PR1ME Maths Programme Overview

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Proven to be the world’s best practice Based on top-performing Singapore, Republic of Korea and Hong Kong Complete coverage of the Cambridge Primary Mathematics curriculum

Supports learning 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 powered by offers a comprehensive, accessible suite of teaching, learning, practice and assessment resources with real-time data for flexibility in planning and instruction.

Programme Overview

TM

Proven pedagogy What teachers are saying

Our data clearly shows that PR1ME Maths works for our students. The end-of-year achievement results speak for themselves: 93% of our students are performing at or above the current expected curriculum level in mathematics.

– Franz Josef School

Mathematics is designed to specifically develop Critical thinking, Collaboration, Communication and Creativity. In building these 4Cs, Mathematics helps students and teachers grow in Confidence as they are motivated to learn and teach and to continue challenging themselves.

works for every student and teacher.

TM

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Why

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works

TM

Supports learning to mastery for all students because it incorporates a pedagogical framework and instructional design based on proven teaching and learning practices of global top-performing education systems

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Mathematics Framework is problem solving.

The central focus of the Learning progressions ensure focus and coherence in content using an instructional design that incorporates the Readiness-Engagement-Mastery model.

Learning experiences designed 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

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Integrates assessment for learning to enable every child to succeed: Formative and summative assessment tasks provide insights for effective teaching and learning

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Offers a comprehensive, accessible suite of teaching and learning resources for flexibility in planning and instruction, and learning

TM

Supports learning to mastery for all students

Learning experiences designed on the Readiness-Engagement-Mastery model 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.

READIN

Every student is a successful mathematics learner.

Learning Progression Principle

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MASTERY

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Think About It and Math Journal encourage development and communication of mathematical thinking. page 10

Consolidation of learning Assessment and Reviews provide summative assessment for consolidation of learning. page 17

Extension of learning Mind Stretcher, Create Your Own and Mission Possible immerse students in problem-solving tasks at various levels of difficulty. page 7

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Reflective review

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Practice book and digital practice exercises incorporate systematic variation for students to achieve proficiency and flexibility. page

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Motivated practice

M AS

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

Skill

Learning Progression Principle

Concepts

Learning Progression Principle

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Every lesson is designed to develop deep conceptual understanding and procedural fluency in every student.

READINESS Checking prior knowledge

Fractions

At the beginning of each chapter, 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.

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Let's Remember 1.

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Learning Progression Principle

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Complete the number line.

48

51

52

Write the missing numbers. a)

15 ÷ 3 =

d)

14 ÷

=7

b)

4×4=

e)

8×

= 24

c)

× 4 = 12

f)

÷ 2 = 10

Janice spent

1 1 of her salary on food. She gave of her 10 5

salary to charity. What fraction of her salary did Janice spend?

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

231

6

EN

s

c)

EXPLORE © 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

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Proc

ac

b)

47

Taking ownership of learning 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. page

Write the fraction of each shape that is shaded. a)

ENGAGEMENT This is the main phase of learning for which 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.

page 12

Gradual Release of Responsibility Concept lessons progress from teacher demonstration and shared demonstration to guided practice, culminating in independent practice and problem solving.

Teacher-led inquiry Purposeful questions provided in the Teacher’s Guide help teachers to encourage students to investigate and explain and reflect on their thinking. page 11

5

a) 47 – 25 =

.

40 and 6 is 40 + 6 =

TM

Suppose the number Supports is 10. learning to mastery for all students 2.

Add or subtract.

Stage 1: 10 + 20 = 30 b) 19 – 4 = c) 13 – 7 = a) 8 + 6 = Stage 2: 30 – 5 = 25 Stage 3: 25 + 20 = 45

Learning mathematics via problem solving 3.

Add or subtract. You may use the number track to help you.

81=– 45 = 36 65 – 14 d) 53 5– 33 =7 of8 learning 9 10 11 12 13 14 15it is16also 17 a tool for learning.

In Mathematics, problem solving is not only a6goal mathematics, The number is 36 more than 10. b) 11 – 2 =

a) 9 + 3 =

c) 5 + 8 + 3 =

10 + 36 = 46 Problem solving for She starts with the number 46. EXPLORE Mexico has 35 UNESCO World Heritage sites. productive struggle has 55 UNESCO World Heritage sites.

Compare the methods in steps 3Italy and 5.more How many UNESCO World Heritage sites does to develop resilience Italy have than Mexico?

Which method do you prefer? Why? At the beginning of each chapter,

can we solve this problem? f)5. Plus 78How – 71 = Discuss in your group and fill in columns 1 and 2.

e)2. Plan 96 – 62 =3. Answer Explore provides the opportunity 4. Check

to...

89 – 46 =

to engage prior knowledge in problem solving, leading to independent thinking and greater ownership of learning.

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

word problems involving addition and subtraction routine problem involving addition and subtraction 24

Throughout the chapter, students revisit the problem and persevere in solving it.

>> Look at EXPLORE on page 24 again.

Fill in column 3. Can you solve the problem now?

Chapter 2: Exercise 2.6

PB

63

>> Look at EXPLORE on page 24 again.

Can you solve the problem now?

What else do you need to know?

Unit 4 Subtracting Fractions

Concept development via problem solving

You will learn to...

• subtract fractions with the same denominator • subtract fractions with different denominators

4.1 Subtracting fractions with the same denominator Let's Learn

Mathematical problems are used as contexts for introducing concepts and to develop deep conceptual understanding.

a)

Elaine had 5 of a loaf of bread. She used 1 of the loaf to make 6

6

bread crumbs. What fraction of the loaf of bread was left?

5 and 1 are like fractions.

6 6

5 6

Concepts are introduced in Let’s Learn in each unit via problems.

1 6

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

Teachers lead students to investigate, explore, and find answers on their own.

6

5 1 4 – = 6 6 6 2 = 3

?

Both 4 and 6 can be divided by 2. ÷2

4 6

=

2 3

÷2

2 of the loaf of bread was left.

3 Remember to write your answer in its simplest form.

To subtract like fractions, subtract only the numerators.

The denominator remains the same.

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© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

c)

b)

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

n way.

My answer is correct.

There are 16 oranges in the basket.

Compare the methods in steps 3 an Which method do you prefer? Why

Develops a problem-solving mindset —students can extrapolate from what they know and apply their Let's Do knowledge of mathematics in a range of situations, Solve the word problems. Use or draw bar models to help you. including new and unfamiliar ones.Show your work clearly.

1. Understand

2. Plan

3. Answer

4. Check

5. Plus

Next, try solving each problem in a different way.

Which method do you prefer? Why?

Multiple opportunities for problem solving at varying levels of difficulty

1. Understand

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

1.

Students learn to solve problems by applying concepts, skills and processes learned to various problem situations both familiar and non-routine.

2. Plan

3. Answer

5. Plus

Mrs. Clark bought some pies.

She gave 43 away and had 5 pies left.

How many pies did she buy? ?

43

43

5

5=

Unit 4 Mrs. Problem Clark Solving bought

Each chapter ends with a problem-solving lesson.

4. Check

pies.

You will learn to…

• solve a non-routine problem on multiplication

5 1 of his 9 3 Let's Learn project on Tuesday. What fraction of his project did he complete altogether

Ken of his project on Monday. He completed another 4.1completed Mind stretcher

2.

Word problems

There are 10 sheep and chickens in a barn. on both days?

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.

The animals have 28 legs altogether.

How many sheep are there?

How many chickens are there?

Let's Practice

1U

Solve the word problems. Show your work clearly.

How many animals are there?

How many legs are there altogether?

nderstand

the problem.

3 of her room on Monday. She painted another Sonia painted What do I have to find?

1.

10

her room on Tuesday. On which day did she paint more?

Non-routine problems

1 of 5

2

1

2.

lan cut into 12 equal of A cake P was pieces.

Pam I can draw a picture to ate 3 pieces. Tina ate 3 what to do. the cake.

Who ate less? show the animals.

3.

Tony used

3A

5 1 of a roll of ribbon for a present. His sister used of the same 8 8 Draw 10 circles to represent 10 animals.

Work out the

roll of ribbon to make a bow. What fraction of the roll of ribbon did they nswer.

4.

Problem-posing tasks

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

use altogether?

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 persisting with challenging problems.

Suppose all the animals are chickens.

7 8

legs for everylong chicken. meter into two pieces. One piece Ali cut a piece of woodDraw that2was

was

1 meter long. How long was the other piece?

4 10 chickens have 20 legs.

PB

Chapter 11: Exercise 5.1

CREATE YOUR OWN Mr. Lewis painted of a wall red. His daughter painted of the same wall white. Was a greater fraction of the wall painted red or white?

Read the word problem. Write the missing fractions.

How did you decide what fractions to use?

Next, solve the word problem. Show your work clearly.

What did you learn?

262 MISSION POSSIBLE

Computational thinking tasks

Tucker has half of a symmetric figure drawn on a grid as shown below.

He wants to program a bot to help him complete the figure.

The bot will color the squares that it lands on.

8 7

Building on the mathematics concepts and skills learned, Mission Possible tasks introduce students to computational thinking, an important foundational skill in STEM education.

6 5 4 3 2 1 A

B

C

D

E

F

G

Help Tucker complete the instructions for the bot.

The bot should not return to a colored grid square.

Use grid references and words such as turn right and turn left.

Start at (D, 5).

Move forward -4813-20-4

7

unit(s) to (

,

).

129

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Mind stretchers are specially crafted problems that require students to solve them using heuristics and higher order thinking skills.

TM

Supports learning to mastery for all students Focus on the problem-solving method Mathematics explicitly teaches students to use various thinking skills and heuristics­— problem-solving strategies—to solve mathematical problems.

Heuristics in

Mathematics

Use a representation

• Draw a picture • Make a list • Choose an operation

Make a calculated guess

• Guess and check • Look for a pattern • Make a supposition • Use logical reasoning

Walk through the process

• Act it out • Work backwards

Change the problem

• Restate the problem in another way • Solve part of the problem

The bar model method The bar model method, a key problem-solving strategy in Mathematics, uses visual representation to help students understand and draw mathematical concepts to solve problems.

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.

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 formulas and abstract representations.

Arithmetic Problem

Algebraic Problem

8

Bar model virtual manipulatives on Math Pro allow students to build problem-solving skills.

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

Focus on the problem-solving process Uniquely designed UPAC+™ to develop flexible problem solvers A unique 5-step Understand-Plan-Answer-Check-Plus™ (UPAC+™) problem solving process that ensures students’ problem-solving efforts are consistently scaffolded and students develop critical and creative thinking skills.

The + in the UPAC+™ problem-solving process 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 alternative solutions.

1

2 3

4

NEW

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 • Solve the problem in another way.

• Compare the methods. Which method do you prefer? Why?

9

TM

Supports learning to mastery 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.

Communicating reasoning via Think About It

THINK ABOUT IT Sarah and David solve this problem in different ways.

5 1 + =?

8 8

In Think About It, carefully crafted questions based on common conceptual misconceptions or procedural mistakes are posed. Using question prompts as scaffolding, students think about the question, communicate their reasoning and justify their conclusions.

5+1=6 8 + 8 = 16 6 My answer is .

5+1=6 6 My answer is .

16

8

Sarah

David

Who is correct?

Why do you say so?

Who is wrong?

Why do you say so?

ng like fractions?

Think of a time in your daily life when you need to add fractions.

PB

252

Being able to reason is essential in making mathematics meaningful for all students.

10

Chapter 11: Exercise 3.1

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

What did you learn about addi

Thinking mathematically is developed as a conscious habit.

Date:

Name:

Date:

Math Journal

Math Journal

1.

Explain what multiplication means.

2.

Draw pictures to show 3 × 4.

3.

Write two related multiplication facts.

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-39-6 Current subscribers of PR1METM Mathematics Teaching Hub Grade 3 may print or photocopy this page for classroom use.

Math Journal tasks are designed for students to use the prompts to reflect on, express and clarify their mathematical thinking, and to allow teachers to observe students’ growth and development in mathematical thinking and reasoning.

Name:

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-38-9 Current subscribers of PR1METM Mathematics Teaching Hub Grade 2 may print or photocopy this page for classroom use.

Expressing mathematical thinking with Math Journal

Let's Practice 1.

Let's Practice

Write the missing numbers.

1.

Write three pairs of hundreds that make 1000.

2.

Show how you can subtract ones or tens from a 3-digit number with regrouping.

3.

Show how you can find half of a 3-digit even number.

a) There are 3 cars in each group.

130Bthrees to Task 1 requires students to count by find the total number of objects and complete Concept-based journaling tasks the multiplication sentences.

3×3=

153A

Let's Practice 1.

Write the missing numbers.

Process-based journaling tasks

a) There are 3 cars in each group.

Count by threes: 3, 6,

Task 2 requires studentsThere to count by threes to are cars altogether. complete the patterns.

9

3×3=

b) There are 3 flowers in each vase.

There are

1.2 Using dot cards

Count by threes: 3, 6,

9

9

cars altogether.

b) There are 3 flowers in each vase.

Teacher-led inquiry through purposeful questions

Let's Learn Objectives: • Observe the commutative and distributive Count by threes: 3, 6, , , 5×3= 15 Count by threes: 3, 6, 9 , 12 , 15 5×3= properties of multiplication Students learn through guided inquiry, a process during which teachers lead students to explore, investigate 15 There are flowers altogether.

There are flowers altogether.

• Relate two multiplication facts using and find answers on their own by posing purposeful ‘3questions.

Posing purposeful questions helps to assess and more’ or ‘32.less’ 2. Count by threes to complete the patterns.

Count by threes to complete the patterns.

12 , 15 , 18 6, 9, • Build up the multiplication table of 3, and advance students’ reasoning and sense making about important mathematical ideas anda) relationships. , 18 a) 6, 9, 24 , 27 , 30 b) 18, 21, commit the multiplication facts to memory ,

b) 18, 21,

, 30

PB

Let's Learn Round the numbers 43, 49 and 55 to the nearest ten.

43

40

49

50

55

60 3.2 Rounding numbers to the nearest ten

Resources:

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

3.2 Rounding numbers to the nearest ten

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

PB

a)

Chapter 10: Exercise 1.1

1.2 Using dot cards Materials: Let's Learn 1.2 Using dot cards • Dot Card F (BM10.1): a) There are 6 plates.

Let's Learn 1 copy per group, There are 3 pears on each plate.

How many pears are there altogether? a) There are 6 plates.

1 enlarged copy for demonstration 1 2 3 There are 3 pears on each plate.

1 • Dot Card G (BM10.2): 2 How many pears are there altogether?

We can use dot cards to help us.

3 4 The dot card shows 6 groups of 3.

1 copy per group, 1 2 3 5 6 3 1 enlarged copy21for demonstration 6 × 3 =us.

18 We can use dot cards to 6help 9 3 • Counters There 12 4 The dot card shows 6 groups ofare 3. 18 pears altogether.

5 6

Chapter 10: Exercise 1.1

3 6 9 12 15 18

15 18

195

3.2 Rounding numbers to the nearest ten 43 is between 40 and 50.

Let's Learn × 3 = 18 • CB: pp. 195–197 6There It is nearer to 40 than to 50.

Let's Learn are 18 pears altogether.

Objective: 43 is 40 when rounded to the nearest ten.

• PB: p. 127 a) Round the numbers 43, 49 and 55 to the nearest ten.Ask: How do we show 195 6 groups of 3 on the dot 43 ≈ 40 • Round a 2-digit or 3-digit number to the

43 49 55 card? (Put counters on 6 rows of the dot card.) (a) Stage: Concrete Experience Demonstrate how the counters are to be Draw 6 circles on the board and stick 50 40 60 placed on the dot card to show 6 groups of 3.

Resources: 3 counters in each circle.

49 is between 40 and 50.

43 is between 40 and 50.

Have students do the same.

• CB: pp.

14–15 It is nearer to 50 than to 40.

It is nearer 40 than toin 50. each Ask: How many counters are tothere 49 is 50 when rounded to the nearest ten.

43 is 40 when rounded to the nearest ten.

Say: Let us count the counters on the dot card.

• PB: p. 18 group? (3) How many groups are there? (6) 49 is approximately 50.

43 ≈ 40 49 ≈ 50 I round 43 to theThere nearest ten. are 3 counters in each row so we count 43 is approximately 40.

Say: We have 6 groups of≈ is 3thecounters.

55 is halfway between 50 and 60.

Vocabulary: approximation sign. by threes. 3, 6, 9, …, 18.

55 is approximately 60.

Take 60 to be the nearest ten.

• approximately 49 is between 40 and 50.

55 is 60 when rounded to the nearest ten.

Stage: Pictorial Representation Point to each row of counters as you count.

It is nearer to 50 than to 40.

• round 55 ≈ 60 Say: We can use a dot card torounded helptous find ten. the Ask: How many counters are there? (18) 49 is 50 when the nearest 49 is approximately 50.

49 ≈ 50 total number of counters. b) Round 197 to the nearest ten.

Say: 6 groups of 3 are 18. (a) Stage: Pictorial Representation 55 is halfway between 50 and 60.

Have 55 is approximately 60.

Take 60 to beDistribute the nearest ten. number line in (a) on CB p. 14students on the work in groups.

197 197 is Draw betweenthe 190 and 200.

Stage: Abstract Representation 55 is 60 when rounded to the nearest ten.

It is nearer to 200 than to 190. counters board but do not label ‘43’, ‘49’ and ‘55’. and a copy of55Dot ≈ 60 Card F (BM10.1) to 197 is 200 when rounded to the nearest ten.

Ask: What is the multiplication sentence to find each students to see that there are 10group. equal 190 200 b) Round 197 to the nearest ten.

197 ≈ Guide 200 6 groups of 3? (6 × 3 = 18) enlarged copy of Dot197Card F (BM10.1) intervals between 40 and 50 andStick eachan interval 197 is between 190 and 200.

Write: c) Round 805 to the nearest ten. is nearer to 200 than to 190. 6 × 3 = 18 on the board. Put counters on the three It197 circles for 1. 800 and 810. is 200 when rounded to the nearest ten.

805 isstands halfway between 805 Say: There are 18 counters altogether.

197 ≈ 200 the first line. row of the dot190card. 200 805 isInvite 810 when to the a rounded student to mark 43 on theinnumber nearest ten.

Round 805 to the nearest ten.

Say: 50.

There is 1 row of c)counters.

There are Say: 43 is between two tens—40 and 805 is halfway between 800 and 810.

800 810 805 805 ≈ 3 counters 1 group805of 3.when rounded to the is 810 Ask: How many intervals are there from 40 toin 1 row. I have shown Gathering information Making mathematics visible nearest ten.

43? (3) How many intervals are there from 43 to 810 800 810 805 ≈ To round a number to the nearest ten, look at the digit in the ones 50?

(7) Is 43 nearer to 40 or to 50?

(Nearer to 40) place. If it is 5 or greater, round up. If it is less than 5, round down.

nearest ten

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

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

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

Repeat the above procedure to show students

11

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

14

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

14

I round 43 to the nearest ten.

43 is approximately 40.

2021 Scholastic Education Ltd 978-981-4813-32-7 ISBN 978-981-4813-20-4 © 2021 Scholastic Education ©International (S) International Pte Ltd (S) Pte ISBN

≈ is the approximation sign.

(b) and (c) Stages: Pictorial and Abstract Representations Follow the procedure in (a).

Conclude that to round a number to the nearest ten, we look at the digit in the ones place. If it is 5 or greater, we round up. If it is less than 5, we Chapter 10: Multiplication Tables of 3 and 4

199

TM

Supports learning to mastery for all students

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 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 Digital Practices

Summative Assessment Objective: evaluating conceptual mastery and procedural fluency: Let’s Practice, Practice Book Exercises, Digital Assessments

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. Throughout the activity, the teacher observes what the students say and do and provides feedback to students.

Unit 3 Adding Fractions Concrete Students use virtual 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.

You will learn to...

• add fractions with the same denominator • add fractions with different denominators

3.1 Adding fractions with the same denominator Let's Learn a)

Diana ate 3 of a pizza. Peter ate 5 of the same pizza.

10

10

What fraction of the pizza did they eat altogether?

3 and 5 have the same denominator.

10 10

They are called like fractions.

3 10 5 10

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.

3 10

5 10

5 8 3 + = 10 10 10 4 = 5

Both 8 and 10 can be divided by 2. ÷2

8 4 = 10 5 ÷2

Abstract Once conceptual understanding is developed, students learn to represent the concept using numbers and mathematical symbols.

They ate 4 of the pizza altogether.

5

Fractions with the same denominator are called like fractions.

To add like fractions, add only the numerators. The denominator remains the same.

250

12

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

?

The CPA approach to mathematics instruction and learning enables students to make and demonstrate mathematical connections, making mathematical understanding deep and long-lasting. b)

Add 2 and 7 .

Concrete-Pictorial-Abstract approach in formative assessment 9

9

2 9

1.

Add. Write each answer in its simplest form. b)

1 4 + = 7 7

Let's Practice Add. Write each answer in its simplest form.

c)

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

Add 2 and 7 .

9

2 5 + 8 8

7

7 1 + 10 10

9 2 7 Let’s Practice, Practice Book Exercises and Digital Practices + = 9 9 9 help students to transition their understanding of concepts from = ?

4 6 e) + 14 14 pictorial to abstract levels.

Let's Do 2 ninths and 7 ninths make 1 whole.

Add. Write each answer in its simplest form. b) +

+

1 4 + = 7 7

Recap 2 9

Let's Practice

b)

1 2 + 3 3

2 3 5 + = 9 9 9

c)

7 1 + 10 10

d)

6 3 + 12 12

When adding fractions with the same denominator, add only the numerators.

The denominator remains the same.

1.

Add. Write each answer in its simplest form. a)

4 6 + 14 14

f)

6 1 + = 8 8

2 3 + 20 20 2.

Coursebook Let’s Practice

6 3 + 12 12

ASSESS with a unique framework that incorporates C-P-A 2 3 approach to evaluate f) + 20 20 student’s level of conceptual understanding

DIAGNOSE each student’s level of conceptual understanding and progress in real time to eliminate learning deficit

b) +

e)

d)

with timely, actionable insights and recommendations to reduce gaps by tailoring each lesson just right for all students

?

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-27-3

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

2 5 + 8 8

1 2 + 3 3

REMEDIATE

3 9

Add. Write each answer in its simplest form. a)

b)

Exercise 3.1 Adding fractions with the same denominator

2 1 + = 6 6 6

=

1.

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Practice Book Exercises

Digital Practice based on the Pictorial and Abstract Framework

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Supports learning to mastery for all students

Focused and coherent curriculum based on learning progression principles Coherent framework, spiral curriculum Singapore’s Mathematics Curriculum Framework is at the center of the curriculum design of Mathematics. The framework stresses conceptual understanding, skills proficiency and mathematical processes and duly emphasizes metacognition and attitudes. It also reflects the 21st century competencies.

Learning Progression Principle

Mathematics has a focused and coherent content framework and developmental continuum in which higher concepts and skills are built upon the more foundational ones.

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The careful spiral sequence of successively more complex ways of reasoning about mathematical concepts ­— the learning progressions ­— makes the curriculum rigorous and effective for all learners.

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Deep focus on fewer topics builds a strong foundation.

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Learning Progression Principle

3

Sequencing of learning objectives within a topic across grades is based on a mathematically logical progression.

For example, learning of fractions is connected across grades. In grade 1, students learn to identify halves and quarters. In grade 2, the concept of fractions is extended to other proper fractions. In grade 3, equivalent fractions are introduced and students apply the knowledge of equivalent fractions to addition and subtraction of fractions.

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. For example, in grade 1, telling time to the half hour is taught after the fractions chapter to reinforce the concept of halves and allow students to make connections between the two topics.

15

TM

Assessment for learning Mathematics enables every child to succeed by integrating formative and Unit 5 Dividing by 5independent learning. summative assessments with instruction for effective teaching and You will learn to…

• divide numbers using the multiplication table of 5

Formative assessment

5.1 Dividing by 5

Let's Learn interactive process by which teachers Formative assessment is a vital part of the ongoing, gather immediate insight about students’ learning inform and support their teaching.

Divide 15 to books into 5 stacks.

Let’s Do

This task assesses students’ understanding

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.

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There are

books in each stack.

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Divide. Use the related multiplication facts to help you. a)

2. © 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-19-8

This task assesses students’ understanding at the abstract level.

15 ÷ 5 = 3 at the pictorial and abstract 5 × levels. = 15

b) 4 × 5 = 20

7 × 5 = 35

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Complete the related multiplication and division facts. a)

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Recap provides a pictorial and abstract 5 × 5 = 25 representation of the concrete activity 25 ÷ 5 = 30 ÷ 5 = carried out in the class.

6 × 5 = 30

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 formative and diagnostic assessment providing essential information to students and teachers on learning progress.

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

16

167

Readiness-Engagement-Mastery model of instructional design

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on the method required to solve the problem, and the problem-solving process.

Teacher’s Guide

• Advocates active learning and adaptivity with self reflection tools and scaffolded thinking processes.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

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

TM

TM

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Teacher’s Guide 2

• Uses technology to enrich the learning and teaching experience with interactive content for whole-class teaching, extensive resources for teachers and diagnostic practice and assessment for students.

• Promotes creative thinking and critical thinking by encouraging learners to innovate and craft alternative solutions to mathematical problems.

For Teachers

TM

TM

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

2

TM

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

Mathematics is based on a pedagogical approach and instructional design that:

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

2

TM

Practice Book in 2 parts

Teacher’s Guide

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

Coursebook in 2 parts

Practice Book in 2 parts

For Students

Teacher’s Guide in 2 parts Interactive Whiteboard

Helping Children Around the World to Read and Learn

For over 90 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

ON EDITI

100% coverage of Cambridge Primary Mathematics Curriculum Framework

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• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

Teacher’s Guide in 2 parts Interactive Whiteboard

Helping Children Around the World to Read and Learn

NEW

I SBN 981- 07- 3291- 0

www.scholastic.com

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

Mathematics is based on a pedagogical approach and instructional design that:

centered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

Practice Book

1A Teacher’s Guide

Coursebook in 2 parts

Teacher’s Guide in 2 parts Interactive Whiteboard

Helping Children Around the World to Read and Learn For over 90 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

TM

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and

A world-class program incorporating the highly effective the problem-solving process.

Readiness-Engagement-Mastery model of instructional design • Is effective, measurable and diagnostic with a learner-

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

1B Practice Book

Practice Book in 2 parts

Scholastic

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

Mathematics is based on a pedagogical approach and instructional design that:

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

1A Coursebook

Coursebook in 2 parts

2

TM

Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

Scholastic

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and the problem-solving process.

Coursebook

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

TM

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Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

TM

Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

TM

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

Scholastic

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and the problem-solving process.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

www.scholastic.com

Focus on Computational Thinking and Math Journaling Builds a Strong Foundation for STEM

Coursebook

I SBN 981- 07- 3064- 0

For over 90 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

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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

Digital

NEW EDITION

Summative assessment Helping Children Around the World to Read and Learn

For 100 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

ON EDITI NEW

ISBN 978-981-4813-32-7

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

Enhanced support for effective implementation of Readiness-Engagement-Mastery pedagogy Digital PR1ME Mathematics Teaching Hub for additional teaching resources and online professional development

Reviews

Review 2 1.

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

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Digital Assessment Digital Assessment provides topical, cumulative and progress monitoring assessments for evaluating fluency, proficiency and for benchmarking throughout the year.

Systematic and regular summative assessments include one after every chapter, two mid year and one end of year assessment help students review what they have learnt.

Chapter assessment

Half-yearly assessment

Quarterly assessment

17

Valuable learning insights and reports in Math Pro Auto-generated reports 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.

Math Pro Teacher Dashboard Accessible on teacher dashboard and at every point of use, learning insights and reports help educators monitor trends and quickly find and address learning gaps and gains.

Identify students’ strengths and weaknesses Access class math wellness at a glance through the class proficiency band.

18

Track Progress and Reports in Math Pro Stay one step ahead with real-time data and reports to ensure that teachers can always make timely decisions, even as they are teaching.​

Monitor progress Student performance is presented in easy to view format for every practice and assessment available.

Teachers can track individual student and class performance and progress at the click of a button.

The practice reports inform teachers about individual students’ Level of Understanding (LU).

Critical Insights give actionable insights to address gaps in learning.

When instruction is informed by insights from assessment, students are more engaged and take greater ownership of their learning.

19

Comprehensive suite of teaching and learning resources A comprehensive range of resources for grades K to 6 to support teaching, learning, practice and assessment in a blended, print or digital environment provides flexibility in planning and instruction, and learning.

STUDENT resources

Print Materials

10mm

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Student Books in 2 parts

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• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

Teacher’s Guide

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For over 90 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

EDITION

100% coverage of Cambridge Primary Mathematics Curriculum Framework Focus on Computational Thinking and Math Journaling Builds a Strong Foundation for STEM

For 100 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

Practice Book in 2 parts

Helping Children Around the World to Read and Learn

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Helping Children Around the World to Read and Learn For over 100 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

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For over 90 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

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Helping Children Around the World to Read and Learn

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Helping Children Around the World to Read and Learn For 100 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

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100% coverage of Cambridge Primary Mathematics Curriculum Framework

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Helping Children Around the World to Read and Learn For over 90 years, teachers and parents have recognized Scholastic as a trusted name in learning. Scholastic continues this successful history by remaining focused on encouraging children to learn to read and love to learn, helping teachers carry out their important jobs and supporting parents in their role as their child’s first teacher.

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Mathematics

Scholastic Mathematics K is an innovative Mathematics program focused on the development of early numeracy and problem-solving skills, based on the effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong.

Scholastic Mathematics K is based on a pedagogical approach and instructional design that:

Student Books in 4 parts

Scholastic Mathematics K is an innovative Mathematics program focused on the development of early numeracy and problem-solving skills, based on the effective Helping Childrenpractices Aroundofthe Read and Learn teaching and learning theWorld globaltotop-performers in Mathematics – Singapore, Republic of Korea and Hong Kong.

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Student Books in 2 parts

in 4 parts

10mm

Practice Book in 2 parts

Teacher’s Guide in 2 parts Interactive Whiteboard

Student Book

Scholastic

Mathematics on the development of early numeracy K is an innovative Mathematics teaching and and problem-solving program focused learning practices Republic of Korea skills, based of the global on the effective top-performers and Hong Kong. in Mathematics – Singapore,

Mathematics Book A Part 1

program focused Mathematics on the effective K is an innovative skills, based Mathematics and problem-solving in Mathematics – Singapore, Scholastic of early numeracy top-performers on the development practices of the global learning teaching and and Hong Kong. approach and Republic of Korea a pedagogical K is based on Mathematics to pictorial Scholastic from concrete design that: instructional as children progress and numbers. models, drawings conceptual understanding to work • Builds deep using manipulatives, encouraged to abstract thinking skills, with students and collaboration and reflect on their understanding. metacognition age• Develops discover, explain of concepts to activities and together on the application Readers. mindset through of engaging Big Books and problem-solving via a series • Creates a real-world scenarios Problem Solving appropriate parts Readers in 4 Teacher’s Guides

Teacher’s Guide

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

Student Books

Coursebook in 2 parts

Mathematics K

centered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

5 Teacher’s Guide

5 Coursebook

1B Practice Book

Practice Book in 2 parts

Mathematics

Practice Book

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

to Read

Coursebook in 2 parts

Part 2

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

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

Mathematics is based on a pedagogical approach and instructional design that:

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and

A world-class program incorporating the highly effective the problem-solving process.

Readiness-Engagement-Mastery model of instructional design • Is effective, measurable and diagnostic with a learner-

Mathematics is based on a pedagogical approach and instructional design that:

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and the problem-solving process.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

Student Book

Scholastic

Helping Children Around the World to Read and Learn

Book A

5

Coursebook

Teacher’s Guide in 2 parts Interactive Whiteboard

Student Book A Part 1

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

Practice Book in 2 parts

Student

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

Mathematics is based on a pedagogical approach and instructional design that:

Student Book

5

TM

TM

Coursebook in 2 parts

K

TM

TM

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Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

Scholastic

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and the problem-solving process.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

For Students

Teacher’s Guide in 2 parts Interactive Whiteboard

Helping Children Around the World to Read and Learn

Teacher’s Guide A

• Uses technology to enrich the learning and teaching experience with interactive content for whole-class teaching, extensive resources for teachers and diagnostic practice and assessment for students.

• Promotes creative thinking and critical thinking by encouraging learners to innovate and craft alternative solutions to mathematical problems.

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

Teacher’s Guide

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

Practice Book in 2 parts

Teacher’s Guide in 2 parts Interactive Whiteboard

Mathematics

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

1A Teacher’s Guide

1A Coursebook

Coursebook in 2 parts

www.scholastic.com

Practice Book in 2 parts

Helping Children Around the World to Read and Learn

K

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

Mathematics is based on a pedagogical approach and instructional design that:

centered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

ISBN 978-981-4781-36-7

Coursebook in 2 parts

Teacher’s Guide in 2 parts Interactive Whiteboard

Mathematics

Practice Book

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

• Creates a problem-solving mindset through the application of concepts to ageappropriate real-world scenarios via a series of engaging Big Books and Readers.

Mathematics K

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

www.scholastic.com

Practice Book in 2 parts

Teacher's Guide A

• Develops metacognition and collaboration skills, with students encouraged to work together on activities and discover, explain and reflect on their understanding.

jobs and supporting parents in their role as their child’s first teacher.

Coursebook in 2 parts

Mathematics K

Teacher’s Guide

• Builds deep conceptual understanding as children progress from concrete to pictorial to abstract thinking using manipulatives, models, drawings and numbers.

• Advocates active learning and adaptivity with self reflection tools and scaffolded thinking processes.

K

TM

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and

A world-class program incorporating the highly effective the problem-solving process.

Readiness-Engagement-Mastery model of instructional design• Is effective, measurable and diagnostic with a learner-

Mathematics is based on a pedagogical approach and instructional design that:

TM

Scholastic

TM

TM

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and the problem-solving process.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

TM

Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

1

TM

Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

Scholastic

TM

1

Coursebook

TM

1

TM

• Develops metacognition in learners enabling them to monitor, direct and communicate their thinking process.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Uses technology to deliver interactive instructional content to facilitate whole-class teaching.

Mathematics is based on a pedagogical approach and instructional design that:

Mathematics

For Teachers

TM

TM

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

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

Mathematics is based on a pedagogical approach and instructional design that:

Teacher’s Guide 1

• Uses technology to enrich the learning and teaching experience with interactive content for whole-class teaching, extensive resources for teachers and diagnostic practice and assessment for students.

TM

TM

TM

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

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A world-class program incorporating effective Scholastic Mathematics K is basedthe on ahighly pedagogical approach and instructional design that: Readiness-Engagement-Mastery model of instructional design

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TM

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Scholastic Mathematics is a forward-thinking and innovative mathematics program based on the curriculum standards and effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong. It is adapted from the highly-acclaimed and widely-proven PRIMARY MATHEMATICS Project developed by the Ministry of Education, Singapore.

Scholastic

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

• Incorporates professional learning into the curriculum framework to develop the pedagogical content knowledge of educators to improve classroom practices.

• Promotes creative thinking and critical thinking by encouraging learners to innovate and craft alternative solutions to mathematical problems.

A world-class program based on top-performing Singapore, Republic of Korea and Hong Kong

Scholastic

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on both the method required to solve the problem, and the problem-solving process.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

TM

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on the method required to solve the problem, and the problem-solving process.

Teacher’s Guide

• Advocates active learning and adaptivity with self reflection tools and scaffolded thinking processes.

• Is effective, measurable and diagnostic with a learnercentered and teacher-directed approach designed to enable assessment of understanding of concepts and mastery of skills at every step of concept development and learning.

Scholastic Mathematics K is an innovative Mathematics program focused on the development of early numeracy and problem-solving skills, based on the effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong.

Scholastic Mathematics (New Edition) is a proven core program that now offers 100% coverage of the Cambridge Primary Mathematics Curriculum Framework. Based on research and feedback from educators, the effective Readiness-Engagement-Mastery instructional design of the first edition is further strengthened and new features ensure a strong foundation for STEM.

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

Mathematics K

Scholastic

• Teaches via problem solving through the systematic development of problem-solving skills and by focusing on the method required to solve the problem, and the problem-solving process.

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

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A world-class program incorporating the highly effective Readiness-Engagement-Mastery model of instructional design Scholastic Mathematics (New Edition) is a proven core program that now offers 100% coverage of the Cambridge Primary Mathematics Curriculum Framework. Based on research and feedback from educators, the effective Readiness-Engagement-Mastery instructional design of the first edition is further strengthened and new features ensure a strong foundation for STEM.

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Comp ehens ve esson p ans suppo o each esson n he Cou sebooks

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A single, comprehensive ecosystem for all your mathematics teaching and learning needs.

Embedded Professional Learning & Lesson Preparation Resources in the PREPARE mode are designed to build teacher knowledge and make lesson planning quick and easy, so that you can help every student can achieve mastery in mathematics.

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Motivation for Mastery

Pro Tools in Math Pro aid teachers in their everyday teaching and best support their learners to set them up for success.

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Pro Tools for Effective, Engaged Teaching

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Rewards and incentives in recognition of effort and progress foster positive behavior and mindset to ensure students continuously strive and thrive.

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Valuable Learning Insights & Reports​ Accessible on teacher dashboard and at every point of use, learning insights and reports help educators monitor trends and quickly find and address learning gaps and gains.

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World Class Pedagogy ​ & Blended Curriculum Scholastic Math Pro incorporates PR1ME Mathematics, the core curriculum proven to be world’s best practice in mathematics, to deliver top-notch seamless blended learning experiences to your students.​

23

Connected Teaching ​ & Learning​ In Math Pro, checks for readiness, on-going formative and summative assessments are integrated with instruction, so that teachers are always one step ahead with accurate data to target those who need intervention.

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Resources to support at every step of teaching

Instructional support for effective teaching Mathematics provides extensive support at point of use to support teacher development along with student learning, making teaching mathematics a breeze.

Teaching Hub in Math Pro This one-stop teacher’s resource center provides all the resources you will need to transform your teaching experience.

With the Teaching Hub, you can: Plan and prepare for lessons with lesson notes from the Teacher’s Guide, Access all content from the Coursebook and Practice Book to plan or teach a lesson on screen, View and share lesson demonstration videos during class time, and Access extra lessons to address learning objectives for regional curricula and view journal tasks.

The Teaching Hub on Math Pro 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.

The Interactive Whiteboard embedded within the Teaching Hub provides teachers with ways to make lessons interactive and helps to facilitate formative assessment during lessons. Teachers can explain concepts with the use of concept videos, virtual manipulatives and other point of use Pro tools.

Teachers can review real-time data to dive into details of students’ abilities and understanding of different topics, chapters or concepts.

Virtual manipulatives allow teachers to explain concepts and demonstrate concrete activities for deep conceptual understanding. Students can also access them to practice and work independently to strengthen concepts.

To address the learning needs of local curricula, additional lessons and resources are available for download in the Teaching Hub. These lessons and resources can be used to supplement teaching out of the print Coursebook and Practice Book.

24

Every mathematics teacher is a master teacher.

Teacher’s Guide developmental Continuum

A comprehensive Teacher’s Guide, available in print and digital format, provides complete program support including:

Teachers can use the Developmental Continuum to understand the links between learning objectives within and across strands and grade levels. It provides a useful overview of prior, current and future learning objectives. Teachers will observe how new learning is built on prior learning across the grades and how each topic forms the foundation for future learning.

Grade 2

Unit 3: Adding Fractions

Grade 3

Developmental continuum, Scheme of Work, Detailed notes for each lesson in the Coursebook,

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-32-7

Answers for practice tasks in the Coursebook and Practice Book, and Reproducibles for class activities.

BM11.2 Fraction Cut-outs 2

Count within 100.

Count within 100.

Count within 1000.

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

Read and write a number within 100—the numeral and the corresponding number word.

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

Recognize conservation of numbers.

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

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

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 ones, tens or hundreds more than or less than a given number within 1000.

Estimate the number of objects in a group of less than 40 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, tens or hundreds within 1000.

Find the number which is 1, 2 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, tens or hundreds within 1000.

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

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

Compare and order numbers within 1000.

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

Read and place numbers within 100 on a number line.

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

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

Use grouping in twos, fives and tens to count groups of up to 100 objects.

Read and place numbers within 1000 on a number line.

Recognize odd and even numbers within 20 by skip counting.

Identify if a group has an odd or even number of objects.

Give a number between two 3-digit numbers.

Read and place numbers within 100 on a number line.

Compare and order numbers within 100.

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

Give a number between two neighboring pairs of tens within 100.

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

Round a 3-digit number to the nearest hundred.

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-33-4

Chapter 11: Fractions

Chapter 11: Fractions

3 10 5 10

Vocabulary: • like fractions

3 10

(a) Stage: Concrete Experience Have students work in groups. Distribute fraction circles to each group.

Write the word problem in (a) on CB p. 250 on the board. Have students read the word problem.

Ask: What fraction of the pizza did Diana eat?

3

Have students show 10 using the fraction circles.

5 10

?

5 8 3 + = 10 10 10 4 = 5

Both 8 and 10 can be divided by 2. ÷2

8 4 = 10 5 ÷2

They ate 4 of the pizza altogether.

5

Fractions with the same denominator are called like fractions.

To add like fractions, add only the numerators. The denominator remains the same.

250

Ask: What fraction of the pizza did Peter eat? ( 10 )

5

Have students show 10 using the fraction circles.

Ask: What do we have to find? (The fraction of the pizza the two children ate altogether) How do we find the fraction of the pizza the two children ate altogether? (Add the two fractions by combining the fraction circles.)

3

Have students combine the fraction circles ( 10 5

and 10 ).

Ask: What fraction of the pizza did the two children eat? ( 10 ) Stage: Pictorial Representation Draw the fraction bar in (a) on the page on the board and relate it to the fraction circle. Guide students to see that we can find the fraction of the pizza that was eaten by counting the number of shaded parts.

Say: From the fraction bar, we can tell that the 3 5 8 sum of 10 and 10 is 10 .

Stage: Abstract Representation 3 5 8 Write: 10 + 10 = 10 8

Ask: Is 10 in its simplest form? (No) How can 8 we express 10 in its simplest form? (Divide the 8 numerator and denominator of 10 by 2.)

3 5 8 Write: 10 + 10 = 10 4 =5

4

Say: The two children ate 5 of the pizza altogether.

3 5 Have students observe that 10 and 10 have the same denominator and introduce the term ‘like fractions’.

Say: To add like fractions, add only the numerators. The denominator remains the same.

Strand: Numbers and Operations

Chapter 11: Fractions

Scheme of Work

241

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

Objectives • Recognize and name proper fractions • Place whole numbers up to 100 on a

Materials PINE TG3 ch11.indd 241

*Resources

Vocabulary 05/11/20 6:53 PM

Lesson notes

• CB: p. 231

number line

• Multiply and divide numbers within

multiplication tables

Unit 1: Fraction of a Whole 1.1 Making a whole

• Find the fraction that must be added to

• 1 enlarged copy of Fraction

• CB: pp. 232–233 • PB: p. 164 • Digital Practice

1.2 Comparing and ordering fractions with the same numerator or denominator

• Compare and order unit fractions

• Fraction Cut-outs 2 (BM11.2):

• CB: pp. 234–237 • PB: p. 165 • Digital Practice

a given fraction to make a whole

• Compare and order fractions which

have a common numerator or denominator

1 1.3 Using benchmark • Use 0, 2 and 1 as benchmark fractions fractions

Cut-outs 1 (BM11.1)

1 copy for demonstration, 1 copy per pair of students

• Fraction Cut-outs 3 (BM11.3):

• 2 copies of Fraction Bars 1

(BM11.5) per student (BM11.6) per student

05/11/20 6:53 PM

© 2021 Scholastic Education International (S) Pte Ltd

• common

denominator

• common

numerator

3 copies for demonstration, 3 copies per pair of students • Fraction Cut-outs 4 (BM11.4): 1 copy for demonstration, 1 copy per pair of students • 3 markers of different colors

• 1 copy of Fraction Bars 2

• CB: pp. 238–239 • PB: p. 166 • Digital Practice

ISBN 978-981-4813-33-4

Scheme of Work

Professional Learning Now! 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.

25

10

3 and 5 have the same denominator.

10 10

3

224

PINE TG3 ch11.indd 224

Reproducible

10

What fraction of the pizza did they eat altogether?

They are called like fractions.

8

Let’s Remember

06/11/20 9:58 AM

Diana ate 3 of a pizza. Peter ate 5 of the same pizza.

5

Unit

Blackline masters

• add fractions with the same denominator • add fractions with different denominators

Resources: • CB: pp. 250–252 • PB: pp. 173–174

( 10 )

Developmental Continuum

PINE TG3 BLM.indd 328

You will learn to...

3.1 Adding fractions with the same denominator Let's Learn a)

Materials: • Fraction circles

T17

328

Unit 3 Adding Fractions

3.1 Adding fractions with the same denominator Let's Learn Objective: • Add like fractions with a sum within 1 whole

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-33-4

Whole Numbers / place Value

© 2021 Scholastic Education International (S) Pte Ltd ISBN 978-981-4813-20-4

Grade 1

Numbers aNd OperaTiONs

Mathematics

Why

Mathematics K works

Scholastic Mathematics K is the foundation level of Mathematics, an innovative world-class mathematics program based on the effective teaching and learning practices of global top performers in Mathematics. The program focuses on the development of early numeracy and problem-solving skills to build a strong foundation for meaningful learning and to develop a problem-solving mindset.

Scholastic Mathematics K follows a consistent and structured implementation model which embeds Singapore’s mathematics pedagogy in its instructional design.

These effective pedagogical practices are:

Learning Mathematics via Problem Solving

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Formative and Summative Assessment Integrated with Instruction

Opportunity for Development & Communication of Mathematical Thinking

Concepts Readiness-Engagement-Mastery Model in Instructional Design Learning Mathematics

by Doing Mathematics

24

Laying a strong foundation for numeracy for all students number of dots on their cards. Have pairs compare the number of dots on their cards using ‘more than’, ‘fewer than’ and ‘the same as’, which are terms students have already encountered. Have students raise their hands as you ask the following questions.

• Who has more dots than their friend?

• Who has fewer dots than their friend?

• Who has the same number of dots as their friend?

Explain that students will now compare numbers. Introduce ‘greater than’, ‘less than’ and ‘equal to’ and tell students that we use these terms to compare numbers. Have them look at their Number-Dot Cards.

Learning mathematics via problem solving

Ask which students have more dots than their partner. Have them read out the number on their NumberDot Card as well as the number on their partner’s Number-Dot Card. Explain how ‘greater than’ is connected to ‘more than’.

Say: has more dots than . We can also say that has a greater number of dots than (e.g. 11) is greater than (e.g. 8). , or that Have those students with more dots than their partner compare their numbers with their partners'. Use the same procedure to connect ‘fewer than’ to ‘less than’ and ‘the same as’ to ‘equal to’. If there are no pairs with the same number of dots, show students Number-Dot Cards with the same number of dots, e.g.

Number-Dot Card ‘12’.

Say: Both of these cards have the same number or an equal number of dots.

Activities throughout the program are designed to support problem solving.

New concepts are always introduced with a hands-on activity. An inquiry-based Observe: NOTE: When comparing sets of objects, we use approach students to explore, investigate, ask questions and find answers.

• Do leads students have difficulty identifying numbers? ‘greater than’, ‘less than’ and ‘equal to’ to compare •

If so, which numbers?

Do students understand ‘greater than’, ‘less than’ and ‘equal to’?

numbers, e.g. Group A has a greater number of apples than Group B. (We would not use ‘greater than’ for countable nouns, e.g. ‘10 apples is greater than 5 apples.’ would be incorrect.)

Chapter Workout Look and talk.

Let’s Learn SB p. 148

Purposeful questions in the Teacher’s Guide help the teacher guide the inquiry process.

Count and say.

1. Compare and write. (a) Circle the set that has more.

12

© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-4781-37-4

Let’s Do

Belle

Bob

Helicopter

© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-4769-02-0

King

© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-4769-02-0

10

Direct students to the numbers on the cats T-shirts and compare the numbers. Ask questions like the following.

• Which number is greater than 12?

• Which number is less than 12?

is greater than

9

.

(b) Circle the set that has fewer.

is less than

11 .

2. Circle the sets that have an equal number of cubes.

8

SB p. 149

© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-4769-02-0

Refer students to the picture on SB p. 148.

Ask questions like the following.

• Who has more toys, King or Belle?

• Who has fewer toys, Bob or Helicopter?

• Which 2 cats have the same number of toys?

8

Task 1 provides practice for students to count and compare the number of objects in groups of up to 15 objects as well as compare the respective numbers using 'greater than' and 'less than'.

Task 2 requires students to circle the sets with the same number of objects.

Chapter Workout appears at the end of each chapter for teachers to guide students to apply what they have learned to solve problems in real-world context.

57

Daily Wrap-Up Reteach

Refer students to the Number Tape they created. Ask: • Which numbers are greater than 10? (11, 12, 13, 14, 15) • Which numbers are less than 5? (0, 1, 2, 3, 4)

Give each pair of students a stick of 10 connecting cubes.

Have them make two other sticks of cubes, one with more and the other with fewer cubes than the stick of 10 cubes.

Each chapter ends with a problem solving lesson using the Problem Solving Kit. Lesson 1: Numbers to 15

167

Each problem solving lesson is built around a story. As students engage with the story and encounter mathematical problems, learning is consolidated in a meaningful context and conceptual understanding is deepened. The problem solving tasks provide opportunities for students to apply learning and to communicate their thinking.

15 mins

There are 8 chocolate cupcakes.

Oh, and 8 strawberry cupcakes!

You knew?

Yes, 8 vanilla cupcakes too!

Learning Center Activities

The stories and accompanying small group, pair and independent learning center activities encourage rich discussion and communication of mathematical ideas and thinking.

Materials and Resources: • Picture Graph (TR 3.1), 1 copy per pair

Materials and Resources: • Sorting and Comparing (TR 3.2), 1 copy per student • 20 teddy bear counters (10 each of 2 different colors), 1 set per pair

Activity 1 Prior to the lesson, prepare different graphs (one for each pair) based one of the following questions. Draw a simple picture for each category.

• What is your favorite flavor of cupcake? Banana, strawberry or apple?

• What is your favorite sandwich filling? Egg, tomato or cheese?

• What is your favorite sport? Swimming, basketball or soccer?

Then, have pairs conduct a survey from 8 students.

Partners will ask the question to their friends and draw the picture or put a tick in the correct box in the Picture Graph (TR 3.1) based on their answers.

Have students share the results of their survey question.

Ask: • What was the question you asked your friends? Were you surprised by the information you collected? Explain your thinking.

• What else can you tell us about your graph? (E.g. More friends like to swim than to play soccer./The same number of friends like basketball and soccer.)

Activity 2

Materials and Resources:

Activity 3

•

Distribute a copy of Favorite Muffin Flavor (TR 3.3) to students and read the directions with students.

Have students write the total for each type of muffin and to indicate which type of muffin has more or fewer. Explain to students when done, they are to share their work with a partner.

Favorite Muffin Flavor (TR 3.3), 1 copy per student

Wrap up

10 mins

3

Distribute a copy of Sorting and Comparing (TR 3.2) to each student and a set of teddy bear counters to each pair.

Students take turns to randomly choose a counter from the bag. Each student chooses 10 times and then, sorts the chosen counters by color on his/her workmat.

Explain to students when done, they are to share what they notice about the number of counters in each circle on their workmat. (E.g. I have more red counters than blue counters./I have 8 red counters and 2 blue counters./I have the same number of red and blue counters.)

25

Have students think about what they learned about sorting and graphs. (E.g. You can sort by color./Sorting helps you show information in a picture graph.)

6

© 2018 Scholastic Education International (S) Pte Ltd ISBN 978-981-4769-65-5

Consolidate and Assess

Mathematics

Laying a strong foundation for numeracy for all students

Opportunities for development and communication of mathematical thinking Activity 1

Think, turn and talk.

Students are encouraged to communicate their ideas, clarify their thoughts and share their thinking to develop mathematical thinking skills throughout the program.

3rd

The yellow teddy bear is first.

The red teddy bear is first.

© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-4769-02-0

As they solve non-routine and open-ended problems, students explain and reflect on their answers. They are encouraged to discuss their solutions, think aloud and reflect on what they are doing.

Belle

King

Who is right?

Why?

5

Learning mathematics by doing mathematics The activity-based Concrete-Pictorial-Abstract approach is a key instructional strategy advocated in the Singapore approach to mathematics learning.

Authentic mathematical experiences in Scholastic Mathematics K to manipulate concrete materials help students relate mathematics to the real world and understand relationships between numbers and their representations.

Concepts in Let’s Learn are taught using the Concrete-Pictorial-Abstract approach to develop deep conceptual understanding. This approach is introduced in grade K and consistently applied in grades 1 to 6.

Lesson 1

Put Together

Add and write. (a)

Count all.

1, 2, 3, 4, 5.

3 ducks stand.

2 ducks sit.

Concrete Hands-on tasks suggested in the Teacher’s Guide allow students to explore, investigate and participate in concrete mathematical experiences.

There are altogether.

ducks

(b)

2 balls are red.

2 balls are blue.

Abstract 82 Finally, students learn to represent concepts or skills in numbers and mathematical symbols.

26

There are © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-4769-02-0

Pictorial A crucial link to build a solid conceptual understanding, students are guided to understand mathematical ideas presented visually.

balls altogether.

(c)

1 umbrella is open.

1 umbrella is closed.

There are

umbrellas in all.

83

Comprehensive suite of teaching and learning resources Mathematics K is your complete suite of easy to use teaching and learning resources to make mathematics fun for your students.

Student and Teacher Access in Math Pro

Problem Solving Kit 20 stories - each story is available in Big Book format and in Reader format (6 copies of each reader)

A platform for front-of-class teaching, and learning engage the whole class

Comprises twenty stories aimed at consolidating students’ understanding of core mathematical concepts through solving problems and developing a problem-solving mindset using age-appropriate contexts

Problem Solving Teacher’s Guide Provides lesson plans that encourage mathematically-rich discussion and communication of mathematical ideas and thinking

Student Book A&B Contains activities and practices for students to reinforce learning

Teacher’s Guide A&B Provides comprehensive lesson plans to support each lesson

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