
Germany 1346
Russia 1556
3. Complete the sentences.
a) In 647, the digit 6 is in the place.
b) In 293, the digit in the tens place is
4. Write the missing numbers.
a) is 3 more than 536.
b) is 20 less than 791.
c) 407 is 40 more than
d) 612 is 200 less than hundreds tens ones
5. Complete the number patterns. a)
Chapter Overview
Let’s Remember
Unit 1: Thousands, Hundreds, Tens and Ones
Unit 2: Order of Numbers
Unit 3: Rounding Numbers
Unit 4: Problem Solving
Let's Remember Let's Remember
Recall:
1. Counting and writing a number within 1000— the numeral and the corresponding number word (CB3 Chapter 1)
2. Writing a 3-digit number in hundreds, tens and ones (CB3 Chapter 1)
3. Identifying the position of each digit in a 3-digit number (CB3 Chapter 1)
4. Finding the number which is ones, tens or hundreds more than or less than a given number within 1000 (CB3 Chapter 1)
5. Completing number patter ns by counting on or backwards (CB3 Chapter 1)
6. Comparing and ordering numbers within 1000 (CB3 Chapter 1)
7. Placing numbers within 1000 on a number line (CB3 Chapter 1)
How can we solve this problem? Discuss in your group and fill in columns 1 and 2. 505 525
Compare and order numbers within 1000.
Arrange the countries in order. Begin with the country with the greatest number of medals in the given period of time.
United States, Russia, Germany
Compare and order numbers within 10 000. Answer varies.
Have students read the word problem on CB p. 2. Discuss with students the following questions:
•Have you ever watched any Summer Olympic Games? If yes, what is your favorite event?
•What is the total number of medals won by your country from 1896 to 2016?
•What do you think are the objectives of the Olympic Games?
Have students form groups to complete the tasks in columns 1 and 2 of the table. Let students know that they do not have to solve the word problem. Ask the groups to present their work.
Tell students that they will come back to this word problem later in the chapter.
Counting,
Let's Learn Let's Learn
Objectives:
•Count within 10 000
•Read and write a number within 10 000— the numeral and the corresponding number word
Materials:
•1 enlarged copy of Place Value Cards (BM1.1)
•Base ten blocks
Resources:
•CB: pp. 3–5
Vocabulary:
•thousand
•Place value disks
•PB: pp. 9–10
(a) Cut out the place value cards in BM1.1.
Stage: Concrete Experience
Show students 10 hundred-squares.
Ask: How many hundreds are there? (10)
Join the hundred-squares to make a thousand-block. Count by hundreds while joining the hundred-squares.
Say: There are 10 hundreds. 10 hundreds is equal to 1 thousand. We use a thousand-block to represent 1 thousand.
Stages: Pictorial and Abstract Representations
Have students look at the base ten blocks in (a) on CB p. 3.
Write: 10 hundreds = 1 thousand
Say: 10 hundreds is equal to 1 thousand.
(b) Stage: Concrete Experience
Use base ten blocks to represent 2354.
Say: Let us count on to find the number that the base ten blocks represent. 1000, 2000, 2100, 2200, 2300, 2310, 2320, 2330, 2340, 2350, 2351, 2352, 2353, 2354.
Point to the blocks as you count.
Say: The base ten blocks represent 2354. Distribute place value disks to each student.
Say: Let us use place value disks to represent 2354.
Show a thousand disk and a thousand-block. Point to the thousand disk.
Say: This is a thousand disk. It represents 1000. A thousand-block and a thousand disk represent the same value.
Note that unlike the base ten blocks where each unit cube represents 1 one, each place value disk represents 1 unit of a place value, such as 1 ten or 1 thousand.
Ask: How many thousand disks do you need to represent 2 thousands? (2)
Have students place 2 thousand disks on their tables. Similarly, introduce a hundred disk, a ten disk and a one disk and have students place 3 hundred disks, 5 ten disks and 4 one disks, respectively, on their tables.
Say: Let us count on to find the number that the place value disks represent.
Guide students to point to each place value disk as they count.
Say: The place value disks represent 2354.
Stage: Pictorial Representation
Have students look at the base ten blocks and place value disks in (b) on CB p. 3.
Ask: What number do the base ten blocks and place value disks represent? (2354) How many thousands are there? (2)
Stick the place value card ‘2000’ on the board. Ask similar questions about the hundreds, tens and ones and stick the corresponding place value cards on the board. Overlap the place value cards to show 2354 as done in (b) on the page.
Say: 2000, 300, 50 and 4 make 2354.
Stage: Abstract Representation
Write: 2000 + 300 + 50 + 4 = 2354
Say: 2354 is read as two thousand, three hundred and fifty-four.
1.
2.
3. Write
4. Write 8201 in words.
(c) Stages: Pictorial and Abstract Representations
Have students look at the place value disks in (c) on CB p. 4. Draw a place value chart, with a thousands, hundreds, tens and ones column, on the board.
Ask: How many thousands are there? (5)
Write ‘5’ in the thousands column in the place value chart.
Ask similar questions about the hundreds, tens and ones and write the corresponding digits in the place value chart.
Say: 5000, 700, 10 and 8 make 5718.
Write: 5000 + 700 + 10 + 8 = 5718
Say: 5718 is read as five thousand, seven hundred and eighteen.
Task 1 requires students to count within 10 000 and write the numbers as numerals. The numbers are represented using base ten blocks.
Task 2 requires students to count within 10 000 and write the numbers as numerals. The numbers are represented using place value disks.
Task 3 requires students to write the numerals, given the numbers in words.
Task 4 requires students to write the numbers in words given the numerals.
Count and
the
3. Write the numerals.
three thousand, five hundred and twelve
one thousand, eight hundred and four 4. Write the numbers in words.
9257
1.2 Identifying values of digits
Let's Learn Let's Learn Objectives:
•Write a 4-digit number in thousands, hundreds, tens and ones
•Identify the values of digits in a 4-digit number
Materials:
•1 enlarged copy of Place Value Cards (BM1.1)
Resources:
•CB: pp. 5–7
•PB: p. 11
(a) Cut out the place value cards in BM1.1.
Stage: Abstract Representation
Overlap the place value cards ‘4000’, ‘300’, ‘50’ and ‘8’ to show 4358 on the board.
Say: 4358 is a 4-digit number.
Separate the place value cards.
Ask: In 4358, what does the digit 4 stand for? (4000)
Ask similar questions about the other digits.
Say: 4000, 300, 50 and 8 make 4358.
Write: 4000 + 300 + 50 + 8 = 4358
Draw a place value chart, with thousands, hundreds, tens and ones columns on the board.
Explain to students that they can write 4358 in the place value chart by writing the digit 4 in the thousands place to represent 4000, the digit 3 in the hundreds place to represent 300, and so on.
Say: We can identify the value of each digit by looking at its place value. In 4358, the digit 8 is in the ones place so there are 8 ones. Its value is 8.
Ask: Which digit is in the tens place? (5) How many tens are there? (5) What is its value? (50) Ask similar questions about the digits in the hundreds and thousands places.
(b)
Follow the procedure in (a) by drawing a place value chart and asking the value of each digit. Write: 9748 = 9 thousands 7 hundreds 4 tens 8 ones
9748 = 9000 + 700 + 40 + 8
Say: 9000 + 700 + 40 + 8 is the expanded form of 9748.
Task 1 requires students to identify and write the value of each digit in 4-digit numbers.
Task 2 requires students to identify the values and place values of digits in a 4-digit number.
In 4358, the digit 8 is in the ones place and its value is 8.
The digit 5 is in the place and its value is 50.
The digit 3 is in the hundreds place and its value is 300.
The digit is in the thousands place and its value is
a) The digit 1 is in the place. b) The digit 3 stands for c) The digit in the thousands place is
The value of the digit 5
Task 3 requires students to write 4-digit numbers given the thousands, hundreds, tens and ones. Students are also required to complete the expanded form of 4-digit numbers.
Let's Practice Let's Practice
Task 1 requires students to identify the values and place values of digits in 4-digit numbers.
Task 2 requires students to identify the values of digits in 4-digit numbers.
Task 3 requires students to write 4-digit numbers given the thousands, hundreds, tens and ones. Students are also required to complete the expanded form of 4-digit numbers.
Task 4 requires students to write the expanded form of 4-digit numbers.
Have students go back to the word problem on CB p. 2.
Ask: Can you solve the problem now? (Answer varies.) What else do you need to know? (Answer varies.)
Students are not expected to be able to solve the problem now. They will learn more skills in subsequent lessons and revisit this problem at the end of the chapter.
3. Write the missing numbers.
a) 1 thousand 3 hundreds 8 tens 5 ones =
b) 3 thousands 7 hundreds 9 ones =
c) 7964 = + 900 + 60 + 4
d) 9082 = 9000 + + 2
Let's Practice Practice
1. Complete the sentences.
a) In 3470, the digit 4 is in the place.
b) In 7286, the digit has a value of 7000.
c) In 9305, the digit 0 has a value of d) In 8749, the digit in the tens place is
2. Write the value of the digit 6 in each number. a) 2461 b) 6
3. Write the missing numbers.
a) 5 thousands 1 hundred 6 tens 8 ones = b) 2 thousands 2 hundreds 3 tens = c) 4895 = + 800 + 90 + 5 d) 7077 = 7000 + + 7
4. Write the expanded form of each number. a) 5217 =
2.1 Finding more than and less than Let's Learn Let's
2.1 Finding more than and less than Let's Learn Let's Learn
Objective:
•Find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000
Materials:
•Counters
Resources:
•CB: pp. 8–9
•PB: p. 12
(a) Stages: Concrete Experience, and Pictorial and Abstract Representations
Draw a place value chart on the board and stick counters on the chart to show 2453, as shown in (a) on CB p. 8.
Ask: What number does the place value chart show? (2453)
Say: Let us find out what number is 20 more than 2453. Finding 20 more than 2453 is the same as adding 20 to 2453.
Ask: Which column of the place value chart do we add 2 counters to? (Tens)
Stick two more counters in the tens column. Ask: What number does the place value chart show now? (2473)
Say: 20 more than 2453 is 2473.
Write: 20 more than 2453 is 2473.
Point out that the digit in the tens place has changed but the other digits have not changed. Repeat the above procedure to guide students to find the number which is 1000 more than 2453 but this time, add one counter to the thousands column.
(b) Stages: Concrete Experience, and Pictorial and Abstract Representations
Follow the procedure in (a), but this time, use counters to show 5816 and remove three counters from the ones column to find the number which is 3 less than 5816. Remove four counters from the hundreds column to find the number which is 400 less than 5816.
Task 1 requires students to find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000.
Let's Learn Let's Learn
Objectives:
•Count on and backwards by ones, tens, hundreds or thousands within 10 000
•Describe, complete and create a number pattern by counting on and backwards by ones, tens, hundreds or thousands within 10 000
Resources:
•CB: pp. 10–11
•PB: p. 13
(a) Stage: Abstract Representation
Write: 1238
Say: Let us count on by tens from 1238.
Ask: What number is 10 more than 1238? (1248)
Write: 1238, 1248
Repeat the above question to form the pattern:
1238, 1248, 1258, 1268, 1278.
Say: Let us find the number that comes next in the number pattern.
Ask: What number is 10 more than 1278? (1288)
Continue the above pattern and write 1288.
Say: The number that comes next is 1288.
(b) Stage: Abstract Representation
Write: 2090, 3090, 4090, ______, 6090, 7090
Say: Let us find the missing number in the number pattern.
Ask: Is each number greater or less than the number before it? (Greater than) How much more is each number than the number before it? (1000) Say: The number pattern is formed by counting on by thousands. The missing number is 1000 more than 4090.
Ask: What is 1000 more than 4090? (5090) Write 5090 in the blank in the number pattern.
Ask: What is 1000 more than 5090? (6090)
Say: The missing number is 5090.
Let's Learn
a) Start at 1238. Count on by tens.
1238, 1248, 1258, 1268, 1278, ?
What number comes next?
10 more than 1278 is 1288. The number that comes next is
b) What is the missing number?
2090, 3090, 4090, ?, 6090, 7090
1000 more than 4090 is 5090. 1000 more than 5090 is 6090.
So, the missing number is
c) Start at 5816. Count backwards by hundreds.
5816, 5716, 5616, 5516, 5416, ?
What number comes next?
100 less than 5416 is 5316. The number that comes next is
d) What are the missing numbers?
5972, 5971, ? ?, 5968, 5967
1 less than 5971 is 5970. 1 less than 5970 is 5969. 1 less than 5969 is 5968.
So, the missing numbers are and
(c) Stage: Abstract Representation
Follow the procedure in (a), but this time count backwards by hundreds.
(d) Stage: Abstract Representation
Follow the procedure in (b). Have students observe that the number pattern is formed by counting backwards by ones.
Let's Do Let's Do
Task 1 requires students to describe number patter ns.
Task 2 requires students to complete number patterns.
Task 3 requires students to make a number pattern.
Let's Practice Let's Practice
Task 1 requires students to complete and then describe number patter ns.
Task 2 requires students to make a number pattern.
Let's Do Do
1. Describe the number patterns. a) 7655, 7555, 7455, 7355, 7255, 7155
Start at 7655. Count by b) 6286, 6296, 6306, 6316, 6326, 6336 Start at 6286. Count by
2. Complete the number patterns. a) 6357, 6358, 6359, , 6361, b) , 6419, 5419, 4419, 3419,
3. Make a number pattern using the rule: ‘Start with 2704. Count on by hundreds.’
1. Complete each number pattern. Then, describe the number pattern. a) 5465, 5466, 5467, 5468, Start at 5465. Count by b) 4568, 4558, 4548, , 4518 Start at 4568. Count by c) 9542, , 7542, 6542, , 4542 Start at 9542. Count by d) 7880, , , 8180, 8280, 8380 Start at 7880. Count by
backwards on on backwards backwards on Answer varies. Sample: 8759, 8749, 8739, 8729, 8719, 8709 6360 7419 2419 5469 4538 8542 5542 79808080 5470 4528 2704, 2804, 2904, 3004, 3104, 3204 6362 tens ones tens thousands hundreds hundreds
2. Make a number pattern that involves counting backwards. Start with 8759. Let's Practice Let's Practice P B
2.3 Comparing and ordering numbers using place values
Let's Learn 361453275351
Compare 5327, 3614 and 5351.
H T O
First, compare the thousands. 3 thousands is less than 5 thousands. 3614 is the least number.
Next, we compare 5327 and 5351. Compare the hundreds. They are the same.
Then, compare the tens. 2 tens is less than 5 tens. 5327 is less than 5351. 5327 < 5351 5351 is the greatest number.
Arrange the numbers in order. Begin with the least. (least)
2.3 Comparing and ordering numbers using place values
Let's Learn Let's Learn
Objectives:
•Compare and order numbers within 10 000
•Use ‘>’ and ‘<’ symbols to compare numbers within 10000
Resources:
•CB: pp. 12–13 •PB: p. 14
Stage: Abstract Representation
Write: 5327, 3614, 5351
Copy the first place value chart on CB p. 12 on the board without filling in the numbers.
Say: Let us compare 5327, 3614 and 5351 using a place value chart.
Invite three students to fill in the place value chart to show the numbers 5327, 3614 and 5351. Say: We start comparing from the highest place value—the thousands place.
Ask: What is the digit in the thousands place in 5327? (5) What is the digit in the thousands place in 3614? (3) What is the digit in the thousands place in 5351? (5)
Say: 3 thousands is less than 5 thousands. So, 3614 is the least number.
Ask: Which numbers do we compare next? (5327 and 5351)
Let's Do Do
1. a) Which is greater, 1902 or 1368? b) Which is less, 4715 or 4517?
Start comparing from the highest place value.
2. Write > or < a) 4135 5134 b) 2847 2748
3. Arrange the numbers in order. Begin with the least. 9853, 7692, 9801 , , (least)
Let's Practice Let's Practice
1. Write > or < a) 3527 1479 b) 4280 4652 c) 6401 6483 d) 8299 8294
769298019853 < < < > > >
2. a) Which is the least, 4792, 4927 or 4279? b) Which is the greatest, 7300, 7003 or 7030?
3. Arrange the numbers in order. Begin with the greatest. a) 2215, 1740, 3860 b) 8719, 8745, 5298, 6273
I have learned to... find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000 describe and complete number patterns compare and order numbers within 10 000 1902 4517 4279 7300 3860 8745 2215 8719 1740 62735298
Say: Since 5327 and 5351 have the same digit in the thousands and hundreds places, we compare the digits in the tens place.
Ask: What is the digit in the tens place in 5327? (2) What is the digit in the tens place in 5351? (5) Say: 2 tens is less than 5 tens. So, 5327 is less than 5351. 5351 is the greatest number. Guide students to arrange the numbers in order, beginning with the least.
Write: 3614, 5327, 5351
Task 1 requires students to compare two numbers within 10 000.
Task 2 requires students to compare two numbers within 10 000 using the symbols ‘>’ and ‘<’.
Task 3 requires students to compare and order three numbers within 10 000.
Task 1 requires students to compare two numbers within 10 000 using the symbols ‘>’ and ‘<’.
Task 2 requires students to compare three numbers within 10 000.
Task 3 requires students to compare and order numbers within 10 000.
3.1 Reading number lines
Let's Learn Let's Learn
Objectives:
•Read numbers within 10 000 on a number line
•Place numbers within 10 000 on a number line
•Give a number between two 4-digit numbers
Resources:
•CB: pp. 14–15
•PB: pp. 15–16
(a) Stages: Pictorial and Abstract Representations
Draw the number line in (a) on CB p. 14 on the board.
Say: The numbers on a number line get greater as we move along the number line from left to right. We use a number line to show the order of numbers.
Ask: How many equal intervals are there between 2000 and 3000 on this number line? (10)
Say: There are 10 equal intervals between 2000 and 3000 on this number line.
Explain to students that there is 1000 between 2000 and 3000 and 10 hundreds make 1 thousand, so each interval stands for 100. Count in steps of 100 from 2000 to 3000, moving from one mark to another on the number line as you count to verify that each interval stands for 100.
Guide students to find the numbers that W, X, Y and Z represent by counting in steps of 100.
(b) Stages: Pictorial and Abstract Representations
Draw the number line in (b) on CB p. 14 on the board.
Ask: How many equal intervals are there between 5600 and 5700 on this number line? (10) What does each interval stand for? (10)
Say: Let us find a number that is between 5600 and 5700.
Mark the number 5625 on the number line.
Ask: Is 5625 more than 5600? (Yes) Is 5625 less than 5700? (Yes)
Say: So, 5625 is between 5600 and 5700. Ask students to name other numbers that are between 5600 and 5700.
You will learn to...
Let's Learn Learn
W represents 2200.
X represents 2600.
represents Z represents
b) Find a number that is between 5600 and 5700.
5625 is more than 5600. 5625 is less than 5700. So, 5625 is between 5600 and 5700. Name three other numbers between 5600 and 5700.
Answers vary. Samples: 5610, 5673, 5694
Let's Do Let's
1. Complete the number line.
more 2800 3100
2. Circle the number between 3100 and 3200. 3300, 3090, 3108
Task 1 requires students to read numbers within 10 000 on a number line.
Task 2 requires students to circle the number that is between two given 4-digit numbers.
Task 1 requires students to read numbers within 10 000 on number lines.
Task 2 requires students to place numbers within 10 000 on a number line.
Task 3 requires students to give a number that is between two 4-digit numbers.
Let's Learn Let's Learn
Objective:
•Round a 3-digit or 4-digit number to the nearest ten
Resources:
•CB: pp. 15–16
•PB: p. 17
(a) Stage: Pictorial Representation
Draw the number line in (a) on CB p. 15 on the board but do not label ‘197’.
Guide students to see that there are 10 equal intervals between 190 and 200 and each interval stands for 1.
Invite a student to mark 197 on the number line. Say: 197 is between two tens—190 and 200. Ask: How many intervals are there from 190 to 197? (7) How many intervals are there from 197 to 200? (3) Is 197 nearer to 190 or to 200? (200)
Stage: Abstract Representation
Say: Since 197 is nearer to 200 than it is to 190, we say 200 is the ten nearest to 197. When we round 197 to the nearest ten, we get 200.
Write: 197 ≈ 200
Say: We read this statement as ‘197 is approximately 200’.
Explain that ‘≈’ is the approximation sign and means ‘approximately’.
(b) Stages: Pictorial and Abstract Representations
Follow the procedure in (a).
(c) Stages: Pictorial and Abstract Representations
Follow the procedure in (a) on TG p. 14. Point out that when a number is halfway between two tens, the greater ten is to be taken as the nearest ten. In this case, the greater ten is 3810.
Conclude that to round a number to the nearest ten, we look at the digit in the ones place. If it is 5 or greater, we round up. If it is less than 5, we round down.
Task 1 requires students to round a 3-digit and a 4-digit number to the nearest ten.
Let's Practice
Task 1 requires students to round the number of items to the nearest ten.
3.3 Rounding numbers to the nearest hundred
Objective:
•Round a 3-digit or 4-digit number to the nearest hundred
Resources:
•CB: pp. 16–17
•PB: p. 18
(a) Stage: Pictorial Representation
Draw the number line in (a) on CB p. 16 on the board.
Say: We have learned to round numbers to the nearest ten. Now let us learn to round numbers to the nearest hundred. Let us round 527 to the nearest hundred.
Ask: What are the hundreds on this number line? (500 and 600)
Point to the halfway mark on the number line and have students observe that 527 is less than halfway between 500 and 600.
Ask: Is 527 nearer to 500 or to 600? (500)
To round a number to the nearest ten, look at the digit in the ones place. If it is 5 or greater, round up. If it is less than 5, round down.
Let's Do Let's
Let's Practice
1. a) 209 children took part in an art competition. Round the number of children to the nearest ten. b) James scored 4803 points in a computer game. Round the number of points to the nearest ten.
3.3 Rounding numbers to the nearest hundred
Round
to
b) Round 6680 to the nearest hundred. 6680 is more than halfway between 6600 and 6700. It is nearer to 6700 than to 6600. 6680 is 6700 when rounded to the nearest hundred.
Stage: Abstract Representation
Say: Since 527 is nearer to 500 than it is to 600, 500 is the hundred nearest to 527. 527 is 500 when rounded to the nearest hundred.
Write: 527 ≈ 500 Say: 527 is approximately 500.
(b) Stages: Pictorial and Abstract Representations Follow the procedure in (a).
(c) Stages: Pictorial and Abstract Representations
Follow the procedure in (a) on TG p. 15. Point out that when a number is halfway between two hundreds, the greater hundred is to be taken as the nearest hundred. In this case, the greater hundred is 3300.
Conclude that to round a number to the nearest hundred, we look at the digit in the tens place. If it is 5 or greater, we round up. If it is less than 5, we round down.
Let's Do Let's and Let's Practice Let's Practice
Task 1 requires students to round 3-digit and 4-digit numbers to the nearest hundred.
3.4 Rounding numbers to the nearest thousand
Let's Learn Let's Learn
Objective:
•Round a 4-digit number to the nearest thousand
Resources:
•CB: pp. 17–18
•PB: p. 19
(a) Stage: Pictorial Representation
Draw the number line in (a) on CB p. 17 on the board.
Say: We have learned to round numbers to the nearest ten and hundred. Now, let us learn to round numbers to the nearest thousand. Let us round 1297 to the nearest thousand.
Ask: What are the thousands on this number line? (1000 and 2000)
Point to the halfway mark on the number line and have students observe that 1297 is less than halfway between 1000 and 2000.
Ask: Is 1297 nearer to 1000 or to 2000? (1000)
Stage: Abstract Representation
Say: Since 1297 is nearer to 1000 than it is to 2000, we say 1000 is the thousand nearest to 1297. We say 1297 is 1000 when rounded to the nearest thousand.
Write: 1297 ≈ 1000
Say: 1297 is approximately 1000.
3.4 Rounding numbers to the nearest thousand
(b) and (c) Stages: Pictorial and Abstract Representations
Follow the procedure in (a) on TG p. 16. For (c), point out that when a number is halfway between two thousands, the greater thousand is to be taken as the nearest thousand. In this case, the greater thousand is 5000.
Conclude that to round a number to the nearest thousand, we look at the digit in the hundreds place. If it is 5 or greater, we round up. If it is less than 5, we round down.
Do Do and Let's Practice
Task 1 requires students to round 4-digit numbers to the nearest thousand.
a number to the
Let's Do Do
4.1 Mind stretcher
Let's Learn Let's Learn
Objective:
•Solve a non-routine problem involving numbers to 10 000 using the strategy of looking for a pattern
Resource:
•CB: pp. 19–20
Vocabulary:
•ter m
Have students read the problem on CB p. 19.
1. Understand the problem. Pose the questions in the thought bubble in step 1.
2. Plan what to do.
Point out to students that they can look for a pattern to find out what number they need to add to the 19th term to get the 20th term.
3. Work out the Answer
Copy the number pattern on the board. Ask: What is the difference between the 1st and the 2nd terms? (3)
Continue to find the difference between the subsequent pairs of consecutive numbers in the pattern.
Copy the table on the page on the board. Have students look at the numbers in the last two rows of the table.
Ask: What do you notice about the numbers in these two rows? (Answer varies. Sample: Each number in the last row is 1 more than the number above it.)
Say: To find the next term, we add a number that is 1 more than the position number of the term to the previous term. For example, the 1st term of this pattern is 6. To find the 2nd term, we need to add ‘1 more than 2’ to the 1st term. So, we need to add 3 to the 1st term, 6, to get the 2nd term, 9.
4.1 Mind stretcher
Let's Learn Let's Learn
The numbers in a number pattern are called terms Look at the number pattern below. 6, 9, 13, 18, 24, 31 1st 2nd 3rd
What number do we add to the 19th term to get the 20th term?
Ask: What is the position number of the 20th term? (20) To get the 20th term, what number should we add to the 19th term? (21) How did you get this answer? (Find 1 more than 20.)
Say: To get the 20th term, we add ‘1 more than 20’ to the 19th term. 1 more than 20 is 21. So, we add 21 to the 19th term to get the 20th term.
4. Check if your answer is correct. Have students check the answer by checking that the number of terms from the 2nd term to the 20th term is the same as the number of numbers from 3 to 21.
5. + Plus Solve the problem in another way. Have students try to solve the problem in a different way.
Have 1 or 2 students share their methods. If students are unable to solve the problem in a different way, explain the method shown on CB p. 20.
Ask: Which method do you prefer? Why? (Answers vary.)
Have students go back to the word problem on CB p. 2. Get them to write down in column 3 of the table what they have learned that will help them solve the problem, and then solve the problem.
Have a student present his/her work to the class.
We add 21 to the 19th term to get the 20th term. Compare the methods in steps 3 and 5. Which method do you prefer? Why?
Exercise 1.1
1. a) 2304 b) 3023
2. a) 8527 b) 5032
3. a) 8556 b) 3043 c) 5109 d) 6002
4. a) eight thousand, three hundred and twenty-one
b) seven thousand, eight hundred and six c) four thousand and eight d) nine thousand and ten e) three thousand, seven hundred and nineteen f) five thousand, five hundred and forty g) six thousand, nine hundred and ninety-nine
Exercise 1.2
1. a) 5 b) 4
c) thousands d) 30
e) tens; 0
2. Circle:
a) 9523 b) 4325
3. a) 800 b) 9
c) 4000 d) 6000
4. a) 3000 + 800 + 40 + 7
b) 4000 + 200 + 8 c) 5000 + 90
Exercise 2.1
1. a) 5234
b) 1919 c) 5878 d) 6670
e) 4341 f) 3227 g) 9020 h) 3897 i) 4208 j) 8646 k) 8226 l) 8726
m) 30 n) 1000 o) 700 p) 3000
Exercise 2.2
1. a) 8701; 8801; on; hundreds b) 6550; 6540; backwards; tens c) 6999; 5999; backwards; thousands d) 3880; 3890; on; tens e) 2230; 1930; 1830; backwards; hundreds f) 6467; 9467; on; thousands g) 7503; 7493; backwards; tens
Exercise 2.3
1. a) < b) >
c) < d) >
2. a) 3228, 3174, 3124
b) 2222, 2220, 2200, 2000
3. a) 1001, 1010, 1100
b) 9896, 9900, 9998, 9999
4. a) 964; 346 b) 5079; 9750
Exercise 3.1
1. a) 6300; 6700; 6900 b) 7010; 7040; 7090
c) 3000; 5000; 7500 d) 5150; 5300; 5400
e) 2900; 3300; 3800
2.
3. Circle:
a) 5504 b) 7011
c) 3454 d) 2335
e) 8899
4. Answers vary. Sample:
a) 1385 b) 6025
c) 9560 d) 4800
e) 2510 f) 5900
g) 9000
Exercise 3.2
1. a) 60 b) 70 c) 100
d) 430 e) 690 f) 840
g) 1240 h) 2700 i) 9900
j) 5210 k) 5100 l) 3000
2. a) 240 b) 3450 meters c) $2810
d) 530 e) 920 f) 3740
Exercise 3.3
1. a) 700 b) 300 c) 900 d) 500 e) 400 f) 1000 g) 2300 h) 9000 i) 4000 j) 4900 k) 6400 l) 7300
2. Tick:
a) 267 b) 1231 c) 5680 d) 9830
3. 2350
Exercise 3.4
1. a) 3000 b) 9000 c) 2000 d) 5000
e) 3000 f) 7000 g) 5000 h) 9000 i) 7000 j) 9000 k) 2000 l) 8000
2. 5000; 9000; 5000; 4000; 4000
• 8-point compass
We can tell directions using an 8-point compass
(N)
East is 90° away from north. So, northeast is 45° away from north and from east.
• 24-hour clock notation
The 24-hour clock notation is a way of writing time by dividing a day into 24 hours.
10:30 a.m. can be written as 10 : 30.
1: 25 p.m. can be written as 13 : 25.
A • acute angle
An acute angle is an angle that is smaller
a 3D shape is usually the face on which it rests. In a prism, the parallel identical faces are known as the bases.
• closed figure
Closed figures start and end at the same point.
These are closed figures.
• cross section
A cross section of a 3D shape is the shape made when the 3D shape is cut parallel to its base.
• decagon
cross section
A decagon is a polygon with 10 sides.
• decimal
A decimal is a number with a whole number part and a fractional part separated by a decimal point. 0.2, 3.02 and 4.53 are decimals.
• decimal place A decimal place is the position of a digit to the right of a decimal point. The decimal 15.49 has two decimal places: the tenths place and the hundredths place.
• decimal point A decimal point is a dot used to separate the whole number part from the fractional part of a number.
whole number partfractional part 1 5
decimal point
I • improper fraction An improper fraction is a fraction that is equal to or greater than 1. Its numerator is equal to or greater than its denominator.
13 6 and 11 11 are improper fractions.
• irregular polygon An irregular polygon is a polygon in which all the sides are not of equal length or all angles are not of equal measure.
These are examples of irregular polygons.
L • legend A map has a legend which explains what each symbol on the map represents. It is also called a key.
• obtuse angle An obtuse angle is an angle that measures greater than
Angle b is an obtuse angle.
• open figure
Open figures start and end at different points.
These are open figures.
• degree A degree is a unit of angle measure.
A right angle measures 90 degrees. Write 90 degrees as 90°.
• divisible
A number is divisible by another number if it can be divided without any remainder.
12 ÷ 4 = 3 12 can be divided by 4 without any remainder.
12 is divisible by 4.
H
• heptagon
A heptagon is a polygon with 7 sides.
• hexagonal prism
See prism
• hexagonal pyramid
See pyramid
• hundredth
1 hundredth is 1 out of 100 equal parts.
1 100 = 0.01
parallel
These two faces of the 3D shape are parallel. They are always the same distance apart.
• pentagonal prism See prism.
• pentagonal pyramid See pyramid.
• polygon A polygon is a closed figure formed by 3 or more line segments that do not cross.
These figures are polygons.
• prism A prism is a 3D shape with two parallel identical faces joined by square or rectangular faces.
• pyramid A pyramid is a 3D shape that has a polygonal base and three or more triangular faces that meet at a common vertex.
The shape of the base of a pyramid gives the pyramid its name.
Q • quadrilateral A quadrilateral is a polygon with 4 sides.
R
• rectangular
The shape of the base of a
gives the
• regular polygon A regular polygon is a polygon in which all sides are of equal length and all angles are of equal measure.
These are examples of regular polygons.
S • second (s) The second is a smaller unit of time than the minute.
1 minute = 60 seconds
• second
The second hand is the clock hand that shows the number of seconds that has passed in a minute.
• square centimeter (cm2)
The area of the square is 1 square centimeter
• square meter (m2) 1 m 1 m The area of the square is 1 square meter.
• square prism See prism
• square pyramid See pyramid
• square unit The area of the figure is 7 square units
T • tenth 1 tenth is 1 out of 10 equal parts. 1 10 = 0.1
• term Numbers in a number pattern are called terms
U • uniform cross section A 3D shape has a uniform cross section when the cross sections of the 3D shape are identical in shape and size. Prisms have uniform cross sections.
V • vertex (angle) The vertex of an angle is the point at which the endpoints of the two rays meet.
of ABC.
the
•
• timetable A timetable shows the events that occur at different times of the day in the order of their occurrence.
• triangular prism See prism
• triangular pyramid See pyramid
BM1.1 Place Value Cards
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
3 0 0 2 0 0 1 0 0 6 0 0 5 0 0 4 0 0 9 0 0 8 0 0 7 0 0 1 0 0 0 0
9 0 0 0 2 0 0 0 1 0 0 0 4 0 0 0 3 0 0 0 6 0 0 0 5 0 0 0 8 0 0 0 7 0 0 0
A world-class program incorporating the highly effective Readiness-Engagement-Mastery model of instructional design
100% coverage of Cambridge Primary Mathematics Curriculum Framework Incorporates Computational Thinking and Math Journaling Builds a Strong Foundation for STEM
Scholastic TM Mathematics (New Edition) covers five strands of mathematics across six grades: Numbers and Operations, Measurement, Geometry, Data Analysis, and Algebra.
The instructional design of the program incorporates the Readiness-Engagement-Mastery process of learning mathematics, making learning meaningful, and lesson delivery easy and effective.
Think About It Practice
Create Your Own Assessment
Mind Stretcher Math Jour nal
Mission Possible Exercises Reviews
Each chapter of the coursebook starts with Let’s Remember and Explore to ready students for learning new content and comprises units of study developed on carefully grouped learning objectives. Each unit is delivered through specially crafted daily lessons that focus on a concept or an aspect of it. Concepts and skills are introduced in Let’s Learn. Let’s Do and Let’s Practice provide opportunities for immediate formative assessment and practice.
Let’s Remember offers an opportunity for systematic recall and assessment of prior knowledge in preparation for new learning.
Explore encourages mathematical curiosity and a positive learning attitude. It gets students to recall prior knowledge, set targeted learning goals for themselves and track their learning as they progress through the unit, seeking to solve the problem.
In Let’s Learn, concepts and skills are introduced and developed to mastery using the concrete-pictorialabstract approach. This proven, research-based approach develops deep conceptual understanding.
Systematic variation of tasks in Let's Do and Let's Practice reinforces students’ understanding and enables teachers to check learning and identify remediation needs.
Practice Book links lead to exercises in the Practice Book to further reinforce understanding of the concepts and skills learnt.
Think About It develops metacognition by providing opportunities for mathematical communication, reasoning and justification. Question prompts take students through the mathematical reasoning process, helping teachers identify misconceptions.
A Problem Solving lesson concludes each chapter. With a focus on both the strategies and the process of problem solving, these word problems provide a meaningful context for students to apply mathematical knowledge and skills.
A 5-step process guides students to systematically solve problems by applying appropriate strategies and to reflect on their problemsolving approach.
Create Your Own and Mind Stretcher develop higher-order thinking skills and metacognitive ability.
Mission Possible develops computational thinking through a scaffolded approach to solving complex problems with newly learnt skills.
Mathematical Modeling provides opportunities for students to model solutions to real-world problem situations.
To make learning and teaching fun and engaging, digital components are available with
Digital practice and assessment further strengthen understanding of key concepts and provide diagnostic insight in students' capabilities and gaps in understanding.
In addition to the course materials for in-class projection, the Hub offers valuable resources including videos, lesson notes, and additional content at point of use.
Let’s
1. Count and write the number in numerals and in words.
Numeral:
Words:
2. Count the hundreds, tens and ones. Then, write the missing numbers.
hundreds tens ones =
3. Complete the sentences.
a) In 647, the digit 6 is in the place.
b) In 293, the digit in the tens place is .
4. Write the missing numbers.
a) is 3 more than 536.
b) is 20 less than 791.
c) 407 is 40 more than .
d) 612 is 200 less than .
5. Complete the number patter ns.
a) 324, 329, 334, , , 349,
b) 580, , , 574, 572, , 568
6. Arrange the numbers in order. Begin with the greatest.
a) 182, 305, 310
b) 453, 437, 457
7. Mark 505 and 525 with crosses on the number line. 490500510520530540
The Summer Olympic Games are held every four years. The total number of medals won by United States, Germany and Russia from 1896 to 2016 are given below.
United States 2523
Ger many 1346 Russia 1556
Arrange the countries in order. Begin with the country with the greatest number of medals in the given period of time.
How can we solve this problem? Discuss in your group and fill in columns 1 and 2.
learn
You will learn to...
• count within 10 000
• read and write numbers up to 10 000
• write 4-digit numbers in thousands, hundreds, tens and ones
• identify the values of digits in 4-digit numbers
1.1 Counting, reading and writing numbers
Let's Learn Learn a) one thousand 10 hundreds = 1 thousand b) 2 thousands 3
Count on from 1000.
1000, 2000, 2100, 2200, 2300, 2310, 2320, 2330, 2340, 2350, 2351, 2352, 2353, 2354
2000 + 300 + 50 + 4 = 2354
2354 is read as two thousand, three hundred and fifty-four.
+ 700 + 10 + 8 =
Let's Do Let's Do
1. Count and write the numeral.
Count the thousands, hundreds, tens and ones.
2. Count and write the numeral.
3000 + 200 + 90 + 3 =
3. Write two thousand, seven hundred and fifteen as a numeral.
4. Write 8201 in words.
1. Count and write the numeral.
2. Count and write the numeral.
6000 + 500 + 8 =
3. Write the numerals.
a) three thousand, five hundred and twelve
b) one thousand, eight hundred and four
4. Write the numbers in words.
a) 9257
b) 4006
c) 8013
a) 4358 is a 4-digit
+ 300 + 50 + 8 = 4358 Let's Learn Learn
digit 8 stands for 8.
digit 5 stands for . The digit 3 stands for . The digit 4 stands for 4000.
In 4358, the digit 8 is in the ones place and its value is 8.
The digit 5 is in the place and its value is 50.
The digit 3 is in the hundreds place and its value is 300.
The digit is in the thousands place and its value is .
The expanded form of 9748 is 9000 + 700 + 40 + 8. b)
9748 = 9 thousands 7 hundreds 4 tens 8 ones
9748 = 9000 + 700 + 40 + 8
Let's Do Do
1. Write the values of the digits.
a) b) 2 9 0 7 8 6 1 5
2. Look at the place value table below and complete the sentences.
a) The digit 1 is in the place.
b) The digit 3 stands for .
c) The digit in the thousands place is .
d) The value of the digit 5 is .
3. Write the missing numbers.
a) 1 thousand 3 hundreds 8 tens 5 ones =
b) 3 thousands 7 hundreds 9 ones =
c) 7964 = + 900 + 60 + 4
d) 9082 = 9000 + + 2
1. Complete the sentences.
a) In 3470, the digit 4 is in the place.
b) In 7286, the digit has a value of 7000.
c) In 9305, the digit 0 has a value of .
d) In 8749, the digit in the tens place is .
2. Write the value of the digit 6 in each number.
a) 2461 b) 6007 c) 5236
d) 9689 e) 3610 f) 7368
3. Write the missing numbers.
a) 5 thousands 1 hundred 6 tens 8 ones =
b) 2 thousands 2 hundreds 3 tens =
c) 4895 = + 800 + 90 + 5
d) 7077 = 7000 + + 7
4. Write the expanded form of each number.
a) 5217 =
b) 3094 =
I have learned to... count within 10 000 read and write numbers up to 10 000 write 4-digit numbers in thousands, hundreds, tens and ones identify the values of digits in 4-digit numbers
>> Look at EXPLORE on page 2 again. Can you solve the problem now? What else do you need to know?
You will learn to...
• find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000
• describe and complete number patterns
• compare and order numbers within 10 000
Let's Learn Let's Learn
20 more than 2453 is 2473. 1000 more than 2453 is . 3 less than 5816 is 5813.
400 less than 5816 is .
Let's Do Let's Do
1. Write the missing numbers.
a)
b)
100 more than 3508 is . 2000 less than 6125 is .
c) 50 more than 1423 is . d) 4 less than 7759 is . e) 3194 is more than 2794. f) 9271 is less than 9331.
Let's Practice Let's Practice
1. Write the missing numbers.
a) 2 more than 4047 is . b) 300 less than 2472 is .
c) is 1 less than 5670. d) is 3000 more than 3087.
e) 9422 is more than 9382. f) 6699 is less than 6729.
a) Start at 1238. Count on by tens.
1238, 1248, 1258, 1268, 1278, ?
What number comes next?
b) What is the missing number?
2090, 3090, 4090, ?, 6090, 7090
1248 is 10 more than 1238. 1258 is 10 more than 1248.
10 more than 1278 is 1288. The number that comes next is .
1000 more than 4090 is 5090. 1000 more than 5090 is 6090.
So, the missing number is .
c) Start at 5816. Count backwards by hundreds.
100 – 100 – 100 + 1000 + 1000 + 1000 + 10 + 10 + 10
100
5816, 5716, 5616, 5516, 5416, ?
What number comes next?
d) What are the missing numbers?
1 – 1
5972, 5971, ?, ?, 5968, 5967
5716 is 100 less than 5816. 5616 is 100 less than 5716.
100 less than 5416 is 5316. The number that comes next is .
1 less than 5971 is 5970. 1 less than 5970 is 5969. 1 less than 5969 is 5968.
So, the missing numbers are and . + 10
1. Describe the number patter ns.
a) 7655, 7555, 7455, 7355, 7255, 7155
Start at 7655. Count by .
b) 6286, 6296, 6306, 6316, 6326, 6336
Start at 6286. Count by .
2. Complete the number patter ns.
a) 6357, 6358, 6359, , 6361,
b) , 6419, 5419, 4419, 3419,
3. Make a number patter n using the rule: ‘Start with 2704. Count on by hundreds.’
Let's Practice Let's
1. Complete each number patter n. Then, describe the number pattern.
a) 5465, 5466, 5467, 5468, ,
Start at 5465. Count by .
b) 4568, 4558, 4548, , , 4518
Start at 4568. Count by .
c) 9542, , 7542, 6542, , 4542
Start at 9542. Count by .
d) 7880, , , 8180, 8280, 8380
Start at 7880. Count by .
2. Make a number patter n that involves counting backwards. Start with 8759.
Let's Learn Let's Learn
Compare 5327, 3614 and 5351.
First, compare the thousands. 3 thousands is less than 5 thousands. 3614 is the least number.
Next, we compare 5327 and 5351.
Compare the hundreds. They are the same.
Then, compare the tens. 2 tens is less than 5 tens. 5327 is less than 5351. 5327 < 5351 5351 is the greatest number.
Arrange the numbers in order. Begin with the least. , , (least)
1. a) Which is greater, 1902 or 1368? b) Which is less, 4715 or 4517?
2. Write > or <.
a) 4135 5134
Start comparing from the highest place value.
b) 2847 2748
3. Arrange the numbers in order. Begin with the least. 9853, 7692, 9801 , , (least)
1. Write > or <.
a) 3527 1479
c) 6401 6483
b) 4280 4652
d) 8299 8294
2. a) Which is the least, 4792, 4927 or 4279?
b) Which is the greatest, 7300, 7003 or 7030?
3. Arrange the numbers in order. Begin with the greatest.
a) 2215, 1740, 3860 , , b) 8719, 8745, 5298, 6273 , , ,
I have learned to... find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000 describe and complete number patterns compare and order numbers within 10 000
You will learn to...
• read numbers to 10 000 on a number line
• round a 3-digit or 4-digit number to the nearest ten or hundred
• round a 4-digit number to the nearest thousand
Let's Learn Let's Learn
W represents 2200.
X represents 2600.
Y represents .
Z represents .
There are 10 equal intervals between 2000 and 3000. Each interval stands for 100. Count in steps of 100. 2000, 2100, 2200, …
b) Find a number that is between 5600 and 5700.
5625 is more than 5600. 5625 is less than 5700. So, 5625 is between 5600 and 5700.
Name three other numbers between 5600 and 5700.
Let's Do Do
1. Complete the number line.
2. Circle the number between 3100 and 3200. 3300, 3090, 3108
1. Complete the number lines.
2. Mark 1450 and 950 with crosses on the number line. b)
3. Write a number that is between the two given numbers. a) 4300 and 4400 b) 2480 and 2495
Let's Learn Let's Learn Let's Practice Let's
a) Round 197 to the nearest ten.
197 is between 190 and 200. It is nearer to 200 than to 190.
197 is 200 when rounded to the nearest ten.
197 ≈ 200
b) Round 7361 to the nearest ten.
7361 is between 7360 and 7370. It is nearer to 7360 than to 7370.
7361 is 7360 when rounded to the nearest ten.
7361 ≈ ≈ is the approximation sign.
c) Round 3805 to the nearest ten.
3805
3800 3810
3805 is halfway between 3800 and 3810. 3805 is 3810 when rounded to the nearest ten.
3805 ≈
To round a number to the nearest ten, look at the digit in the ones place. If it is 5 or greater, round up. If it is less than 5, round down.
Let's Do Let's Do
1. Round each number to the nearest ten.
Let's Practice Let's Practice
1. a) 209 children took part in an art competition. Round the number of children to the nearest ten.
b) James scored 4803 points in a computer game. Round the number of points to the nearest ten.
Let's Learn Let's Learn
a) Round 527 to the nearest hundred.
527 is less than halfway between 500 and 600. It is nearer to 500 than to 600.
527 is 500 when rounded to the nearest hundred.
527 ≈ 500
b) Round 6680 to the nearest hundred.
6680 is more than halfway between 6600 and 6700. It is nearer to 6700 than to 6600.
6680 is 6700 when rounded to the nearest hundred.
6680 ≈
c) Round 3250 to the nearest hundred.
3250 3200 3300
3250 is halfway between 3200 and 3300. 3250 is 3300 when rounded to the nearest hundred. 3250 ≈
To round a number to the nearest hundred, look at the digit in the tens place. If it is 5 or greater, round up. If it is less than 5, round down.
Let's Do Let's Do
1. Round each number to the nearest hundred.
≈
Let's Practice Let's Practice
1. Round each number to the nearest hundred.
693
2739
975
Let's Learn Learn
a) Round 1297 to the nearest thousand.
1297
1297 is less than halfway between 1000 and 2000. It is nearer to 1000 than to 2000. 1297 is 1000 when rounded to the nearest thousand. 1297 ≈ 1000
b) Round 8760 to the nearest thousand.
8760 is more than halfway between 8000 and 9000. It is nearer to 9000 than to 8000.
8760 is 9000 when rounded to the nearest thousand.
8760 ≈
c) Round 4500 to the nearest thousand.
4500 is halfway between 4000 and 5000.
4500 is 5000 when rounded to the nearest thousand.
4500 ≈
To round a number to the nearest thousand, look at the digit in the hundreds place. If it is 5 or greater, round up. If it is less than 5, round down.
Let's Do Let's Do
1. Round each number to the nearest thousand.
Let's Practice Let's Practice
1. Round each number to the nearest thousand.
I have learned to... read numbers to 10 000 on a number line round a 3-digit or 4-digit number to the nearest ten or hundred round a 4-digit number to the nearest thousand
B Chapter 1: Exercise 3.4
You will learn to...
• solve a non-routine problem involving numbers to 10 000
Let's Learn Let's Learn
The numbers in a number pattern are called terms. Look at the number pattern below.
6, 9, 13, 18, 24, 31 1st 2nd 3rd
What number do we add to the 19th term to get the 20th term?
How do we get the second term from the first term?
How do we get the third term from the second term?
What do I have to find?
I can look for the pattern 6, 9, 13, 18, 24, 31
1 Plan what to do. 2 Work out the Answer. 3 + 3+ 4+ 5+ 6+ 7 Term 6913182431
To find the next term, we add a number that is 1 more than the position number of the term to the previous term. Understand the problem.
Position of term 1st2nd 3rd 4th5th6th Add to previous term 34567
4
5
Check if your answer is correct.
+ Plus Solve the problem in another way.
To get the 20th term, we add 1 more than 20 to the 19th term. 1 more than 20 is 21. So, we add 21 to the 19th term to get the 20th term.
1st, 2nd, 3rd, …, 20th
There are 19 terms from the 2nd term to the 20th term. 3, 4, 5, …, 21
There are also 19 numbers from 3 to 21. So, my answer is correct.
Continue the pattern until you get the 20th term.
6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th
81, 94, 108, 123, 139, 156, 174, 193, 213, 234 11th 12th 13th 14th 15th 16th 17th 18th 19th 20th
We add 21 to the 19th term to get the 20th term.
Compare the methods in steps 3 and 5. Which method do you prefer? Why?
Understand 2. Plan 3. Answer 4. Check 5. Plus
I have learned to... solve a non-routine problem involving numbers to 10 000
>> Look at EXPLORE on page 2 again. Fill in column 3. Can you solve the problem now?
• 8-point compass
We can tell directions using an 8-point compass
Northwest (NW)
Southwest (SW)
East is 90° away from north. So, northeast is 45° away from north and from east.
• 24-hour clock notation
The 24-hour clock notation is a way of writing time by dividing a day into 24 hours.
10 :30 a.m. can be written as 10 : 30. 1: 25 p.m. can be written as 13 : 25.
A
• acute angle
An acute angle is an angle that is smaller than a right angle. It measures less than 90°.
• area
The area of a figure is the number of units needed to cover the sur face of the figure.
Angle a is an acute angle. a
The area of the figure is 8 square units.
• base (3D shape)
The base of a 3D shape is usually the face on which it rests. In a prism, the parallel identical faces are known as the bases.
• closed figure
Closed figures start and end at the same point.
These are closed figures.
• cross section
A cross section of a 3D shape is the shape made when the 3D shape is cut parallel to its base.
cross section
• degree
A degree is a unit of angle measure.
• divisible
D
• decagon
A decagon is a polygon with 10 sides.
• decimal
A decimal is a number with a whole number part and a fractional part separated by a decimal point. 0.2, 3.02 and 4.53 are decimals.
• decimal place
A decimal place is the position of a digit to the right of a decimal point. The decimal 15.49 has two decimal places: the tenths place and the hundredths place.
• decimal point
A decimal point is a dot used to separate the whole number part from the fractional part of a number.
1.5
whole number partfractional part
decimal point
A right angle measures 90 degrees. Write 90 degrees as 90°.
A number is divisible by another number if it can be divided without any remainder.
12 ÷ 4 = 3
12 can be divided by 4 without any remainder.
12 is divisible by 4.
H
• heptagon
A heptagon is a polygon with 7 sides.
• hexagonal prism
See prism.
• hexagonal pyramid
See pyramid.
• hundredth
1 hundredth is 1 out of 100 equal parts.
1 100 = 0.01
• improper fraction
An improper fraction is a fraction that is equal to or greater than 1. Its numerator is equal to or greater than its denominator.
13 6 and 11 11 are improper fractions.
• irregular polygon
An irregular polygon is a polygon in which all the sides are not of equal length or all angles are not of equal measure.
These are examples of irregular polygons. L
• legend
A map has a legend which explains what each symbol on the map represents. It is also called a key.
• mixed number
A mixed number is made up of a whole number and a fraction.
7 + 1 2 = 7 1 2 mixed number whole number fraction
• nonagon
A nonagon is a polygon with 9 sides. O
• obtuse angle
An obtuse angle is an angle that measures greater than 90° but less than 180°.
b
Angle b is an obtuse angle.
• open figure
Open figures start and end at different points.
These are open figures.
• parallel
These two faces of the 3D shape are parallel. They are always the same distance apart.
• pentagonal prism See prism.
• pentagonal pyramid See pyramid.
• polygon
A polygon is a closed figure formed by 3 or more line segments that do not cross.
These figures are polygons.
• prism
A prism is a 3D shape with two parallel identical faces joined by square or rectangular faces.
• pyramid
A pyramid is a 3D shape that has a polygonal base and three or more triangular faces that meet at a common vertex.
• rectangular pyramid See pyramid. parallel faces
The shape of the base of a pyramid gives the pyramid its name. Q
• quadrilateral
A quadrilateral is a polygon with 4 sides.
The shape of the base of a prism gives the prism its name.
R
• rectangular prism See prism.
• regular polygon
A regular polygon is a polygon in which all sides are of equal length and all angles are of equal measure.
These are examples of regular polygons.
• square prism
See prism.
• square pyramid
See pyramid.
• square unit
S
• second (s)
The second is a smaller unit of time than the minute. 1 minute = 60 seconds
• second hand
The second hand is the clock hand that shows the number of seconds that has passed in a minute.
The area of the figure is 7 square units.
• tenth 1 tenth is 1 out of 10 equal parts. 1 10 = 0.1
• term
Numbers in a number patter n are called terms.
2, 4, 6, 8, 10
The area of the square is 1 square centimeter.
• square meter (m2) 1 m 1 m
The area of the square is 1 square meter.
• thousand 1 thousand = 10 hundreds = 1000
• timetable
A timetable shows the events that occur at different times of the day in the order of their occurrence.
• triangular prism
See prism.
• triangular pyramid
See pyramid.
• uniform cross section
A 3D shape has a uniform cross section when the cross sections of the 3D shape are identical in shape and size.
Prisms have unifor m cross sections. V
• vertex (angle)
cross sections
The vertex of an angle is the point at which the endpoints of the two rays meet.
Point B is the vertex of ABC.
A world-class program incorporating the highly effective
Readiness-Engagement-Mastery model of instructional design
PR1ME Mathematics Digital Practice and Assessment provides individualized learning support and diagnostic performance reports
Scholastic TM Mathematics (New Edition) covers five strands of mathematics across six grades: Numbers and Operations, Measurement, Geometry, Data Analysis, and Algebra.
Each Practice Book comprises chapters with several Exercises. Chapters end with Problem Solving exercises. A Review follows after every four or five chapters.
Exercises provide comprehensive practice for students to attain fluency and mastery of topics.
Recap helps students to recall what was taught in the coursebook and assist them with the exercise.
Tasks in each exercise are systematically varied to provide comprehensive practice and formative assessment.
Reviews provide summative assessment and enable consolidation of concepts and skills learnt across various topics.
Chapter 1 Whole Numbers
Exercise 1.1 Counting, reading and writing numbers 9
Exercise 1.2 Identifying values of digits 11
Exercise 2.1 Finding more than and less than 12
Exercise 2.2 Number patter ns 13
Exercise 2.3 Comparing and ordering numbers using place values 14
Exercise 3.1 Reading number lines 15
Exercise 3.2 Rounding numbers to the nearest ten 17
Exercise 3.3 Rounding numbers to the nearest hundred 18
Exercise 3.4 Rounding numbers to the nearest thousand 19
Chapter 2 Addition and Subtraction Within 10 000
Exercise 1.1 Adding without regrouping
Exercise 1.2 Adding with regrouping once
Exercise 1.3 Adding with regrouping twice
Exercise 1.4 Adding with regrouping three times
Exercise 1.5 Estimating sums
Exercise 1.6 Solving word problems
Exercise 2.1 Subtracting without regrouping
Exercise 2.2 Subtracting with regrouping once
Exercise 2.3 Subtracting with regrouping twice
Exercise 2.4 Subtracting with regrouping three times
Exercise 2.5 Regrouping from thousands or hundreds
Exercise 2.6 Estimating differences
Exercise 2.7 Solving word problems
Exercise 3.1 Word problems
Chapter 3 Multiplication and Division of Whole Numbers
Exercise 1.1 Multiplying ones, tens or hundreds by a 1-digit number 38
Exercise 1.2 Multiplying 3-digit numbers by 1-digit numbers 39
Exercise 1.3 Multiplying three 1-digit numbers 40
Exercise 1.4 Multiplying whole numbers by 10
Exercise 1.5 Estimating products
Exercise 1.6 Solving word problems
Exercise 2.1 Dividing hundreds or tens by a 1-digit numbers
Exercise 2.2 Dividing 3-digit numbers by 1-digit numbers
Exercise 2.3 Dividing whole numbers by 10
Exercise 2.4 Estimating quotients
Exercise 2.5 Solving word problems
Exercise 3.1 Word problems
Exercise 1.1 Writing mixed numbers 59
Exercise 1.2 Comparing and ordering mixed numbers on a number line 60
Exercise 2.1 Writing improper fractions 61
Exercise 2.2 Expressing improper fractions as mixed numbers 62
Exercise 2.3 Expressing mixed numbers as improper fractions 63
Exercise 2.4 Expressing a mixed number as another mixed number 64
Exercise 3.1 Associating fractions with division 65
Exercise 3.2 Expressing improper fractions as whole numbers or mixed numbers 66
Exercise 3.3 Solving word problems 67
Chapter 5 Operations of Fractions
Exercise 1.1 Adding two fractions 69
Exercise 1.2 Adding three fractions 70
Exercise 1.3 Solving word problems 71
Exercise 2.1 Subtracting a fraction from a whole number 73
Exercise 2.2 Subtracting two fractions from a whole number 74
Exercise 2.3 Completing number patter ns 75
Exercise 2.4 Solving word problems 76
Exercise 3.1 Understanding fraction of a set 78
Exercise 3.2 Finding a fraction of a set 79
Exercise 3.3 Multiplying a fraction and a whole number 80
Exercise 3.4 Solving word problems 82
Exercise 4.1 Word problems 84
Exercise 1.1 Understanding the relationship between units of measurement 87
Exercise 1.2 Comparing readings on different scales 88
Exercise 1.3 Converting measurements in different units 90
Exercise 1.4 Comparing measurements 91
Exercise 1.5 Measuring and drawing line segments 92
Exercise 1.6 Adding and subtracting measurements in compound units 94
Exercise 2.1 Solving word problems 95
Chapter 7 Handling Data
Exercise 1.1 Collecting, presenting and interpreting data 97
Exercise 2.1 Sorting data in Venn diagrams with 2 criteria 99
Exercise 2.2 Sorting data in Venn diagrams with 3 criteria 101
Chapter 8 Angles
Exercise 1.1 Naming angles 103
Exercise 1.2 Estimating and measuring angles 104
Exercise 1.3 Drawing angles 105
Chapter 9 Position and Movement
Exercise 1.1 Relating tur ns to right angles 108
Exercise 1.2 Telling directions using an 8-point compass 109
Exercise 1.3 Giving directions 111
Chapter 10 Decimals
Exercise 1.1 Reading and writing decimals less than 1 121
Exercise 1.2 Expressing decimals as fractions with a denominator of 10 122
Exercise 1.3 Reading and writing decimals greater than 1 123
Exercise 1.4 Interpreting decimals in terms of tens, ones and tenths 124
Exercise 1.5 Identifying values of digits 125
Exercise 1.6 Writing tenths as decimals 126
Exercise 1.7 Reading number lines 127
Exercise 1.8 Measuring and drawing line segments 128
Exercise 1.9 Expressing decimals as fractions or mixed numbers in their simplest for m 130
Exercise 1.10 Comparing and ordering decimals 131
Exercise 2.1 Reading and writing decimals 132
Exercise 2.2 Interpreting decimals in terms of tens, ones, tenths and hundredths 133
Exercise 2.3 Identifying values of digits 134
Exercise 2.4 Expressing fractions and mixed numbers as decimals 135
Exercise 2.5 Reading number lines 136
Exercise 2.6 Expressing decimals as fractions or mixed numbers in their simplest for m 137
Exercise 2.7 Comparing and ordering decimals 138
Exercise 2.8 Finding ‘more than’ and ‘less than’ 139
Exercise 3.1 Rounding decimals to the nearest whole number 140
Exercise 3.2 Rounding decimals to 1 decimal place 141
Chapter 11 Mental Strategies
Exercise 1.1 Making 1000 142
Exercise 2.1 Adding two 2-digit numbers using the ‘add the tens, then add the ones’ strategy 143
Exercise 2.2 Adding two 2-digit numbers by making tens 144
Exercise 2.3 Adding numbers using the compensation strategy 145
Exercise 2.4 Adding three or four numbers 146
Exercise 3.1 Subtracting 2-digit numbers with regrouping 147
Exercise 3.2 Subtracting 2-digit numbers from tens 148
Exercise 3.3 Subtracting numbers using the compensation strategy 149
Exercise 4.1 Finding doubles of 2-digit numbers 150
Exercise 4.2 Finding doubles of tens or hundreds 151
Exercise 4.3 Finding halves of numbers up to 200 152
Exercise 4.4 Finding halves of tens or hundreds 153
Review 3 154
Chapter 12 2D Shapes
Exercise 1.1 Identifying open and closed figures 163
Exercise 1.2 Identifying polygons 164
Exercise 1.3 Naming polygons 165
Exercise 1.4 Making and drawing polygons 166
Exercise 2.1 Symmetry in polygons 168
Exercise 2.2 Sorting polygons 170
Exercise 2.3 Symmetry in patter ns 171
Chapter 13 3D Shapes
Exercise 1.1 Identifying types of prisms 172
Exercise 1.2 Understanding cross sections of prisms 174
Exercise 1.3 Identifying types of pyramids 175
Exercise 1.4 Understanding cross sections of pyramids 177
Exercise 1.5 Sorting prisms and pyramids 178
Exercise 2.1 Making prisms and pyramids 179
Chapter 14 Area
Exercise 1.1 Understanding area 180
Exercise 1.2 Area in square units 181
Exercise 2.1 Area in square centimeters 183
Exercise 2.2 Area in square meters 184
Chapter 15 Time
Exercise 1.1 Telling time 185
Exercise 1.2 Finding duration in seconds 186
Exercise 2.1 Understanding the relationship between units of time 187
Exercise 2.2 Converting minutes and seconds 188
Exercise 2.3 Converting years and months 189
Exercise 2.4 Converting weeks and days 190
Exercise 3.1 Telling time 191
Exercise 3.2 Finding duration in hours and minutes 192
Exercise 3.3 Finding end time 194
Exercise 3.4 Finding start time 196
Exercise 4.1 Reading and interpreting timetables 198
Exercise 4.2 Using timetables 200
Exercise 5.1 Word problems 204
Review 4 207
Recap
1 thousand 2 hundreds 6 tens 5 ones
1000 + 200 + 60 + 5 = 1265 1265 is read as one thousand, two hundred and sixty-five.
1. Count and write the numerals.
2. Count and write the numerals. a)
8000 + 500 + 20 + 7 =
b)
5000 + 30 + 2 =
3. Write the numerals.
a) eight thousand, five hundred and fifty-six
b) three thousand and forty-three
c) five thousand, one hundred and nine
d) six thousand and two
4. Write the numbers in words.
a) 8321
b) 7806
c) 4008
d) 9010
e) 3719
f) 5540
g) 6999
1. Complete the sentences.
In 7861, the digit 7 is in the thousands place. It stands for 7000 and its value is 7000. 7861 = 7000 + 800 + 60 + 1
a) In 7534, the digit has a value of 500.
b) In 5843, the digit is in the tens place.
c) In 6180, the digit 6 is in the place.
d) In 1230, the value of the digit 3 is .
e) In 2309, the digit 0 is in the place and its value is .
2. Circle the correct number for the given place.
a) 5 is in the hundreds place.b) 4 is in the thousands place.
3. Write the missing numbers.
a) 8856 = 8000 + + 50 + 6 b) 7609 = 7000 + 600 + c) 4098 = + 90 + 8 d) 6530 = + 500 + 30
4. Write the expanded form of each number.
a) 3847 =
b) 4208 =
c) 5090 = Recap
Recap
1000 more than 4567 is 5567.
1. Write the missing numbers.
a) 3 more than 5231 is .
b) 40 more than 1879 is .
c) 200 more than 5678 is .
d) 3000 more than 3670 is .
e) 4 less than 4345 is .
f) 40 less than 3267 is .
g) 200 less than 9220 is .
h) 4000 less than 7897 is .
i) is 300 more than 3908.
j) is 2000 more than 6646.
k) is 300 less than 8526.
l) is 60 less than 8786.
m) 2879 is less than 2909.
n) 2599 is more than 1599.
o) 4555 is less than 5255.
p) 6456 is less than 9456.
Recap
Start at 4321. Count on by thousands.
+ 1000 + 1000 + 1000
4321, 5321, 6321, 7321, ?
1000 more than 7321 is 8231. The number that comes next is 8231.
1. Complete each number pattern. Then, describe the number pattern.
a) 8301, 8401, 8501, 8601, ,
Start at 8301. Count by .
b) 6590, 6580, 6570, 6560, ,
Start at 6590. Count by .
c) 9999, 8999, 7999, , , 4999
Start at 9999. Count by .
d) 3870, , , 3900, 3910, 3920
Start at 3870. Count by .
e) 2330, , 2130, 2030, ,
Start at 2330. Count by .
f) 4467, 5467, , 7467, 8467,
Start at 4467. Count by .
g) 7513, , , 7483, 7473, 7463
Start at 7513. Count by .
Recap
Compare 4634, 5632 and 5623.
4634 4 634
5632 5 632
5623 5 623
First, compare the thousands. Next, compare the hundreds. Then, compare the tens. Lastly, compare the ones.
4 thousands is less than 5 thousands. 4634 is the least number. In 5632 and 5623, the thousands and hundreds are the same. So, we compare the tens. 3 tens is greater than 2 tens. So, 5632 > 5623. 5632 is the greatest number.
1. Write > or <.
a) 4675 5678
b) 6890 6789
c) 8880 8885 d) 1245 1234
2. Arrange the numbers in order. Begin with the greatest.
a) 3124, 3228, 3174
b) 2200, 2220, 2222, 2000
3. Arrange the numbers in order. Begin with the least.
a) 1010, 1001, 1100
b) 9999, 9896, 9998, 9900
4. a) Form the greatest and the least 3-digit numbers using the digits 4, 3, 6 and 9. Use each digit only once.
Greatest:
Least:
b) Form the least and the greatest 4-digit numbers using the digits 5, 0, 9 and 7. Use each digit only once.
Least:
Greatest:
A represents 3400. B represents 3700.
There are 10 equal intervals between 3000 and 4000. Each interval stands for 100.
1. Complete the number lines.
2. Mark 4200 with crosses on the number lines below.
3.
a) Circle the number between 5500 and 5600. 5605 5504 5455
b) Circle the number between 7010 and 7020. 7100 7010 7011
c) Circle the number between 3445 and 3455. 3544 3454 3545
d) Circle the number between 2330 and 2345. 2335 2435 2325
e) Circle the number between 8890 and 8900. 8980 8899 8809
4. Write a number that is between the two given numbers.
a) 1350 and 1450
b) 6000 and 6050
c) 9555 and 9570
d) 4790 and 4805
e) 2500 and 2525
f) 5800 and 6000
g) 8900 and 9100
To round a number to the nearest ten, look at the digit in the ones place. If it is 5 or greater, round up. If it is less than 5, round down.
5217
5210 5220 5215
5217 is nearer to 5220 than to 5210. So, 5217 is 5220 when rounded to the nearest ten.
5217 ≈ 5220
1. Round each number to the nearest ten.
a) 58 ≈ b) 71 ≈ c) 95 ≈ d) 425 ≈ e) 693 ≈ f) 836 ≈ g) 1235 ≈ h) 2704 ≈ i) 9898 ≈
j) 5212 ≈ k) 5097 ≈ l) 2996 ≈
2.
a) Mathew went to school for 237 days in a year. Round the number of days to the nearest ten.
b) A bus traveled a distance of 3453 meters between two bus stops. Round the distance traveled to the nearest ten.
c) Meg has $2814. Round the amount to the nearest ten.
d) Maria has 525 stickers. Round the number of stickers to the nearest ten.
e) Eva has 923 stamps. Round the number of stamps to the nearest ten.
f) Jon wrote 3744 words for his book. Round the number of words to the nearest ten.
Recap
To round a number to the nearest hundred, look at the digit in the tens place. If it is 5 or greater, round up. If it is less than 5, round down.
5250 is halfway between 5200 and 5300.
So, 5250 is 5300 when rounded to the nearest hundred.
5250 ≈ 5300
1. Round each number to the nearest hundred.
a) 684 ≈ b) 281 ≈ c) 908 ≈ d) 549 ≈ e) 352 ≈ f) 995 ≈ g) 2310 ≈ h) 8952 ≈ i) 3965 ≈ j) 4890 ≈ k) 6439 ≈ l) 7253 ≈
2. Tick (✓) the correct answer.
a) Which number when rounded to 227 267 the nearest hundred is 300?
b) Which number when rounded to 1231 1271 the nearest hundred is 1200?
c) Which number when rounded to 5630 5680 the nearest hundred is 5700?
d) Which number when rounded to 9897 9830 the nearest hundred is 9800?
3. What is the least number that is 2400 when rounded to the nearest hundred?
Recap
To round a number to the nearest thousand, look at the digit in the hundreds place. If it is 5 or greater than 5, round up. If it is less than 5, round down.
4152 is nearer to 4000 than to 5000.
So, 4152 is 4000 when rounded to the nearest thousand. 4152 ≈ 4000
1. Round each number to the nearest thousand. a) 3407 ≈ b) 8553 ≈ c) 1781 ≈ d) 4917 ≈ e) 2657 ≈ f) 7182 ≈ g) 5055 ≈ h) 9289 ≈ i) 6501 ≈ j) 8670 ≈ k) 1812 ≈ l) 7571 ≈
2. The table below shows the points scored by five friends in a game. Round the scores to the nearest thousand.