PR1ME Maths Book 1: Sample chapters of Teacher Guide, Course Book and Practice Book

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

Teacher’s Guide

Enhanced support for effective implementation of Readiness-Engagement-Mastery pedagogy

Digital PR1ME Mathematics Teaching Hub for additional teaching resources and online professional development

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.

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

Let's Remember

Recall:

1. Recognizing and naming proper fractions (CB2 Chapter 12)

Explore encourages mathematical curiosity and a positive learning attitude by getting students to recall the requisite prior knowledge, set learning goals and track their learning as they progress through the unit.

2. Placing whole numbers up to 100 on a number line (CB2 Chapter 1)

3. Multiplying and dividing numbers within multiplication tables (CB3 Chapter 3)

EXPLORE

Have students read the word problem on CB p. 231. Discuss with students the following questions:

•Do you donate money to charity ?

•Why do you think Janice donated a part of her salary to charity?

•Besides donating money to charity, what can we do to support charity?

Have students form groups to complete the tasks in columns 1 and 2 of the table. Let students know that they do not have to solve the word problem. Ask the groups to present their work.

Tell students that they will come back to this word problem later in the chapter.

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.

page T24

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.

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.

and

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.

Solve the problem in another way.

Suppose the number is 10.

Stage 1: 10 + 20 = 30

Stage 2: 30 – 5 = 25

Stage 3: 25 + 20 = 45

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.

She starts with the number 46.

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

Addition and Subtraction Within

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

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.

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

and his father? Who is heavier? How many kilograms heavier? What do I have to find? Understand the problem. 1 Plan what to do. 2 CREATE YOUR OWN

Brian and his father have a total mass of 90 kilograms. Brian’s father is 50 kilograms heavier than Brian. What is Brian’s mass? I can draw a

model to compare their masses. What is the total mass of

Using the bar model method

Brian’s mass is 20 kilograms.

Step-by-step guidance in the lesson plans as well as complete worked solutions assist the teachers in teaching students how to solve mathematical problems using the bar model method with confidence.

Develops a growth mindset in every student –the understanding that each effort is instrumental to growth and to be resilient and persevere when initial efforts fail.

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.

Concept-based

Process-based tasks help teachers understand students’ thinking process through a concept.

Teacher-led enquiry through purposeful questions

Let's Practice Let's Practice

Task 1 requires students to count by threes to find the total number of objects and complete the multiplication sentences.

Task 2 requires students to count by threes to complete the patterns.

Students learn through guided enquiry, a process during which instead of giving the answers, teachers lead students to explore, investigate and find answers on their own by posing purposeful questions provided in the Teacher’s Guide. Purposeful questions are used to gather information, probe thinking, make the mathematics visible and encourage reflection and justification. Posing purposeful questions helps to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.

1.2 Using dot cards

Let's Learn

Objectives:

• Observe the commutative and distributive properties of multiplication

• Relate two multiplication facts using ‘3 more’ or ‘3 less’

• Build up the multiplication table of 3 and commit the multiplication facts to memory

Materials:

• Dot Card F (BM10.1): 1 copy per group, 1 enlarged copy for demonstration

• Dot Card G (BM10.2): 1 copy per group, 1 enlarged copy for demonstration

•Counters

Resources:

• CB: pp. 195–197

are 18 pears altogether.

Gathering information

• PB: p. 127

(a) Stage: Concrete Experience Draw 6 circles on the board and stick

3 counters in each circle.

Ask: How many counters are there in each group? (3) How many groups are there? (6)

Say: We have 6 groups of 3 counters.

Stage: Pictorial Representation

Say: We can use a dot card to help us find the total number of counters. Have students work in groups. Distribute counters and a copy of Dot Card F (BM10.1) to each group. Stick an enlarged copy of Dot Card F (BM10.1) on the board. Put counters on the three circles in the first row of the dot card.

Say: There is 1 row of counters. There are 3 counters in 1 row. I have shown 1 group of 3.

Ask: How do we show 6 groups of 3 on the dot card? (Put counters on 6 rows of the dot card.)

Demonstrate how the counters are to be placed on

Making the mathematics visible

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

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.

Dividing by

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.

Dividing

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. Divide. Use the

Let's Practice

1. Divide. Use

Let’s Do enables teachers to immediately assess students’ understanding of the concepts just taught and identify remediation needs.

Task 1 assesses students’ understanding of division by 5 at the pictorial and abstract levels.

Task 2 assesses students’ understanding of division by 5 at the abstract level.

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

2.

1.

Tasks are ordered by level of difficulty and are systematically varied to gradually deepen the student’s conceptual

understanding.

Easy to assign and with instant access, Digital Practice includes hints to support students and provides immediate feedback to teachers on students’ learning.

Summative 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.

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.

Let's Remember Recall: 1. Writing tens and ones as a 2-digit number (CB1 Chapter 15)

2. Adding and subtracting within 20 using number bonds (CB1 Chapter 7)

3. Adding and subtracting within 20 using the ‘counting on’ or ‘counting backwards’ method (CB1 Chapter 7)

EXPLORE

Have students read the word problem on CB p. 24.

Discuss with students the following questions:

•What is a UNESCO World Heritage site ?

•Are there any UNESCO World Heritage sites in your country? What are the sites?

•Do you think we should protect such sites ?

•What can we do to protect them ?

•What will happen if we do not protect such sites?

Have students form groups to complete the tasks in columns 1 and 2 of the table. Let students know that they do not have to solve the word problem. Ask the groups to present their work.

Tell students that they will come back to this word problem later in the chapter.

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 Do

Task 1 requires students to associate the terms ‘sum’ and ‘difference’ with addition and subtraction respectively. A comparison

model is provided to help students find the sum and difference.

Task 2 requires students to associate the

‘sum’ with addition.

Let's Practice

Tasks 1 and 3 require students to associate the term ‘sum’ with addition.

Tasks 2 and 4 require students to associate the term ‘difference’ with subtraction.

•difference

•sum

Stage: Concrete Experience

(a)

Have students work in pairs. Distribute connecting cubes in two colors, for example, red and blue, to each pair and have students follow each step of your demonstration.

Join 3 red connecting cubes to show 3. Then, join 8 blue connecting cubes to show 8.

Ask: How many red cubes do you see? (3) How many blue cubes do you see? (8)

Join the bar of red cubes and the bar of blue cubes together.

Ask: How many cubes are there altogether? (11)

Stage: Pictorial Representation

Use two markers in different colors to draw a part-whole bar model with 3 equal units and 8 equal units to illustrate the numbers 3 and 8, as shown by the connecting cubes. Relate this model to the earlier connecting cubes activity.

Erase the lines between the units in the bar model to create a simplified version of the model as shown on the right in (a) on CB p. 25.

Say: This is a bar model.

Point out that the length of each part of the model corresponds to the number of connecting cubes of each color.

Say: The two parts form a whole. This model shows the total or the sum of 3 and 8. The sum of two numbers is the total of the two numbers.

We found earlier that the total of 3 cubes and 8 cubes is 11 cubes, so the sum of 3 and 8 is 11.

Separate the bar of connecting cubes into its two parts, 3 and 8, again. Place the bar of 3 cubes above the bar of 8 cubes and left align the bars.

Chapter 2: Addition and Subtraction Within 100 30

Say: Notice that the total number of cubes has not changed. Let us represent the sum of 3 and 8 in another model.

Draw the comparison bar model as shown in the thought bubble in (a) on the page.

Conclude that we can represent the sum in two types of bar models.

Stage: Abstract Representation

Say: We want to find the sum of 3 and 8. The sum of 3 and 8 is the total of 3 and 8. We find the sum by adding the two numbers.

Write: 3 + 8 = 11

Say: The sum of 3 and 8 is 11.

(b) Stage: Concrete Experience

Have students continue to work in pairs and follow each step of your demonstration.

Reuse the two bars of connecting cubes formed in (a). Place the bar of 3 cubes above the bar of 8 cubes and left align the bars.

Ask: How many red cubes are there? (3) How many blue cubes are there? (8) Which bar is shorter, the bar of red cubes or the bar of blue cubes? (Red cubes) Which is less, 3 or 8? (3)

Say: Let us find out how many more blue cubes than red cubes there are by counting the number of cubes.

For each Let’s Do task, the objective is listed for teachers to reteach the relevant concepts. Answers are provided for all tasks.

For each task in the Practice Book Exercise, the objectives and skills assessed are identified in the Teaching Hub to enable teachers to check learning and address remediation needs. Answers are provided for all tasks.

Digital Practice provides immediate feedback to teachers on students’ learning so that teachers can provide early intervention if required. The items come with hints to promote independent learning for students.

1

2

David is checking his friend's answer to a subtraction.

THINK ABOUT IT

Students

Students

What did you learn about subtracting a 1-digit number from a 2-digit

Think

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

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

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

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

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

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.

2

4 To solve 1-step word problems involving subtraction with regrouping

Students

Students

Students

To solve 1-step word problems involving addition with regrouping

To solve 1-step word problems involving subtraction with regrouping

a) How many storybooks does Kevin have?

b) How many storybooks do they have altogether?

CREATE YOUR OWN

Nathan has 46 stamps.

He has 19 more stamps than Tim.

a) How many stamps does Tim have?

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

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

Let's Practice

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

CREATE YOUR OWN

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

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

solve the word problem.

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

4.2 Mind stretcher

Let's Learn Let's

Objective:

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

Resource:

•CB: pp. 62–63

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

Have students read the problem on CB p. 62.

1. Understand the problem.

Pose the questions in the thought bubble

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.

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

Go through the task using the prompts given below.

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

money left after buying each combination)

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

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

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

Digital Chapter Assessment enables consolidation of learning in every chapter. Auto-generated reports provide actionable data for teachers to carry out remediation or extension as required.

Math Journal tasks in the Teaching Hub allows teachers to gain insight into students’ thinking. Rubrics are provided to help teachers give feedback to students.

1To

2To

3

4To

6To

7To

Digital Quarterly and Half-Yearly Assessments provide opportunities for summative assessment at regular intervals throughout the year. Auto-generated reports help teachers to measure and report students’ learning against the curriculum.

1.

2.

Practice Book Reviews provide opportunities for summative assessment. They consolidate learning across several chapters. The last review in each grade assesses learning in the entire grade. For each task, the objectives assessed are identified in the Teaching Hub to enable teachers to check learning and address remediation needs.

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

Rote count within 100 by ones and tens.

Read and write 0 to 10 —the numeral and the corresponding number word.

Identify the last number counted as the number of objects in the group.

Count on and backwards within 10.

Count groups of up to 20 objects in different arrangements.

Compare the number of objects in two groups.

Compare and order numbers within 20.

Understand that the number that comes next is 1 more.

Break apart 4 to 10 objects into two parts.

Count within 100.

Read and write a number from 0 to 100—the numeral and the corresponding number word.

Recognize conservation of numbers.

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

Estimate the number of objects in a group of less than 40 objects.

Find the number which is 1, 2 or 10 more than or less than a given number within 100.

Give a number that comes before or after a number or between two numbers within 100.

Count on and backwards by ones, twos or tens within 100.

Describe and complete a number pattern by counting on or backwards by ones, twos or tens within 100.

Make 4 to 10 with two parts.Recognize odd and even numbers within 20 by skip counting.

Write a number bond for 4 to 10.

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.

Read and place numbers within 100 on a number line. Compare and order numbers within 100.

Use ordinal numbers 1st to 10th to indicate position. Give a number between two neighboring pairs of tens within 100.

Estimate the number of objects in a group of fewer than 10 objects.

Compare the number of objects in two or more groups.

Subitize up to 6 objects.Compare and order numbers within 100.

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

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

Grade K

Grade 1

Grade 2

NUMBERS AND OPERATIONS (continued)

Whole Numbers / Place Value (continued)

Compose and decompose numbers from 10 to 19 as 10 ones and some more ones.

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

Use the ‘=’ sign to represent equality.

Make number stories to illustrate number bonds for 5 to 10.

Break a group of 5 to 10 objects into two parts in different ways.

Write a number bond for 5 to 10.

Name the missing part or whole in a number bond.

Name a position using an ordinal number from 1st to 10th.

*Count within 120.

*Read and write a number from 101 to 120—the numeral and the corresponding number word.

Addition / Subtraction

Add or subtract within 10.Use picture cut-outs (or other manipulatives) to illustrate the meanings of addition and subtraction.

Act out addition and subtraction stories to illustrate the meanings of addition and subtraction.

Make addition or subtraction stories with the given illustrations.

Count all to add two quantities within 10.

Illustrate addition and subtraction stories and problems with number bonds.

Use drawings to represent addition and subtraction stories.

Write addition and subtraction facts within 5.

Count on to add or count backwards to subtract within 10.

Make a number story for a given addition or subtraction sentence.

Write a number sentence for a given situation involving addition or subtraction.

Apply the identity, commutative and associative properties of addition.

Observe the answer when 0 is subtracted from a number.

Write a family of four addition and subtraction facts for a given number bond.

Identify doubles facts within 20.

Mentally add: - two or three 1-digit whole numbers within 20 - a 1-digit whole number and a 2-digit whole number within 20

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.

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.

Grade K

Grade 1

Grade 2

NUMBERS AND OPERATIONS (continued)

Addition / Subtraction (continued) Write a number sentence for an addition or subtraction problem.

Mentally subtract:

- a 1-digit whole number from another 1-digit whole number

- a 1-digit whole number from a 2-digit whole number within 20

Check the answer to addition or subtraction.

Use ‘+’, ‘–’ or ‘=’ correctly to complete number sentences.

Find pairs of multiples of 10 with a total of 100 and write the addition and subtraction facts for each number pair.

Find the missing part in an addition sentence.

Find the missing part or whole in a subtraction sentence.

Find the missing part in an addition sentence. Use the ‘=’ sign to represent equality.

Find the missing part or whole in a subtraction sentence.

Solve 1-step word problems involving addition or subtraction of numbers within 20.

*Add and subtract within 40.

*Solve 1-step word problems involving addition or subtraction of numbers within 40.

Multiplication / Division

Find doubles of numbers up to 10.

Find halves of even numbers of objects up to 10 by sharing.

Identify odd and even numbers by sharing.

Recognize equal groups and find the total number in the groups by repeated addition.

Use mathematical language such as ‘4 threes’ and ‘3 groups of 5’ to describe equal groups.

Use manipulatives to illustrate the meaning of multiplication and the sharing and grouping concepts of division.

Understand that division can leave some left over.

Tell multiplication and division stories for given pictures.

Write a number sentence for a given situation involving multiplication or division.

Work out a multiplication fact within 40 by repeated addition.

Use arrays to show multiplication sentences.

Grade K

Grade 1

Grade 2

NUMBERS AND OPERATIONS (continued)

Multiplication / Division (continued)

Associate the term ‘product’ with multiplication.

Use the commutative property of multiplication.

Write a family of four multiplication and division facts.

Solve 1-step word problems on multiplication or division.

Count by twos, threes, fours, fives and tens.

Observe the commutative and distributive properties of multiplication.

Build up the multiplication tables of 2, 3, 4, 5 and 10 and commit the multiplication facts to memory.

Multiply numbers within the multiplication tables of 2, 3, 4, 5 and 10.

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.

Grade K

Grade 1

Grade 2

NUMBERS AND OPERATIONS (continued)

Fractions / Concepts

Recognize and name one half of a whole which is divided into 2 equal parts.

Recognize and name one fourth or one quarter of a whole which is divided into 4 equal parts.

Find one half of a small number of objects by putting the objects into 2 equal groups.

Find one fourth or one quarter of a small number of objects by putting the objects into 4 equal groups.

Use the fraction 1 2 to describe a half of a whole or a set.

Use the fraction 1 4 to describe a fourth or a quarter of a whole or a set.

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 and fourths or quarters of a whole or a set. Find halves, thirds and quarters of a set.

Use the fractions 2 2 , 2 4 , 3 4 and 4 4 to describe halves and fourths or quarters of a whole or a set.

MEASUREMENT

Length

Describe an object using ‘long’, ‘tall’ and ‘short’.

Compare up to three objects.

Compare the lengths of two or more objects.

Arrange objects in order according to their lengths.

Measure using up to 10 non-standard units. Estimate and measure the length of an object in non-standard units.

Compare the lengths of two or more objects measured in non-standard units.

Recognize and name unit fractions up to 1 12

Recognize and name proper fractions.

Identify the numerators and denominators of proper fractions.

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.

Grade K Grade 1 Grade 2

MEASUREMENT (continued)

Length (continued)

Volume and Capacity

Compare the volume of liquids in 2 identical containers.

Mass / Weight

Describe an object using ‘heavy’ and ‘light’.

Compare up to three objects.

Understand the meaning of capacity.

Compare the capacities of two or more containers visually.

Arrange containers in order according to their capacities.

Estimate and measure the capacity of a container in non-standard units.

Compare the capacities of two or more containers measured in non-standard units.

Compare the masses of two or more objects.

Arrange objects in order according to their masses.

Explore mass by hefting. Estimate and measure the mass of an object in non-standard units.

Measure with a pan balance using up to 10 non-standard units.

Explore estimation.

Understand a big object is not necessarily heavier than a smaller one.

Size Describe an object using ‘big’ and ‘small’.

Compare up to three objects.

Time: Calendar

Name the days of the week in sequence.

Link specific days to familiar events.

Name the months of the year in sequence.

Compare the masses of two or more objects measured in non-standard units.

*Measure the length of a line or curve in inches.

*Draw a line given its length in inches.

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

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

Estimate, measure and compare capacities of containers in liters.

Arrange containers in order according to their capacities.

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

Name and order the days of the week.

Know that there are 7 days in a week.

Name the months of the year.

Measure and compare masses in kilograms.

Estimate, measure and compare masses in grams.

Arrange objects in order according to their masses.

Choose a suitable unit of measure when measuring masses.

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

Read a calendar.

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

Associate months with events.

Grade K

Grade 1

Grade 2

Grade K

MEASUREMENT (continued)

Time: Calendar (continued)

Link familiar events to months.

Grade 1

Know that there are 12 months in a year.

Time: Clock

Grade 2

Understand the relationships between units of time.

Count the days in a month. Read and write a date. Choose suitable units of measure when measuring time intervals.

Sequence events in order of ‘morning’, ‘afternoon’ and ‘night’.

Measure and compare short periods of time in informal ways and using ‘longer’, ‘shorter’, ‘faster’ and ‘slower’.

Tell time to the hour and half hour on analog and digital clocks.

*Tell time to the quarter hour on analog and digital clocks.

Relate time to events of a day.

Sequence events according to the time of the day.

Tell time by 5-minute intervals on analog and digital clocks.

Tell time using a.m. and p.m.

Money

Recognize and name one-cent, five-cent, ten-cent, twenty-cent and fifty-cent coins.

Count and tell the amount of money up to twenty cents in one-cent coins.

Compare two amounts of money between one and ten cents.

Add or subtract amounts of money in one cents up to 10 cents and represent the result with drawings.

Recognize and name five-cent, ten-cent, fifty-cent and one-dollar coins.

Count and tell the amount of money in a group of coins up to $1.

Exchange a coin for more coins in one denomination.

Make up an amount of money using a group of coins.

Compare amounts of money.

Relate time to events of a day.

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

Develop a sense of the duration of daily activities.

Measure duration of activities in minutes.

Solve word problems on time.

Recognize and name five-dollar, ten-dollar and fifty-dollar notes.

Count and tell the amount of money in a group of notes and/or coins up to $100.

Exchange a note for more coins and/or notes.

Make up an amount of money using a group of coins and/or notes.

Compare amounts of money.

Read the price of an item and pay for it.

Add and subtract money in cents up to $1.

Add and subtract money in dollars up to $100.

Count change like a cashier in a purchasing situation.

Solve 1-step word problems on money.

GEOMETRY

Lines and Curves

2D Shapes

Recognize and name five basic plane shapes: circle, triangle, rectangle, square and hexagon.

Count the sides and corners of a shape.

Build awareness of attributes: shape, size and color.

Sort and group (and re-sort) plane shapes according to attributes: shape, size and color.

Describe the location of plane shapes using positional and directional words.

Identify plane shapes on real-world objects.

Use plane shapes to create a new shape and items commonly found in the environment.

Describe objects by their shapes.

Recognize and name the four basic 2D shapes: circle, triangle, rectangle and square.

Identify the sides and corners of a 2D shape.

Sort 2D shapes according to each of these attributes: shape, size and color.

Describe and continue a pattern with 2D shapes according to one or more of these attributes: shape, size and color.

*Make pictures using shapes.

Fit suitable pieces together to form a 2D shape.

Identify a line segment and a curve.

Name, describe and draw 2D shapes: circle, triangle, rectangle, square, pentagon and hexagon.

Find 2D shapes in the environment.

3D Shapes

Recognize and name basic solid shapes: sphere, cylinder, cone and cube.

Describe the attributes of solid shapes: slide, stack and roll.

Identify real-world objects as solids.

Describe the location of solid shapes using positional and directional words.

Recognize and name 3D shapes: cube, cuboid, cylinder, cone and sphere.

Identify basic 2D shapes in 3D shapes.

Sort 3D shapes according to each of these attributes: shape, size and color.

*Identify a 3D shape that can slide, stack or roll.

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.

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.

Grade K

Grade 1

Grade 2

GEOMETRY (continued)

3D Shapes (continued)

Identify plane shapes on solid shapes.

Use solids to build and compare two structures.

Position and Movement

Use ordinal numbers 1st to 10th to indicate position.

Describe the location of plane shapes using positional and directional words.

Describe the location of solid shapes using positional and directional words.

DATA ANALYSIS

Data Collection Participate in a class survey to collect data.

Describe and continue a pattern with 3D shapes according to one or more of these attributes: shape, size and color.

Use 3D shapes to make models.

Describe the location of objects using positional words.

Name a position using an ordinal number from 1st to 10th.

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.

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

Recognize whole, half and quarter turns.

Identify left and right turns. Describe turns using the words 'clockwise' and 'counterclockwise'.

Use everyday language of direction and distance to describe movement of objects.

Follow and give instructions involving position, direction and movement.

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

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

Read and interpret a list. Present data given in a list as a block graph.

Tables

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

Read and interpret a table.Present data given in a table as a block graph.

Group objects in a Carroll diagram using different criteria.

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

Grade K

Grade 1

Grade 2

Grade K

DATA ANALYSIS (continued)

Graphs

Grade 1

Sort and group up to 10 objects by color or pattern.

Sort and count data to create a 3-column or 3-row picture graph of up to 10 objects per category.

Visually compare data.

Make a simple pictogram using one-to-one representation.

Read and interpret a pictogram.

Grade 2

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.

ALGEBRA

Patterns

Equations

Identify visual patterns in the environment.

Describe, copy and extend AB, ABC and AAB shape, sound and action patterns.

Transfer patterns to a different format.

Describe and complete a number pattern by counting on or backwards by ones, twos or tens within 100.

Describe and continue a pattern with 2D shapes according to one or more of these attributes: shape, size and color.

Describe and continue a pattern with 3D shapes according to one or more of these attributes: shape, size and color.

Find the missing part in an addition sentence.

Find the missing part or whole in a subtraction sentence.

*Solve 1-step word problems by finding missing numbers in addition or subtraction sentences.

*Lessons are available in PR1ME Mathematics Teaching Hub.

Describe and complete a number pattern by counting on or backwards by ones, twos, threes, fours, fives or tens within 100.

*Continue a pattern with 2D shapes according to one or two of these attributes: shape, size, color and orientation.

*Continue a pattern with 3D shapes according to one or two of these attributes: shape, size, color and orientation.

Find the missing part in an addition sentence.

Find the missing part or whole in a subtraction sentence.

Strand: Numbers and Operations

Chapter 1: Numbers 0 to 10

*Digital Practice is available in PR1ME Mathematics Digital Practice and Assessment.

*ResourcesVocabulary

Materials

• CB: p. 1

Objectives

• Count up to 5 objects arranged in different ways

Scheme of Work Unit

Let’s Remember

• count backwards

• count on

• number track

• CB: pp. 2–5

• PB: pp. 9–10

• 1 copy of Ten Frame (BM1.1) per student

• Digital Practice

Unit 1: Counting and Comparing

• Counters

• Count within 10 (including the use of zero)

• Read and write a number from 0 to 10—the numeral and the corresponding number word

1.1 Counting, r eading and writing numbers

• Recognize conservation of numbers

• CB: pp. 5–6

• PB: p. 11

• Digital Practice

• Connecting cubes (blue and red)

• Count on and backwards within 10

1.2 Counting on and backwards

• same number

• CB: pp. 7–8

• PB: p. 12

• Digital Practice

• 1 bag of 4 red connecting cubes and 4 blue connecting cubes per pair of students

• Compare the number of objects in two groups within 10 by matching

1.3 Comparing number of objects by matching

• 1 bag of 5 red connecting cubes and 3 blue connecting cubes per pair of students

• 1 copy of Books and Pencils Picture Cards (BM1.2) per pair of students

• 1 copy of Bread and Cheese Picture Cards (BM1.3) per pair of students

• as many as

• equal (=)

• greater than • less

less than

• more

• CB: pp. 8–11

• PB: pp. 13–14

• 1 enlarged copy of Cats and Flowers Picture Cards (BM1.4)

• Compare the number of objects in two groups within 10 by counting

• Digital Practice

• 1 enlarged copy of Bees and Ants Picture Cards (BM1.5)

• Compare two numbers within 10

1.4 Comparing number of objects by counting

• greatest

• least

• CB: pp. 11–12

• PB: p. 15

• Digital Practice

• 1 enlarged copy of Rabbits and Carrots Picture Cards (BM1.6)

• Use the ‘=’ sign to represent equality

• Compare and order numbers within 10

1.5 Comparing and ordering numbers

Digital Practice and Assessment

Digital Chapter Assessment — Available in PR1ME Mathematics

The suggested duration for each lesson is 1 hour.

Chapter 1 Numbers 0 to 10

Chapter Overview

Let’s Remember Unit 1: Counting and Comparing

Let's Remember Let's Remember

Recall:

1. Counting up to 5 objects arranged in different ways (Grade K Chapter 1)

EXPLORE

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

•Who are your family members?

•What do you do together as a family?

•Is your family important to you? Why?

Have students form groups to complete the tasks in columns 1 and 2 of the table.

Let students know that they do not have to solve the problem. Ask the groups to present their work.

Tell students that they will come back to this problem later in the chapter.

Mary and her family are at the beach. a) How many people are there in your family? b) Are there more people in your family than in Mary’s? Answers vary.

Discuss in your group and fill in columns 1 and 2.

Count up to 5. Compare numbers.

Unit 1: Counting and Comparing

1.1 Counting, reading and writing numbers

Let's Learn Let's Learn

Objectives:

•Count within 10 (including the use of zero)

•Read and write a number from 0 to 10—the numeral and the corresponding number word

•Recognize conservation of numbers

Materials:

•1 copy of Ten Frame (BM1.1) per student

•Counters

Resources:

•CB: pp. 2–5

•PB: pp. 9–10

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

Distribute a copy of Ten Frame (BM1.1) and counters to each student.

Stick 1 counter on the board.

Ask: How many counters are there? (1)

Draw a ten frame on the board.

Say: Let us put 1 counter in the ten frame. Place the counter in the ten frame as shown on CB p. 1 to show the number 1. Have students count 1 counter and place it in their ten frame.

Write: 1 one

Point to the numeral and word form of ‘1’ on the board and read them aloud. Write the numeral ‘1’ again and have students observe how it is written. Stick 2 counters on the board.

Say: Let us count the counters. 1, 2. There are 2 counters.

Draw a ten frame on the board.

Say: Let us put the 2 counters in the ten frame. Place the 2 counters in the ten frame as shown on CB p. 1 to show the number 2. Have students count 2 counters and place them in their ten frame.

Write: 2 two

Point to the numeral and word form of ‘2’ on the board and read them aloud. Write the numeral ‘2’ again and have students observe how it is written. Repeat the above procedure for 3 to 5.

Counting, reading and writing numbers

Repeat the procedure in (a) on TG p. 4 for 6 to 10. Ensure that students place the counters side by side in the ten frame, starting from the left, and fill up the first row before moving to the second row.

Ask: What if there are no counters? How do we show nothing? (Answers vary.)

Say: We use zero to show nothing. Write: 0 zero

Ask: Why is ‘zero’ not said aloud when we count? (‘Zero’ means nothing and we do not count when there is nothing. We start counting from 1.)

To reinforce students’ counting skill, have them work in groups. Call out any number up to 10 and have students take out that number of counters. The first group to form the correct set wins a point. Play several rounds. The group with the most points wins.

(b) Stage: Concrete Experience

Ask 5 students to stand in front of the class.

Ask: How many students are there? (5) Ask the students to rearrange themselves.

Ask: How many students are there now? (5) Did the number of students change? (No)

Stages: Pictorial and Abstract Representations

Have students look at the pictures in (b) on CB p. 3. Ask them to count and write the number of beans on the page.

Say: The beans are rearranged.

Ask: How many beans are there at first? (6) How many beans are there after the rearrangement? (6) Did the number of beans change? (No)

Say: The number of objects does not change when we rearrange the objects.

Let's Do Let's Do

Task 1 requires students to count within 10 and pick the matching numerals or word forms.

Encourage students to avoid counting the same object twice by striking it off as they count or count systematically from left to right (and top to bottom when there are more objects).

Highlight the importance of writing numerals neatly using the correct strokes and being able to recognize numerals correctly. Some common mistakes include:

•0 is written as 6 (and vice versa),

•1 is written as 7 (and vice versa),

•2 is written as z,

•5 is written as s, and

•2, 3 and 5 are written as their mirror images.

Let's Practice Let's

Task 1 requires students to count and write numbers within 10.

b) Count the beans.

Task 2 requires students to draw objects to show numbers within 10.

Task 3 requires students to write numbers within 10 in word form.

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.

1.2 Counting on and backwards

Let's Learn Let's Learn

Objective:

•Count on and backwards within 10

Materials:

•Connecting cubes (blue and red)

Resources:

•CB: pp. 5–6

•PB: p. 11

Vocabulary:

•count backwards

•count on

•number track

(a) Stage: Concrete Experience

Have students work in groups. Distribute some blue and red connecting cubes to each group. Guide students to set up the connecting cubes as shown in (a) on CB p. 5. Recap the number sequence by getting each student to count the number of connecting cubes from left to right to their group members.

Say: When we count the number of cubes from left to right, we start counting from 1. We call this counting on from 1. Demonstrate the counting to students.

Stage: Pictorial Representation

Draw the number track in (a) on the page on the board. Relate the number track to the connecting cubes in the earlier activity.

Say: We can count on using a number track. Have students count on from 1 to 10. Move your finger from each number to the next on the number track as students count.

1.2 Counting on and backwards

12345678910

2, 3, 4, 5, 6, 7, 8, 9, 10

Stage: Abstract Representation

Write: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Have students count on in steps of 1 from numbers other than 1. For example, 4, 5, 6.

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

Follow the procedure in (a) on TG p. 6 but count backwards.

Let's Do Let's Do and Let's Practice Let's Practice Task 1 requires students to count on and backwards within 10.

We can count backwards using a number track.

1.3 Comparing number of objects by matching

Let's Learn Let's Learn

Objective:

•Compare the number of objects in two groups within 10 by matching

Materials:

•1 bag of 4 red connecting cubes and 4 blue connecting cubes per pair of students

•1 bag of 5 red connecting cubes and 3 blue connecting cubes per pair of students

•1 copy of Books and Pencils Picture Cards (BM1.2) per pair of students

•1 copy of Bread and Cheese Picture Cards (BM1.3) per pair of students

Resources:

•CB: pp. 7–8

•PB: p. 12

Vocabulary:

•same number

(a) Stage: Concrete Experience

Have students work in pairs. Distribute a bag of 4 red connecting cubes and 4 blue connecting cubes to each pair.

Have students put the connecting cubes into two groups by color.

Say: Let us compare the two groups. Have students take one connecting cube from each group and join the two connecting cubes and repeat this step until they cannot form any more pairs.

Ask: Are all the red connecting cubes matched to the blue connecting cubes? (Yes) Are there any red or blue connecting cubes that are not matched? (No)

Say: Since all the connecting cubes are matched, and there are no connecting cubes left unmatched, the two groups have the same number of connecting cubes.

Stage: Pictorial Representation

Have students continue to work in pairs. Distribute a copy of Books and Pencils Picture Cards (BM1.2) to each pair.

Draw 4 books and 4 pencils as shown in (a) on CB p. 7 on the board. Label the group of books ‘A’ and the group of pencils ‘B’.

Say: We can compare the groups by drawing a line from each book to each pencil. Draw a line from each book to each pencil. Have students do the same.

Conclude that all the books and pencils are matched, so group A and group B have the same number of objects.

Comparing number of objects by matching

(b) Stages: Concrete Experience and Pictorial Representation

Follow the procedure in (a) but use the bag of 5 red connecting cubes and 3 blue connecting cubes and the Bread and Cheese Picture Cards (BM1.3). Label the group of loaves of bread ‘C’ and the group of cheese blocks ‘D’.

Conclude that not all the objects are matched, so the two groups do not have the same number of objects.

Let's Do Let's Do

Task 1 requires students to compare the number of objects in two groups within 10 by matching.

Let's Practice

Let's Practice

Task 1 requires students to compare the number of objects in two groups within 10 by matching.

1.4 Comparing number of objects by counting

Let's Learn Let's Learn Objectives:

•Compare the number of objects in two groups within 10 by counting

•Compare two numbers within 10

•Use the ‘=’ sign to represent equality

Materials:

•1 enlarged copy of Cats and Flowers Picture Cards (BM1.4)

•1 enlarged copy of Bees and Ants Picture Cards (BM1.5)

•1 enlarged copy of Rabbits and Carrots Picture Cards (BM1.6)

Resources:

•CB: pp. 8–11

•PB: pp. 13–14

Vocabulary:

•as many as

•equal (=)

•greater than

•less

•less than

•more

(a) Stage: Pictorial Representation

Stick an enlarged copy of the Cats and Flowers Picture Cards (BM1.4) on the board. Label the group of cats ‘A’ and the group of flowers ‘B’.

Say: Let us count the number of cats. 1, 2, 3, 4.

Point to each cat as you count.

Say: There are 4 cats.

Write the number of cats below the group of cats.

Repeat the above procedure for the flowers.

Ask: Do group A and group B have the same number of objects? (Yes)

Stage: Abstract Representation

Say: Since group A has 4 objects and group B also has 4 objects, we say that group A has as many objects as group B.

Write: Group A has as many objects as group B. 4 = 4

Point to the number sentence on the board.

Say: We read the number sentence as 4 is equal to 4.

1.4 Comparing number of objects by counting

(b) Stage: Pictorial Representation

Stick an enlarged copy of the Bees and Ants Picture Cards (BM1.5) on the board. Label the group of bees ‘C’ and the group of ants ‘D’.

Say: Let us count the number of bees. 1, 2, 3, 4, 5, 6.

Point to each bee as you count.

Say: There are 6 bees. Write the number of bees below the group of bees.

Repeat the above procedure for the ants.

Ask: Do group C and group D have the same number of objects? (No)

Stage: Abstract Representation

Say: Since group C has 6 objects and group D has 4 objects, group C has more.

Write: Group C has more.

Ask: Is 6 equal to 4? (No)

Say: 6 is not equal to 4. 6 is greater than 4.

Write: 6 is greater than 4.

(c) Stage: Pictorial Representation

Follow the procedure in (b) but use the Rabbits and Carrots Picture Cards (BM1.6). Label the group of rabbits ‘E’ and the group of carrots ‘F’.

Ask: Do group E and group F have the same number of objects? (No)

Stage: Abstract Representation

Say: Since group E has 4 objects and group F has 8 objects, group E has less.

Write: Group E has less.

Ask: Is 4 equal to 8? (No)

Say: 4 is not equal to 8. 4 is less than 8.

Write: 4 is less than 8.

Let's Do Let's Do

Task 1 requires students to compare the number of objects in two groups within 10 by counting. Students have to compare two numbers within 10.

Task 2 requires students to use the = sign to represent equality.

Let's Practice

Task 1 requires students to count the objects in each group to identify two groups with equal number of objects.

Task 2 requires students to compare the number of objects in two groups within 10 by counting. Students have to compare two numbers within 10.

Task 3 requires students to use the ‘=’ sign to represent equality.

1.5 Comparing and ordering numbers

Let's Learn Let's Learn

Objective:

•Compare and order numbers within 10

Resources:

•CB: pp. 11–12

•PB: p. 15

Vocabulary: •greatest •least

Stages: Pictorial and Abstract Representations

Have students look at the pictures on CB p. 11.

Ask: How many ducklings are there in group A? (4)

Write: Group A – 4

Ask: How many ducklings are there in group B? (6)

Write: Group B – 6

Ask: How many ducklings are there in group C? (2)

Write: Group C – 2

Ask: Which group has more, group A or group B? (Group B) Which group has more, group B or group C? (Group B)

Say: The number of ducklings in group B is more than the number of ducklings in the other groups. So, group B has the greatest number of ducklings.

Write: Group B has the greatest number of ducklings.

Ask: Compare the numbers, 4, 6 and 2. Which is the greatest number? (6)

Write: 6 is the greatest number. Have students compare the number of ducklings in the groups again.

Ask: Which group has less, group A or group B? (Group A) Which group has less, group A or group C? (Group C)

Say: The number of ducklings in group C is less than the number of ducklings in the other groups. So, group C has the least number of ducklings.

Ask: Compare the numbers, 4, 6 and 2. Which is the least number? (2)

Write: 2 is the least number.

Say: We can arrange the numbers 4, 6 and 2 in order. Let us start with the greatest number.

Write: 6

Say: The least number is 2.

Write: 6, 2

b) Which group has less? is less than G

3. Tick (✓) the correct number sentences.

1.5 Comparing and ordering numbers

Group B has the greatest number of ducklings. 6 is the greatest number.

Group C has the least number of ducklings. 2 is the least number.

Arrange the numbers in order. Begin with the greatest.

Say: We write the last number between the greatest number and the least number.

Write: 6, 4, 2

Say: We have arranged the numbers in order, beginning with the greatest. We can also arrange the numbers in order, beginning with the least.

Ask: Which number should we start with? (2) Why? (2 is the least number.)

Write: 2

Ask: What number should we write after 2? (4) Why? (4 is greater than 2 but less than 6.)

Write: 2, 4, 6

Let's Do Do

Tasks 1 and 2 require students to compare and order numbers within 10.

Let's Practice Let's Practice

Task 1 requires students to compare numbers within 10.

Task 2 requires students to compare and order numbers within 10.

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.

a) Compare the number of ice cream cones. Which number is the greatest?

b) Arrange the numbers in order. Begin with the least. , , (least)

2. Arrange 6, 3 and 10 in order. Begin with the greatest. , , (greatest)

Circle the least number.

Arrange the numbers in order. Begin with the greatest.

Let's Practice Let's Practice

Practice Book Chapter 1: Answers

Exercise 1.1

1. a) 5 b) 3 c) 4 d) 2

2. a) Circle any 7 cars.

b) Circle any 5 hats.

c) Do not circle any flower.

3. 10

3. Count and match.

d) Circle any 8 bells.

Exercise 1.2 Counting on and backwards

ninesixtenseven eight

4. a) Draw 9 flowers.

4. Draw the correct number of objects.

b) Draw 4 oranges.

a) NINE flowers

c) Draw 6 leaves.

Students should draw 9 flowers.

5. a) zero b) six c) three d) one

Recap 12345678910 count on count backwards

b) FOUR oranges

1. Count on. Trace the route.

Exercise 1.3

1. a) No b) Yes c) No d) Yes

Exercise 1.4

1. a) P; 6; 5 b) M; 6; 8 2. a) Circle the second and fourth pictures. b) Circle the first and fourth pictures. c) Circle the first and fourth pictures. d) Circle the first and third pictures. 3. Tick: a; d; e; g

Exercise 1.5

1. a) Circle: 8; Cross out: 0 b) Circle: 9; Cross out: 5 c) Circle: 8; Cross out: 2 d) Circle: 6; Cross out: 1

2. a) 5; 7; 9; 10 b) 8; 7, 5; 3; 1

Exercise 1.2 1. 11

2. Count on or backwards to write the missing

5. Write each number in words. a) 0 b) 6 c) 3 d) 1

Students should draw 4 oranges. zero six three one

2. a) 9, 6, 2 b) 5, 3, 1 c) 7, 5, 4, 0 d) 9, 7, 6, 2 e) 8, 7, 3, 2 f) 5, 4, 1, 0

3. a) 0, 4, 7 b) 5, 8, 9

c) 0, 2, 5, 9 d) 1, 3, 6, 8 e) 2, 4, 6, 8 f) 0, 4, 7, 9

Glossary

• 2D shape

A 2D shape is a flat shape. For example, circles, triangles, squares and rectangles are 2D shapes.

• 3D model

A 3D model is formed using 3D shapes.

• 3D shape

A 3D shape is not a flat shape. For example, cubes, cuboids, cylinders, cones and spheres are 3D shapes.

1 straw The pen is about 5 straws long.

3 + 3 = 6 Three plus three

DoraJosie

Josie is in front of Dora.

DoraJosie Dora is behind Josie.

BM1.1 Ten Frame

BM1.2 Books and Pencils Picture Cards

BM1.5 Bees and Ants Picture Cards

BM1.6 Rabbits and Carrots Picture Cards

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. In Coursebook In Practice Book

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

Mind Stretcher enables students to apply knowledge gained to non-routine problem situations to develop higher-order thinking skills.

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 0 to 10

Chapter 2 Number Bonds

Chapter 3 Addition

Chapter 4 Subtraction

Chapter 5 Position and Movement

Chapter 6 Numbers to 20

Chapter 7 Addition and Subtraction Within 20

Chapter 8 2D Shapes

Let’s

Chapter 9 3D Shapes

Chapter

Length

Chapter 11 Mass

Chapter 12 Capacity

Let’s Remember

Unit 1: Comparing Capacities

Chapter 13 Comparing Numbers

Let’s Remember

Chapter 14 Handling Data

Let’s Remember

Chapter 15 Numbers to 40

Let’s

Chapter 16 Fractions

Let’s Remember

Chapter

17

Doubles and Halves

Let’s Remember

Chapter 18 Calendar and Time

Chapter 19 Numbers to 100

Chapter 20 Money

Numbers 0 to 10

Let's Remember Let's Remember

1. Count and match.

EXPLORE

Mary and her family are at the beach.

a) How many people are there in your family?

b) Are there more people in your family than in Mary’s?

How can we solve this problem?

Discuss in your group and fill in columns 1 and 2.

Unit 1 Counting and Comparing

You will learn to...

• count within 10

• read and write numbers from 0 to 10

• count on and backwards within 10

• compare and order numbers within 10

1.1 Counting, reading and writing numbers

b) Count the beans. beans beans

The number of objects does not change when we rearrange the objects.

Let's Do Let's

1. Count and match.

Let's Practice Let's Practice

1. Count and write the numbers.

1.3 Comparing number of objects by matching

Let's Learn Let's Learn

a) Match the objects in group A to the objects in group B.

All the objects are matched.

Group A and group B have the same number of objects.

b)

Not all the objects in group C are matched. Group C and group D do not have the same number of objects.

Let's Do Do

1. Match.

Do group E and group F have the same number of objects?

Do group G and group H have the same number of objects?

Do group J and group K have the same number of objects?

1.4 Comparing number of objects by counting Count and compare. Let's Learn Learn

c)

Group C has more. 6 is not equal to 4. 6 is greater than 4.

Group E has less. is not equal to . is less than .

Let's Do Let's Do

1. Count and compare.

G H Group has more. is greater than . Group has less. is less than .

2. Tick (✓) the correct number sentences.

a) 3 = 2 b) 5 = 5

d) 8 = 8

Let's Practice Let's Practice

c) 6 = 9

e) 7 = 7 f) 10 = 0

1. Circle the two groups that have equal number of objects.

2. Compare the number of objects. Then, write the answers in the blanks.

Which group has more? is greater than . a)

Which group has less? is less than .

3. Tick (✓) the correct number sentences.

a) 6 = 6 b) 5 = 4 c) 1 = 1

d) 3 = 7 e) 9 = 9 f) 2 = 5

1.5 Comparing and ordering numbers

Group B has the greatest number of ducklings. 6 is the greatest number.

Group C has the least number of ducklings. 2 is the least number.

Arrange the numbers in order.

Begin with the greatest.

a) Compare the number of ice cream cones. Which number is the greatest?

b) Arrange the numbers in order. Begin with the least. , , (least)

2. Arrange 6, 3 and 10 in order. Begin with the greatest. , , (greatest)

Let's Practice Let's Practice

1. Circle the least number.

a) 5, 3, 2 b) 2, 0, 1 c) 4, 9, 6

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

a) 1, 4, 7 b) 6, 8, 2 c) 0, 9, 3

I have learned to... count within 10 read and write numbers from 0 to 10 count on and backwards within 10 compare and order numbers within 10

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

1.5

Number Bonds

Let's Remember Let's Remember

1. Count and write the numbers.

2. What can you say about the number of leaves?

EXPLORE

There are 6 children at a playground. 4 speak Spanish. The rest speak Portuguese. How many children speak Portuguese?

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 Telling Number Stories

You will learn to...

• tell number stories

• make and complete number bonds

1.1 Making 5

Let's Learn Let's Learn This is a number bond. 3 and 2 make 5. Tell another number story about the children.

Let's Do Let's Do

1. Complete the number bond.

There are 5 children. 3 are girls. 2 are boys. part part whole 3 2 5 5 A number bond is made up of parts and a whole.

THINK ABOUT IT

David and Sarah make number bonds about the apples.

Who is correct?

Why do you say so?

Who is wrong?

Why do you say so?

What did you learn about number bonds?

Think of a time in your daily life when you can use number bonds.

1. Match pairs of numbers that make 5.

1.2 Making 6 Let's Learn Let's Learn

There are 6 keys. 4 are on the keychain. 2 are loose. 4 and 2 make 6. Tell another number story about the keys. part part whole

Let's Do Let's Do

1. Complete the number bond.

1. Match pairs of numbers that make 6. Let's Practice Let's Practice

1.3 Making 7

Let's Learn Let's Learn

There are 7 cats. 5 are playing. 2 are not playing. 5 and 2 make 7. Tell another number story about the cats. part

Let's Do Let's Do

1. Complete the number bond.

1. Match pairs of numbers that make 7.

1.4 Making 8 Let's Learn Let's Learn

Let's Do Let's Do

1. Complete the number bond.

There are 8 butterflies. 2 have yellow spots. 6 do not have yellow spots. 2 and 6 make 8. Tell another number story about the butterflies. part part whole 2 6 8 8

Let's Practice Let's Practice

1. Match pairs of numbers that make 8.

1.5 Making 9

Let's Learn Let's Learn

There are 9 T-shirts. 2 are blue. 7 are not blue. 2 and 7 make 9.

Let's Do Let's Do

1. Complete the number bond.

Tell another number story about the T-shirts. part part whole 2 7 9 9

1. Match pairs of numbers that make 9.

1.6 Making 10 Let's Learn Let's Learn

There are 10 toys. 6 are stuffed toys. 4 are robots. 6 and 4 make 10. Tell another number story about the toys. and make 10. part part whole 6 4 10 10

There are 10 counters. 5 are red. 5 are yellow.

Let's Practice Practice

1. Match pairs of numbers that make

Put 9 blocks into two bags. 5 are in the blue bag. and 5 make 9. blocks are in the green bag. a) and

Let's Learn Let's Learn ? 5 9

6 and make 6. party hats are in the box. 6 ? 6

Let's Do Let's Do

1. Draw the missing part.

The number of oranges should be the same.

1. Draw the missing part.

2. Complete the number bonds.

3. Write the missing numbers.

and 4 make 5.5 and 2 make .

I have learned to... tell number stories make and complete number bonds

>> Look at EXPLORE on page 13 again. Fill in column 3. Can you solve the problem now?

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

Practice Book

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

1 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.

Chapter 1 Numbers 0 to 10

Exercise

Chapter 2 Number Bonds

Exercise

Chapter 3 Addition

Chapter 4 Subtraction

Exercise

Chapter 5 Position and Movement

Exercise

Chapter 6 Numbers to 20

Exercise 1.1 Counting, reading and writing numbers 58

Exercise 1.2 Understanding 2-digit numbers 60

Exercise 1.3 Counting on and backwards 61

Exercise 1.4 Comparing numbers 63

Exercise 1.5 Comparing and ordering numbers 64

Chapter 7 Addition and Subtraction Within 20

Exercise 1.1 Adding two 1-digit numbers by making 10 65

Exercise 1.2 Adding a 1-digit number and a 2-digit number 66

Exercise 1.3 Adding by counting on 67

Exercise 1.4 Doubles facts within 20 68

Exercise 1.5 Using doubles facts to add 69

Exercise 1.6 Adding three 1-digt numbers by grouping numbers 70

Exercise 1.7 Adding three 1-digt numbers by making 10 71

Exercise 2.1 Subtracting a 1-digit number from a 2-digit number using the ‘subtract from ones’ method 72

Exercise 2.2 Subtracting a 1-digit number from a 2-digit number using the ‘subtract from 10’ method 73

Exercise 2.3 Subtracting by counting backwards 74

Exercise 2.4 Subtracting by counting on 75

Exercise 3.1 Finding the missing part in an addition or subtraction sentence 76

Exercise 3.2 Finding the missing whole in a subtraction sentence 77

Exercise 4.1 Word problems 78

Chapter 8 2D Shapes

Exercise 1.1 Identifying 2D shapes 80

Exercise 1.2 Sides and cor ners of shapes 81

Exercise 1.3 Sorting 2D shapes 82

Exercise 2.1 Continuing a patter n 83

Exercise 2.2 Making shapes 85

Chapter 9 3D Shapes

Exercise 1.1 Identifying 3D shapes 87

Exercise 1.2 Sorting 3D shapes 88

Exercise 2.1 Continuing a patter n 89

Exercise 2.2 Making models 91

Review 2 92

Chapter 10 Length

Exercise 1.1 Comparing lengths and heights 97

Exercise 1.2 Comparing lengths by counting 99

Exercise 1.3 Using a start line 100

Exercise 2.1 Measuring length 102

Exercise 2.2 Measuring length in units 103

Chapter 11 Mass

Exercise 1.1 Comparing masses of two objects 105

Exercise 1.2 Comparing masses of three objects 107

Exercise 2.1 Measuring mass in units 109

Exercise 2.2 Comparing masses in units 111

Chapter 12 Capacity

Exercise 1.1 Comparing capacities 113

Exercise 2.1 Measuring capacity 114

Exercise 2.2 Comparing capacities in units 115

Chapter 13 Comparing Numbers

Exercise 1.1 Understanding ‘more than’ 117

Exercise 1.2 Finding 1 or 2 more 119

Exercise 1.3 Finding 1 or 2 less 120

Exercise 2.1 Understanding ‘fewer than’ 121

Exercise 2.2 Comparing by subtraction 122

Exercise 3.1 Word problems 124

Chapter 14 Handling Data

Exercise 1.1 Making, reading and interpreting a list or a table 126

Exercise 2.1 Making, reading and interpreting pictograms 128

Exercise 2.2 Understanding symbols in pictograms 130

Chapter 15 Numbers to 40

Exercise 1.1 Counting, reading and writing numbers within 40 132

Exercise 1.2 Writing numbers in different ways 134

Exercise 1.3 Showing tens and ones 136

Exercise 1.4 Estimating number of objects 137

Exercise 2.1 Finding more than and less than 138

Exercise 2.2 Number patter ns 139

Exercise 2.3 Reading number lines 140

Exercise 2.4 Comparing and ordering numbers using number lines 142

Exercise 2.5 Comparing and ordering numbers using place values 143

Chapter 16 Fractions

Exercise 1.1 Using fractions to describe one half and one quarter of a whole 150

Exercise 1.2 Finding one half and one quarter of a set 152

Exercise 1.3 Using fractions to describe halves and quarters of a whole or a set 154

Chapter 17 Doubles and Halves

Exercise 1.1 Finding doubles 156

Exercise 2.1 Finding halves 157

Chapter 18 Calendar and Time

Exercise 1.1 Naming days of the week 158

Exercise 1.2 Naming months of the year 159

Exercise 1.3 Writing the date 160

Exercise 2.1 Telling time to the hour 161

Exercise 2.2 Telling time to the half hour 163

Exercise 2.3 T ime of the day 165

Chapter 19 Numbers to 100

Exercise 1.1 Counting, reading and writing numbers in tens 167

Exercise 1.2 Numbers in tens and ones 168

Exercise 2.1 Finding more than or less than 170

Exercise 2.2 Number patter ns to 100 171

Exercise 2.3 Reading number lines 173

Exercise 2.4 Comparing and ordering numbers using number lines 175

Exercise 2.5 Comparing and ordering numbers using place values 176

Chapter 20 Money

Exercise 1.1 Naming coins 178

Exercise 1.2 Counting money 179

Exercise 1.3 Exchanging coins 180

Exercise 1.4 Counting money in different denominations 181

Exercise 1.5 Making up an amount of money 182

Exercise 1.6 Comparing amounts of money 184 Review 4 186

Numbers 0 to 10

Exercise 1.1 Counting, reading and writing numbers Recap 8 eight

1. Count and write the missing numbers.

2. Circle the correct number of objects.

7 cars b) 5 hats c) 0 flowers

8 bells

3. Count and match.

4. Draw the correct number of objects.

a) NINE flowers

b) FOUR oranges

c) SIX leaves

5. Write each number in words.

a) 0 b) 6 c) 3 d) 1

Exercise 1.2 Counting on and backwards

1. Count on. Trace the route.

2. Count on or backwards to write the missing numbers.

Exercise 1.3 Comparing number of objects by matching

Recap

Not all the objects in group C are matched.

Group C and group D do not have the same number of objects.

1. Do the groups have the same number of objects? Write Yes or No.

Group A has less. 4 is not equal to 5. 4 is less than 5.

1. Count and compare.

Group P has as many objects as group Q. 4 = 4 4 is equal to 4.

2. Circle the two groups that have equal number of objects.

3. Tick (✓) the correct number sentences.

a) 7 = 7 b) 8 = 6

c) 9 = 5 d) 2 = 2

e) 1 = 1 f) 3 = 8 g) 4 = 4 h) 6 = 5

Exercise 1.5 Comparing and ordering numbers

Recap

1. Circle the greatest number. Cross out the least number.

6 is the greatest number. 3 is the least number.

Arranging the numbers in order, beginning with the greatest: 6, 5, 3 (greatest)

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

a) 6, 2, 9

c) 0, 5, 7, 4

a) 3 0 8 b) 7 9 5 c) 2

b) 3, 5, 1

d) 9, 6, 2, 7

e) 3, 7, 8, 2 f) 1, 4, 0, 5

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

a) 7, 0, 4 b) 8, 5, 9

c) 2, 9, 0, 5 d) 3, 6, 1, 8

e) 6, 2, 4, 8 f) 4, 7, 0, 9 5 3 6