PR1ME Maths Book 3: Sample chapters of Teacher Guide, Course Book and Practice Book

Teacher’s Guide

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

Teacher’s Guide

About Mathematics

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.

works for every student and teacher.

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.

Learning experiences based on the Readiness-Engagement-Mastery model

Every student is a successful mathematics learner.

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.

Readiness

Because mathematical knowledge is cumulative in nature, a student’s readiness to learn new concepts or skills is vital to learning success.

Checking prior knowledge

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.

Chapter 11 Fractions

Taking ownership of learning

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.

Engagement

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.

Concrete-Pictorial-Abstract approach

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.

Gradual Release of Responsibility

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.

Teacher-led enquiry

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.

Mastery

There are multiple opportunities in each lesson for students to consolidate and deepen their learning.

Motivated practice

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.

2.

There are a range of activities, from simple recall of facts to application of concepts, for students to deepen their understanding.

Reflective review

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.

Consolidation of learning

Assessment after each chapter and quarterly Reviews provide summative assessment for consolidation of learning throughout the year.

1.

2.

3.

4.

5.

Summative

Extension of learning

Mind Stretcher, Create Your Own and Mission Possible immerse students in problem solving tasks at various levels of difficulty.

Learning mathematics via problem solving

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

Concepts

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.

Suppose the number is 10.

Stage 1: 10 + 20 = 30

Stage 2: 30 – 5 = 25

Stage 3: 25 + 20 = 45

Problem solving for productive struggle to develop resilience

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.

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.

Concept development via problem solving

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.

Multiple opportunities for learning problem solving at varying levels of difficulty

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

Word problems help students recognize the role that mathematics plays in the world by applying the concepts and skills they have learned within a context.

Word problems assess students’ ability to apply the knowledge learned.

Non-routine problems

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.

Problem posing tasks

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.

Computational thinking tasks

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.

Focus on the problem-solving method

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.

The bar model method

The bar model method, a key problem-solving strategy in TM Mathematics, helps students understand and draw representations of a problem using mathematical concepts to solve the problem.

In arithmetic word problems, the bar model method helps students visualize the situations involved so that they are able to construct relevant number sentences. In this way, it helps students gain a deeper understanding of the operations they may use to solve problems.

CREATE YOUR OWN

Bottle A contains 75 grams of salt.

Bottle B contains 15 grams more salt than bottle A.

a) What is the mass of salt in bottle B?

b) If Mrs. Chen uses 8 grams of salt from bottle B, what is the mass of salt left in bottle B?

Read the problem. Change the masses in the word problem. How did you decide what masses to use?

Next, solve the word problem. Show your work clearly. What did you learn?

The model method lays the foundation for learning formal algebra because it enables students to understand on a conceptual level what occurs when using complex for mulas and abstract representations. Using the model method to solve algebraic word problems helps students derive algebraic expressions, construct algebraic equations and simplify algebraic equations.

3.3 Mind stretcher

Let's Learn Let's Learn

Using algebra

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

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 bar model to compare their masses. What is the total mass of Brian and his father? Who is heavier? How many kilograms heavier? What do I have to find? Understand the problem. 1 Plan what to do.

2

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.

Focus on the problem-solving process UPAC+TM

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.

Development and communication of mathematical thinking and reasoning

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.

Think About It

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.

Math Journal

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.

Process-based

Teacher-led enquiry through purposeful questions

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 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

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

Learning mathematics by doing mathematics

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

Concrete-Pictorial-Abstract approach in concept development

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.

Concrete-Pictorial-Abstract approach in formative assessment

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.

Concrete-Pictorial-Abstract approach in independent practice

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.

Focused and coherent curriculum based on learning progression principles

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

READ

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 six grades, about 90% of the chapters are on Numbers and Operations, Measurement and Geometry The remaining chapters are on Data Analysis and Algebra

Learning Progression Principle

2: Sequencing within strands supports in-depth and efficient development of mathematics content.

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.

Assessment for learning

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.

Formative assessment

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.

Let’s Do

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.

1. Divide. Use the

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.

Practice

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 out in

2.

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 assessment

Summative assessments enable teachers to assess student learning at the end of each chapter and beyond.

Reviews

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.

Review 2

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

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.

Meaningful insight to help every student succeed.

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

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.

Monitor 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.

Identify students’ strengths and weaknesses

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

Reports for Assessments provide in-depth mastery analysis in an easy to access and view format.

Monitor progress

Class List by Assessment Report shows student performance on each assessment.

This report informs teachers on how well students have learned each chapter.

Identify students’ strengths and weaknesses

Class List by Learning Objective Report shows student performance against a topic or learning objective by aggregating the results for it across multiple assessments.

Benchmark performance

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.

Student materials

Coursebook

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.

Practice Book

Correlates to the coursebooks and contains exercises and reviews for independent practice and for mative and summative assessments.

Student Hub

Coursebook in online format with embedded videos to ensure that learning never stops.

Digital Practice and Assessment

Online opportunities for students to consolidate learning and demonstrate understanding.

Teacher support

Teacher’s Guide

Comprehensive lesson plans support instruction for each lesson in the Coursebooks.

Teaching Hub

This one-stop teacher’s resource center provides access to lesson notes, demonstration videos and Coursebook pages for on-screen projection.

Digital Practice and Assessment

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.

Professional Learning Now!

Video tutorials and related quizzes in this online resource provide anytime, anywhere professional learning to educators.

Classroom Posters

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.

Instructional support

TM Mathematics provides extensive support at point of use to support teacher development along with student lear ning, making teaching mathematics a breeze.

Teacher’s Guide

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.

Teaching Hub

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!

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.

Plan Start of school year

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

Start of chapter

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.

Start of lesson

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.

Check for readiness to learn

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.

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.

Teach concepts and skills

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

Task 2 requires students to associate

Let's

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

THINK ABOUT IT

Students

Students

Have students work in groups to discuss the tasks. Ask the groups to present their answers.

Point out to students that 12 in the ones column represents 1 ten 2 ones and not 3 ones. David has mixed up addition and subtraction with regrouping in the vertical form. Conclude that David is not correct.

Reiterate that if there are not enough ones to subtract from, we need to first regroup the tens and ones before we subtract.

Make use of the examples presented by the groups to let students understand the importance and usefulness of knowing how to subtract numbers.

Think About It poses purposeful questions to facilitate meaningful mathematical discourse and promote reasoning and communication. Students work in groups to discuss the task and present and justify their answers to the class.

Teach problem solving

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.

a) How many storybooks does Kevin have?

b) How many storybooks do they have altogether?

CREATE YOUR OWN

Nathan has 46 stamps.

He has 19 more stamps than Tim.

a) How many stamps does Tim have?

b) If Tim gives 8 stamps to Zoe, how many stamps will he have left?

Read the word problem. Replace ‘more’ with ‘fewer’. Next, solve the word problem. Show your work clearly. What did you learn?

To

To solve 1-step word problems involving subtraction with regrouping

Tasks 1 to 3 require students to solve 2-step word problems involving addition and subtraction.

CREATE YOUR OWN

Have students work in groups to create and solve the word problem. Have a few groups present their work.

Students are expected to replace ‘more’ with ‘fewer’ in the word problem. So, they have to add in the first part and subtract in the second part to solve the word problem.

Students

solve the word problem.

Students are expected to solve a 1-step subtraction word problem involving a comparison situation by finding the difference given the two quantities. They can draw a comparison bar model to help them solve the word problem.

4.2 Mind stretcher

Let's Learn Let's Learn

Objective:

•Solve a non-routine problem involving addition and subtraction using the strategy of working backwards

Resource:

•CB: pp. 62–63

Create Your Own tasks facilitate meaningful mathematical discourse and promote reasoning and problem solving. Students work in pairs or groups to discuss the task and present their work to the class.

Have students read the problem on CB p. 62.

1. Understand the problem.

Pose the questions in the thought

2.

3.

Let's Practice Practice

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.

up Chapter 2: Addition and Subtraction Within 100 63

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.

Have students work in groups to complete the task on CB p. 329.

Go through the task using the prompts given below.

1. Decomposition Ask: How can we break down the problem into smaller and simpler problems? (Answer varies. Sample: Find out how much money Miguel has, find all the combinations of two presents Miguel can buy, find the total cost of each combination of presents, find the amount of money left after buying each combination)

2. Pattern Recognition Lead students to say that every time they find the total cost of the combination of presents, they have to check which of the total cost is closest to $78 and less than $78.

3. Abstraction Ask: What information will help you solve the problem? (The notes that Miguel has, the cost of the book, the costs of the presents, and he wants to use up as much of his money as possible)

4. Algorithms Guide students to draw a simple flow chart to show the steps used to solve the problem. Ask a group to write their solution on the board.

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

7To

8To

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.

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.

Math Journal: Rubric

Flexibility for use in print, blended or digital environment

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

Developmental Continuum

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.

NUMBERS AND OPERATIONS

Whole Numbers / Place Value

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.

Name a position using an ordinal number from 1st to 100th.

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.

Identify odd and even numbers.

Read and write a number within 10 000—the numeral and the corresponding number word.

Use number notation and place values (thousands, hundreds, tens, ones).

Find the number which is ones, tens, hundreds or thousands more than or less than a given number within 10 000.

*Identify patterns in a hundred chart.

Count on and backwards by ones, tens, hundreds or thousands within 10 000.

Describe, complete and create a number pattern by counting on or backwards by ones, tens, hundreds or thousands within 10 000.

Compare and order numbers within 10 000.

Use ‘>’ and ‘<’ symbols to compare numbers.

Read and place numbers within 10 000 on a number line.

Give a number between two 4-digit numbers.

Round a 3-digit or 4-digit number to the nearest ten.

Round a 3-digit or 4-digit number to the nearest hundred.

Round a 4-digit number to the nearest thousand.

Grade 2

Grade 3

Grade 4

NUMBERS AND OPERATIONS (continued)

Addition / Subtraction

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.

Add and subtract within 10 000.

Estimate sums and differences.

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.

Check reasonableness of answers in addition or subtraction using estimation.

Solve 1-step and 2-step word problems involving addition and subtraction.

Find pairs of multiples of 50 with a total of 1000 and write the addition and subtraction facts for each number pair.

Mentally add:

- two 2-digit numbers with regrouping

- a 2-digit, 3-digit or 4-digit number to a 3-digit or 4-digit number with regrouping

- three or four 1-digit or 2-digit numbers

- three 2-digit multiples of 10

Mentally subtract: - a 2-digit number from another 2-digit number with regrouping

- a 2-digit, 3-digit or 4-digit number from a 3-digit or 4-digit number

*Identify patterns in an addition chart.

Find pairs of multiples of 100 with a sum of 1000 and write the addition and subtraction facts for each number pair.

Find the missing part in an addition sentence. Find pairs of numbers with a sum of 100 and write the addition and subtraction facts for each number pair.

Find the missing part or whole in a subtraction sentence.

Use the ‘=’ sign to represent equality.

Find the missing part in an addition or subtraction sentence.

Use the ‘=’ sign to represent equality.

Grade 2

Grade 3

Grade 4

NUMBERS AND OPERATIONS (continued)

Addition / Subtraction (continued)

Multiplication / Division 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.

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

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 ones, tens or hundreds by a 1-digit number.

Multiply a 3-digit whole number by a 1-digit number.

Multiply three 1-digit numbers.

Apply the commutative and associative properties of multiplication in computation.

Multiply a whole number up to 3 digits by 10.

Divide hundreds or tens by a 1-digit number.

Divide a 3-digit whole number by a 1-digit number.

Multiply a number by 0 or 1. Divide a whole number up to 4 digits by 10.

Multiply ones or tens by a 1-digit number.

Estimate products and quotients.

Grade 2

Grade 3

Grade 4

NUMBERS AND OPERATIONS (continued)

Multiplication / Division (continued)

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.

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.

Multiply a 2-digit number by a 1-digit number.

Check reasonableness of answers in multiplication or division using estimation.

Divide a number by 1. Solve up to 3-step word problems involving multiplication and division.

Divide ones or tens by a 1-digit number.

Associate the terms ‘quotient’ and ‘remainder’ with division.

Divide a 2-digit number by a 1-digit number.

Estimate products and quotients.

Check reasonableness of answers in multiplication or division using estimation.

Use a part-whole bar model or a comparison bar model to represent a multiplication or division situation.

Solve 1-step and 2-step word problems on multiplication and division.

Find doubles of 2-digit numbers mentally.

Find halves of even numbers up to 200 mentally.

Find doubles of 2-digit numbers mentally.

Find doubles of multiples of 10 up to 1000 mentally.

Find doubles of multiples of 100 up to 10 000 mentally.

Find halves of 2-digit numbers mentally.

Find halves of multiples of 20 up to 2000 mentally.

Find halves of multiples of 200 up to 20 000 mentally.

Grade 2

Grade 3

Grade 4

NUMBERS AND OPERATIONS (continued)

Fractions / Concepts

Fractions / Arithmetic Operations

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.

Recognize and name unit fractions up to 1 12

Recognize and name proper fractions.

Identify the numerators and denominators of proper fractions.

Find the fraction that must be added to a given fraction to make a whole.

Compare and order fractions which have a common numerator or denominator.

Use 0, 1 2 and 1 as benchmark fractions.

Read fractions on a number line.

Compare and order fractions with different numerators and denominators.

Recognize and name equivalent fractions of a given fraction with denominator up to 12.

Find equivalent fractions of a given fraction using multiplication or division.

Express a fraction in its simplest form.

Write the sum of a whole number and a proper fraction as a mixed number.

Read and place mixed numbers on a number line.

Compare and order mixed numbers on a number line.

*Decompose a mixed number or a non-unit fraction into a sum of fractions with the same denominator.

*Interpret a non-unit fraction as a multiple of unit fraction.

Write an improper fraction.

Distinguish among whole numbers, proper fractions, improper fractions and mixed numbers.

Write an improper fraction as a whole number or a mixed number.

Write a whole number or a mixed number as an improper fraction.

Associate a fraction with division.

Express a whole number as a fraction.

Add and subtract like and related fractions within 1 whole.

Solve 1-step word problems involving fractions.

Divide a whole number by another whole number and write the quotient as a mixed number.

Add two or three like or related fractions with a sum more than 1 whole.

Subtract one or two fractions from a whole number.

Grade 2

Grade 3

Grade 4

NUMBERS AND OPERATIONS (continued)

Fractions / Arithmetic Operations (continued)

Decimals

Describe and complete a number pattern involving addition and subtraction of fractions with the same denominator.

Understand a fraction of a set of objects.

Find the value of a fractional part of a quantity.

Multiply a fraction and a whole number.

Solve 1-step and 2-step word problems involving fractions.

Read and write a decimal up to 2 decimal places.

Express a fraction or mixed number whose denominator is a factor of 100 as a decimal.

Interpret a decimal up to 2 decimal places in terms of tens, ones, tenths and hundredths.

Identify the values of digits in a decimal up to 2 decimal places.

Express a decimal up to 2 decimal places as a fraction or mixed number in its simplest form.

Read and place decimals on a number line with intervals of 0.1 or 0.01.

Express an amount of money as a decimal with 2 decimal places.

Compare and order decimals up to 2 decimal places.

Find the number which is 0.1 or 0.01 more than or less than a given number.

Round a decimal to the nearest whole number or 1 decimal place.

Grade 2

Grade 3

Grade 4

MEASUREMENT

Length

Perimeter / Area

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.

Measure the length of a line segment or a curve in centimeters.

Draw a line segment given its length in centimeters.

Measure lengths in meters and centimeters.

Understand that a kilometer is longer than a meter and a millimeter is shorter than a centimeter.

Measure and compare lengths in kilometers or millimeters.

Choose a suitable unit or tool of measure.

Solve 1-step and 2-step word problems on length.

*Measure and compare lengths to the nearest half or quarter inch.

Recall the units of measurements of length.

Know the meanings of the prefixes 'kilo', 'centi' and 'milli'.

Know the relationship between units of length.

Measure the length of a line segment or a curve in centimeters and millimeters.

Draw a line segment given its length in centimeters and millimeters.

Convert a measurement of length from compound units to a smaller unit, and vice versa.

Compare and order measurements of length in compound units.

Add and subtract lengths in compound units.

*Measure and compare lengths in yards and feet.

*Express yards and feet in feet, and vice versa.

*Add and subtract lengths in yards and feet.

*Measure and compare lengths in miles.

*Choose a suitable unit or tool of measure when measuring lengths.

Solve 1-step and 2-step word problems on length.

Measure area in non-standard units.

Find the area of a figure made up of unit squares and half squares.

Compare areas of figures made up of unit squares and half squares.

Visualize the sizes of 1 square centimeter and 1 square meter.

Grade 2

Grade 3

Grade 4

MEASUREMENT (continued)

Perimeter / Area (continued)

Volume and Capacity

Mass / Weight

Estimate, measure and compare capacities of containers in liters.

Arrange containers in order according to their capacities.

Solve 1-step and 2-step word problems on capacity.

Compare volume of liquid in two containers visually.

Measure and compare volume of liquid in two or more containers in liters.

Tell the difference between volume and capacity.

Measure and compare volumes and capacities in milliliters.

Measure volumes and capacities in liters and milliliters.

Choose a suitable unit or tool of measure.

Solve 1-step and 2-step word problems involving volume and capacity.

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.

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.

Find the area of a figure made up of 1-centimeter or 1-meter squares and half squares.

Compare areas of figures made up of 1-centimeter or 1-meter squares and half squares.

*Visualize the sizes of 1 square inch and 1 square foot.

*Find the area of a figure made up of 1-inch or 1-foot squares and half squares.

*Compare areas of figures made up of 1-inch or 1-foot squares and half squares.

Recall the units of measurements of volume of liquid.

Know the relationship between liter and milliliter.

Express liters and milliliters in milliliters, and vice versa.

Compare and order volumes in liters and milliliters.

Add and subtract volumes in liters and milliliters.

Solve 1-step and 2-step word problems on volume.

Recall the units of measurements of mass.

Know the relationship between kilogram and gram.

Express kilograms and grams in grams, and vice versa.

Compare and order masses in kilograms and grams.

Grade 2

Grade 3

Grade 4

MEASUREMENT (continued)

Mass / Weight (continued)

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

Read a calendar.

Name and order the days of the week and months of the year.

Associate months with events.

Understand the relationships between units of time.

Choose suitable units of measure when measuring time intervals.

Time: Clock

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.

Add and subtract masses in kilograms and grams.

Solve 1-step and 2-step word problems on mass.

*Measure and compare weights in pounds and ounces.

*Express pounds and ounces in ounces, and vice versa.

*Add and subtract weights in pounds and ounces.

*Measure and compare weights in tons.

*Know the relationship between tons, pounds and ounces.

*Choose a suitable unit of measure when measuring weights.

*Solve 1-step and 2-step word problems on weight.

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.

Relate time to events of a day. Express hours and minutes in minutes, and vice versa.

Find the duration of a time interval in hours or minutes.

Add and subtract durations in hours and minutes.

Develop a sense of the duration of daily activities. Solve 1-step and 2-step word problems involving time.

Tell time to the second.

Find the duration of a time interval in seconds.

Measure duration of activities in seconds.

Recall the units of measurements of time.

Know the relationship between units of time.

Grade 2

Grade 3

Grade 4

MEASUREMENT (continued)

Time: Clock (continued)

Measure duration of activities in minutes.

Solve word problems on time.

Temperature

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.

*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.

Choose suitable units to measure time intervals.

Express minutes and seconds in seconds, and vice versa.

Express years and months in months, and vice versa.

Express weeks and days in days, and vice versa.

Tell time using the 24-hour clock notation.

Convert time between the 12-hour and 24-hour clock notations.

Compare times using digital and analog clocks.

Find the duration of a time interval given time in 24-hour clock notation.

Read and interpret timetables in 12-hour and 24-hour clock notations.

Use a timetable to solve problems.

Solve word problems on time.

Grade 2

Grade 3

Grade 4

MEASUREMENT (continued)

Money (continued) Add and subtract money in dollars up to $100.

Count change like a cashier in a purchasing situation.

GEOMETRY

Lines and Curves

2D Shapes

Solve 1-step word problems on money.

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.

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.

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.

Identify open and closed figures.

Differentiate between polygons and non-polygons.

Name polygons according to the number of sides.

Identify and describe polygons.

Identify regular and irregular polygons.

Find examples of polygons in the environment and in art.

Make polygons on geoboards.

Draw polygons on dot grids.

Classify polygons using criteria such as the number of right angles, whether or not they are regular and their symmetrical properties.

Identify a symmetric polygon.

Count the number of lines of symmetry in polygons.

Draw lines of symmetry in polygons and patterns.

Find examples of symmetry in the environment and in art.

Grade 2

Grade 3

Grade 4

GEOMETRY (continued)

2D Shapes (continued)

3D Shapes 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.

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.

Understand that 3D shapes can be formed by nets.

Angles

Make a symmetric pattern with one line of symmetry.

Identify, describe and draw different types of prisms and pyramids.

Identify the nets of a cube. Find examples of prisms and pyramids in the environment and in art.

Understand that cross sections of a prism are of the same shape and size as the parallel faces of the prism.

Understand that cross sections of a pyramid are of the same shape as the base but of different sizes.

Classify prisms and pyramids according to the number and shape of faces, number of vertices and edges.

Identify the nets of a cube, a cuboid, a prism or a pyramid.

Identify the 3D shape which can be formed by a net.

Make 3D shapes from nets. Make nets of 3D shapes.

Identify, name and draw a point, a line, a line segment and a ray.

Name an angle using notations such as ∠ABC and ∠x.

Identify an angle. Recognize that the measure of a right angle is 90°.

Compare sizes of angles. Estimate and measure the size of an angle in degrees and classify the angles as acute, right or obtuse.

Identify angles on an object or in a shape.

Draw acute and obtuse angles using a protractor.

Identify right angles. Relate turns to 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.

Relate a 1 4 -tur n to 90°, a 1 2 -tur n to 180°, a 3 4 -turn to 270° and a complete tur n to 360°.

Grade 2

Grade 3

Grade 4

GEOMETRY (continued)

Angles (continued)

Position and Movement

Name a position using an ordinal number from 1st to 100th.

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 -tur n, 2 right angles is a 1 3 -tur n, 3 right angles is a 3 4 -tur n, 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 -tur n, 2 right angles is a 1 2 -tur n, 3 right angles is a 3 4 -tur n, and 4 right angles is a complete turn.

Recognize whole, half and quarter turns.

Describe turns using the words 'clockwise' and 'counterclockwise'.

Follow and give instructions involving position, direction and movement.

DATA ANALYSIS

Data Collection

Collect and record data in a list or table and present it as a pictogram.

Lists Collect and record data in a list and present it as a pictogram.

Present data given in a list as a block graph.

Tables Collect and record data in a table and present it as a pictogram.

Present data given in a table as a block graph.

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.

Relate turns to right angles.

Relate a 1 4 -tur n to 90°, a 1 2 -tur n to 180°, a 3 4 -tur n to 270° and a complete turn to 360°.

Tell direction using the 8-point compass.

Give and follow directions to a place on a grid.

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.

Identify the data to collect to answer a question.

Collect data by observation or survey.

Grade 2

Grade 3

Grade 4

DATA ANALYSIS (continued)

Tables (continued)

Group objects in a Carroll diagram using different criteria.

Sort data in a Carroll diagram with 1 criterion and read the Carroll diagram.

Graphs 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.

Sort data in a Carroll diagram with 2 or 3 criteria.

Make, read and interpret a bar graph with a scale of 1 or greater.

*Make, read and interpret a line plot with a scale marked in whole numbers, halves or quarters.

Venn Diagrams

Group objects in a Venn diagram using different criteria.

Sort data in a Venn diagram with 1 criterion and read the Venn diagram.

ALGEBRA

Patterns

Equations

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.

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 sentence. Find the missing part in an addition or subtraction sentence.

Find the missing part or whole in a subtraction sentence.

*Lessons are available in PR1ME Mathematics Teaching Hub.

Present data in an appropriate data display.

Compare the impact of representations where scales have different intervals.

*Make, read and interpret a line plot with a scale marked in whole numbers, halves, quarters or eighths.

Sort data in a Venn diagram with 2 or 3 criteria.

*Identify patterns in a hundred chart.

Describe, complete and create a number pattern by counting on or backwards by ones, tens, hundreds or thousands within 10 000.

Describe and complete a number pattern involving addition and subtraction of fractions with the same denominator.

Grade 2

Grade 3

Grade 4

Strand: Numbers and Operations

Scheme of Work

• CB: p. 1

• CB: pp. 2–4

• PB: pp. 9–10

• Digital Practice

• expanded form

• CB: pp. 4–5

• PB: p. 11

• Digital Practice

• 1 enlarged copy of Place Value Cards (BM1.1)

• Base ten blocks

• Base ten blocks

• Write a 2-digit number in tens and ones

• Compare and order numbers within 100

• Read numbers within 100 on a number line

Let’s Remember

Unit 1: Hundreds, Tens and Ones

• Count within 1000

• Read and write a number within 1000—the numeral and the corresponding number word

1.1 Counting, r eading and writing numbers

• Read and write a 3-digit number in hundreds, tens and ones

• Identify the position of each digit in a 3-digit number

1.2 Reading a number in hundreds, tens and ones

Unit 2: Order of Numbers

• CB: pp. 6–7

• PB: p. 12

• Digital Practice

• Base ten blocks

• Find the number which is ones, tens or hundreds more than or less than a given number within 1000

2.1 Finding mor e than and less than

• CB: pp. 8–9

• PB: pp. 13–14

• Digital Practice

• CB: pp. 10–11

• PB: p. 15

• Digital Practice

• CB: pp. 12–13

• PB: pp. 16–17

• Digital Practice

• approximately • round

• CB: pp. 14–15

• PB: p. 18

• Digital Practice

• CB: pp. 15–16

• PB: p. 19

• Digital Practice

• CB: pp. 17–18

• Count on and backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000

2.2 Number patterns

• Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000

• Base ten blocks

• Compare and order numbers within 1000

• Use ‘>’ and ‘<’ symbols to compare numbers within 1000

2.3 Comparing and ordering numbers

Unit 3: Rounding Numbers

• Read numbers within 1000 on a number line

• 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

• Solve a non-routine problem involving numbers to 1000 using the strategy of logical reasoning

Reading number lines

3.1

3.2 Rounding numbers to the nearest ten

3.3 Rounding numbers to the nearest hundred

Unit 4: Problem Solving

4.1 Mind str etcher

Digital Chapter Assessment — Available in PR1ME Mathematics Digital Practice and Assessment

The suggested duration for each lesson is 1 hour.

Chapter 1 Numbers to 1000

Chapter Overview

Let’s Remember

Unit 1: Hundreds, Tens and Ones

Unit 2: Order of Numbers

Unit 3: Rounding Numbers

Unit 4: Problem Solving

Let's Remember

Recall:

1. Writing a 2-digit number in tens and ones (CB2 Chapter 1)

2. Comparing and ordering numbers within 100 (CB2 Chapter 1)

3. Reading numbers within 100 on a number line (CB2 Chapter 1)

EXPLORE

Have students read the word problem on CB p. 1. Discuss with students the following questions:

•What is the population of your country?

•The Vatican City has the world’s smallest population. Which country do you think has the world’s largest population?

•Why do you think some countries have larger populations than other countries?

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: Hundreds, Tens and Ones

1.1 Counting, reading and writing numbers

Let's Learn Learn

Objectives:

•Count within 1000

•Read and write a number within 1000—the numeral and the corresponding number word

Materials:

•1 enlarged copy of Place Value Cards (BM1.1)

•Base ten blocks

Resources:

•CB: pp. 2–4

•PB: pp. 9–10

(a) Before the lesson, cut out the place value cards in BM1.1.

Stages: Concrete Experience, and Pictorial and Abstract Representations

Show students a ten-rod.

Say: We use a ten-rod to represent 1 ten. Show students 10 ten-rods.

Ask: How many ten-rods are there? (10)

Join the ten-rods together to make a hundredsquare and show students the hundred-square. Count by tens while joining the ten-rods.

Say: There are 10 tens. 10 tens are equal to 1 hundred. We use a hundred-square to represent 1 hundred.

Write: 10 tens = 1 hundred 1 hundred = 100

Stick the place value card ‘100’ on the board. Show students another hundred-square. Guide students to count by hundreds. (100, 200)

Say: So, 2 hundreds is equal to 200. Write: 2 hundreds = 200

Stick the place value card ‘200’ on the board. Repeat the above procedure for the numbers 300 to 900.

(b) Stage: Concrete Experience

Use base ten blocks to represent 167.

Say: Let us count on to find the number that the base ten blocks represent. 100, 110, 120, …, 160, 161, 162, …, 167.

Point to the blocks as you count.

Say: The base ten blocks represent 167.

Unit 1 Hundreds, Tens and Ones

1.1 Counting, reading and writing numbers

Stage: Pictorial Representation

Have students look at the base ten blocks in (b) on CB p. 2.

Ask: How many hundreds are there? (1) Stick the place value card ‘100’ on the board. Ask similar questions about the tens and ones and stick the corresponding place value cards on the board.

Overlap the place value cards to show 167.

Stage: Abstract Representation

Write: 167 one hundred and sixty-seven

Point to the numeral and word form of 167 on the board and read them aloud. Repeat the above procedure to provide another example on reading and writing another 3-digit number, 542.

(c) Stages: Concrete Experience, and Pictorial and Abstract Representations

Show students 10 hundred-squares.

Ask: How many hundred-squares are there? (10)

Join the hundred-squares together to make a thousand-block and show students the thousand-block. Count by hundreds while joining the hundred-squares.

Say: There are 10 hundreds. 10 hundreds are equal to 1 thousand. We use a thousand-block to represent 1 thousand.

Write: 10 hundreds = 1 thousand 1 thousand = 1000

Stick the place value card ‘1000’ on the board.

Let's Do Let's Do

Task 1 requires students to count within 1000 and write the numbers as numerals.

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.

4

Let's Practice Practice

1. Write the numerals.

a) two hundred and three b) six hundred and eighty c) eight hundred and seventy-nine

2. Write the numbers in words.

a) 514

b) 738

c) 609

five hundred and fourteen seven hundred and thirty-eight six hundred and nine

203 680 879

1.2 Reading a number in hundreds, tens and ones

Let's Learn

3 hundreds 300 1 ten 10 5 ones 5

Hundreds (H) Tens (T)Ones (O) 3 1 5

300 + 10 + 5 = 315

The expanded form of 315 is 300 + 10 + 5. The digit 3 is in the hundreds place. The digit 1 is in the tens place. The digit 5 is in the ones place.

Read 315 as three hundred and fifteen.

In the expanded form, we break up a number to show the value of each digit.

Let's Practice Let's Practice

Task 1 requires students to write the numerals given the numbers in words.

Task 2 requires students to write the numbers in words given the numerals.

1.2 Reading a number in hundreds, tens and ones

Let's Learn Let's Learn

Objectives:

•Read and write a 3-digit number in hundreds, tens and ones

•Identify the position of each digit in a 3-digit number

Materials:

•Base ten blocks

Resources:

•CB: pp. 4–5

Vocabulary:

•expanded for m

•PB: p. 11

Stages: Concrete Experience, and Pictorial and Abstract Representations

Use base ten blocks to represent 315. Copy the place value chart on CB p. 4 on the board but leave out the numbers.

Let's Do

1. Write the numerals. a)

2 hundreds 4 tens 5 ones = b)

500 + 50 =

2. Write the place values of the digits.

a) In 847, the digit 7 is in the place.

b) In 794, the digit 9 is in the place. c) In 305, the digit 3 is in the place.

1. Write each of the following as a numeral. a) 8 hundreds 6 tens 2 ones

2. Write the expanded form of each number. a) 683 b) 908 c) 540 d) 372 Let's Practice Let's Practice

I have learned to... count within 1000 read and write numbers up to 1000 write 3-digit numbers in hundreds, tens and ones identify the position of each digit in 3-digit numbers

Ask: How many hundreds are there? (3)

Write ‘3’ in the hundreds column in the place value chart. Stick the place value card ‘300’ on the board. Repeat the above procedure with the tens and the ones.

Overlap the place value cards to show 315.

Write: 300 + 10 + 5 = 315

Say: 300 plus 10 plus 5 is the expanded form of 315. 315 is the numeral. 315 is read as ‘three hundred and fifteen’.

Have students look at the place value chart.

Say: The digit 3 is in the hundreds place.

Ask: In which place is the digit 1? (Tens) Which digit is in the ones place? (5)

Let's Do Let's Do

Task 1 requires students to write hundreds, tens and ones as 3-digit numbers.

Task 2 requires students to identify the positions of digits in 3-digit numbers.

Let's Practice Let's Practice

Task 1 requires students to write hundreds, tens and ones as 3-digit numbers.

Task 2 requires students to write the expanded form of 3-digit numbers.

Unit 2 Order of Numbers

2.1 Finding more than and less than

Unit 2: Order of Numbers

2.1 Finding more than and less than

Let's Learn Let's Learn

Objective:

•Find the number which is ones, tens or hundreds more than or less than a given number within 1000

Materials:

•Base ten blocks

Resources:

•CB: pp. 6–7 •PB: p. 12

(a) Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students work in groups. Distribute base ten blocks to each group. Ask students to use base ten blocks to represent 435.

Say: Let us find out what number is 1 more than 435. Finding 1 more than 435 is the same as adding 1 to 435.

Have students add 1 unit cube to the base ten blocks.

Ask: What number do the base ten blocks represent now? (436) What is 1 more than 435? (436)

Write: 1 more than 435 is 436.

Repeat the above procedure to guide students to find 20 more than 435.

(b) Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students continue to work in groups. Ask students to use base ten blocks to represent 517.

Say: Let us find out what number is 2 less than 517. Finding 2 less than 517 is the same as subtracting 2 from 517.

Have students remove 2 unit cubes from the base ten blocks.

Ask: What number do the base ten blocks represent now? (515) What is 2 less than 517? (515) Write: 2 less than 517 is 515.

Repeat the above procedure to guide students to find 100 less than 517.

Let's Do Let's Do

Tasks 1 and 2 require students to find the number that is ones, tens or hundreds more than or less than a given number within 1000.

Let's Practice Let's Practice

Task 1 requires students to find the number that is ones, tens or hundreds more than or less than a given number within 1000.

2.2 Number patterns

12345678910

11121314151617181920

21222324252627282930

31323334353637383940

41424344454647484950

51525354555657585960

61626364656667686970

71727374757677787980

81828384858687888990

919293949596979899100

a) pattern: Start at 32. Count on by twos. 32, 34, 36, , 40

b) pattern: Start at 97. Count backwards by tens.

c) pattern: Start at 51. Count on by fives. 51, , , , 38 67

1. Read each rule. Then, continue the number pattern.

a) Start at 86. Count on by tens. 86, 96, 106, 116, b) Start at 306. Count backwards by fours. 306, 302, 298, 294,

c) Start at 793. Count on by twos. 793, 795, 797, 799, , ,

Let's Practice

1. Complete each pattern. Then, describe the number pattern.

a) 48, 43, , 33, 28, , 18

Start at 48.

Count by

b) 172, 272, , , , 672, Start at 172.

Count by

c) 507, , , , , 492, 489

Start at 507.

Count by

2. Write the numbers in order to make a number pattern.

a) 65, 50, 60, 45, 55 40,

b) 13, 9, 7, 5, 11 15, , , , ,

c) 488, 508, 538, 518, 528, 498 478,

2.2 Number patterns

Let's Learn Learn

Objectives:

•Count on and backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000

•Describe and complete a number patter n by counting on or backwards by ones, twos, threes, fours, fives, tens or hundreds within 1000

Resources:

•CB: pp. 8–9 •PB: pp. 13–14

(a) Stages: Pictorial and Abstract Representations

Have students look at the hundreds chart on CB p. 8.

Write: 32, 34, 36, , 40

Say: Let us find the missing number in the number pattern.

Have students locate the given numbers on the hundreds chart.

Ask: What do you notice about the numbers circled in blue? (Answer varies. Samples: There is 1 number between each of the numbers; the second number is 2 more than the first number and the third number is 2 more than the second number.)

Guide students to observe that we can count on by twos to make the number pattern. Have 8

students count on by twos from 32 to 40 using the hundreds chart to find the missing number, 38. Write 38 in the number pattern on the board.

Ask: What are the next two numbers in the pattern? (42 and 44)

(b) Stages: Pictorial and Abstract Representations

Follow the procedure in (a). Have students observe that the number pattern is formed by counting backwards by tens.

(c) Stages: Pictorial and Abstract Representations

Follow the procedure in (a). Have students observe that the number pattern is formed by counting on by fives.

Let's Do Let's Do

Task 1 requires students to continue number patterns within 1000.

Let's Practice Let's Practice

Task 1 requires students to describe and complete number patterns within 1000.

Task 2 requires students to arrange the given numbers to make number patterns.

2.3 Comparing and ordering numbers

Let's Learn Let's Learn

Objectives:

•Compare and order numbers within 1000

•Use ‘>’ and ‘<’ symbols to compare numbers

Materials:

•Base ten blocks

Resources:

•CB: pp. 10–11

•PB: p. 15

(a) Stage: Concrete Experience

Have students work in groups. Distribute base ten blocks to each group.

Write: 255 and 270

Say: Let us compare the numbers 255 and 270. Have students form the two numbers using base ten blocks.

Ask: Which number is formed by fewer blocks? (255)

Say: So, 255 is less than 270.

Stages: Pictorial and Abstract Representations

Have students look at the base ten blocks in (a) on CB p. 10. Copy the place value chart in (a) on the page on the board but leave out the numbers.

Ask: How many hundreds, tens and ones make 255? (2 hundreds 5 tens 5 ones)

Write ‘2’, ‘5’ and ‘5’ in the place value chart to show 255.

Ask: How many hundreds, tens and ones make 270? (2 hundreds 7 tens 0 ones)

Write ‘2’, ‘7’ and ‘0’ in the place value chart to show 270.

Say: We can compare the numbers by looking at the number of hundreds, tens and ones in each number. Let us compare the number of hundreds first.

Ask: Which number has fewer hundreds, 255 or 270? (Both numbers have the same number of hundreds.)

Say: Since both numbers have 2 hundreds, we compare the number of tens.

Ask: Which number has fewer tens, 255 or 270? (255)

Say: 5 tens is less than 7 tens, so 255 is less than 270.

Write: 255 is less than 270. 255 < 270

Say: Since 255 is less than 270, 270 is greater than 255.

Write: 270 is greater than 255. 270 > 255

a) Compare 255 and 270.

b) Compare 238, 170 and 209.

We compare three numbers the same way we compare two numbers. First, we compare the hundreds. Next, we compare the tens and finally the ones. Arrange the numbers in order. Begin with the greatest. (greatest)

(b) Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students continue to work in groups.

Write: 238, 170 and 209

Say: Let us compare the numbers 238, 170 and 209. Have students form the three numbers using base ten blocks.

Copy the place value chart in (b) on CB p. 10 on the board but leave out the numbers.

Ask: How many hundreds, tens and ones make 238? (2 hundreds 3 tens 8 ones)

Write ‘2’, ‘3’ and ‘8’ in the place value chart to show 238.

Continue to ask students to express 170 and 209 in hundreds, tens and ones and write in the place value chart.

Say: Let us compare the number of hundreds first.

Ask: Which number has the fewest hundreds—238, 170 or 209? (170)

Say: 170 is the least number.

Write: 170 is the least number.

Say: Since both the remaining numbers have 2 hundreds, we compare the number of tens.

Ask: Which number has more tens, 238 or 209? (238)

Say: 3 tens is greater than 0 tens, so 238 is greater than 209. 238 is the greatest number.

Write: 238 is the greatest number.

Guide students to arrange the numbers in order, beginning with the greatest. (238, 209, 170)

Let's Do Let's

Do

Task 1 requires students to compare two numbers within 1000.

Task 2 requires students to compare two numbers within 1000 using the ‘>’ and ‘<’ symbols.

Task 3 requires students to compare and order three numbers within 1000.

Do Do 1. Write greater than or less than

Let's Practice

Let's Practice

Task 1 requires students to compare two numbers within 1000 using the ‘>’ and ‘<’ symbols.

Task 2 requires students to compare and order three numbers within 1000.

3. Arrange the numbers in order. Begin with the least. 625, 652, 256 , , (least)

Let's Practice

2. Arrange the numbers in order. Begin with the greatest. a) 590, 509, 950 b) 443, 497, 446 c) 898, 899, 988 d) 742, 427, 472

950, 590, 509 988, 899, 898

I have learned to... find the number which is ones, tens or hundreds more than or less than a given number within 1000 describe and complete number patterns compare and order numbers within 1000

Unit 3: Rounding Numbers

3.1 Reading number lines

Let's Learn Let's Learn Objectives:

•Read numbers within 1000 on a number line

•Place numbers within 1000 on a number line

• Give a number between two 3-digit numbers

Resources:

•CB: pp. 12–13

•PB: pp. 16–17

(a) Stages: Pictorial and Abstract Representations

Draw the number line as shown in (a) on CB p. 12 on the board but leave out the curved arrows.

Have students look at the first two numbers on the number line and count aloud: 100, 110. Elicit from students that they are counting on by tens.

Point out to students that the intervals on a number line are equal.

Ask: What does each interval on the number line stand for? (10)

Say: Each number on the number line is 10 more than the number on the left.

Draw arrows from 100 to 110 and from 110 to 120 on the number line and label the arrows ‘10 more’.

Say: Each letter on the number line stands for a number. Let us find the numbers that A and B stand for.

Guide students to count on by tens from 100, pointing to each mark on the number line as they do so. Count on with students from 100: 100, 110, 120, 130, 140.

Say: A stands for 130 and B stands for 140. Write ‘130’ and ‘140’ on the number line. Point to the numbers 200 and 190 on the number line and count backwards. Elicit from students that they are counting backwards by tens.

Say: Each number on the number line is 10 less than the number on the right.

Draw arrows from 200 to 190 and from 190 to D on the number line and label the arrows ‘10 less’.

Say: Let us now find the numbers that C and D stand for.

Guide students to count backwards by tens from 200, pointing to each mark on the number line as they do so. Count backwards with students from 200: 200, 190, 180, 170.

Unit 3 Rounding Numbers

3.1 Reading number lines

Say: C stands for 170 and D stands for 180.

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.

(b) Stages: Pictorial and Abstract Representations Draw the number line as shown in (b) on CB p. 12. Point out to students that there are 10 equal intervals between 440 and 450 on the number line.

Ask: What does each interval on the number line stand for? (1)

Mark a cross at 443 on the number line.

Ask: What number does the cross represent? (443) Say: 443 is more than 440.

Ask: Is 443 more than or less than 450? (Less than) Say: 443 is more than 440 but less than 450. 443 is between 440 and 450.

Guide students to use the number line to name other numbers between 440 and 450.

Let's Do Let's Do

Task 1 requires students to read numbers within 1000 on number lines.

Task 2 requires students to circle the number that is between the two given 3-digit numbers.

Let's Practice Let's Practice

Task 1 requires students to read numbers within 1000 on number lines.

Task 2 requires students place a number within 1000 on a number line.

Task 3 requires students to give a number between two 3-digit numbers.

3.2 Rounding numbers to the nearest ten

Let's Learn Let's Learn

Objective:

•Round a 2-digit or 3-digit number to the nearest ten

Resources:

•CB: pp. 14–15

•PB: p. 18

Vocabulary:

•approximately

•round

(a) Stage: Pictorial Representation

Draw the number line in (a) on CB p. 14 on the board but do not label ‘43’, ‘49’ and ‘55’.

Guide students to see that there are 10 equal intervals between 40 and 50 and each interval stands for 1.

Invite a student to mark 43 on the number line.

Say: 43 is between two tens—40 and 50.

Ask: How many intervals are there from 40 to 43? (3) How many intervals are there from 43 to 50? (7) Is 43 nearer to 40 or to 50? (Nearer to 40)

Stage: Abstract Representation

Say: Since 43 is nearer to 40 than it is to 50, we say 40 is the ten nearest to 43. When we round 43 to the nearest ten, we get 40.

Write: 43 ≈ 40

Say: We read this statement as ‘43 is approximately 40’.

Explain that ‘≈’ is the approximation sign and it means ‘approximately’.

Repeat the above procedure to show students how to round 49 to the nearest ten. Guide students to conclude that 49 is nearer to 50 than it is to 40 on the number line, so when we round 49 to the nearest ten, we get 50.

Write: 49 ≈ 50

Similarly, show students how to round 55 to the nearest ten. Have students see that 55 is halfway between 50 and 60.

Say: When a number is halfway between two tens, we take the greater ten as the nearest ten. In this case, the greater ten is 60. So, the ten nearest to 55 is 60. When we round 55 to the nearest ten, we get 60. We say 55 is approximately 60.

Have a student write 55 ≈ 60 on the board.

(b) and (c) Stages: Pictorial and Abstract Representations

Follow the procedure in (a).

Conclude that to round a number to the nearest ten, we look at the digit in the ones place. If it is 5 or greater, we round up. If it is less than 5, we round down.

Let's Do Let's Do

Tasks 1 and 2 require students to round 2-digit and 3-digit numbers to the nearest ten.

Let's Practice Let's Practice

Task 1 requires students to round 2-digit and 3-digit numbers to the nearest ten.

Task 2 requires students to round the number of items to the nearest ten.

EXPLORE

Have students go back to the word problem on CB p. 1.

Ask: Can you solve the problem now? (Answer varies.) What else do you need to know? (Answer varies.)

Students are not expected to be able to solve the problem now. They will learn more skills in subsequent lessons and revisit this problem at the end of the chapter.

3.3 Rounding numbers to the nearest hundred

Let's Learn Let's Learn

Objective:

•Round a 3-digit number to the nearest hundred

Resources:

•CB: pp. 15–16

•PB: p. 19

(a) Stage: Pictorial Representation

Draw the number line in (a) on CB p. 15 on the board.

Say: We have learned to round numbers to the nearest ten. Now, we will learn to round numbers to the nearest hundred. Let us round 527 to the nearest hundred.

Ask: What are the hundreds on this number line? (500 and 600)

Point out the halfway mark on the number line and have students observe that 527 is less than halfway between 500 and 600.

Ask: Is 527 nearer to 500 or to 600? (500)

Stage: Abstract Representation

Say: Since 527 is nearer to 500 than it is to 600, we say 500 is the hundred nearest to 527. We say 527 is 500 when rounded to the nearest hundred.

Write: 527 ≈ 500

Say: 527 is approximately 500.

To round a number to the nearest hundred, look at the digit in the tens place. If it is 5 or greater, round up. If it is less than 5, round down.

Let's Do Let's Do

1. Round each number to the nearest hundred.

2. Round each number to the nearest hundred. a) 123 ≈ b) 384 ≈ c) 750 ≈ d) 249 ≈ b) 923 ≈ 923

1. Round each number to the nearest hundred. a) 483 ≈ b) 823 ≈ c) 209 ≈ d) 985 ≈ e) 739 ≈ f) 350 ≈

2. a) There are 393 mangoes in a crate. Round the number of mangoes to the nearest hundred.

b) 743 people visited a zoo on a Friday. Round the number of people to the nearest hundred.

c) There are 550 cows on a farm. Round the number of cows to the nearest hundred.

I have learned to... read numbers to 1000 on a number line round a 2-digit or 3-digit number to the nearest ten round a 3-digit number to the nearest hundred

(b) Stages: Pictorial and Abstract

Representations

Follow the procedure in (a) on TG p. 14. Explain that 250 is halfway between 200 and 300 and the greater hundred is taken as the nearest hundred. So, 250 is 300 when rounded to the nearest hundred. Conclude that to round a number to the nearest hundred, we look at the digit in the tens place. If it is 5 or greater, we round up. If it is less than 5, we round down.

Let's Do Do and Let's Practice

Tasks 1 and 2 require students to round 3-digit numbers to the nearest hundred.

Unit 4: Problem Solving

4.1 Mind stretcher

Let's Learn Let's Learn

Objective:

•Solve a non-routine problem involving numbers to 1000 using the strategy of logical reasoning

Resource:

•CB: pp. 17–18

Mind stretcher

Have students read the problem on CB p. 17.

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 use logical reasoning to find the 3-digit number.

3. Work out the Answer.

Draw a number line from 250 to 350 as shown on the page. Guide students to see that the any 3-digit number from 250 to 349 is 300 when rounded to the nearest hundred.

Say: The number is less than 300. So, the number can only be from 250 to 299.

Ask: What is the digit in the ones place? (0) What do you know about the digit in the tens place? (It is an odd number.) What can the digit be? (5, 7 or 9) What can the number be? (250, 270 or 290)

Copy the table on CB p. 18 on the board but leave the last two columns empty.

Say: Let us check if the number is 250.

Ask: What is the sum of all digits in 250? (7) Write ‘7’ in the correct row in the table.

Ask: Is the number 250? (No) Put a cross in the ‘Check’ row.

Repeat the above procedure to determine if the number is 270 or 290.

Say: The sum of all digits in 270 is 9. So, the number is 270.

4. Check if your answer is correct. Have students check the answer by matching each piece of infor mation about the 3-digit number with the answer 270.

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. 18.

Ask: Which method do you prefer? Why? (Answers vary.)

EXPLORE

Have students go back to the word problem on CB p. 1. 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.

Practice Book Chapter 1: Answers

Exercise 1.1

1. a) 325 b) 460 c) 907

2. a) six hundred and eighteen b) 191

c) five hundred and fifty d) 360

e) two hundred and eighty-eight f) 397

g) one thousand h) 501

i) nine hundred and four j) 473

Exercise 1.2

1. a) 353 b) 806 c) 231 d) 609

2. a) 700 + 20 + 8

b) 500 + 40 + 3

c) 200 + 9

d) 900 + 10

3. a) 3 b) hundreds c) 4 d) tens

Exercise 2.1

1. a) 150 b) 440 c) 700 d) 269 e) 539 f) 700 g) 20 h) 300 i) 357 j) 586 k) 863 l) 868

Exercise 2.2

1. a) 69; 89; 119; 59; on; tens b) 352; 351; 350; 349; 354; backwards; ones c) 231; 331; 631; 831; 231; on; hundreds d) 649; 647; 643, 641; 653; backwards; twos e) 809; 813; 817; 821; 797; on; fours

f) 614; 611; 602; 599; 617; backwards; threes

2. a) 31; 34; 37; 40; 43 b) 664; 659; 654; 649; 644; 639 c) 129; 131; 133; 135; 137; 139 d) 773; 673; 573; 473; 373; 273 e) 305; 301; 297; 293; 289; 285 f) 553; 543; 533; 523; 513; 503

Exercise 2.3

1. a) > b) < c) >

d) < e) > f) <

2. a) 679, 675, 623

b) 226, 222, 212, 210 c) 999, 991, 919, 911 d) 748, 747, 729, 725

3. a) 324, 325, 345

b) 931, 935, 938, 945

c) 225, 242, 252, 255 d) 887, 888, 889, 897

Exercise 3.1

1. a) 72; 76; 84 b) 425; 445; 455 c) 139; 151; 155 d) 550; 650; 850 2. a) to d) e) X 3. a)

4. a) Accept any number from 302 to 389. b) 985

Exercise 3.2

1. a) 60 b) 70 c) 100 d) 430 e) 690 f) 840 g) 260 h) 700 i) 900 j) 210 k) 990 l) 1000 2. a) 70 b) 90 c) 240 d) 450 m e) $280

Exercise 3.3

1. a) 700 b) 300 c) 900 d) 500 e) 400 f) 700 g) 200 h) 1000 i) 900 j) 900 k) 600 l) 500 2. Tick: a) 267 b) 238 c) 680 d) 770 3. 350

• common numerator 3 4 3 8 3 10

These fractions have a common numerator

The numerator of all these fractions is the same number.

E • equivalent fractions

These fractions have a common denominator

The denominator of all these fractions is the same number.

H • hexagon

A hexagon is a 2D shape with 6 sides.

K • kilometer (km) We use kilometer to measure long distances.

The distance between Bogotá and Medellín is 416 kilometers.

L • leap year

A leap year has 366 days. In a leap year, there are 29 days in February.

2 2 4 and 4 8 are equivalent fractions. They have different numerators and denominators, but are equal.

• estimate An estimate is close to the actual value.

312 + 476 ≈ 300 + 500 = 800

The estimated value of 312 + 476 is 800.

• even number

An even number has the digit 0, 2, 4, 6 or 8 in the ones place. It can be divided by 2 with no remainder.

2, 4, 6, 8, 10, 12, ... are even numbers.

• expanded form 200 + 30 + 6 is the expanded form of 236.

F • frequency table

A frequency table is a table that lists items and shows the number of each item.

This frequency table shows the favorite sport of a group of students.

• front-end estimation

We can check if an answer is reasonable using front-end estimation.

To estimate the value of 402 + 351, we keep the leftmost digits of each number and replace the other digits of the number with 0. 402 + 351 ≈ 400 + 300 = 700

The value of 402 + 351 is about 700.

Like fractions have the same denominator.

5 and 2 5 are like fractions.

• line A line is a straight path extending endlessly in both directions with no endpoints.

P Q Line PQ passes through points P and Q.

• line segment A line segment is part of a line with two endpoints.

P Q Line segment PQ has endpoints P and Q.

We use millimeter to measure the length of very short objects.

• net

• milliliter (ml) 1 L 500 ml

There are 200 milliliters of liquid in the beaker. We use milliliter to measure small volumes and capacities.

• round (number) 162167

12 ÷ 2 = 6 When 12 is divided by 2, the quotient is 6.

• ray A ray is a part of a line with one endpoint and extends endlessly in one direction.

P Q Ray PQ has an endpoint P and passes through point Q.

• remainder

13 ÷ 2 = 6 R1 When 13 is divided by 2, the remainder is 1.

• right angle

A right angle is maked as c Angle

c is a right angle.

170

When we round 162 to the nearest ten, we round it down to 160. When we round 167 to the nearest ten, we round it up to 170.

• semicircle

When a circle is divided into two equal parts, a half of the circle is also called a semicircle

• simplest form

The numerator and denominator cannot be further divided by the same number, except 1.

T • tally chart

A tally chart is a table that uses tally marks to keep count.

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

3 0 0 6 0 0 9 0 0 2 0 0 5 0 0 8 0 0 1 0 0 4 0 0 7 0 0 1 0 0 0

A world-class program incorporating the highly effective Readiness-Engagement-Mastery model of instructional design

Coursebook

100% coverage of Cambridge Primary Mathematics Curriculum Framework

Incorporates Computational Thinking and Math Journaling Builds a Strong Foundation for STEM

Coursebook

About Mathematics (New Edition)

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.

Enhanced

New

A 5-step process guides students to systematically solve problems by applying appropriate strategies and to reflect on their problemsolving approach.

Digital Components

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).

For Students

Digital practice and assessment further strengthen understanding of key concepts and provide diagnostic insight in students' capabilities and gaps in understanding.

ForTeachers

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 1000

Chapter 2 Addition and Subtraction Within 1000

Chapter 3 Multiplication Tables

Chapter 4 Multiplication and Division

Chapter 5 Money

Chapter 6 Mental Strategies

Chapter 7 Handling Data

Chapter 8 Length

Chapter 9 Mass

Chapter 10 Volume and Capacity

Let’s

Chapter 11 Fractions

Let’s

Chapter 12 Time

Chapter 13 Angles

Chapter 14 2D and 3D Shapes

Chapter 15 Position and Movement

Numbers to 1000

Let's Remember Let's Remember

1. Count and write the number. 70 4 Tens Ones 74 7 tens 4 ones =

2. Arrange the numbers in order. Begin with the greatest. a) 62, 29, 36 b) 54, 45, 55, 44

3. Complete the number line.

EXPLORE

The country with the smallest population in the world is the Vatican City. In 2019, it had a population of 799 residents. What is this number rounded to the nearest hundred?

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 2. What I need to find out and learn 3. What I have learned

Unit 1 Hundreds, Tens and Ones

You will learn to...

• count within 1000

• read and write numbers up to 1000

• write 3-digit numbers in hundreds, tens and ones

• identify the position of each digit in 3-digit numbers

1.1 Counting, reading and writing numbers

Let's Learn Let's Learn

Count by hundreds.

10 tens = 1 hundred

100, 200, 300, 400, 500

5 hundreds = 500 ones = 500 500 five hundred

Count on from 100.

100, 110, 120, 130, 140, 150, 160, 161, 162, 163, 164, 165, 166, 167

one hundred and sixty-seven

1000 10 hundreds = 1 thousand one thousand

Let's Do Let's Do

1. Count and write the numerals.

100, 200, 300, 400, 500, 600, 700, 800, 900, 1000

2. Write the numerals.

a) one hundred and one

b) four hundred and sixty-nine

c) three hundred and forty

d) eight hundred and fifty

3. a) Write 610 in words. b) Write 403 in words.

600 10

400 3

1. Write the numerals.

a) two hundred and three

b) six hundred and eighty

c) eight hundred and seventy-nine

2. Write the numbers in words.

a) 514

b) 738

c) 609

1.2 Reading a number in hundreds, tens and ones

Let's Learn Let's Learn

300 + 10 + 5 = 315

The expanded form of 315 is 300 + 10 + 5.

The digit 3 is in the hundreds place. The digit 1 is in the tens place. The digit 5 is in the ones place.

Read 315 as three hundred and fifteen.

In the expanded form, we break up a number to show the value of each digit.

Let's Do Do

1. Write the numerals.

a) 2 hundreds 4 tens 5 ones = b) 500 + 50 =

2. Write the place values of the digits.

a) In 847, the digit 7 is in the place.

b) In 794, the digit 9 is in the place.

c) In 305, the digit 3 is in the place.

Let's Practice Let's Practice

1. Write each of the following as a numeral.

a) 8 hundreds 6 tens 2 ones

b) 2 hundreds 5 ones

c) 400 + 9 d) 900 + 70

2. Write the expanded form of each number.

a) 683 b) 908

c) 540 d) 372

I have learned to... count within 1000 read and write numbers up to 1000 write 3-digit numbers in hundreds, tens and ones identify the position of each digit in 3-digit numbers

Unit 2 Order of Numbers

You will learn to...

• find the number which is ones, tens or hundreds more than or less than a given number within 1000

• describe and complete number patterns

• compare and order numbers within 1000

2.1 Finding more than and less than

Let's Learn Let's Learn

1 more than 435 is 436.

20 more than 435 is .

2 less than 517 is 515.

100 less than 517 is .

Let's Do Let's Do

1. Write the missing numbers.

a)

10 more than 532 is . b)

5 less than 307 is .

2. Answer the questions.

a) What number is 20 more than 465?

b) What number is 300 less than 812?

Let's Practice

1. Write the missing numbers.

a) is 3 more than 268. b) is 30 less than 145.

c) is 200 more than 326.

d) 477 is 3 more than .

e) 596 is 20 less than . f) 740 is 100 less than .

Let's Learn

Use the hundreds chart to find the missing numbers in each pattern.

a) pattern: Start at 32. Count on by twos. 32, 34, 36, , 40

b) pattern: Start at 97. Count backwards by tens. 97, 87, 77, , 57

c) pattern: Start at 51. Count on by fives. 51, , , ,

When we count on, the numbers get greater. When we count backwards, the numbers get less.

1. Read each rule. Then, continue the number pattern.

a) Start at 86. Count on by tens. 86, 96, 106, 116, , ,

b) Start at 306. Count backwards by fours. 306, 302, 298, 294, , ,

c) Start at 793. Count on by twos. 793, 795, 797, 799, , ,

Let's Practice

Let's Practice

1. Complete each pattern. Then, describe the number pattern.

a) 48, 43, , 33, 28, , 18

Start at 48.

Count by .

b) 172, 272, , , , 672, Start at 172.

Count by .

c) 507, , , , , 492, 489 Start at 507.

Count by .

2. Write the numbers in order to make a number pattern.

a) 65, 50, 60, 45, 55 40, , , , ,

b) 13, 9, 7, 5, 11 15, , , , ,

c) 488, 508, 538, 518, 528, 498 478, , , , , ,

2.3 Comparing and ordering numbers

Let's Learn

a) Compare 255 and 270.

255 is less than 270.

255 < 270

270 is greater than 255.

270 > 255

b) Compare 238, 170 and 209.

First, compare the hundreds. They are the same. Then, compare the tens. 5 tens is less than 7 tens.

First, compare the hundreds. 1 hundred is less than 2 hundreds. 170 is the least. Then, compare the tens of 238 and 209. 3 tens is greater than 0 tens. 238 is greater than 209. 238 is the greatest.

We compare three numbers the same way we compare two numbers. First, we compare the hundreds. Next, we compare the tens and finally the ones. Arrange the numbers in order. Begin with the greatest.

, , (greatest)

1. Write greater than or less than.

2. Write > or <.

3. Arrange the numbers in order. Begin with the least. 625, 652, 256 , , (least) Let's Practice Let's Practice

1. Write > or <.

2. Arrange the numbers in order. Begin with the greatest. a) 590, 509, 950 b) 443, 497, 446 c) 898, 899, 988 d) 742, 427, 472

I have learned to... find the number which is ones, tens or hundreds more than or less than a given number within 1000 describe and complete number patterns compare and order numbers within 1000

Unit 3 Rounding Numbers

You will learn to...

• read numbers to 1000 on a number line

• round a 2-digit or 3-digit number to the nearest ten

3.1 Reading number lines

Let's Learn

We can show numbers on a number line. Find out the number that each letter stands for.

• round a 3-digit number to the nearest hundred a) 100120110 10 less10 less 150160 190200 10 more10 more

I start at 100. Then, I count on by tens to find A and B.

100, 110, 120, 130, 140

I start at 200. Then, I count backwards by tens to find C and D. 200, 190, 180, 170

A stands for 130. C stands for 170.

B stands for . D stands for .

b) Find a number that is between 440 and 450.

440 443 450

443 is more than 440. 443 is less than 450. So, 443 is between 440 and 450.

What other numbers are between 440 and 450? Name as many as you can.

Let's Do Do

1. Complete the number lines.

2. Circle the correct number.

a) A number between 76 and 80 b) A number between 269 and 300

Let's Practice

1. Complete the number lines. a)

2. Mark 630 with a cross on the number line below.

3. Write a number that is between the two numbers.

a) 367 and 371 b) 249 and 289 c) 164 and 764 d) 668 and 662

3.2 Rounding numbers to the nearest ten

Let's Learn

a) Round the numbers 43, 49 and 55 to the nearest ten.

43 is between 40 and 50. It is nearer to 40 than to 50.

43 is 40 when rounded to the nearest ten.

43 ≈ 40

≈ is the approximation sign.

49 is between 40 and 50. It is nearer to 50 than to 40.

I round 43 to the nearest ten. 43 is approximately 40.

49 is 50 when rounded to the nearest ten.

49 ≈ 50

55 is halfway between 50 and 60. Take 60 to be the nearest ten.

55 is 60 when rounded to the nearest ten.

55 ≈ 60

b) Round 197 to the nearest ten.

197

c) Round 805 to the nearest ten. 805

49 is approximately 50.

55 is approximately 60.

197 is between 190 and 200. It is nearer to 200 than to 190.

197 is 200 when rounded to the nearest ten.

197 ≈ 200

805 is halfway between 800 and 810. 805 is 810 when rounded to the nearest ten. 805 ≈

To round a number to the nearest ten, look at the digit in the ones place. If it is 5 or greater, round up. If it is less than 5, round down.

Let's Do Do

1. Round each number to the nearest ten. a) b) 270 280 275 24 20 30 24 ≈ 275 ≈

2. Round each number to the nearest ten.

a) 52 ≈ b) 85 ≈ c) 179 ≈ d) 495 ≈

Let's Practice Let's Practice

1. Round each number to the nearest ten.

a) 29 ≈ b) 72 ≈ c) 411 ≈ d) 962 ≈ e) 235 ≈ f) 604 ≈

2. a) 67 children took part in a summer camp. Round the number of children to the nearest ten.

b) Gwen’s class folded 493 paper stars altogether. Round the number of paper stars to the nearest ten.

>> Look at EXPLORE on page 1 again. Can you solve the problem now? What else do you need to know?

3.3 Rounding numbers to the nearest hundred

Let's Learn Let's Learn 527

a) Round 527 to the nearest hundred.

527 is less than halfway between 500 and 600. It is nearer to 500 than to 600. 527 is 500 when rounded to the nearest hundred.

527 ≈ 500

b) Round 250 to the nearest hundred.

250 is halfway between 200 and 300. 250 is 300 when rounded to the nearest hundred.

≈

To round a number to the nearest hundred, look at the digit in the tens place. If it is 5 or greater, round up. If it is less than 5, round down.

Let's Do Let's Do

1. Round each number to the nearest hundred.

2. Round each number to the nearest hundred. a) 123 ≈ b) 384 ≈ c) 750 ≈ d) 249 ≈

Let's Practice

Let's Practice

1. Round each number to the nearest hundred.

a) 483 ≈ b) 823 ≈ c) 209 ≈ d) 985 ≈ e) 739 ≈ f) 350 ≈

2. a) There are 393 mangoes in a crate. Round the number of mangoes to the nearest hundred.

b) 743 people visited a zoo on a Friday. Round the number of people to the nearest hundred.

c) There are 550 cows on a farm. Round the number of cows to the nearest hundred.

I have learned to... read numbers to 1000 on a number line round a 2-digit or 3-digit number to the nearest ten round a 3-digit number to the nearest hundred

Unit 4 Problem Solving

You will learn to...

• solve a non-routine problem involving numbers to 1000

4.1 Mind stretcher

Let's Learn Let's Learn

A 3-digit number when rounded to the nearest hundred is 300. The number is less than 300. The digit in the ones place is 0 and the digit in the tens place is an odd number. The sum of all the three digits in the number is 9. What is the number?

1

What do we get when we round the number to the nearest hundred?

Is the number greater or less than 300? What do I know about the digits in the ones place and tens place?

What is the sum of all the three digits in the number?

What do I have to find?

The digit in the tens place is an odd number, so it can only be 5, 7 or 9. Understand the problem.

I can use logical reasoning to find the answer.

Any 3-digit number from 250 to 349 is 300 when rounded to the nearest hundred. Since the number is less than 300, the number can only be from 250 to 299.

5

4 + Plus Solve the problem in another way.

The number is 270.

270 is a 3-digit number. ✓

I have learned to... solve a non-routine problem involving numbers to 1000 Check if your answer is correct.

270 is 300 when rounded to the nearest hundred. ✓

270 is less than 300. ✓

The digit in the ones place is 0. ✓

The digit in the tens place is an odd number. ✓

The sum of all the three digits in the number is 9. ✓

My answer is correct.

Any 3-digit number from 250 to 349 is 300 when rounded to the nearest hundred. The number is less than 300. So, the hundreds digit is 2.

The digit in the ones place is 0 and the sum of all three digits in the number is 9. 2 + ? + 0 = 9 2 and 7 make 9.

The tens digit is 7. 7 is an odd number. The number is 270.

Compare the methods in steps 3 and 5. Which method do you prefer? Why?

>> Look at EXPLORE on page 1 again. Fill in column 3. Can you solve the problem now?

Glossary

A

• acute angle

An acute angle is an angle that is smaller than a right angle.

Angle a is an acute angle.

• angle

An angle can be formed by two rays or two line segments with a common endpoint.

• bar graph

A bar graph shows classified information in different categories. This bar graph shows the favorite subject of a group of students.

Ray OP and ray OQ for m an angle. Line segment OR and line segment OS also for m an angle.

• approximately

79 is about 80.

79 is approximately 80. We write it as 79 ≈ 80.

These fractions have a common denominator. The denominator of all these fractions is the same number.

• common numerator 3 4 3 8 3 10

These fractions have a common numerator. The numerator of all these fractions is the same number. E

• equivalent fractions 1 2 1

8

1 2 = 2 4 = 4 8 1 2 , 2 4 and 4 8 are equivalent fractions. They have different numerators and denominators, but are equal.

• estimate

An estimate is close to the actual value.

312 + 476 ≈ 300 + 500 = 800

The estimated value of 312 + 476 is 800.

• even number

An even number has the digit 0, 2, 4, 6 or 8 in the ones place. It can be divided by 2 with no remainder. 2, 4, 6, 8, 10, 12, ... are even numbers.

• expanded form

200 + 30 + 6 is the expanded form of 236.

F

• frequency table

A frequency table is a table that lists items and shows the number of each item.

This frequency table shows the favorite sport of a group of students.

• front-end estimation

We can check if an answer is reasonable using front-end estimation.

To estimate the value of 402 + 351, we keep the leftmost digits of each number and replace the other digits of the number with 0. 402 + 351 ≈ 400 + 300 = 700

The value of 402 + 351 is about 700.

grid reference

(B, 3) is a grid reference. First, name the column. Then, name the row. The elephant is at (B, 3).

H

• hexagon

A hexagon is a 2D shape with 6 sides.

K

• kilometer (km)

We use kilometer to measure long distances.

The distance between Bogotá and Medellín is 416 kilometers.

• like fractions

Like fractions have the same denominator.

1 5 and 2 5 are like fractions.

• line

A line is a straight path extending endlessly in both directions with no endpoints.

L

• leap year

A leap year has 366 days. In a leap year, there are 29 days in February.

Line PQ passes through points P and Q.

• line segment

A line segment is part of a line with two endpoints.

Q

Line segment PQ has endpoints P and Q. M

• milliliter (ml)

There are 200 milliliters of liquid in the beaker. We use milliliter to measure small volumes and capacities.

millimeter (mm)

We use millimeter to measure the length of very short objects.

• net

A net is a flat figure that can be folded to form a 3D shape.

• obtuse angle

An obtuse angle is an angle that is bigger than a right angle but smaller than 2 right angles.

• odd number

An odd number has the digit 1, 3, 5, 7 or 9 in the ones place. When divided by 2, it leaves a remainder of 1.

1, 3, 5, 7, 9, 11, 13, ... are odd numbers.

• past

The time is 10 minutes past 12. It is 12 : 10.

• pentagon

A pentagon is a 2D shape with 5 sides.

• point

A point shows an exact location in space.

Angle b is an obtuse angle.

• octagon

An octagon is a 2D shape with 8 sides. b

This is point P.

• quotient

12 ÷ 2 = 6

When 12 is divided by 2, the quotient is 6.

• ray

A ray is a part of a line with one endpoint and extends endlessly in one direction.

P Q

Ray PQ has an endpoint P and passes through point Q.

• remainder

13 ÷ 2 = 6 R1

When 13 is divided by 2, the remainder is 1.

• right angle

A right angle is maked as . c

Angle c is a right angle.

• round (number) 162167 160

When we round 162 to the nearest ten, we round it down to 160. When we round 167 to the nearest ten, we round it up to 170. • row

S

• semicircle

When a circle is divided into two equal parts, a half of the circle is also called a semicircle.

simplest form

The time is 15 minutes to 11. It is 10 : 45.

1 2 is the simplest form of 3 6 .

The numerator and denominator cannot be further divided by the same number, except 1.

• tally chart

A tally chart is a table that uses tally marks to keep count.

tally mark //// shows 4. //// shows 5.

A Venn diagram helps us sort data. • volume

The volume of a liquid is the amount of space it takes up.

A world-class program incorporating the highly effective Readiness-Engagement-Mastery model of instructional design

Practice Book

Name

PR1ME Mathematics Digital Practice and Assessment provides individualized learning support and diagnostic performance reports

Practice Book

About TM Mathematics (New Edition)

Scholastic TM Mathematics (New Edition) covers five strands of mathematics across six grades: Numbers and Operations, Measurement, Geometry, Data Analysis, and Algebra.

Each Practice Book comprises chapters with several Exercises. Chapters end with Problem Solving exercises. A Review follows after every four or five chapters.

Exercises provide comprehensive practice for students to attain fluency and mastery of topics.

Recap helps students to recall what was taught in the coursebook and assist them with the exercise.

Tasks in each exercise are systematically varied to provide comprehensive practice and formative assessment.

Reviews provide summative assessment and enable consolidation of concepts and skills learnt across various topics.

Review 3

Chapter 1 Numbers to 1000

Exercise 1.1 Counting, reading and writing numbers

Exercise 1.2 Reading a number in hundreds, tens and ones

Exercise 2.1 Finding more than and less than

Exercise 2.2 Number patter ns

Exercise 2.3 Comparing and ordering numbers

Exercise 3.1 Reading number lines

Exercise 3.2 Rounding numbers to the nearest ten

Exercise 3.3 Rounding numbers to the nearest hundred

Chapter 2 Addition and Subtraction Within 1000

Exercise

Exercise 2.1 Adding with regrouping in ones

Exercise 2.2 Adding with regrouping in tens

Exercise 2.3 Adding with regrouping in tens and ones

Exercise 2.4 Adding more than two numbers

Exercise 2.5 Estimating sums

Exercise 2.6 Solving word problems

Exercise 3.1 Subtracting with regrouping in tens and ones

Exercise 3.2 Subtracting with regrouping in hundreds and tens

Exercise 3.3 Subtracting with regrouping in hundreds, tens and ones

Exercise 3.4 Estimating differences

Exercise 3.5 Solving word problems

Exercise 4.1 Word problems

Chapter 3 Multiplication Tables

Exercise 1.1 Multiplying numbers by 2, 3, 4, 5 and 10

Exercise 1.2 Dividing numbers by 2, 3, 4, 5 and 10

Exercise 2.1 Multiplying by 6

Exercise 2.2 Dividing by 6

Exercise 3.1 Multiplying by 7

Exercise 3.2 Dividing by 7

Exercise 4.1 Multiplying by 8

Exercise 4.2 Dividing by 8

Exercise

Exercise

Chapter 6 Mental Strategies

Exercise 1.1 Making 1000 103

Exercise 1.2 Making 100 104

Exercise 2.1 Adding ones, tens or hundreds to a 2-digit or 3-digit number without regrouping 105

Exercise 2.2 Adding ones or tens to a 2-digit or 3-digit number with regrouping 106

Exercise 2.3 Adding two 2-digit numbers without regrouping 107

Exercise 3.1 Subtracting ones, tens or hundreds from a 2-digit or 3-digit number without regrouping 108

Exercise 3.2 Subtracting ones or tens from a 2-digit or 3-digit number with regrouping 109

Exercise 3.3 Subtracting a 2-digit number from another 2-digit number without regrouping 110

Exercise 4.1 Finding doubles of 2-digit numbers 111

Exercise 4.2 Finding halves of even numbers up to 200 112

Review 2 113

Chapter 7 Handling Data

Exercise 1.1 Making tally charts and frequency tables 119

Exercise 2.1 Making, reading and interpreting bar graphs with a scale of 1 121

Exercise 2.2 Making, reading and interpreting bar graphs with a scale greater than 1 123

Exercise 3.1 Sorting data in Venn diagrams with 1 criterion 126

Exercise 4.1 Sorting data in Carroll diagrams with 2 or 3 criteria 128

Chapter 8 Length

Exercise 1.1 Measuring and drawing lengths in centimeters 130

Exercise 1.2 Length in meters and centimeters 134

Exercise 2.1 Length in kilometers 135

Exercise 2.2 Length in millimeters 136

Exercise 3.1 Word problems 137

Chapter 9 Mass

Exercise 1.1 Mass in kilograms 139

Exercise 1.2 Mass in grams 141

Exercise 1.3 Mass in kilograms and grams 143

Exercise 2.1 Word problems 145

Chapter 10 Volume and Capacity

Exercise 1.1 Understanding volume 147

Exercise 1.2 Measuring and comparing volumes in liters 149

Exercise 1.3 Volume and capacity 151

Exercise 2.1 Liters and milliliters 153

Exercise 3.1 Word problems 155

Review 3 157

Chapter 11 Fractions

Exercise 1.1 Making a whole 164

Exercise 1.2 Comparing and ordering fractions with the same numerator or denominator 165

Exercise 1.3 Using benchmark fractions 166

Exercise 1.4 Comparing and ordering fractions on a number line 167

Exercise 2.1 Understanding equivalent fractions 169

Exercise 2.2 Finding equivalent fractions by multiplying 170

Exercise 2.3 Finding equivalent fractions by dividing 171

Exercise 2.4 Comparing using equivalent fractions 172

Exercise 3.1 Adding fractions with the same denominator 173

Exercise 3.2 Adding fractions with different denominators 175

Exercise 4.1 Subtracting fractions with the same denominator 177

Exercise 4.2 Subtracting fractions with different denominators 179

Exercise 5.1 Word problems 181

Chapter 12 Time

Exercise 1.1 Reading time 183

Exercise 1.2 Duration of time 185

Exercise 1.3 Converting hours and minutes 187

Exercise 1.4 Adding and subtracting hours and minutes 188

Exercise 2.1 Duration of time in days and weeks 189

Exercise 3.1 Word problems 190

Chapter 13 Angles

Exercise 1.1 Identifying and naming points, lines, line segments and rays 192

Exercise 1.2 Identifying and comparing angles 193

Exercise 1.3 Identifying angles on objects and in shapes 194

Exercise 2.1 Identifying right angles 196

Exercise 2.2 Drawing right angles 198

Chapter 14 2D and 3D Shapes

Exercise 1.1 Naming and describing 2D shapes

Exercise 1.2 Sorting 2D shapes

Exercise 2.1 Completing symmetric figures

Exercise 3.1 Making cubes

Chapter 15 Position and Movement

Exercise 1.1 Relating tur ns to right angles

Exercise 2.1 Reading grid references

Exercise 2.2 Giving directions

Numbers to 1000

Exercise 1.1 Counting, reading and writing numbers

Recap

Numeral: 124

Number in words: one hundred and twenty-four

1. Count and write the numerals.

10 hundreds = 1 thousand

2. Write the missing numerals or numbers in words.

one hundred and ninety-one

three hundred and sixty

three hundred and ninety-seven

five hundred and one

four hundred and seventy-three

Exercise 1.2 Reading a number in hundreds, tens and ones

Recap

Hundreds (H)Tens (T)Ones (O) 1 2 4

100 + 20 + 4 = 124

1. Write the numerals.

a) 3 hundreds 5 tens 3 ones =

b) 8 hundreds 6 ones =

c) 200 + 30 + 1 =

d) 600 + 9 =

2. Write the expanded form of each number.

a) 728

c) 209

3. Complete the sentences.

100 + 20 + 4 is the expanded form of 124.

b) 543

d) 910

a) In 832, the digit in the tens place is .

b) In 503, the digit 5 is in the place.

c) In 394, the digit in the ones place is .

d) In 701, the digit 0 is in the place.

Exercise 2.1 Finding more than and less than

Recap

20 less than 227 is 207.

1. Write the missing numbers.

a) 4 less than 154 is .

b) 100 more than 340 is

c) 10 more than 690 is .

d) 2 more than 267 is .

e) 30 less than 569 is .

f) 200 less than 900 is .

g) less than 984 is 964.

h) more than 438 is 738.

i) 407 is 50 more than .

j) is 70 less than 656.

k) 903 is 40 more than .

l) 778 is 90 less than .

Exercise 2.2 Number patterns

Recap

231232233234235236237238239240

241242243244245246247248249250

251252253254255256257258259260

pattern: Start at 255. Count backwards by threes. The number pattern is 255, 252, 249, 246, 243, 240. The next two numbers in the pattern are 237 and 234.

1. Complete each number pattern. Then, describe the number pattern.

a) 59, , 79, , 99, 109, Start at . Count by .

b) 354, 353, , , , , 348 Start at . Count by .

c) , , 431, 531, , 731, Start at . Count by .

d) 653, 651, , , 645, , Start at . Count by .

e) 797, 801, 805, , , , Start at . Count by .

f) 617, , , 608, 605 , Start at . Count by .

2. Write the numbers in order to make a number pattern.

a) 37, 31, 40, 34, 43 28, , , , ,

b) 644, 654, 664, 639, 649, 659

669, , , , , ,

c) 133, 139, 131, 135, 129, 137

127, , , , , ,

d) 573, 773, 273, 473, 673, 373

873, , , , , ,

e) 301, 293, 297, 285, 289, 305

309, , , , , ,

f) 513, 533, 553, 503, 523, 543

563, , , , , ,

Chapter 1: Practice 2.2 Online

Exercise 2.3 Comparing and ordering numbers

3 48 3 41

First, compare the hundreds and tens. They are the same.

348 is greater than 341. 348 > 341

Then, compare the ones. 8 ones is greater than 1 one.

341 is less than 348. 341 < 348

1. Compare the numbers using > or <.

a) 345 224 b) 654 786 c) 939 919

d) 885 899 e) 536 534 f) 852 858

2. Arrange the numbers in order. Begin with the greatest.

a) 675, 679, 623

b) 210, 222, 212, 226

c) 911, 991, 919, 999

d) 748, 725, 747, 729

3. Arrange the numbers in order. Begin with the least.

a) 345, 325, 324

b) 931, 938, 945, 935

c) 242, 252, 255, 225

d) 888, 887, 897, 889

Exercise 3.1 Reading number lines

Recap

Start at 200 and count on by tens to find A. 200, 210, 220, 230 A stands for 230.

From the number line, we can see that: 210 is more than 200. 210 is less than 300. So, 210 is between 200 and 300.

1. Complete the number lines.

Start at 300 and count backwards by tens to find B. 300, 290, 280, 270 B stands for 270.

2. Look at the number line.

870890 930 970990

a) Label the number that is 30 more than 930 with W.

b) Label the number that is 20 less than 930 with X.

c) Label the number that is 30 more than 890 with Y.

d) Label the number that is 40 less than 980 with Z.

e) Which letter stands for a number that is 30 less than Z?

3. Mark 557 with a cross on each number line below.

a) b)

c)

d)

4. Write a number that is between the two given numbers. Draw number lines to help you.

a) 301 and 390 b) 986 and 984

Exercise 3.2 Rounding numbers to the nearest ten

Recap

217 is nearer to 220 than to 210.

So, 217 is 220 when rounded to the nearest ten.

≈ 220

To round a number to the nearest ten, look at the digit in the ones place. If it is 5 or greater, round up. If it is less than 5, round down.

1. Round each number to the nearest ten.

a) 58 ≈ b) 71 ≈ c) 95 ≈ d) 425 ≈ e) 693 ≈ f) 836 ≈ g) 255 ≈ h) 704 ≈ i) 898 ≈

j) 212 ≈ k) 989 ≈ l) 996 ≈

2.

a) Maria has 65 stickers. Round the number of stickers to the nearest ten.

b) Eva has 93 stamps.

Round the number of stamps to the nearest ten.

c) Mathew went to school for 237 days in a year. Round the number of days to the nearest ten.

d) The distance between Kevin’s home and his office is 453 meters. Round the distance to the nearest ten.

e) Meg has $281. Round the amount to the nearest ten.

Exercise 3.3 Rounding numbers to the nearest hundred

Recap

250 is halfway between 200 and 300.

So, 250 is 300 when rounded to the nearest hundred.

To round a number to the nearest hundred, look at the digit in the tens place. If it is 5 or greater, round up. If it is less than 5, round down.

1. Round each number to the nearest hundred.

a) 725 ≈ b) 281 ≈ c) 908 ≈ d) 549 ≈ e) 352 ≈ f) 684 ≈ g) 231 ≈ h) 954 ≈ i) 945 ≈ j) 890 ≈ k) 643 ≈ l) 495 ≈

2. Tick (✓) the correct answer.

a) Which number is 300 when rounded to the nearest hundred?

b) Which number is 200 when rounded to the nearest hundred?

c) Which number is 700 when rounded to the nearest hundred?

d) Which number is 800 when rounded to the nearest hundred?

3. What is the least number that is 400 when rounded to the nearest hundred?