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
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 and 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. Recognizing and naming proper fractions (CB2 Chapter 12)
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.
2. Placing whole numbers up to 100 on a number line (CB2 Chapter 1)
3. Multiplying and dividing numbers within multiplication tables (CB3 Chapter 3)
EXPLORE
Have students read the word problem on CB p. 231. Discuss with students the following questions:
•Do you donate money to charity ?
•Why do you think Janice donated a part of her salary to charity?
•Besides donating money to charity, what can we do to support charity?
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.
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.
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.
and
Assessment after each chapter and quarterly Reviews provide summative assessment for consolidation of learning throughout the year.
1.
2.
3.
4.
5.
Summative
Mind Stretcher, Create Your Own and Mission Possible immerse students in problem solving tasks at various levels of difficulty.
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.
Solve the problem in another way.
Suppose the number is 10.
Stage 1: 10 + 20 = 30
Stage 2: 30 – 5 = 25
Stage 3: 25 + 20 = 45
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.
She starts with the number 46.
Compare the methods in steps 3 and 5. Which method do you prefer? Why?
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
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.
2.
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.
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.
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.
Let the mass of Brian’s father be y.
x + y = 90
y = 50 + x
x + y = 90
x + 50 + x = 90
2x + 50 = 90
2x = 40
x = 20
and his father? Who is heavier? How many kilograms heavier? What do I have to find? Understand the problem. 1 Plan what to do. 2 CREATE YOUR OWN
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
model to compare their masses. What is the total mass of
Using the bar model method
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
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?
Plan what to do.
• What can you do to solve the problem?
• Which strategies/heuristics can you use?
Work out the 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.
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 tasks help teachers understand students’ thinking process through a concept.
Let's Practice 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’
• 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
are 18 pears altogether.
• 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. I 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 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.
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
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.
Dividing
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.
1. Divide. Use the
Let's Practice
1. Divide. Use
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
1.
Recap provides a pictorial and abstract representation of the concrete activity carried
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.
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.
1. Write the missing numerals or numbers in words. Numeral Number in words a) 50 b) forty-nine c) 68 d) one hundred
2. Count the tens and ones. Then, write the missing numbers.
3. Arrange the numbers in order. Begin with the greatest.
4. Complete the number patterns.
a) 66, , 76, , 86, b) , , 44, , 36, 32 c) 37, , 67, 77, d) , 85, , 79, 76, tens ones = TensOnes
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.
High-value learning analytics 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.
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.
Class Result by Curriculum Stage Report shows student performance in assessments by chapter and Cambridge Primary Mathematics Curriculum stage, for teachers to compare students’ progress against the curriculum.
All class reports can be drilled down to the individual student level.
Actionable, real-time reports accessible on the teacher’s dashboard help to monitor student progress and make timely instructional decisions.
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.
Coursebook in online format with embedded videos to ensure that learning never stops.
Online opportunities for students to consolidate learning and demonstrate understanding.
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.
* TM Mathematics Grades K–3 are available now. Grades 4–6 will be available in Fall 2021.
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
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 answer from
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.
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.
Let's Remember Recall: 1. Writing tens and ones as a 2-digit number (CB1 Chapter 15)
2. Adding and subtracting within 20 using number bonds (CB1 Chapter 7)
3. Adding and subtracting within 20 using the ‘counting on’ or ‘counting backwards’ method (CB1 Chapter 7)
EXPLORE
Have students read the word problem on CB p. 24.
Discuss with students the following questions:
•What is a UNESCO World Heritage site ?
•Are there any UNESCO World Heritage sites in your country? What are the sites?
•Do you think we should protect such sites ?
•What can we do to protect them ?
•What will happen if we do not protect such sites?
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 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 Do
Task 1 requires students to associate the terms ‘sum’ and ‘difference’ with addition and subtraction respectively. A comparison
model is provided to help students find the sum and difference.
Task 2 requires students to associate the
‘sum’ with addition.
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
Stage: Concrete Experience
(a)
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.
Chapter 2: Addition and Subtraction Within 100 30
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
Students
What did you learn about subtracting a 1-digit number from a 2-digit
Think
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.
3.6 Solving word problems
Let's Learn Learn
Objectives: •Solve 1-step word problems involving addition or subtraction with regrouping
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.
•Use a part-whole bar model or a comparison bar model to represent an addition or subtraction situation
Resources:
•CB: pp. 55–57
•PB: pp. 47–48
Have students read the word problem on CB p. 55.
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 draw a bar model to show the number of cupcakes.
3. Work out the Answer Say: Emma buys 24 cupcakes. Draw a bar and label it ‘24’.
Say: She gives away 16 cupcakes. Split the bar into two unequal parts and label the longer part ‘16’.
Say: We have to find how many cupcakes are left.
Draw a brace over the shorter part and label it with a ‘?’. Explain that we use a question mark to indicate 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.
She has 13 more storybooks than Kevin.
2
4 To solve 1-step word problems involving subtraction with regrouping
Students
Students
Students
To solve 1-step word problems involving addition with regrouping
To solve 1-step word problems involving subtraction with regrouping
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?
Let's Practice
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.
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
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 thought bubble
4.2
Have
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.
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
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. Wrap up
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 and report students’ learning against the curriculum.
1.
2.
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 and to eliminate the impact of disruption.
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
Digital Chapter Assessment
Math Journal Practice Book Reviews
Digital Quarterly Assessment
Digital Half-Yearly Assessment
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.
Whole Numbers / Place Value
Count within 100.
Read and write a number from 0 to 100—the numeral and the corresponding number word.
Recognize conservation of numbers.
Use number notation and place values (tens, ones).
Estimate the number of objects in a group of less than 40 objects.
Find the number which is 1, 2 or 10 more than or less than a given number within 100.
Give a number that comes before or after a number or between two numbers within 100.
Count on and backwards by ones, twos or tens within 100.
Describe and complete a number pattern by counting on or backwards by ones, twos or tens within 100.
Recognize odd and even numbers within 20 by skip counting.
Read and place numbers within 100 on a number line.
Give a number between two neighboring pairs of tens within 100.
Count within 100.
Read and write a number within 100—the numeral and the corresponding number word.
Use number notation and place values (tens, ones).
Estimate the number of objects in a group of less than 100 objects.
Find the number which is 1, 2, 3, 4, 5 or 10 more than or less than a given number within 100.
Count on and backwards by ones, twos, threes, fours, fives or tens within 100.
Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives or tens within 100.
Read and place numbers within 100 on a number line.
Use grouping in twos, fives and tens to count groups of up to 100 objects.
Identify if a group has an odd or even number of objects.
Compare and order numbers within 100.
Use ‘>’ and ‘<’ symbols to compare numbers.
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.
Give a number between two 3-digit numbers.
Round a 2-digit or 3-digit number to the nearest ten.
Round a 3-digit number to the nearest hundred.
Whole Numbers / Place Value (continued)
Compare the number of objects in two or more groups.
Compare and order numbers within 100.
Use ‘>’ and ‘<’ symbols to compare numbers.
Use the ‘=’ sign to represent equality.
Make number stories to illustrate number bonds for 5 to 10.
Break a group of 5 to 10 objects into two parts in different ways.
Write a number bond for 5 to 10.
Name the missing part or whole in a number bond.
Name a position using an ordinal number from 1st to 10th.
*Count within 120.
*Read and write a number from 101 to 120—the numeral and the corresponding number word.
Name a position using an ordinal number from 1st to 100th.
Identify odd and even numbers.
Addition / Subtraction
Use picture cut-outs (or other manipulatives) to illustrate the meanings of addition and subtraction.
Make a number story for a given addition or subtraction sentence.
Write a number sentence for a given situation involving addition or subtraction.
Apply the identity, commutative and associative properties of addition.
Observe the answer when 0 is subtracted from a number.
Write a family of four addition and subtraction facts for a given number bond.
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 situation.
Add and subtract within 100.
Add three or more 1-digit or 2-digit numbers.
Check the answer to addition or subtraction.
Solve 1-step and 2-step word problems involving addition and 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.
Addition / Subtraction (continued)
Identify doubles facts within 20.
Mentally add:
- two or three 1-digit whole numbers within 20
- a 1-digit whole number and a 2-digit whole number within 20
Mentally subtract:
- a 1-digit whole number from another 1-digit whole number
- a 1-digit whole number from a 2-digit whole number within 20
Check the answer to addition or subtraction.
Use ‘+’, ‘–’ or ‘=’ correctly to complete number sentences.
Find the missing part in an addition sentence.
Find the missing part or whole in a subtraction sentence.
Find pairs of 1-digit numbers with a total up to 18 and write the addition and subtraction facts for each number pair.
Find number pairs with a total of 20 and write the addition and subtraction facts for each number pair
Find pairs of multiples of 10 with a total of 100 and write the addition and subtraction facts for each number pair.
Solve 1-step and 2-step word problems involving addition and subtraction.
*Identify patterns in an addition chart.
Solve 1-step word problems involving addition or subtraction of numbers within 20.
Find the missing part in an addition sentence.
Find the missing part or whole in a subtraction sentence.
Use the ‘=’ sign to represent equality.
Find pairs of multiples of 100 with a sum of 1000 and write the addition and subtraction facts for each number pair.
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
*Add and subtract within 40.
*Solve 1-step word problems involving addition or subtraction of numbers within 40.
Multiplication / Division
Find doubles of numbers up to 10.
Find halves of even numbers of objects up to 10 by sharing.
Identify odd and even numbers by sharing.
Recognize equal groups and find the total number in the groups by repeated addition.
Use mathematical language such as ‘4 threes’ and ‘3 groups of 5’ to describe equal groups.
Use manipulatives to illustrate the meaning of multiplication and the sharing and grouping concepts of division.
Understand that division can leave some left over.
Tell multiplication and division stories for given pictures.
Write a number sentence for a given situation involving multiplication or division.
Work out a multiplication fact within 40 by repeated addition.
Use arrays to show multiplication sentences.
Associate the term ‘product’ with multiplication.
Use the commutative property of multiplication.
Write a family of four multiplication and division facts.
Solve 1-step word problems on multiplication or division.
Count by twos, threes, fours, fives and tens.
Observe the commutative and distributive properties of multiplication.
Build up the multiplication tables of 2, 3, 4, 5 and 10 and commit the multiplication facts to memory.
Multiply numbers within the multiplication tables of 2, 3, 4, 5 and 10.
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.
*Identify patterns in a multiplication chart.
Multiply a number by 0 or 1.
Multiply ones or tens by a 1-digit number.
Multiply a 2-digit number by a 1-digit number.
Divide a number by 1.
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.
Multiplication / Division (continued)
Fractions / Concepts
Recognize and name one half of a whole which is divided into 2 equal parts.
Recognize and name one fourth or one quarter of a whole which is divided into 4 equal parts.
Find one half of a small number of objects by putting the objects into 2 equal groups.
Find one fourth or one quarter of a small number of objects by putting the objects into 4 equal groups.
Use the fraction 1 2 to describe a half of a whole or a set.
Use the fraction 1 4 to describe a fourth or a quarter of a whole or a set.
Find halves and fourths or quarters of a whole or a set.
Use a related multiplication fact to divide.
Divide numbers using the multiplication tables of 2, 3, 4, 5 and 10.
Use a part-whole bar model to represent a multiplication or division situation.
Solve 1-step word problems on multiplication or division using the multiplication tables of 2, 3, 4, 5 or 10.
*Relate doubling to multiplying by 2.
*Relate halving to dividing by 2.
Find doubles of 2-digit numbers up to 50 mentally.
Understand the relationship between halving and doubling.
Find halves of even numbers up to 100 mentally.
Recognize and name one half, one third and one quarter of a whole.
Find one half, one third and one quarter of a small number of objects by sharing.
Use the fractions 1 2 , 1 3 and 1 4 to describe one half, one third and one quarter of a whole or a set.
Recognize and name halves, thirds and quarters of a whole.
Use the fractions 2 2 , 2 3 , 3 3 , 2 4 , 3 4 and 4 4 to describe halves, thirds and quarters of a whole or a set.
Recognize that 2 2 , 3 3 and 4 4 make a whole.
Find halves, thirds and quarters of a set.
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 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.
Fractions / Concepts (continued)
Use the fractions 2 2 , 2 4 , 3 4 and 4 4 to describe halves and fourths or quarters of a whole or a set.
Fractions / Arithmetic Operations
Length
Compare the lengths of two or more objects.
Arrange objects in order according to their lengths.
Estimate and measure the length of an object in non-standard units.
Compare the lengths of two or more objects measured in non-standard units.
Recognize and name unit fractions up to 1 12.
Recognize and name proper fractions.
Identify the numerators and denominators of proper fractions.
Express a fraction in its simplest form.
Volume and Capacity
Understand the meaning of capacity.
Compare the capacities of two or more containers visually.
Arrange containers in order according to their capacities.
Understand that a meter is longer than a centimeter.
Estimate, measure and compare lengths in meters or centimeters.
Arrange objects in order according to their lengths.
*Understand that a foot is longer than an inch and a yard is longer than a foot.
*Estimate, measure and compare lengths in inches, feet or yards.
*Measure the length of a line or curve in inches.
*Draw a line given its length in inches.
Choose a suitable unit or tool of measure when measuring lengths.
Solve 1-step and 2-step word problems on length.
Estimate, measure and compare capacities of containers in liters.
Arrange containers in order according to their capacities.
Add and subtract like and related fractions within 1 whole.
Solve 1-step word problems involving fractions.
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.
Compare volume of liquid in two containers visually.
Measure and compare volume of liquid in two or more containers in liters.
Solve 1-step and 2-step word problems on capacity. Tell the difference between volume and capacity.
Volume and Capacity (continued)
Estimate and measure the capacity of a container in non-standard units.
Compare the capacities of two or more containers measured in non-standard units.
Mass / Weight
Compare the masses of two or more objects.
Arrange objects in order according to their masses.
Estimate and measure the mass of an object in non-standard units.
Compare the masses of two or more objects measured in non-standard units.
Measure and compare masses in kilograms.
Estimate, measure and compare masses in grams.
Arrange objects in order according to their masses.
Choose a suitable unit of measure when measuring masses.
Solve 1-step and 2-step word problems on mass.
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.
Estimate, measure and compare masses of objects in kilograms or grams using weighing scales.
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.
Time: Calendar
Time: Clock
Name and order the days of the week.
Know that there are 7 days in a week.
Name the months of the year.
Read a calendar.
Name and order the days of the week and months of the year.
Associate months with events.
Know that there are 12 months in a year. Understand the relationships between units of time.
Read and write a date. Choose suitable units of measure when measuring time intervals.
Tell time to the hour and half hour on analog and digital clocks.
*Tell time to the quarter hour on analog and digital clocks.
Tell time by 5-minute intervals on analog and digital clocks.
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.
Tell time using a.m. and p.m. Find the duration of a time interval in hours and minutes.
Time: Clock (continued)
Relate time to events of a day. Relate time to events of a day.
Sequence events according to the time of the day. Find the duration of a time interval in hours or minutes.
Develop a sense of the duration of daily activities.
Measure duration of activities in minutes.
Solve word problems on time.
Express hours and minutes in minutes, and vice versa.
Add and subtract durations in hours and minutes.
Solve 1-step and 2-step word problems involving time.
Temperature
Money Recognize and name five-cent, ten-cent, fifty-cent and one-dollar coins.
Count and tell the amount of money in a group of coins up to $1.
Exchange a coin for more coins in one denomination.
Make up an amount of money using a group of coins.
Compare amounts of money.
Recognize and name five-dollar, ten-dollar and fifty-dollar notes.
Count and tell the amount of money in a group of notes and/or coins up to $100.
Exchange a note for more coins and/or notes.
Make up an amount of money using a group of coins and/or notes.
Compare amounts of money.
Read the price of an item and pay for it.
Add and subtract money in cents up to $1.
Add and subtract money in dollars up to $100.
Count change like a cashier in a purchasing situation.
Solve 1-step word problems on 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.
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
3D Shapes
Describe objects by their shapes.
Recognize and name the four basic 2D shapes: circle, triangle, rectangle and square.
Identify the sides and corners of a 2D shape.
Sort 2D shapes according to each of these attributes: shape, size and color.
Describe and continue a pattern with 2D shapes according to one or more of these attributes: shape, size and color.
*Make pictures using shapes.
Fit suitable pieces together to form a 2D shape.
Identify a line segment and a curve.
Name, describe and draw 2D shapes: circle, triangle, rectangle, square, pentagon and hexagon.
Find 2D shapes in the environment.
Identify the sides and vertices of a 2D shape.
Sort 2D shapes according to the following: shape, size, color, number of sides and number of vertices.
*Continue a pattern with 2D shapes according to one or two of these attributes: shape, size, color and orientation.
*Make new 2D shapes by combining 2D shapes.
*Name 2D shapes that make up a new shape.
*Copy 2D shapes on a dot grid or square grid.
Identify symmetry in the environment.
Identify a symmetric figure.
Cut out a symmetric figure from a folded piece of paper.
Identify and draw lines of symmetry.
Recognize and name 3D shapes: cube, cuboid, cylinder, cone and sphere.
Identify basic 2D shapes in 3D shapes.
Sort 3D shapes according to each of these attributes: shape, size and color.
*Identify a 3D shape that can slide, stack or roll.
Name, describe and make 3D shapes: cube, cuboid, cone, cylinder, sphere and pyramid.
Find 3D shapes in the environment.
Identify the flat and curved surfaces of a 3D object in the shape of cube, cuboid, cone, cylinder, sphere or pyramid.
Identify the faces, edges and vertices of a 3D object in the shape of cube, cuboid, cone, cylinder, sphere or pyramid.
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.
*Name 2D shapes that make up a new shape.
Complete a symmetric figure given half of the figure and the line of symmetry.
Understand that 3D shapes can be formed by nets.
Identify the nets of a cube.
3D Shapes (continued)
Describe and continue a pattern with 3D shapes according to one or more of these attributes: shape, size and color.
Use 3D shapes to make models.
Angles
Sort 3D shapes according to their properties.
*Continue a pattern with 3D shapes according to one or two of these attributes: shape, size, color and orientation.
Position and Movement
Describe the location of objects using positional words.
Name a position using an ordinal number from 1st to 100th.
Name a position using an ordinal number from 1st to 10th.
Recognize whole, half and quarter turns.
Identify left and right turns. Describe turns using the words 'clockwise' and 'counterclockwise'.
Identify, name and draw a point, a line, a line segment and a ray.
Identify an angle.
Compare sizes of angles.
Identify angles on an object or in a shape.
Identify right angles.
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.
Give and follow directions to a place on a grid.
Position and Movement (continued)
Use everyday language of direction and distance to describe movement of objects.
Data Collection
Follow and give instructions involving position, direction and movement.
Collect and record data in a list or table and present it as a pictogram.
Lists Present data in a list. Collect and record data in a list and present it as a pictogram.
Read and interpret a list. Present data given in a list as a block graph.
Tables Present data in a table. Collect and record data in a table and present it as a pictogram.
Read and interpret a table. Present data given in a table as a block graph.
Group objects in a Carroll diagram using different criteria.
Sort data in a Carroll diagram with 1 criterion and read the Carroll diagram.
Collect and record data in a tally chart and a frequency table.
Read and interpret a tally chart and a frequency table.
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
Venn Diagrams
Make a simple pictogram using one-to-one representation.
Read and interpret a pictogram.
Collect and record data in a list or table and present it as a pictogram.
Make, read and interpret a pictogram with a scale of 1, 2, 3, 4, 5 or 10.
Present data given in a list or table as a block graph.
Read and interpret a block graph.
*Make, read and interpret a line plot with a scale marked in whole numbers.
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.
Group objects in a Venn diagram using different criteria.
Sort data in a Venn diagram with 1 criterion and read the Venn diagram.
Patterns
Equations
Describe and complete a number pattern by counting on or backwards by ones, twos or tens within 100.
Describe and continue a pattern with 2D shapes according to one or more of these attributes: shape, size and color.
Describe and continue a pattern with 3D shapes according to one or more of these attributes: shape, size and color.
Find the missing part in an addition sentence.
Find the missing part or whole in a subtraction sentence.
*Solve 1-step word problems by finding missing numbers in addition or subtraction sentences.
Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives or tens within 100.
*Continue a pattern with 2D shapes according to one or two of these attributes: shape, size, color and orientation.
*Continue a pattern with 3D shapes according to one or two of these attributes: shape, size, color and orientation.
Find the missing part in an addition sentence.
Find the missing part or whole in a subtraction sentence.
*Lessons are available in PR1ME Mathematics Teaching Hub.
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.
*Identify patterns in a multiplication chart.
Find the missing part in an addition or subtraction sentence.
Strand: Numbers and Operations
Practice is available in
Objectives Materials *ResourcesVocabulary
• CB: pp. 1–2
• Count within 40 by making tens first, and read and write numbers from 21 to 40
• Write tens and ones as a 2-digit number
Let’s Remember
• Place numbers within 40 on a number line
• Compare numbers within 40 using place values
• Name positions using ordinal numbers from 1st to 10th and the words ‘left’ and ‘right’
Unit 1: Counting, Reading and Writing Numbers
• CB: pp. 3–4
• PB: p. 9
• Digital Practice
• 1 enlarged copy of Place Value Cards (BM1.1)
• 1 rubber band
• 9 bundles of 10 straws
• 10 straws
• CB: pp. 5–7
• PB: pp. 10–11
• Digital Practice
• 1 enlarged copy of Place Value Cards (BM1.1)
• Base ten blocks
• Counters
• Count by tens within 100
• Read and write tens within 100—the numeral and the corresponding number word
1.1 Counting, reading and writing numbers in tens
• Count within 100 by making tens
• Read and write a number within 100— the numeral and the corresponding number word
1.2 Numbers in tens and ones
• Write a 2-digit number in tens and ones
• CB: pp. 8–9
• PB: p. 12
• Digital Practice
• 1 jar with about 50 beads
• Estimate the number of objects in a group of less than 100 objects
1.3 Estimating the number of objects
Unit 2: Order of Numbers
• CB: pp. 10–11
• PB: p. 13
• Digital Practice
• 1 copy of Number Chart (BM1.2) per student
• Find the number which is 1, 2, 3, 4, 5 or 10 more than or less than a given number within 100
2.1 Finding more than and less than
• CB: pp. 12–14
• PB: pp. 14–15
• Digital Practice
• CB: pp. 14-15
• PB: p. 16
• Digital Practice
• even number
• CB: pp. 16–17
• odd number
• PB: pp. 17–18
• Digital Practice
• 1 copy of Number Chart (BM1.2) per student
• Count on or backwards by ones, twos, threes, fours, fives or tens within 100
2.2 Number patterns
• Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives or tens within 100
• Read numbers within 100 on a number line
2.3 Reading number lines
• Place numbers within 100 on a number line
• Counters
• Use grouping in twos, fives and tens to count groups of up to 100 objects
• Identify if a group has an odd or even number of objects
2.4 Counting in groups of 2, 5 and 10
• CB: pp. 18–19
• PB: p. 19
• Digital Practice
• Base ten blocks
• Compare and order numbers within 100 using place values
2.5 Comparing and ordering numbers
• Use ‘>’ and ‘<’ symbols to compare numbers within 100
Unit 3: Ordinal Numbers
• CB: pp. 20–21
• PB: pp. 20–21
• Digital Practice
• CB: pp. 22–23
• Name a position using an ordinal number from 1st to 100th
3.1 Knowing 1st to 100th
• Solve a non-routine problem involving numbers within 100 using the strategy of making a list
Digital Practice and Assessment
Unit 4: Problem Solving 4.1
Mind stretcher
Digital Chapter Assessment — Available in PR1ME Mathematics
The suggested duration for each lesson is 1 hour.
1. Count. Then, write the number in numerals and in words. Numeral: Word:
5. Look at the picture. Then, write in the blanks.
ant bee butterfly grasshopper snail
a) The is 2nd from the left.
b) The is 1st from the right.
2. Count the sticks and write the number.
3. Complete the number line.
4. Compare the numbers. Then, write the missing numbers.
c) The is 4th from the left.
d) The is 5th from the right.
e) The is 3rd from the left.
The number of countries in each continent is shown below.
North America: 23 South America: 12 Europe: 44 Africa: 54 Asia: 48 Oceania: 14
Arrange the continents in order.
Begin with the continent that has the greatest number of countries.
How can we solve this problem?
Africa, Asia, Europe, North America, Oceania, South America
Discuss in your group and fill in columns 1 and 2. 1. What I already know that will help me solve the problem
Compare and order numbers within 40.
Chapter Overview
Let’s Remember
Unit 1: Counting, Reading and Writing Numbers
Unit 2: Order of Numbers
Unit 3: Ordinal Numbers
Unit 4: Problem Solving
Let's Remember
Recall:
1. Counting within 40 by making tens first, and reading and writing numbers from 21 to 40 (CB1 Chapter 15)
2. Writing tens and ones as a 2-digit number (CB1 Chapter 15)
3. Placing numbers within 40 on a number line (CB1 Chapter 15)
4. Comparing numbers within 40 using place values (CB1 Chapter 15)
5. Naming positions using ordinal numbers from 1st to 10th and the words ‘left’ and ‘right’ (CB1 Chapter 5)
What I need to find out and learn
Compare and order numbers within 100. Answer varies.
Have students read the problem on CB p. 2. Discuss with students the following questions:
• How is the world organized?
•How many continents are there?
•What are the continents?
•What countries are in South America? How about countries in North America and Europe?
• How are the countries different?
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 problem. Ask the groups to present their work.
Tell students that they will come back to this problem later in the chapter.
1.1 Counting, reading and writing numbers in tens
Let's Learn Let's Learn Objectives:
• Count by tens within 100
• Read and write tens within 100—the numeral and the corresponding number word
Materials:
• 1 enlarged copy of Place Value Cards (BM1.1)
• 1 rubber band
• 9 bundles of 10 straws
• 10 straws
Resources:
• CB: pp. 3–4
•PB: p. 9
(a) Before the lesson, cut out the place value cards in BM1.1.
Stages: Concrete Experience, and Pictorial and Abstract Representations
Put 10 straws on the table in front of the class. Count the straws with the class and tie them in a bundle of 10 with a rubber band.
Say: There are 10 straws in one bundle. So, this is 1 group of 10. We know that 10 ones is the same as 1 ten.
Write: 10 ones = 1 ten 1 ten = 10
Stick the place value card ‘10’ on the board. Put another bundle of straws on the table. Guide students to count by tens to find the total number of straws in the two bundles. (10, 20)
Say: So, 2 tens is equal to 20. Write: 2 tens = 20 ones 2 tens = 20
Stick the place value card ‘20’ on the board. Repeat the above procedure for the numbers 30 to 90.
(b) Stage: Pictorial Representation
Have students look at the ten frames in (b) on CB p. 3.
Ask: What number does each ten frame represent? (10)
Say: Let us count the counters in the ten frames. 10, 20, 30, …, 100. There are 100 counters.
Write: 10 tens = 100 ones 10 tens = 100 10 tens = 1 hundred
Stick the place value card ‘100’ on the board.
Stage: Abstract Representation
Write some tens within 100 on the board. Read aloud the numbers on the board with students.
Say: A numeral is a symbol used to represent a number of objects. The numbers on the board are numerals.
Task 1 requires students to count by tens within 100 and write the number as a numeral.
Task 2 requires students to write the numerals given the numbers in words.
Let's Practice
Task 1 requires students to count by tens within 100 and write the number as a numeral.
Task 2 requires students to write the numerals given the numbers in words.
Task 3 requires students to write the numbers in words given the numerals.
Let's Do
1.
1.
Let's Learn Let's Learn
Objectives:
• Count within 100 by making tens
• Read and write a number within 100—the numeral and the corresponding number word
• Write a 2-digit number in tens and ones
Materials:
• 1 enlarged copy of Place Value Cards (BM1.1)
•Base ten blocks
•Counters
Resources:
• CB: pp. 5–7
• PB: pp. 10–11
Before the lesson, cut out the place value cards in BM1.1.
(a) Stage: Concrete Experience
Stick 44 counters randomly on the board.
Say: Let us count the counters. 1, 2, 3, …, 10. There are more than 10 counters. Let us count the counters again by putting them in groups of 10. Arrange the counters in rows of 10 as you count. You should have 4 rows of 10 counters and 1 row of 4 counters.
Say: Let us count the counters. 10, 20, 30, 40, 41, 42, 43, 44. There are 44 counters.
Stage: Pictorial Representation
Have students look at the picture in (a) on CB p. 5.
Say: Each group shows 10 erasers.
Ask: How many groups are there? (4) How many erasers are there in 4 groups? (40)
Stick the place value card ‘40’ on the board.
Ask: How many erasers are not in groups? (4) Stick the place value card ‘4’ on the board. Overlap the place value cards to show 44. Say: 40 and 4 make 44. There are 44 erasers.
Stage: Abstract Representation
Write: 44 forty-four
Point to the numeral and word form of 44 on the board and read them aloud.
(b) Stages: Concrete Experience, and Pictorial and Abstract Representations
Follow the procedure in (a). Copy the place value chart in (b) on CB p. 5 on the board but leave out the numbers.
Explain to students that each bracelet stands for 1 ten. There are 5 tens. Write ‘5’ in the tens column of the place value chart. Next, explain to students that each bead stands for 1 one. There are 3 ones. Write ‘3’ in the ones column of the place value chart. Tell students that there are 5 tens and 3 ones in 53.
(c) Stages: Concrete Experience and Pictorial Representation
Show 75 using base ten blocks. Count the base ten blocks aloud with students.
Point to the ten-rods as you count: 10, 20, 30, …, 70.
Say: The ten-rods stand for 70.
Stick the place value card ‘70’ on the board.
Point to the unit cubes as you count: 1, 2, 3, 4, 5.
Say: The unit cubes stand for 5.
Stick the place value card ‘5’ on the board.
Say: We have 70 and 5.
Overlap the place value cards to show 75.
Say: 70 and 5 make 75.
Stage: Abstract Representation
Write: 75 seventy-five
Copy the place value chart in (c) on CB p. 5 on the board but leave out the numbers.
Guide students to count the number of tens and ones and write in the place value chart.
Say: There are 7 tens 5 ones in 75.
Write: 75 = 7 tens 5 ones
Draw a number bond as shown in (c) on the page.
Say: Since 70 is 7 tens and 5 is 5 ones, 75 is 7 tens 5 ones.
Write: 75 = 70 + 5
1.
2.
Task 1 requires students to count within 100 and write the number as a numeral.
Task 2 requires students to write 2-digit numbers in tens and ones.
Task 3 requires students to write the numerals given the numbers in words.
Task 1 requires students to count within 100 and write the number as a numeral.
Task 2 requires students to count within 100 and write the 2-digit number in tens and ones.
Task 3 requires students to write 2-digit numbers in tens and ones, and vice versa.
Task 4 requires students to write the numerals given the numbers in words.
Task 5 requires students to write the numbers in words given the numerals.
Have students go back to the 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.
a) 1 Maya grabs a handful of 2 She estimates the number marbles from the jar. of marbles she is holding.
5 Maya counts the marbles in the jar. I am holding about 10 marbles.
3 Maya counts the 4 She estimates the marbles in her hands. number of marbles left in the jar.
Let's Learn Let's Learn
Objective:
• Estimate the number of objects in a group of less than 100 objects
Materials:
• 1 jar with about 50 beads
Resources:
• CB: pp. 8–9
• PB: p. 12
(a) Stage: Concrete Experience
Place a jar of about 50 beads on a table in front of the class. Have a student come up to the table and grab a handful of beads from the jar.
Ask: How many beads do you think your classmate is holding? (Answers vary.)
Have another student count the number of beads their classmate is holding.
Ask: Is your estimate close to the actual number of beads? (Yes or no)
Say: Now, estimate the number of beads left in the jar. (Answers vary.)
Estimate the number of toy robots. There are about 50 toy robots. Now, let us count the number of toy robots. There are toy robots.
Let's Do Let's 1. Make an estimate. Then, count.
Estimate: There are about erasers. Count: There are erasers.
Let's Practice Practice 1. Make an estimate. Then, count.
Estimate: There are about buttons. Count: There are buttons.
Lead students to form reasonable estimates by having them imagine the number of handful of beads they can grab from the jar and then estimating the number of beads left in the jar. Ask another student to count the number of beads left in the jar to check if the estimates are close to the actual number of beads.
(b) Stages: Pictorial and Abstract Representations Have students look at the pictures in (b) on CB p. 9.
Say: Count 10 toy robots and circle them. Use the 10 toy robots to estimate the total number of toy robots.
Ask: How many toy robots do you think there are? (Answers vary.)
Say: Now, count the toy robots.
Ask: How many toy robots are there? (56)
Say: There are 56 toy robots.
Ask: Is your estimate close to 56? (Yes or no) Did you make a good estimate? (Yes or no)
Let's Do Let's and Let's Practice Let's Practice
Task 1 requires students to estimate and count the number of objects in a group of less than 100 objects.
2.1 Finding more than and less than
Let's Learn Let's Learn
Objective:
• Find the number which is 1, 2, 3, 4, 5 or 10 more than or less than a given number within 100
Materials:
• 1 copy of Number Chart (BM1.2) per student
Resources:
• CB: pp. 10–11
• PB: p. 13
(a) Stages: Pictorial and Abstract Representations
Distribute a copy of Number Chart (BM1.2) to each student.
Guide students to read the numbers on the chart to ensure that they are familiar with number sequences up to 100.
Ask students to circle 13 on the number chart.
Say: Let us count on 3 ones from 13.
Have students place a finger on 13 and move 3 steps to the right.
Guide them to see that this is the same as counting on 3 ones from 13.
Ask: What number are you pointing at now? (16)
Say: 13, 14, 15, 16. 3 more than 13 is 16.
Provide another example to guide students to find 5 more than 77.
(b) Stages: Pictorial and Abstract Representations
Follow the procedure in (a) but guide students to count backwards 4 ones from 56 to reach 52. Provide another example to guide students to find 3 less than 42.
(c) Stages: Pictorial and Abstract Representations
Ask students to circle 19 on the number chart. Say: Let us count on 1 ten from 19. Have students place a finger on 19 and count on 10 ones.
Ask: What number are you pointing at now? (29) Have students place a finger on 19 again and move it 1 row downwards to 29.
Guide students to see that this is counting on 1 ten which is the same as counting on 10 ones, and they will still end up at 29.
Say: 19, 29. 10 more than 19 is 29.
Repeat the above procedure to guide students to count backwards 1 ten from 87 to find 10 less than 87.
You will learn to... • find 1, 2, 3, 4, 5 or 10 more than or less than a given number • describe and complete number patterns • read numbers to 100 on a number line • count objects in twos, fives or tens • identify odd and even numbers • compare and order numbers within 100
2.1 Finding more than and less than Let's Learn
12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100
a) Count on 3 ones from 13. 13, 14, 15, 16 3 more than 13 is 16.
b) Count backwards 4 ones from 56. 56, 55, 54, 53, 52 4 less than 56 is c) Count on 1 ten from 19. 19 29 10 more than 19 is
Let's Do Let's Do
Task 1 requires students to find the number which is 1, 2, 5 or 10 more than or less than a given number within 100.
Let's Practice Let's Practice
Tasks 1 and 2 require students to find the number which is 3, 4, 5 or 10 more than or less than a given number within 100.
1. Write the missing numbers.
a) is 1 more than 65. b) is 1 less than 65.
c) is 2 more than 65. d) is 2 less than 65.
e) is 5 more than 65. f) is 5 less than 65.
g) is 10 more than 65. h) is 10 less than 65. Let's Do
1. Write the missing numbers. a) is 5 more than 53. b) is 5 less than 53.
c) is 10 more than 53. d) is 10 less than 53.
e) is 3 more than 53. f) is 3 less than 53.
g) is 4 more than 53. h) is 4 less than 53.
2. Answer the questions.
a) What number is 3 more than 34?
b) What number is 4 less than 45?
c) What number is 5 more than 75?
d) What number is 10 less than 82?
Let's Learn Let's Learn
Objectives:
• Count on or backwards by ones, twos, threes, fours, fives or tens within 100
• Describe and complete a number patter n by counting on or backwards by ones, twos, threes, fours, fives or tens within 100
Materials:
• 1 copy of Number Chart (BM1.2) per student
Resources:
• CB: pp. 12–14
• PB: pp. 14–15
(a) Stages: Pictorial and Abstract Representations
Distribute a copy of Number Chart (BM1.2) to each student. Have students locate the number 61 on the number chart and color the box blue. Get them to count on 5 ones from 61.
Ask: What number do you reach? (66) Have students color the box with the number 66 blue. Ask them to now count on 5 ones from 66.
Ask: What number do you reach? (71) Have students color the box with the number 71 blue. Ask them to count on 5 ones from 71.
Ask: What number do you reach? (76)
Have students color the box with the number 76 blue.
Have students look at the blue boxes in the number chart. Guide them to observe that they have counted on by fives from 61 to 76. Write: 61, 66, 71, 76
Tell students that this is a number pattern. Have them see how each number is related to the number before it.
Ask: How are 61 and 66 related? (66 is 5 more than 61.) How are 66 and 71 related? (71 is 5 more than 66.) How are 71 and 76 related? (76 is 5 more than 71.)
Say: Each number in the number pattern is 5 more than the number before it.
Ask: So, how can we find the next number in this pattern? (By adding 5 to the number 76/ by counting on by fives from 76) What is the next number in this pattern? (81) What number comes after 81 in this pattern? (86)
Let's Learn Learn
12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100
a) pattern: Start at 61. Count on by fives. The number pattern is 61, 66, 71, 76.
b) pattern: Start at 89. Count backwards by twos. The number pattern is 89, 87, 85, 83. The next two numbers in the pattern are and Each number is 2 less than the number before it. Each number is 5 more than the number before it. We can find number patterns on a number chart.
The next two numbers in the pattern are 81 and 86.
(b) Stages: Pictorial and Abstract Representations
Follow the procedure in (a) but guide students to count backwards by twos from 89 to 83. Conclude with students that each number is 2 less than the number before it. So, the next two numbers in the pattern are 81 and 79.
Task 1 requires students to describe and continue number patterns within 100.
Task 2 requires students to complete number patterns within 100.
Let's Do Do
1. Describe each number pattern. Then, continue the number pattern.
12345678910
11121314151617181920
21222324252627282930
31323334353637383940 41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100
a) pattern: Start at 28. Count on by 28, , , , , b) pattern: Start at 80. Count by 80,
2. Complete the number patterns. a) 73, 72, 71,
Task 1 requires students to describe and continue number patterns within 100.
Task 2 requires students to complete number patterns within 100.
Let's Learn
Objectives:
• Read numbers within 100 on a number line
• Place numbers within 100 on a number line
Resources:
• CB: pp. 14–15
• PB: p. 16
Stages: Pictorial and Abstract Representations
Draw the number line as shown on CB p. 14 on the board but leave out the curved arrows. Have students look at the first two numbers on the number line and count aloud. (40, 41) Elicit from students that they are counting on by ones. Remind students that the intervals on a number line are equal.
Ask: What does each interval on the number line stand for? (1)
Say: Each number on the number line is 1 more than the number on the left.
Draw arrows from 40 to 41 and from 41 to 42 on the number line and label the arrows ‘1 more’.
Say: Each shape on the number line stands for a number. Let us find the number that the first shape stands for.
Guide students to count on by ones from 40, pointing to each mark as they do so. Count on with students from 40. (40, 41, 42)
Say: The shape stands for 42. Write ‘42’ on the number line.
Repeat the above procedure to guide students to find the number the circle stands for by counting on by ones.
Point to the numbers 50 and 49 on the number line and count backwards. Elicit from students that they are counting backwards by ones. Say: Each number on the number line is 1 less than the number on the right.
Draw arrows from 50 to 49 and from 49 to 48 on the number line and label the arrows ‘1 less’.
Let's Practice Let's Practice
1. Continue each number pattern. Then, describe the number pattern. a) 88, 84, 80, 76, , Count by b) 19, 22, 25, 28, , Count by
2.3 Reading number lines
Say: Let us now find the number that the triangle stands for.
Guide students to count backwards by ones from 50, pointing to each mark as they do so. Count backwards with students from 50. (50, 49, 48)
Say: The triangle stands for 48.
Lead students to see that they can either count on or backwards from a known number to find the missing numbers on a number line. Emphasize that they should first identify the number that each interval represents on the number line before finding the missing numbers.
Task 1 requires students to read numbers within 100 on number lines.
Task 1 requires students to read numbers within 100 on number lines.
Task 2 requires students to find 3, 4 or 5 more than or less than each given number within 100 and read the numbers on a number line.
Task 3 requires students to place a number within 100 on a number line.
Complete the number lines.
a) Label the number that is 3 more than 47 with A.
b) Label the number that is 3 less than 56 with B.
c) Label the number that is 4 more than 51 with C.
d) Which letter stands for a number that is 5 less than letter C?
Mark 97 with a cross on the number line below.
Let's Learn Let's Learn
Objectives:
• Use grouping in twos, fives and tens to count groups of up to 100 objects
• Identify if a group has an odd or even number of objects
Materials:
•Counters
Resources:
• CB: pp. 16–17
• PB: pp. 17–18
Vocabulary:
•even number
• odd number
(a) Stage: Concrete Experience
Stick 6 counters on the board.
Say: Let us count the counters by putting them in groups of 2.
Put 2 counters in a group and circle the group. Say: There are still 4 counters left so we continue to put counters in groups of 2.
Repeat the grouping process until there are no counters left.
Ask: How many counters are there in each group? (2)
Count on by twos with the class. (2, 4, 6)
Ask: How many counters are there? (6)
Stages: Pictorial and Abstract Representations
Refer students to the pictures of cars on CB p. 16 and relate them to the earlier activity. Say: Let us count the cars by counting on by ones. 1, 2, 3, 4, 5, 6.
Ask: Is it faster to count the cars by counting on by ones or by twos? (Twos)
(b) Stages: Concrete Experience, and Pictorial and Abstract Representations
Follow the procedure in (a) but count the mangoes by grouping them in fives and in tens.
(c) Stages: Concrete Experience, and Pictorial and Abstract Representations
Follow the procedure in (a). Point out to students that 12 beans can be put into groups of 2. So, 12 is an even number. Have students see that 15 beans cannot be put into groups of 2. There is 1 bean left over. So, 15 is an odd number.
Say: An even number of objects can be put into groups of 2. An odd number of objects cannot be put into groups of 2. There will be 1 object left over.
Task 1 requires students to use grouping in twos, fives or tens to count groups of up to 100 objects.
Task 2 requires students to identify the group that shows an even number.
Let's Practice Let's Practice
Task 1 requires students to use grouping in twos, fives or tens to count groups of up to 100 objects.
Task 2 requires students to identify the group that shows an odd number.
Count and write the number of objects. Circle groups of 2, 5 or 10 objects to help you count.
Cross out the group that shows an even number.
Let's Learn Let's Learn
Objectives:
• Compare and order numbers within 100 using place values
• Use ‘>’ and ‘<’ symbols to compare numbers within 100
Materials:
•Base ten blocks
Resources:
• CB: pp. 18–19
• PB: p. 19
(a) Stage: Concrete Experience
Have students work in groups. Distribute base ten blocks to each group.
Say: Let us compare the numbers 53 and 47. Have students form the two numbers using base ten blocks.
Ask: Which number is formed by more blocks? (53)
Say: So, 53 is greater than 47.
Stages: Pictorial and Abstract Representations
Have students look at the base ten blocks in (a) on CB p. 18 and relate them to the earlier activity.
Say: Each ten-rod represents 1 ten. Each unit cube represents 1 one.
Copy the place value chart in (a) on the page on the board but leave out the numbers.
Ask: How many tens and ones make 53? (5 tens 3 ones)
Write ‘5’ and ‘3’ in the place value chart to show 53.
Ask: How many tens and ones make 47? (4 tens 7 ones)
Write ‘4’ and ‘7’ in the place value chart to show 47.
Say: We can compare the numbers by looking at the number of tens and ones in each number. Let us compare the number of tens first.
Ask: Which number has more tens, 53 or 47? (53)
Say: Since 53 has more tens than 47, 53 is greater than 47.
Write: 53 is greater than 47. 53 > 47
(b) Stage: Concrete Experience
Have students continue to work in groups. Say: Let us compare the numbers 53 and 59. Have students form the two numbers using base ten blocks.
Ask: Which number is formed by fewer blocks? (53)
Say: So, 53 is less than 59.
2.5 Comparing and ordering numbers
Let's Learn Let's Learn
Stages: Pictorial and Abstract Representations
Have students look at the base ten blocks in (b) on CB p. 18 and relate them to the earlier activity.
Copy the place value chart in (b) on the page on the board but leave out the numbers.
Ask: How many tens and ones make 53? (5 tens 3 ones) How many tens and ones make 59? (5 tens 9 ones)
Complete the place value chart to show the numbers 53 and 59.
Say: We can compare the numbers by looking at the number of tens and ones in each number. Let us compare the number of tens first.
Ask: Which number has fewer tens, 53 or 59? (Both numbers have the same number of tens.)
Say: Since both numbers have 5 tens, we compare the number of ones. 3 ones is less than 9 ones so 53 is less than 59.
Write: 53 is less than 59. 53 < 59
(c) Stage: Abstract Representation
Write 53, 47 and 59 in a place value chart. Guide students to compare the number of tens before comparing the number of ones. Then, guide students to arrange the numbers in order, beginning with the greatest. (59, 53, 47)
Task 1 requires students to compare two numbers within 100 using place values.
Task 2 requires students to compare two numbers within 100 using the ‘>’ and ‘<’ symbols.
Task 3 requires students to compare and order three numbers within 100.
Let's Practice
Task 1 requires students to compare two numbers within 100 using the ‘>’ and ‘<’ symbols.
Task 2 requires students to compare and order three numbers within 100.
1. Write greater than or less than a) TensOnes 62
Write
Let's Practice
3. Arrange 86, 49 and 94 in order. Begin with the least. , , 1. Write > or
2. Arrange the numbers in order. Begin with the given number. a) 786382 63, ,
945791 94,
I have learned to... find 1, 2, 3, 4, 5 or 10 more than or less than a given number describe and complete number patterns read numbers to 100 on a number line count objects in twos, fives or tens identify odd and even numbers compare and order numbers within 100
Let's Learn Let's Learn
Objective:
• Name a position using an ordinal number from 1st to 100th
Resources:
• CB: pp. 20–21
• PB: pp. 20–21
Stage: Pictorial Representation
Write the letters of the English alphabet in a row on the board.
Ask: Which is the first letter of the English alphabet? (A) Which is the second letter of the English alphabet? (B) In which position is the letter J? (10th)
Point to each letter in the English alphabet and, together with students, say its position aloud until the 10th position.
Stage: Abstract Representation
Say: Let us learn to name positions beyond the 10th position.
Read aloud the ordinal numbers from 11th to 20th. As you say each ordinal number, write it on the board. For example, 11th, eleventh. Have students look at the ordinal numbers from 11th to 20th. Guide them to observe that the ordinal numbers are written by adding –th to the end of the numbers. The same is true for the word form except for the words twelfth and twentieth.
Next, introduce ordinal numbers from 21st to 30th to the students.
Ask: In which position is the letter Y? (25th) Which letter is the 23rd letter of the English alphabet? (W) Write: 10th tenth 20th twentieth 30th thirtieth . .
100th hundredth
You will learn to… • name a position using an ordinal number from 1st to 100th
These are the 26 letters of the English alphabet. ABCDEFGHIJKLMNOPQRSTUVWXYZ
‘A’ is the first letter of the alphabet. We can write ‘first’ as ‘1st’.
‘N’ is the fourteenth letter of the alphabet. We can write ‘fourteenth’ as ‘14th’.
1st, 14th and 22nd are ordinal numbers. Here are some others.
WriteReadWriteReadWriteRead 11theleventh21sttwenty-first10thtenth 12thtwelfth 22nd twenty-second 20thtwentieth 13ththirteenth23rdtwenty-third30ththirtieth 14thfourteenth24thtwenty-fourth40thfortieth 15thfifteenth25thtwenty-fifth50thfiftieth 16thsixteenth26thtwenty-sixth60thsixtieth 17thseventeenth27th twenty-seventh 70thseventieth 18theighteenth28thtwenty-eighth80theightieth 19thnineteenth29thtwenty-ninth90thninetieth 20thtwentieth30ththirtieth100thhundredth
‘Y’ is the 25th letter of the alphabet.
‘W’ is the letter of the alphabet.
Read aloud the ordinal numbers 10th, 20th, 30th, ... , 100th on the board and point to each number as you read.
Write: 54th 32nd seventy-eighth ninety-fifth
Ask students to write the other form of these four ordinal numbers on the board.
Let's Do Let's Do
Task 1 requires students to match the ordinal numbers.
Task 2 requires students to identify stars given their positions in ordinal numbers.
Let's Practice Let's Practice
Task 1 requires students to identify the child given its position in ordinal number and name a position using ordinal number.
Task 2 requires students to name the positions of selected beads in a row, using ordinal numbers. Students have to read the ordinal numbers either from left to right or from right to left.
Beth is 12th in the line and Jayden is 13th in the line. a) is 15th in the line b) Sam is in the line. 2. Write the positions of the yellow beads. a) Write the positions in words.
b) Write the positions in ordinal numbers.
4.1 Mind stretcher
Let's Learn Let's Learn Objective:
• Solve a non-routine problem involving numbers within 100 using the strategy of making a list
Resource:
• CB: pp. 22–23
Have students read the problem on CB p. 22.
1. Understand the problem. Pose the questions in the thought bubble in step 1.
2. Plan what to do.
Point out to students that we can make a list to solve the problem.
3. Work out the Answer.
Say: Since the greatest number is 33 and the least number is 24, the third number is greater than 24 but less than 33.
Ask: What numbers are greater than 24 but less than 33? (25, 26, 27, 28, 29, 30, 31, 32)
Write: 25, 26, 27, 28, 29, 30, 31, 32
Have students read sentence 3 of the problem.
Say: The third number has 3 tens and at least 1 one.
Point to the numbers on the board.
Ask: Which of these numbers have 3 tens and at least 1 one? (31 and 32) Why is 30 not included? (It has 3 tens and 0 ones.)
Say: Since only 31 and 32 have 3 tens and at least 1 one, the third number can be 31 or 32.
Adele arranges three numbers in order. 33 is the greatest and 24 is the least. The third number has 3 tens and at least 1 one. What can the third number be?
How many numbers are there? What number is the greatest? What number is the least? What do I know about the third number? What do I have to find? Let's Learn Let's Learn
Understand the problem.
I can make a list to solve the problem.
The third number is greater than 24 but less than 33. The third number can be 25, 26, 27, 28, 29, 30, 31 or 32.
The third number has 3 tens and at least 1 one. Only 31 and 32 have 3 tens and at least 1 one. So, the third number can be 31 or 32.
Both 31 and 32 are greater than 24 but less than 33. Both 31 and 32 have 3 tens and at least 1 one. My answer is correct.
4. Check if your answer is correct.
Guide students to check their answer by reading the problem again to check if the problem matches the answer.
Ask: Is 31 greater than 24 but less than 33? (Yes) Is 32 greater than 24 but less than 33? (Yes) Do both 31 and 32 have 3 tens and at least 1 one? (Yes)
Conclude that the answer is correct.
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. 23.
Ask: Which method do you prefer? Why? (Answers vary.)
Have students go back to the 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.
From the number line, 25, 26, 27, 28, 29, 30, 31 and 32 are greater than 24, but less than 33. The third number has 3 tens and at least 1 one. So, the third number can be 31 or 32. Compare the methods in steps 3 and 5. Which method do you prefer? Why?
Exercise 1.1
1. a) 5; 50; 50 b) 6; 60; 60
2. Match: thirty—30; eighty—80; fifty—50; ninety—90
3. a) sixty b) twenty c) one hundred d) forty
Exercise 1.2
1. a) 59 b) 47
2. eighty-one; forty-nine; 63; 72; fifty-five; 98; forty-seven; 86; seventy-four
3. a) 5; 4; 50; 4; b) 40; 3; c) 70; 6;
4. a) 55 b) 60
c) 94 d) 4; 2
e) 3; 8 f) 88
Exercise 1.3
1. a) Estimate varies; 53 b) Estimate varies; 37 c) Estimate varies; 42
Exercise 2.1
1. a) 48; 52; 43 b) 61; 54; 66
2. a) 54 b) 40 c) 59 d) 90
e) 29 f) 87 g) 67 h) 44
Exercise 2.2
1. A: 23; 25; count on by twos
B: 7; 22; count backwards by fives
C: 31; 51; count on by tens
2. a) 66; 65; 64; backwards; ones b) 45; 48; 51; on; threes
c) 55; 45; 35; backwards; tens
d) 61; 65; 69; on; fours
e) 41; 39; 37; backwards; twos
3. a) 48; 49; 51; 52
b) 90; 80; 60; 40
c) 89; 86; 74; 71
d) 64; 74; 79
e) 100; 92; 84; 80 f) 11; 21; 41; 61; 81
g) 84; 82; 78; 74
Exercise 2.3
1. a) 59; 60; 64; 66; 68 b) 81; 82; 85; 86; 90; 91
2.
3.
Exercise 2.4
1. a) 25 b) 30 c) 44
2. a) Circle the second group.
b) Circle the first group.
c) Circle the second group.
3. a) Cross out the second group.
b) Cross out the third group.
Exercise 2.5
1. a) < b) < c) < d) > e) < f) > g) > h) < i) >
2. a) 56, 49, 47 b) 68, 61, 59 c) 87, 82, 78, 63 d) 99, 95, 59, 55
3. a) 56, 71, 72 b) 39, 42, 45 c) 38, 50, 53, 59 d) 83, 89, 93, 98
Exercise 3.1
1. Match: 22nd—twenty-second; 85th—eighty-fifth; 56th—fifty-sixth; 98th—ninety-eighth; 60th—sixtieth
2. a) robot C b) robot F c) robot G d) 14th/fourteenth e) 18th/eighteenth f) 19th/nineteenth 3. a) forty-fourth; thirty-eighth; thirty-third b) fiftieth; fifty-seventh; sixty-second c) 98th; 94th; 89th; 83rd; 79th
•
• change The amount of change is the amount of money you get back after paying for an item.
Anne buys a pencil for 20¢ She pays for the pencil with a 50¢ coin. She gets
•
D
• denominator
In a fraction, the denominator is the total number of equal parts in a whole. In the fraction 3 4 , 4 is the denominator.
• difference A difference is the answer we get when we subtract numbers.
The difference between 8 and 5 is 3.
• divide (÷) Put 6 marbles in 3 equal groups. 6 ÷ 3 = 2 We divide to find the number of objects in each group.
Put 6 marbles in groups of 3.
We divide to find the number of equal groups.
There
The mass of the strawberry is 20 grams.
kilogram (kg) The kilogram is a unit of mass. We write kg for kilogram. We use kilogram to measure the mass of heavy objects.
The mass of the watermelon is 3 kilograms.
leap year A year that has 29 days in February is called a leap year
• line of symmetry
A line of symmetry is a line that divides a figure into two halves that match exactly when folded along this line. A figure can have more than 1 line of symmetry.
In these figures, the dotted lines are lines of symmetry.
• line segment
These are line segments
• liter (L)
The liter is a unit of capacity. For example, we use liter to measure the capacity of a container.
The meter is a unit of length. We use meter to measure long lengths and distances.
•
• multiplication Multiplication means putting together equal groups.
• multiplication sentence
2 × 3 = 6
× 5 = 20 These are multiplication sentences
• multiply ( )
× 3 = 6 We multiply to find the total in equal groups.
• numerator
In a fraction, the numerator is the number of equal parts being counted or used.
In the fraction 3 4 , 3 is the numerator.
O • odd number
An odd number of objects cannot be put into groups of 2. There is one left over. 5 is an odd number.
• pentagon
A pentagon is a shape with 5 sides and 5 vertices.
• product
The answer we get by multiplying numbers is the product of the numbers.
2 × 3 = 6
The product of 2 and 3 is 6.
• proper fraction A proper fraction is a fraction with a numerator less than the denominator. 1 4 and 2 3 are proper fractions.
• pyramid pyramid
This pyramid has a square for the bottom face and 4 triangular faces.
Q
• symmetry A figure has symmetry if we can fold it into halves that match exactly along the fold line.
T • third third
Each part is one third of the square. One third is 1 out of 3 equal parts.
• times ( ) 4 × 5 = 20
We read this multiplication sentence as 4 times 5 is equal to 20.
U • unit fraction
• vertex (plural: vertices) (3D shapes) vertex
A vertex in a 3D shape is a point where edges meet.
The pencil and arrow show a whole turn
A unit fraction has 1 as the numerator.
1 2 and 1 4 are unit fractions.
V • vertex (plural: vertices) (2D shapes)
vertex vertex
A vertex in a 2D shape is a corner. It is a point where two sides meet.
Z • zero mark zero mark cm
To measure the length of an object using a ruler, we start measuring from the zero mark
= 3 These are related division facts
• related multiplication facts 2 × 5 = 10 5 × 2 = 10 These are related multiplication facts S • sum A sum is the answer we get when we add numbers.
8 + 5 = 13 The sum of 8 and 5 is 13.
• symmetric figure
A symmetric figure is a figure with two halves that match exactly when folded along the line of symmetry.
The pencils and arrows show a quarter turn
line of symmetry line of symmetry These are symmetric figures.
4 9 3 8 2 7 1 6 0 5 4 9 3 8 2 7 1 6 0 5
3 0 2 0 1 0 6 0 5 0 4 0 9 0 8 0 7 0 1 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.
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.
To make learning and teaching fun and engaging, digital components are available with TM Mathematics (New Edition).
PR1ME Mathematics Digital Practice and Assessment
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.
Chapter 1 Numbers to 100
Chapter 2 Addition and Subtraction Within 100
Chapter 3 Metric Units of Length
Chapter 4 Mass
Chapter 5 Capacity
Chapter 10 Multiplication Tables of 3 and 4
Chapter 11 Money
Chapter 12 Fractions
Chapter 13 Time
Chapter 14 Position and Movement
Let’s
Let's Remember Let's Remember
1. Count. Then, write the number in numerals and in words.
Numeral: Word:
2. Count the sticks and write the number.
3 tens 4 ones = 3. Complete the number line. 30323334
1 ten = 10
4. Compare the numbers. Then, write the missing numbers.
22 is the greatest. is the least.
5. Look at the picture. Then, write in the blanks.
ant bee butterfly grasshopper snail
a) The is 2nd from the left.
b) The is 1st from the right.
c) The is 4th from the left.
d) The is 5th from the right.
e) The is 3rd from the left.
The number of countries in each continent is shown below.
North America: 23 South America: 12 Europe: 44 Africa: 54 Asia: 48 Oceania: 14
Arrange the continents in order.
Begin with the continent that has the greatest number of countries.
How can we solve this problem?
Discuss in your group and fill in columns 1 and 2.
1. What I already know that will help me solve the problem
You will learn to...
• count within 100
• read and write numbers up to 100
• write 2-digit numbers in tens and ones
• estimate the number of objects
1.1 Counting, reading and writing numbers in tens
Let's Learn Let's Learn
10 ones = 1 ten
b)
10, 20, ..., 100 are numerals.
10 tens = 1 hundred
10, 20, 30, 40, 50, 60
6 tens = 60 ones = 60
60
sixty
10, 20, 30, ..., 80, 90, 100
10 tens = 100 ones = 100
100
one hundred
A numeral is a symbol used to represent a number of objects.
Let's Do Let's Do
1. Count the tens. Then, write the missing numbers.
tens = ones =
2. Write the numerals.
a) forty b) ninety
1. Count the tens. Then, write the missing numbers.
tens =
3. Write the numbers in words. a) 30 b) 70 Let's Practice
2. Write the numerals. a) fifty b) one hundred
a) Count the number of erasers. Make tens first. 40 and 4 make 44. There are 44 erasers. 40 4 forty-four 4 4 b) 53 is 50 and 3. 53 = 5 tens 3 ones c)
1. Count and write the number of buttons. There are buttons.
2. Count the tens and ones. Then, write the missing numbers.
56 = 5 tens ones 56 = 50 +
= tens 4 ones
= + 4
3. Write the numerals. a) sixty-eight b)
1. Count and write the number of sticks. There are sticks.
2. Count the tens and ones. Then, write the missing numbers. = tens ones = +
3. Write the missing numbers.
a) 4 tens 6 ones = b) 7 tens 9 ones = c) is 90 and 3. d) 50 and 8 make .
4. Write the numerals.
a) fifty-four
c) seventy-one
5. Write the numbers in words.
b) eighty-two
d) thirty-nine
a) 45 b) 99
P B Chapter 1: Exercise 1.2
>> Look at EXPLORE on page 2 again. Can you solve the problem now? What else do you need to know?
Let's Learn Let's Learn
a) 1 Maya grabs a handful of 2 She estimates the number marbles from the jar. of marbles she is holding.
3 Maya counts the
I am holding about 10 marbles.
4 She estimates the marbles in her hands. number of marbles left in the jar.
1, 2, 3, … I am holding 12 marbles.
There are about 40 marbles left in the jar.
5 Maya counts the marbles in the jar.
We count the marbles in groups of 10. Then, count on.
There are 45 marbles in the jar.
Estimate the number of toy robots. There are about 50 toy robots. Now, let us count the number of toy robots. There are toy robots.
Let's Do Let's Do
1. Make an estimate. Then, count.
Estimate: There are about erasers. Count: There are erasers.
Let's Practice Let's Practice
1. Make an estimate. Then, count.
I can circle groups of 10 toy robots to help me count.
Estimate: There are about buttons. Count: There are buttons.
I have learned to... count within 100 read and write numbers up to 100 write 2-digit numbers in tens estimate the number of objects and ones
You will learn to...
• find 1, 2, 3, 4, 5 or 10 more than or less than a given number
• describe and complete number patterns
• read numbers to 100 on a number line
• count objects in twos, fives or tens
• identify odd and even numbers
• compare and order numbers within 100
41424344454647484950 51525354555657585960
a) Count on 3 ones from 13. 13, 14, 15, 16
3 more than 13 is 16.
b) Count backwards 4 ones from 56. 56, 55, 54, 53, 52 4 less than 56 is .
c) Count on 1 ten from 19. 19, 29 10 more than 19 is . 12345678910
61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 1 ten = 10
Let's Do Let's Do
1. Write the missing numbers.
a) is 1 more than 65. b) is 1 less than 65.
c) is 2 more than 65. d) is 2 less than 65.
e) is 5 more than 65. f) is 5 less than 65.
g) is 10 more than 65. h) is 10 less than 65.
Let's Practice Let's Practice
1. Write the missing numbers.
a) is 5 more than 53. b) is 5 less than 53.
c) is 10 more than 53. d) is 10 less than 53.
e) is 3 more than 53. f) is 3 less than 53.
g) is 4 more than 53. h) is 4 less than 53.
2. Answer the questions.
a) What number is 3 more than 34?
b) What number is 4 less than 45?
c) What number is 5 more than 75?
d) What number is 10 less than 82?
Let's Learn Let's Learn
We can find number patterns on a number chart.
11121314151617181920
21222324252627282930
31323334353637383940 41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100
a) pattern: Start at 61. Count on by fives.
The number pattern is 61, 66, 71, 76.
The next two numbers in the pattern are 81 and 86. 12345678910
Each number is 5 more than the number before it.
b) pattern: Start at 89. Count backwards by twos.
The number pattern is 89, 87, 85, 83.
The next two numbers in the pattern are and . Each number is 2 less than the number before it.
Let's Do Let's Do
1. Describe each number pattern. Then, continue the number pattern.
12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100
a) pattern: Start at 28. Count on by . 28, , , , ,
b) pattern: Start at 80. Count by . 80, , , , ,
2. Complete the number patterns.
a) 73, 72, 71, , b) 42, 46, 50, , c) 20, 30, , 50, 60, d) 95, 93, , , 87, 85
1. Continue each number pattern. Then, describe the number pattern.
a) 88, 84, 80, 76, , Count by .
b) 19, 22, 25, 28, , Count by .
2. Complete the number patterns.
a) 55, 60, 65, , b) 20, 17, 14, ,
c) , 90, 80, , 60, 50
d) 34, , , 46, 50, 54
Let's Learn Let's Learn
What numbers do , and stand for on the number line?
Count on by ones: 40, 41, 42. stands for 42.
Count on by ones: 44, . stands for .
Count backwards by ones: 50, 49, . stands for .
1. Complete the number lines. a)
Let's Do Let's Do Let's Practice Let's Practice
1. Complete the number lines. a)
2. Look at the number line.
a) Label the number that is 3 more than 47 with A.
b) Label the number that is 3 less than 56 with B.
c) Label the number that is 4 more than 51 with C.
d) Which letter stands for a number that is 5 less than letter C?
3. Mark 97 with a cross on the number line below.
Let's Learn Let's Learn
a) 2, 4, 6
Count on by twos. 2, 4, 6
There are 6 toy cars.
b)
5, 10, 15, 20 10, 20 or
Count on by fives. or Count on by tens. 5, 10, 15, 20 10, 20
There are mangoes.
c)
12 beans can be put into groups of 2. 12 is an even number.
15 beans cannot be put into groups of 2. There is 1 bean left over. 15 is an odd number.
An even number of objects can be put into groups of 2. An odd number of objects cannot be put into groups of 2. There will be 1 object left over.
Let's Do Let's Do
1. Count and write the number of objects. Circle groups of 2, 5 or 10 objects to help you count.
2. Cross out the group that shows an even number.
Let's Practice
Let's Practice
1. Count and write the number of objects. a) b)
2. Circle the group that shows an odd number.
Let's Learn Let's Learn
a) Compare 53 and 47.
53 is greater than 47. 53 > 47
b) Compare 53 and 59.
53 is less than 59. 53 < 59
c) Compare 53, 47 and 59.
59 is the greatest number. 47 is the least number.
Arrange the numbers in order. Begin with the greatest. , , (greatest)
Compare the tens. 5 tens is greater than 4 tens. TensOnes
First, compare the tens. They are the same. Then, compare the ones. 3 ones is less than 9 ones.
First, compare 1
Then, use the greater number 53 and compare 2 .
Let's Do Let's Do
1. Write greater than or less than. a) TensOnes 62 75 b) TensOnes 98 93 62 is 75. 98 is 93.
2. Write > or <. a) 44 69 b) 87 84
3. Arrange 86, 49 and 94 in order. Begin with the least. , ,
Let's Practice Let's Practice
1. Write > or <.
2. Arrange the numbers in order. Begin with the given number.
a) 786382 63, , b) 945791 94, ,
I have learned to... find 1, 2, 3, 4, 5 or 10 more than or less than a given number describe and complete number patterns read numbers to 100 on a number line count objects in twos, fives or tens identify odd and even numbers compare and order numbers within 100
You will learn to… • name a position using an ordinal number from 1st to 100th
Let's Learn Let's
These are the 26 letters of the English alphabet. ABCDEFGHIJKLMNOPQRSTUVWXYZ
‘A’ is the first letter of the alphabet. We can write ‘first’ as ‘1st’.
‘N’ is the fourteenth letter of the alphabet. We can write ‘fourteenth’ as ‘14th’.
1st, 14th and 22nd are ordinal numbers. Here are some others.
WriteReadWriteReadWriteRead 11theleventh21sttwenty-first10thtenth 12thtwelfth 22nd twenty-second 20thtwentieth 13ththirteenth23rdtwenty-third30ththirtieth 14thfourteenth24thtwenty-fourth40thfortieth 15thfifteenth25thtwenty-fifth50thfiftieth 16thsixteenth26thtwenty-sixth60thsixtieth 17thseventeenth27th twenty-seventh 70thseventieth 18theighteenth28thtwenty-eighth80theightieth 19thnineteenth29thtwenty-ninth90thninetieth 20thtwentieth30ththirtieth100thhundredth
‘Y’ is the 25th letter of the alphabet.
‘W’ is the letter of the alphabet. 1st first 14th fourteenth 22nd twenty-second
Let's Do Let's Do
1. Match.
2. Circle the 75th star. Cross out the eighty-first star.
Practice
Practice
1. These children are in a line to buy movie tickets.
BethJaydenSamDarrenEllie
Beth is 12th in the line and Jayden is 13th in the line.
a) is 15th in the line. b) Sam is in the line.
2. Write the positions of the yellow beads.
a) Write the positions in words.
b) Write the positions in ordinal numbers.
You will learn to… • solve a non-routine problem with numbers up to 100
Let's Learn Let's Learn
Adele arranges three numbers in order.
33 is the greatest and 24 is the least. The third number has 3 tens and at least 1 one. What can the third number be?
1 Plan what to do. 2 Work out the Answer. 3 Check if your answer is correct. 4
How many numbers are there? What number is the greatest? What number is the least?
What do I know about the third number? What do I have to find?
I can make a list to solve the problem.
The third number is greater than 24 but less than 33.
The third number can be 25, 26, 27, 28, 29, 30, 31 or 32.
The third number has 3 tens and at least 1 one. Only 31 and 32 have 3 tens and at least 1 one. So, the third number can be 31 or 32.
Both 31 and 32 are greater than 24 but less than 33.
Both 31 and 32 have 3 tens and at least 1 one. My answer is correct. Understand the problem.
The third number is greater than 24 but less than 33.
Draw a number line.
I have learned to... solve a non-routine problem with numbers up to 100 + Plus Solve the problem in another way.
From the number line, 25, 26, 27, 28, 29, 30, 31 and 32 are greater than 24, but less than 33.
The third number has 3 tens and at least 1 one. So, the third number can be 31 or 32.
Compare the methods in steps 3 and 5. Which method do you prefer? Why?
1. Understand 2. Plan 3. Answer 4. Check 5. Plus
>> Look at EXPLORE on page 2 again. Fill in column 3. Can you solve the problem now?
• a.m.
We use a.m. for the time just after midnight to just before noon.
The boy wakes up at 7 : 00 a.m.
• after
• before
The time is 5 minutes after 7 o'clock. It is 7 : 05.
We read 7 : 05 as seven o five.
• array
An array is an arrangement of objects in rows and columns. This array has 2 rows and 5 columns. It shows 2 × 5.
The time is 5 minutes before 7 o'clock. It is 6 : 55.
We read 6 : 55 as six fifty-five.
• block graph Herrings caught on a fishing trip
Han LeeJacinthaColinSheila
C
• Carroll diagram
Odd numbersEven numbers 11, 15, 3, 7 16, 4, 20, 2
• centimeter (cm) cm
The centimeter is a unit of length. We use centimeter to measure short lengths.
• change
The amount of change is the amount of money you get back after paying for an item.
Anne buys a pencil for 20¢. She pays for the pencil with a 50¢ coin. She gets 30¢ in change.
• clockwise
The clockwise direction is the direction in which clock hands turn.
• counterclockwise
The counterclockwise direction is the direction opposite to which clock hands tur n.
• curve
These are curves.
• curved surface curved surface
• denominator
In a fraction, the denominator is the total number of equal parts in a whole.
In the fraction 3 4 , 4 is the denominator.
• difference
A difference is the answer we get when we subtract numbers.
difference
8 – 5 = 3
The difference between 8 and 5 is 3.
• divide (÷)
Put 6 marbles in 3 equal groups.
6 ÷ 3 = 2
We divide to find the number of objects in each group.
Put 6 marbles in groups of 3.
6 ÷ 3 = 2
We divide to find the number of equal groups.
• division
See divide.
• division sentence
6 ÷ 3 = 2
8 ÷ 2 = 4
These are division sentences.
• edge edge
The sides of two faces meet at an edge.
• equal groups
There is an equal number of objects in each group. The three groups are equal groups.
• even number
An even number of objects can be put into groups of 2. There is no leftover. 4 is an even number.
• evening
The part of the day from the end of after noon to night is evening
• face face
A face is a flat surface of a 3D shape.
• fact family
2 × 10 = 20 10 × 2 = 20
20 ÷ 10 = 2 20 ÷ 2 = 10
This is a multiplication and division fact family.
• flat surface flat surface
• gram (g)
The gram is a unit of mass. We write g for gram. We use gram to measure the mass of light objects.
The mass of the strawberry is 20 grams.
H half turn
The pencils and arrows show a half turn.
• hexagon
A hexagon is a shape with 6 sides and 6 vertices.
• hour (h)
An hour is a unit of time. 1 hour = 60 minutes
K
• kilogram (kg)
The kilogram is a unit of mass. We write kg for kilogram. We use kilogram to measure the mass of heavy objects.
The mass of the watermelon is 3 kilograms.
L
• leap year
A year that has 29 days in February is called a leap year.
• line of symmetry
A line of symmetry is a line that divides a figure into two halves that match exactly when folded along this line. A figure can have more than 1 line of symmetry.
In these figures, the dotted lines are lines of symmetry.
• line segment
These are line segments
• liter (L) 1 L
The liter is a unit of capacity. For example, we use liter to measure the capacity of a container.
• meter (m)
1 meter meter ruler
The meter is a unit of length. We use meter to measure long lengths and distances.
• midnight
12 o’clock at night is midnight.
• noon
12 o’clock in the day is noon.
• numerator
In a fraction, the numerator is the number of equal parts being counted or used.
In the fraction 3 4 , 3 is the numerator.
• odd number
• minute
A minute is a unit of time. 60 minutes = 1 hour
• multiplication
Multiplication means putting together equal groups.
• multiplication sentence 2 × 3 = 6 4 × 5 = 20
These are multiplication sentences.
• multiply ( )
2 × 3 = 6
We multiply to find the total in equal groups.
An odd number of objects cannot be put into groups of 2. There is one left over. 5 is an odd number.
• p.m.
We use p.m. for the time just after noon to just before midnight.
The boy is studying at 2 : 00 p.m.
• pentagon
A pentagon is a shape with 5 sides and 5 vertices.
• product
The answer we get by multiplying numbers is the product of the numbers.
2 × 3 = 6
The product of 2 and 3 is 6.
• proper fraction
A proper fraction is a fraction with a numerator less than the denominator. 1 4 and 2 3 are proper fractions.
• pyramid pyramid
This pyramid has a square for the bottom face and 4 triangular faces.
R• regroup
13 ones = 1 ten 3 ones
We can regroup 10 ones into 1 ten.
• related division facts
15 ÷ 3 = 5
15 ÷ 5 = 3
These are related division facts.
• related multiplication facts
2 × 5 = 10
5 × 2 = 10
These are related multiplication facts
S• sum
A sum is the answer we get when we add numbers.
sum
8 + 5 = 13
The sum of 8 and 5 is 13.
• symmetric figure
A symmetric figure is a figure with two halves that match exactly when folded along the line of symmetry.
line of symmetry
line of symmetry
pencils and arrows show a quarter turn
These are symmetric figures.
• symmetry
A figure has symmetry if we can fold it into halves that match exactly along the fold line.
• third third
• vertex (plural: vertices) (3D shapes)
vertex
A vertex in a 3D shape is a point where edges meet.
Each part is one third of the square. One third is 1 out of 3 equal parts.
• times ( )
4 × 5 = 20
We read this multiplication sentence as 4 times 5 is equal to 20.
The pencil and arrow show a whole turn
• unit fraction
A unit fraction has 1 as the numerator. 1 2 and 1 4 are unit fractions.
• vertex (plural: vertices) (2D shapes)
• zero mark zero mark cm
To measure the length of an object using a ruler, we start measuring from the zero mark.
vertex
vertex
A vertex in a 2D shape is a corner. It is a point where two sides meet.
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.
4.
3.
Reviews provide summative assessment and enable consolidation of concepts and skills learnt across various topics.
Chapter 1 Numbers to 100
Exercise 1.1 Counting, reading and writing numbers in tens 9
Exercise 1.2 Numbers in tens and ones 10
Exercise 1.3 Estimating the number of objects 12
Exercise 2.1 Finding more than and less than 13
Exercise 2.2 Number patter ns 14
Exercise 2.3 Reading number lines 16
Exercise 2.4 Counting in groups of 2, 5 and 10 17
Exercise 2.5 Comparing and ordering numbers 19
Exercise 3.1 Knowing 1st to 100th 20
Chapter 2 Addition and Subtraction Within 100
Exercise 1.1 Understanding the meanings of sum and difference 22
Exercise 2.1 Adding a 1-digit number to a 2-digit number 23
Exercise 2.2 Adding tens to a 2-digit number 25
Exercise 2.3 Adding two 2-digit numbers 27
Exercise 2.4 Subtracting a 1-digit number from a 2-digit number 29
Exercise 2.5 Subtracting tens from a 2-digit number 31
Exercise 2.6 Subtracting a 2-digit number from another 2-digit number 33
Exercise 2.7 Solving word problems 35
Exercise 3.1 Adding a 1-digit number to a 2-digit number with regrouping 37
Exercise 3.2 Adding two 2-digit numbers with regrouping 39
Exercise 3.3 Adding more than two numbers 41
Exercise 3.4 Subtracting a 1-digit number from a 2-digit number with regrouping 43
Exercise 3.5 Subtracting a 2-digit number from another 2-digit number with regrouping 45
Exercise 3.6 Solving word problems 47
Exercise 4.1 Word problems 49
Chapter 3 Metric Units of Length
Exercise 1.1 Measuring and comparing lengths in meters 51
Exercise 2.1 Measuring and comparing lengths in centimeters 52
Exercise 2.2 Choosing units or tools of measure 53
Exercise 3.1 Word problems 54
Exercise 3.2 More word problems 56
Chapter 4 Mass
Exercise 1.1 Measuring and comparing masses in kilograms
Exercise 2.1 Measuring and comparing masses in grams
Exercise 2.2 Choosing units of measure
Exercise 3.1 Word problems
Exercise 3.2 More word problems
Chapter 5 Capacity
Exercise 1.1 Measuring and comparing capacities in liters
Exercise 2.1 Word problems
Exercise 2.2 More word problems
Chapter 6 Multiplication
Exercise 1.1 Adding the same number
Exercise 3.1 Completing multiplication sentences
Exercise 3.2 Related multiplication facts
Exercise 3.3 Solving multiplication problems
Chapter 7 Division
Exercise 1.1 Finding the number of objects in each group
Exercise 1.2 Finding the number of equal groups 91
Exercise 1.3 Telling division stories 93
Exercise 2.1 Finding the number of objects in each group 94
Exercise 2.2 Finding the number of equal groups
Exercise 2.3 Related division facts
Exercise 2.4 Writing a fact family
Chapter 8 Multiplication Tables of 2, 5 and 10
Exercise 1.1 Counting by twos
Exercise 1.2 Using dot cards 101
Exercise 2.1 Counting by fives 102
Exercise 2.2 Using dot cards 103
Exercise 3.1 Counting by tens 104
Exercise 3.2 Using dot cards 105
Exercise 4.1 Dividing by 2 106
Exercise 5.1 Dividing by 5 107
Exercise 6.1 Dividing by 10 108
Exercise 7.1 Word problems involving multiplication
Exercise 7.2 Word problems involving division
Chapter 9 Mental Strategies
Exercise 1.1 Pairing 1-digit numbers
Exercise 1.2 Making 20
Exercise 1.3 Making 100 121
Exercise 2.1 Finding doubles of numbers up to 10 122
Exercise 2.2 Finding doubles of 2-digit numbers up to 50 123
Exercise 2.3 Finding halves of even numbers up to 20 124
Exercise 2.4 Finding halves of even numbers up to 100 125
Chapter 10 Multiplication Tables of 3 and 4
Exercise 1.1 Counting by threes
Exercise 1.2 Using dot cards
Exercise 2.1 Counting by fours
Exercise 2.2 Using dot cards
Exercise 3.1 Dividing by 3 130
Exercise 4.1 Dividing by 4 131
Exercise 5.1 Word problems involving multiplication 132
Exercise 5.2 Word problems involving division 134
Chapter 11 Money
Exercise 1.1 Naming notes 136
Exercise 1.2 Counting money 137
Exercise 1.3 Exchanging money 138
Exercise 1.4 Counting money in different denominations 139
Exercise 1.5 Exchanging money in more ways 140
Exercise 1.6 Making up an amount of money 141
Exercise 1.7 Comparing amounts of money 143
Exercise 2.1 Adding amounts of money 145
Exercise 2.2 Subtracting amounts of money 147
Exercise 3.1 Word problems 149
Chapter 12 Fractions
Exercise 1.1 Using fractions to describe one half, one third and one quarter of a whole 151
Exercise 1.2 Finding one half, one third and one quarter of a set 152
Exercise 1.3 Using fractions to describe halves, thirds and quarters of a whole 153
Exercise 1.4 Finding halves, thirds and quarters of a set 154
Exercise 2.1 Recognizing and naming unit fractions 155
Exercise 2.2 Recognizing and naming other fractions 157
Review 3 159
Chapter 13 Time
Exercise 1.1 Telling time by 5-minute intervals 165
Exercise 1.2 Telling time using a.m. and p.m. 167
Exercise 2.1 Duration of time from the hour 168
Exercise 2.2 Duration of time 170
Exercise 3.1 Reading a calendar 172
Exercise 3.2 Understanding the relationship between units of time 173
Exercise 4.1 Word problems 174
Chapter 14 Position and Movement
Exercise 1.1 Turns 176
Exercise 1.2 Giving directions 178
Chapter 15 Handling Data
Exercise 1.1 Making, reading and interpreting pictograms 180
Exercise 1.2 Making, reading and interpreting pictograms with scale 183
Exercise 2.1 Making, reading and interpreting block graphs 186
Exercise 3.1 Sorting data in Carroll diagrams 188
Chapter 16 2D Shapes
Exercise 1.1 Identifying line segments and curves 189
Exercise 2.1 Naming and describing 2D shapes 190
Exercise 2.2 Identifying sides and vertices 191
Exercise 2.3 Sorting 2D shapes 192
Exercise 3.1 Identifying and making symmetric figures 194
Exercise 3.2 Identifying and drawing lines of symmetry 195
Chapter 17 3D Shapes
Exercise 1.1 Naming and describing 3D shapes 197
Exercise 1.2 Identifying flat and curved sur faces 198
Exercise 1.3 Identifying faces, edges and vertices 199
Exercise 1.4 Sorting 3D shapes 200
Review 4 202
7 tens = 70 ones = 70 seventy
1. Count in tens. Then, write the missing numbers. tens = ones tens = ones = =
2. Match the numerals and the numbers in words. thirty eighty
3. Write the numbers in words.
sixty-five 6 tens and 5 ones make 65. 60 and 5 make 65.
1. Count and write the missing numbers.
There are cans. There are eggs.
2. Write the missing numerals or number words.
3. Count the tens and ones. Then, write the missing numbers. a) b) 43 = + c)
= tens ones
= +
76 = +
4. Write the missing numbers.
a) 5 tens 5 ones = b) 6 tens 0 ones = c) is 90 and 4.
d) tens ones = 42
e) tens ones = 38 f) 80 and 8 make .
Recap
Estimate: There are about 20 flags.
Count: There are 23 flags.
1. Make an estimate. Then, count.
a)
Estimate: There are about flowers.
Count: There are flowers.
b)
Estimate: There are about rabbits.
Count: There are rabbits.
c)
Estimate: There are about leaves.
Count: There are leaves.
Recap
575859606162 count on count backwards
1. Write the missing numbers.
Count 4 ones from 57. 4 more than 57 is 61.
Count backwards 3 ones from 62. 3 less than 62 is 59.
a) is 1 more than 47. is 5 more than 47. is 4 less than 47.
b) is 3 less than 64. is 10 less than 64. is 2 more than 64.
2. Answer the questions.
a) What number is 2 more than 52?
b) What number is 5 less than 45?
c) What number is 4 more than 55?
d) What number is 3 more than 87?
e) What number is 10 less than 39?
f) What number is 4 less than 91?
g) What number is 3 less than 70?
h) What number is 5 more than 39?
61626364656667686970
71727374757677787980
81828384858687888990
pattern: Start at 62. Count on by fours.
The number pattern is 62, 66, 70, 74, 78.
The next two numbers in the pattern are 82 and 86.
1. Complete the number patterns. Then, describe the number patterns.
2. Continue each number pattern. Then, describe the number pattern.
a) 69, 68, 67, , , Count by _.
b) 36, 39, 42, , , Count by .
c) 85, 75, 65, , , Count by .
d) 49, 53, 57, , , Count by .
e) 47, 45, 43, , , Count by .
3. Complete the number patterns.
a) 45, 46, 47, , , 50, , , 53
b) , , 70, , 50, , 30, 20, 10
c) , , 83, 80, 77, ,
d) 59, , 69, , , 84, 89
e) , 96, , 88, , , 76
f) , , 31, , 51, , 71,
g) 86, , , 80, , 76, , 72
Recap
1. Complete the number lines.
b) 2. Look at the number line.
1 more than 73 is 74. represents 74.
1 less than 79 is 78. represents 78.
a) Label the number that is 10 more than 64 with A.
b) Label the number that is 3 less than 71 with B.
c) Label the number that is 5 more than 67 with C.
d) Label the number that is 4 less than 69 with D.
3. Mark 82 with a cross on the number line below.
Recap
Count on by twos.
2, 4, 6, 8, 10, 12, 14
There are 14 cans.
14 cans can be put into groups of 2. 14 is an even number.
An even number of objects can be put into groups of 2. An odd number of objects cannot be put into groups of 2. There will be 1 object left over.
1. Count and write the number of objects. Circle groups of 2, 5 or 10 objects to help you count. a)
2. Circle the group that shows an even number.
3. Cross out the group that shows an odd number.
Recap
65 is less than 69.
65 < 69
1. Compare the numbers using < or >.
First, compare the tens. They are the same. Then, compare the ones. 5 ones is less than 9 ones.
a) 35 85 b) 38 48 c) 57 64
d) 56 52 e) 96 98 f) 66 62
g) 79 75 h) 68 69 i) 88 87
2. Arrange the numbers in order. Begin with the greatest number.
a) 47, 49, 56
b) 61, 59, 68
c) 82, 63, 87, 78
d) 95, 59, 99, 55
3. Arrange the numbers in order. Begin with the least number.
a) 56, 72, 71
b) 42, 39, 45
c) 50, 59, 53, 38
d) 83, 98, 93, 89
Recap
We can name a position using ordinal numbers. 20th 30th
Star A is at the 21st position. We read 21st as ‘twenty-first’. Star B is at the 40th position. We read 40th as ‘fortieth’.
1. Match.
22nd fifty-sixth 85th ninety-eighth 56th twenty-second 98th sixtieth 60th eighty-fifth
2. Answer the questions.
10th 17th
a) Which robot is in the 12th place?
b) Which robot is in the 15th place?
c) Which robot is in the 16th place?
d) In which place is robot E?
e) In which place is robot I?
f) In which place is robot J?
3. a) Write the positions of the eaten apples in words.
b) Write the positions of the shaded flowers in words.
c) Write the positions of the cones with ice cream in ordinal numbers.
