REVISED EDITION
BASED ON THE SINGAPORE BAR MODEL METHOD
1
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AS PER LATESTCBSE CURRICULUM
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First Published in 2018Revised Edition 2019Re-print Edition 2020
ISBN 978-81-932005-0-6
Published by
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Yan Kow Cheong Yan Kow Cheong, based out of Singapore has been active on the Singapore’s mathematics educational scene for over two decades with teaching appointments at the ACS (Independent), NUS Extension, Institute of Technical Education, and Singapore Science Centre. He regularly conducts workshops and seminars for primary and secondary school students, teachers and parents.Kow-Cheong is the author of Singapore’s best-selling Mathematical Quickies & Trickies series and the co-author of the MOE-approved Additional Maths 360. Besides editing primary and secondary MOE-approved textbooks, co-writing Teachers’ Guides, and ghost-writing assessment titles, he has also written contests questions and on-line assessment tests, and provided contents for maths apps.A contributor to mathematics periodicals and journals, such as The Mathematics Educator, Mathematics Medley; he is also the author of The Stack Model Method: An Intuitive and Creative Approach to Solving Word Problems [Primary 3–4 & 5–6] and many other titles. His academic interests involve research in mathematics education, in particular, the psychology of learning and teaching mathematics, and creative problem solving.Kow-Cheong writes about the good, the bad and the not-so-ugly of Singapore’s maths education and of the local educational publishing industry. Read his two maths blogs at www.singaporemathplus.com and www.singaporemathplus.net. He can be reached at: [email protected]
Our Advisors
Dr. Kevin MahoneyDr. Kevin Mahoney, based out of America has been a teacher of mathematics since 1989. A "math war" veteran, he has worked on wide variety of mathematics pedagogy and curricular materials in both public and private schools. In 2012, he became the first American to investigate Singapore's elementary teaching methods at the doctoral level, publishing original academic research on the effects of Singaporean pedagogy on American math students.Dr. Kevin worked as Math Curriculum Coordinator at an independent school outside Boston, Massachusetts. He consults with large numbers of schools and teacher training institutes in U.S., Canada, Europe and India, training the faculty and helping schools effectively implement mathematics curriculum and instruction.
WOW MATHS based on the Singapore model is a series of eight textbooks specially designed to meet the mathematical needs and wants of primary and middle school students in India, by incorporating the proven problem solving strategies and heuristics commonly used in the Singapore maths curriculum.Besides promoting critical and creative thinking in mathematics, the WOW MATHS series introduces the Singapore Bar (or Model) Method-a powerful visualization and problem-solving heuristic used to solve word problems and to help students gain a better insight into mathematical concepts across all the eight grades.
ApproachThe series infuses the Concrete-Pictorial-Abstract (CPA) approach of learning and teaching interwoven with the bar model method. This blend makes the teaching of mathematical concepts much simple and easier. The simpler and effective strategies will not only motivate the students to learn a new topic, concept or skill, but will also make the learning of mathematics more meaningful and relevant to their everyday life.
Preface
Abstract
Concrete
Pictorial
=3
They have 5 cars in all.
Venu has 3 cars. Siya has 2 cars.
2 5+?
3 2
Venu Siya
The WOW series has 15 unique features.
WOW KIDS
They are your Maths buddies. They stimulate interest, explain concepts and create involvement in learning.
Venu Siya Tina Irfan
I Can
Consolidated check of the concepts learnt in the previous class.
Show scaffolded introduction of concepts. Develop conceptual learning.
Topics Covered
Graded exercises assess understanding of mathematical concepts.
Exercise
Theme based checking of how much the children have learned about the concepts taught.
WorksheetAddition
Relates the concepts taught to every situations and shows how mathematical concepts are applied to everyday situations.
Everyday Maths
Think Smart
Helps students enhance their critical and creative thinking skills, and to arouse mathematical curiosity.
Trains children to perform mental calculations quickly.
Mental Maths
Mathematical facts about the topics.
Fact ZoneCautions/Alerts children of the common mistakes and errors.
Mind It
Includes suggestions/ideas for teacher and parents to make the learning of the topic comprehensive and complete.
TipTeaching
Consists of graded questions that test understanding and application of concepts taught with an integrated approach.
Hands on activities to further consolidate the concepts taught.
Maths Lab Activity
Quick recap of the concepts learnt in the previous class.
Warm UpEncourages active student participation and creates opportunity for interaction and discussion.
WOW MATHS based on the Singapore model is a series of eight textbooks specially designed to meet the mathematical needs and wants of primary and middle school students in India, by incorporating the proven problem solving strategies and heuristics commonly used in the Singapore maths curriculum.Besides promoting critical and creative thinking in mathematics, the WOW MATHS series introduces the Singapore Bar (or Model) Method-a powerful visualization and problem-solving heuristic used to solve word problems and to help students gain a better insight into mathematical concepts across all the eight grades.
ApproachThe series infuses the Concrete-Pictorial-Abstract (CPA) approach of learning and teaching interwoven with the bar model method. This blend makes the teaching of mathematical concepts much simple and easier. The simpler and effective strategies will not only motivate the students to learn a new topic, concept or skill, but will also make the learning of mathematics more meaningful and relevant to their everyday life.
Preface
Abstract
Concrete
Pictorial
=3
They have 5 cars in all.
Venu has 3 cars. Siya has 2 cars.
2 5+?
3 2
Venu Siya
The WOW series has 15 unique features.
WOW KIDS
They are your Maths buddies. They stimulate interest, explain concepts and create involvement in learning.
Venu Siya Tina Irfan
I Can
Consolidated check of the concepts learnt in the previous class.
Show scaffolded introduction of concepts. Develop conceptual learning.
Topics Covered
Graded exercises assess understanding of mathematical concepts.
Exercise
Theme based checking of how much the children have learned about the concepts taught.
WorksheetAddition
Relates the concepts taught to every situations and shows how mathematical concepts are applied to everyday situations.
Everyday Maths
Think Smart
Helps students enhance their critical and creative thinking skills, and to arouse mathematical curiosity.
Trains children to perform mental calculations quickly.
Mental Maths
Mathematical facts about the topics.
Fact ZoneCautions/Alerts children of the common mistakes and errors.
Mind It
Includes suggestions/ideas for teacher and parents to make the learning of the topic comprehensive and complete.
TipTeaching
Consists of graded questions that test understanding and application of concepts taught with an integrated approach.
Hands on activities to further consolidate the concepts taught.
Maths Lab Activity
Quick recap of the concepts learnt in the previous class.
Warm UpEncourages active student participation and creates opportunity for interaction and discussion.
SINGAPORE BAR MODEL
Singapore Maths Curriculum is recognized around the world for its innovative and effective teaching and learning practices. Singapore uses heuristics (problem solving strategies) and Bar Model Method (an effective pedagogical strategy recognized in over 30 countries and ranked the highest in TIMSS).
Bar or the Model drawing is a powerful visualization problems solving heuristic that is used to solve both arithmetic and algebraic problems. The Model method enables word problems that we traditionally set at higher grades (using algebra) to be set at lower grades.
The Bar (or Model) method:• helps students to gain a better insight into mathematical concepts such as
fraction, ratio and percentage• helps students to plan for the solution steps for solving a maths problem• is comparable to, but is less abstract than, the algebraic method• empowers students to solve challenging problems
Venu spent 21 of his pocket money on a movie and 4
1 on a new pen. What fraction of his pocket money was left?
Let’s solve some problems by both the traditional and bar model methods.
Money spent on movie = 21
Money spent on pen = 41
Total money spent = 21
41+
= 42
41
43+ =
Money left = 1– 43
= 44 – 4
341=
41 of his pocket money was left.
41 of his pocket money was
left.
Money left = 41
Traditional Method Model Method
Movie Pen
Money left
Number of stamps = x
Stamps given to one brother = 61 x
Remaining stamp collection = 65 x
Stamps given to other brother
= 52 × 6
5 x = 31 x
Remaining stamps = 12According to the question,
61 x + 3
1 x + 12 = x
62 72x x+ + = x
63 72x+ = x
3x + 72 = 6x 3x – 6x = – 72 –3x = – 72 x = 24
Sahil earned a profit of `20.00 by selling a pair of shoes for `300.00. What was the cost of the pair of shoes?
Bar modeling is also helpful in solving mathematical problems of higher grades.
Tanya has two brothers. She gave 61 of her stamp collection to one of them and
52 of the remainder to the other. In the end, she was left with 12 stamps. How many stamps did Tanya have at first?
3 units = 121 unit = 12 ÷ 3 = 46 units = 6 × 4 = 24Tanya had 24 stamps at first.Tanya had 24 stamps at first.
Total Stamps
?
Remainder Given to first
brother
Remainder12
First brother
Second brother
Selling price (S.P.) = `300.00Profit (P) = `20.00Cost price (C.P.) = ?
C.P. = S.P. – Profit
C.P. = `300.00 – `20.00C.P. = `280.00The cost price of the pair of shoes was `280.00.
C.P. = `300.00 – `20.00C.P. = `280.00The cost price of the pair of shoes was `280.00.
Traditional Method
Traditional Method
Model Method
Model Method
`300.00
`20.00
C.P. =? Profit
S.P.
SINGAPORE BAR MODEL
Singapore Maths Curriculum is recognized around the world for its innovative and effective teaching and learning practices. Singapore uses heuristics (problem solving strategies) and Bar Model Method (an effective pedagogical strategy recognized in over 30 countries and ranked the highest in TIMSS).
Bar or the Model drawing is a powerful visualization problems solving heuristic that is used to solve both arithmetic and algebraic problems. The Model method enables word problems that we traditionally set at higher grades (using algebra) to be set at lower grades.
The Bar (or Model) method:• helps students to gain a better insight into mathematical concepts such as
fraction, ratio and percentage• helps students to plan for the solution steps for solving a maths problem• is comparable to, but is less abstract than, the algebraic method• empowers students to solve challenging problems
Venu spent 21 of his pocket money on a movie and 4
1 on a new pen. What fraction of his pocket money was left?
Let’s solve some problems by both the traditional and bar model methods.
Money spent on movie = 21
Money spent on pen = 41
Total money spent = 21
41+
= 42
41
43+ =
Money left = 1– 43
= 44 – 4
341=
41 of his pocket money was left.
41 of his pocket money was
left.
Money left = 41
Traditional Method Model Method
Movie Pen
Money left
Number of stamps = x
Stamps given to one brother = 61 x
Remaining stamp collection = 65 x
Stamps given to other brother
= 52 × 6
5 x = 31 x
Remaining stamps = 12According to the question,
61 x + 3
1 x + 12 = x
62 72x x+ + = x
63 72x+ = x
3x + 72 = 6x 3x – 6x = – 72 –3x = – 72 x = 24
Sahil earned a profit of `20.00 by selling a pair of shoes for `300.00. What was the cost of the pair of shoes?
Bar modeling is also helpful in solving mathematical problems of higher grades.
Tanya has two brothers. She gave 61 of her stamp collection to one of them and
52 of the remainder to the other. In the end, she was left with 12 stamps. How many stamps did Tanya have at first?
3 units = 121 unit = 12 ÷ 3 = 46 units = 6 × 4 = 24Tanya had 24 stamps at first.Tanya had 24 stamps at first.
Total Stamps
?
Remainder Given to first
brother
Remainder12
First brother
Second brother
Selling price (S.P.) = `300.00Profit (P) = `20.00Cost price (C.P.) = ?
C.P. = S.P. – Profit
C.P. = `300.00 – `20.00C.P. = `280.00The cost price of the pair of shoes was `280.00.
C.P. = `300.00 – `20.00C.P. = `280.00The cost price of the pair of shoes was `280.00.
Traditional Method
Traditional Method
Model Method
Model Method
`300.00
`20.00
C.P. =? Profit
S.P.
• Workout the solution• Tryout di�erent
strategies
• Draw a model• Work backwards • Look for a pattern• Guess & Check • Simplify a problem
Polya's
4-step problem solving process
Step - 1
Step - 2
Step - 3
Step - 4
Understanding the problem
Devising a Plan
Doing
Checking
Polya’s four-step model, named a�er the Hungarian mathematician, George Polya (1887-1985), is commonly used in
mathematical problem solving.
WomenMen?60
90Total People
WomenMen3060
• Identify wanted, Given & Needed information• Restate the problem
• Check the solution 60 + 30 = 90 • Seek alternatives solutions, if required• Extend the method to other problems
solve the problem
explain your work
choose a strategy
READ, VISUALIZE & THINK
90Total People
Men People (Given)
Women
1. Rewind 11 Think Smart, Everyday Maths
2. Number Bonds 27 Maths Fun, Maths Lab
3. Addition to 10 35 Mental Maths, Practice Sheet
4. Subtraction to 10 52 Think Smart, Maths Lab
5. Numbers 11 to 20 67 Everyday Maths, Maths Lab
6. Numbers 20 to 100 94 Practice Sheet, Maths Lab
7. Addition and Subtraction within 100 116 Mental Maths, Worksheet
8. Multiplication 134 Maths Fun, Worksheet, Maths Lab
9. Shapes and Patterns 149 Everyday Maths, Worksheet, Maths Lab
10. Measurement 164 Mental Maths, Maths Lab
11. Time 177 Maths Fun, Worksheet, Maths Lab
12. Money 185 Mental Maths, Maths Lab
13. Data Handling 191 Everyday Maths, Practice Sheet, Maths Lab
Contents
10 9 8 7 6 5 4 3 2 1 10987654321
• Workout the solution• Tryout di�erent
strategies
• Draw a model• Work backwards • Look for a pattern• Guess & Check • Simplify a problem
Polya's
4-step problem solving process
Step - 1
Step - 2
Step - 3
Step - 4
Understanding the problem
Devising a Plan
Doing
Checking
Polya’s four-step model, named a�er the Hungarian mathematician, George Polya (1887-1985), is commonly used in
mathematical problem solving.
WomenMen?60
90Total People
WomenMen3060
• Identify wanted, Given & Needed information• Restate the problem
• Check the solution 60 + 30 = 90 • Seek alternatives solutions, if required• Extend the method to other problems
solve the problem
explain your work
choose a strategy
READ, VISUALIZE & THINK
90Total People
Men People (Given)
Women
• Workout the solution• Tryout di�erent
strategies
• Draw a model• Work backwards • Look for a pattern• Guess & Check • Simplify a problem
Polya's
4-step problem solving process
Step - 1
Step - 2
Step - 3
Step - 4
Understanding the problem
Devising a Plan
Doing
Checking
Polya’s four-step model, named a�er the Hungarian mathematician, George Polya (1887-1985), is commonly used in
mathematical problem solving.
WomenMen?60
90Total People
WomenMen3060
• Identify wanted, Given & Needed information• Restate the problem
• Check the solution 60 + 30 = 90 • Seek alternatives solutions, if required• Extend the method to other problems
solve the problem
explain your work
choose a strategy
READ, VISUALIZE & THINK
90Total People
Men People (Given)
Women
1. Rewind 11 Think Smart, Everyday Maths
2. Number Bonds 27 Maths Fun, Maths Lab
3. Addition to 10 35 Mental Maths, Practice Sheet
4. Subtraction to 10 52 Think Smart, Maths Lab
5. Numbers 11 to 20 67 Everyday Maths, Maths Lab
6. Numbers 20 to 100 94 Practice Sheet, Maths Lab
7. Addition and Subtraction within 100 116 Mental Maths, Worksheet
8. Multiplication 134 Maths Fun, Worksheet, Maths Lab
9. Shapes and Patterns 149 Everyday Maths, Worksheet, Maths Lab
10. Measurement 164 Mental Maths, Maths Lab
11. Time 177 Maths Fun, Worksheet, Maths Lab
12. Money 185 Mental Maths, Maths Lab
13. Data Handling 191 Everyday Maths, Practice Sheet, Maths Lab
Contents
10 9 8 7 6 5 4 3 2 1 10987654321
• Workout the solution• Tryout di�erent
strategies
• Draw a model• Work backwards • Look for a pattern• Guess & Check • Simplify a problem
Polya's
4-step problem solving process
Step - 1
Step - 2
Step - 3
Step - 4
Understanding the problem
Devising a Plan
Doing
Checking
Polya’s four-step model, named a�er the Hungarian mathematician, George Polya (1887-1985), is commonly used in
mathematical problem solving.
WomenMen?60
90Total People
WomenMen3060
• Identify wanted, Given & Needed information• Restate the problem
• Check the solution 60 + 30 = 90 • Seek alternatives solutions, if required• Extend the method to other problems
solve the problem
explain your work
choose a strategy
READ, VISUALIZE & THINK
90Total People
Men People (Given)
Women
11
I have a glass of juice in my left hand.
I have an apple in my right hand.
Thicker Thinner Heavier Lighter
Longer
Shorter
Taller
Shorter
Bigger Smaller
Outside Inside
Top
Bottom
Use real objects or pictures of various objects. Show these to children and ask them to guess the names. Ask the children to make comparison statements, such as “Which is bigger?, Which is smaller?, Which is heavier?, Which is lighter?”
Near Far
Teaching Tip
Observe as you read.
Rewind1
11
I have a glass of juice in my left hand.
I have an apple in my right hand.
Thicker Thinner Heavier Lighter
Longer
Shorter
Taller
Shorter
Bigger Smaller
Outside Inside
Top
Bottom
Use real objects or pictures of various objects. Show these to children and ask them to guess the names. Ask the children to make comparison statements, such as “Which is bigger?, Which is smaller?, Which is heavier?, Which is lighter?”
Near Far
Teaching Tip
Observe as you read.
Rewind1
12
1. For each item in column A, circle an item in column B that shows the opposite of it.
Exercise 1
Heavier
A B
Lighter
Thicker
Taller
Bigger Smaller
Shorter
Thinner
2. Tick ( ) the picture that matches the description.
a)
a) b) c)
d) e) f)
b)
c)
d)
Taller building Heavier glass
Shorter snake Longer rope Lighter object
Shorter girl
13
instructions.A smaller rectanglea)
A longer linec)
A bigger squareb)
A shorter ribbond)
4. Circle the correct option. What isnear the ball?
inside the box?
a)
c)
e)
d)
f)
b) far from the girl?
outside the house?
on the top of the cupboard? at the bottom of the stairs?
Think Smart
Look at the scene on the right. Discuss it with your classmates.Talk about the position of the animals and objects using the following words.
near far down in out longershorter up taller smaller bigger
12
1. For each item in column A, circle an item in column B that shows the opposite of it.
Exercise 1
Heavier
A B
Lighter
Thicker
Taller
Bigger Smaller
Shorter
Thinner
2. Tick ( ) the picture that matches the description.
a)
a) b) c)
d) e) f)
b)
c)
d)
Taller building Heavier glass
Shorter snake Longer rope Lighter object
Shorter girl
13
instructions.A smaller rectanglea)
A longer linec)
A bigger squareb)
A shorter ribbond)
4. Circle the correct option. What isnear the ball?
inside the box?
a)
c)
e)
d)
f)
b) far from the girl?
outside the house?
on the top of the cupboard? at the bottom of the stairs?
Think Smart
Look at the scene on the right. Discuss it with your classmates.Talk about the position of the animals and objects using the following words.
near far down in out longershorter up taller smaller bigger
14
1 One
2 Two
3 Three
4 Four
5 Five
6 Six
7 Seven
8 Eight
9 Nine
10 Ten
ZeroMy basket is empty. There are no objects
kept in it.
Counting
This means you have ‘zero’
objects in the basket.
In counting, zero (0)comes before 1.
Fact Zone
10 2 3 4 5
We always use plural to denote zero of something: zero cats, zero fruits. A common mistake is to associate the number zero with nothing. Zero is the absence of something.
Teaching Tip
15
a) b)
c) d)
e) f)
g) h)
j)i)
1. How many are there in each group? Draw a line from each
you.1
2
3
4
5
6
7
8
9
10
2. Write the missing numbers on the number line.
2 5 8
Exercise 2
3. Count the circles on each balloon. Match it with the correct number.
1 2 3 4 5 6 7 8 9
14
1 One
2 Two
3 Three
4 Four
5 Five
6 Six
7 Seven
8 Eight
9 Nine
10 Ten
ZeroMy basket is empty. There are no objects
kept in it.
Counting
This means you have ‘zero’
objects in the basket.
In counting, zero (0)comes before 1.
Fact Zone
10 2 3 4 5
We always use plural to denote zero of something: zero cats, zero fruits. A common mistake is to associate the number zero with nothing. Zero is the absence of something.
Teaching Tip
15
a) b)
c) d)
e) f)
g) h)
j)i)
1. How many are there in each group? Draw a line from each
you.1
2
3
4
5
6
7
8
9
10
2. Write the missing numbers on the number line.
2 5 8
Exercise 2
3. Count the circles on each balloon. Match it with the correct number.
1 2 3 4 5 6 7 8 9
16
4. Look at the picture given below. Count the objects and write their number in the given boxes.
5. Count and write.a) How many fish are there in the pond?
b) How many books are there on the desk?
c) How many objects are there on the table?
d) How many pens are there in the pen holder?
17
6. Count the objects. Write their numbers and number names.
7. Read the given numbers.
Complete the sequence.
8 9 5 2 1 4 7 3 6
1
1. Count the number of books you have in your school bag. Write the number of books. Write its number name. ____________________
2. Look around in your classroom. Count the given objects and write their number in the boxes.
Doors Display boards Charts Windows
Everyday Maths
16
4. Look at the picture given below. Count the objects and write their number in the given boxes.
5. Count and write.a) How many fish are there in the pond?
b) How many books are there on the desk?
c) How many objects are there on the table?
d) How many pens are there in the pen holder?
17
6. Count the objects. Write their numbers and number names.
7. Read the given numbers.
Complete the sequence.
8 9 5 2 1 4 7 3 6
1
1. Count the number of books you have in your school bag. Write the number of books. Write its number name. ____________________
2. Look around in your classroom. Count the given objects and write their number in the boxes.
Doors Display boards Charts Windows
Everyday Maths
18
Which set has more marbles?
Set B > Set A So, 6 > 4.
Set B has more marbles than Set A.Set B has 2 more marbles than Set A.So, 6 is greater than 4.
moreSet A
Set B
Which set has less balls?
Compare the beads in Set A and Set B.
Set B has less balls than Set A.Set B has 2 less balls than Set A.So, 5 is smaller than 7.
Set B < Set A So, 5 < 7.
Set A
Set Bless
Set A and Set B have equal beads.
Set A has as many beads as Set B.Set B has as many beads as Set A.So, 5 equals 5.
Set A = Set B So, 5 = 5.
Set A
Set B
Comparing Numbers
1
2
3
We use ‘>’ sign to represent
‘more’.
We use ‘<’ sign to represent
‘less’.
We use ‘=’ to represent
‘is equal to’.
Everyday Maths
How many wheels does each vehicle have?
Bicycle Bus Auto rickshaw Car
19
2. Read and draw. Count and then write ‘more’ or ‘less’.
1. Count and write the number of objects. Tick ( ) the set that has more objects.
5 rectangles
a)
a)
b)
b)
3 triangles 5 triangles
2 rectangles
Remember to count
correctly and draw neatly.
Set A
Set A has more kites than Set B.
So, is more than .
Set B
Exercise 3
Set A
Set A has less apples than Set B.
So, is less than .
Set B
Set A Set B
18
Which set has more marbles?
Set B > Set A So, 6 > 4.
Set B has more marbles than Set A.Set B has 2 more marbles than Set A.So, 6 is greater than 4.
moreSet A
Set B
Which set has less balls?
Compare the beads in Set A and Set B.
Set B has less balls than Set A.Set B has 2 less balls than Set A.So, 5 is smaller than 7.
Set B < Set A So, 5 < 7.
Set A
Set Bless
Set A and Set B have equal beads.
Set A has as many beads as Set B.Set B has as many beads as Set A.So, 5 equals 5.
Set A = Set B So, 5 = 5.
Set A
Set B
Comparing Numbers
1
2
3
We use ‘>’ sign to represent
‘more’.
We use ‘<’ sign to represent
‘less’.
We use ‘=’ to represent
‘is equal to’.
Everyday Maths
How many wheels does each vehicle have?
Bicycle Bus Auto rickshaw Car
19
2. Read and draw. Count and then write ‘more’ or ‘less’.
1. Count and write the number of objects. Tick ( ) the set that has more objects.
5 rectangles
a)
a)
b)
b)
3 triangles 5 triangles
2 rectangles
Remember to count
correctly and draw neatly.
Set A
Set A has more kites than Set B.
So, is more than .
Set B
Exercise 3
Set A
Set A has less apples than Set B.
So, is less than .
Set B
Set A Set B
20
4. Count the objects and write their number in the box. Circle the groups which have an equal number of objects.
5. Put the correct sign (>, < or =).
a) 3 5 b) 2 1 c) 6 3
d) 7 7 e) 1 0 f) 9 2
To get the number that comes just after 5, count 1 forward from 5. So, 6 comes just after 5.
What comes just before 5?
What comes just after 5?
To get the number that comes just before 5, count 1 backward from 5. So, 4 comes just before 5.
Before, After and Between
Jump 1 number backward from 5
1 2 3 4 5 6 7 8
Jump 1 number forward from 5
1 2 3 4 5 6 7 8
1
2
1 less
1 more
21
What comes in between?
4 comes before 5 and 6 comes after 5.
This means 5 is between 4 and 6.
Between
3
1. Which number comes just before and just after? Count on the number line.
comes just before 7.a)
a)
b)
b)
comes just before 3.c)
c)
d)
d)
comes just after 7.
comes just after 3.
2. For each middle number, write the numbers that come before and after it.
1 3
5 8
Exercise 4
a) b)
c) d)
3. Write the number that comes in between the two given numbers.
1 3 4 6
7 9 8 10
Guide the children to draw arrows on the number line to show a number just before and just after.
Teaching Tip
0 1 2 3 4 5 6 7 8 9
Before After
0 1 2 3 4 5 6 7 8 9 10
20
4. Count the objects and write their number in the box. Circle the groups which have an equal number of objects.
5. Put the correct sign (>, < or =).
a) 3 5 b) 2 1 c) 6 3
d) 7 7 e) 1 0 f) 9 2
To get the number that comes just after 5, count 1 forward from 5. So, 6 comes just after 5.
What comes just before 5?
What comes just after 5?
To get the number that comes just before 5, count 1 backward from 5. So, 4 comes just before 5.
Before, After and Between
Jump 1 number backward from 5
1 2 3 4 5 6 7 8
Jump 1 number forward from 5
1 2 3 4 5 6 7 8
1
2
1 less
1 more
21
What comes in between?
4 comes before 5 and 6 comes after 5.
This means 5 is between 4 and 6.
Between
3
1. Which number comes just before and just after? Count on the number line.
comes just before 7.a)
a)
b)
b)
comes just before 3.c)
c)
d)
d)
comes just after 7.
comes just after 3.
2. For each middle number, write the numbers that come before and after it.
1 3
5 8
Exercise 4
a) b)
c) d)
3. Write the number that comes in between the two given numbers.
1 3 4 6
7 9 8 10
Guide the children to draw arrows on the number line to show a number just before and just after.
Teaching Tip
0 1 2 3 4 5 6 7 8 9
Before After
0 1 2 3 4 5 6 7 8 9 10
22
Moving from a smaller number to a greater number is known as increasing order.
10
23
45
67
89
10
23
45
67
89
10
Moving from a greater number to a smaller number is known as decreasing order.
In increasing order, numbers
go upward.
In decreasing order, numbers go downward.
Increasing and Decreasing Order
1. Write each set of numbers in increasing order. 6, 4, 5, 1 a) b) 8, 3, 9, 10
1
10 9
3
Go down
Go down
2. Write the given numbers in decreasing order. 1, 10, 5, 6a) b) 9, 2, 8, 0
Exercise 5
Call five children in front of the class. Ask their roll numbers and get them to arrange themselves in increasing or decreasing order.
Maths Fun
Increasin
g Decreasing
Go upGo up
23
Maths Fun
3. Write the numbers in increasing order.
Six 9 3 Two 7 Five
Smallest
a)
b)
Greatest
Four Two Zero Ten Nine Six
Smallest Greatest
An ordinal number is used to show the position or order of an object.
Take out any five books from your school bag.Arrange them in a stack and label the position.Rearrange the books for each round and complete the given table.
Position of the book
Book name
Round 1 ThirdRound 2 FifthRound 3 Second Round 4 FirstRound 5 Fourth
Ordinal Numbers
Teaching Tip
Encourage the children to notice that the numbers they have written in both the cases of question 3, are in increasing order.
Mind It
Forth Fourth Nineth Ninth
First
Sixth
Third
Eighth
Fifth
Tenth
Second
Seventh
Fourth
Ninth
22
Moving from a smaller number to a greater number is known as increasing order.
10
23
45
67
89
10
23
45
67
89
10
Moving from a greater number to a smaller number is known as decreasing order.
In increasing order, numbers
go upward.
In decreasing order, numbers go downward.
Increasing and Decreasing Order
1. Write each set of numbers in increasing order. 6, 4, 5, 1 a) b) 8, 3, 9, 10
1
10 9
3
Go down
Go down
2. Write the given numbers in decreasing order. 1, 10, 5, 6a) b) 9, 2, 8, 0
Exercise 5
Call five children in front of the class. Ask their roll numbers and get them to arrange themselves in increasing or decreasing order.
Maths Fun
Increasin
g Decreasing
Go upGo up
23
Maths Fun
3. Write the numbers in increasing order.
Six 9 3 Two 7 Five
Smallest
a)
b)
Greatest
Four Two Zero Ten Nine Six
Smallest Greatest
An ordinal number is used to show the position or order of an object.
Take out any five books from your school bag.Arrange them in a stack and label the position.Rearrange the books for each round and complete the given table.
Position of the book
Book name
Round 1 ThirdRound 2 FifthRound 3 Second Round 4 FirstRound 5 Fourth
Ordinal Numbers
Teaching Tip
Encourage the children to notice that the numbers they have written in both the cases of question 3, are in increasing order.
Mind It
Forth Fourth Nineth Ninth
First
Sixth
Third
Eighth
Fifth
Tenth
Second
Seventh
Fourth
Ninth
24
a) Fill in the blanks. The shirt is first from the left. The skirt is second from the left. The __________ is third from the left. The __________ is fourth from the left. The __________ is fifth from the left.b) What is second from the right? ______________c) What is fourth from the right? ______________d) What is fifth from the right? ______________
Left Right
a) Colour the last three boxes.
b) Circle first six leaves.
Colour the third box from the left.
Circle the sixth leaf from the left.
Exercise 6
1. Look at the picture given below.
2. Compare the numbers with ordinal numbers.
25
8 14 10
53 6
F I V E A P S
O C Y G T E I
U E I G H T X
R T H R E E S
T A V D O N E
1. Find and circle the number names of the given numbers.
2. Which number comes just before and after? Count and mark on the number line.
3. Put the correct sign (>, < or =).
4. Look at the picture and answer the questions.
0 1 2 3 4 5 6 7 8 9 10
comes just before 9.a) b)
Name the animala) on the third step. _______________b) on the first step. _______________c) between the third and the fifth step. _______________
comes just after 7.
7 9 10 1
4 4 2 5
FirstSecond
ThirdFourth
Fifth
24
a) Fill in the blanks. The shirt is first from the left. The skirt is second from the left. The __________ is third from the left. The __________ is fourth from the left. The __________ is fifth from the left.b) What is second from the right? ______________c) What is fourth from the right? ______________d) What is fifth from the right? ______________
Left Right
a) Colour the last three boxes.
b) Circle first six leaves.
Colour the third box from the left.
Circle the sixth leaf from the left.
Exercise 6
1. Look at the picture given below.
2. Compare the numbers with ordinal numbers.
25
8 14 10
53 6
F I V E A P S
O C Y G T E I
U E I G H T X
R T H R E E S
T A V D O N E
1. Find and circle the number names of the given numbers.
2. Which number comes just before and after? Count and mark on the number line.
3. Put the correct sign (>, < or =).
4. Look at the picture and answer the questions.
0 1 2 3 4 5 6 7 8 9 10
comes just before 9.a) b)
Name the animala) on the third step. _______________b) on the first step. _______________c) between the third and the fifth step. _______________
comes just after 7.
7 9 10 1
4 4 2 5
FirstSecond
ThirdFourth
Fifth
2626
Aim: To recognise numbers from 1 to 10 and compare them.Requirements: 10 number cards, sketch pensSteps:1. Play this game in pairs.2. Take 10 cards and write 0 to 9 on them with
different coloured sketch pens. Give one set of cards to each pair.3. Lay the cards in a single line (upside down).4. Take turns and draw a card one by one.5. Compare the numbers on the cards.6. The child having a greater number will
keep both the cards.7. Write your numbers on the table. Use ‘>’
or ‘<’ for comparison.8. Repeat steps 4 to 7 until all the cards are
used.9. The child having more cards will win the game.
Teaching Tip
You can make the number cards using a cardboard or a paper.
MATHS LAB ACTIVITY
Maths Lab Activity
Record Table
Turn Number on my card
Number on my friend's card Compare
1 4 3 4 > 3
2
3
4
5
27
3 dogs are sitting.3 dogs are standing.There are 6 dogs.
2 flowers are red. 4 flowers are yellow.There are 6 flowers.
Warm Up
3
2
3
4
6
6
Number Bonds2
2626
Aim: To recognise numbers from 1 to 10 and compare them.Requirements: 10 number cards, sketch pensSteps:1. Play this game in pairs.2. Take 10 cards and write 0 to 9 on them with
different coloured sketch pens. Give one set of cards to each pair.3. Lay the cards in a single line (upside down).4. Take turns and draw a card one by one.5. Compare the numbers on the cards.6. The child having a greater number will
keep both the cards.7. Write your numbers on the table. Use ‘>’
or ‘<’ for comparison.8. Repeat steps 4 to 7 until all the cards are
used.9. The child having more cards will win the game.
Teaching Tip
You can make the number cards using a cardboard or a paper.
MATHS LAB ACTIVITY
Maths Lab Activity
Record Table
Turn Number on my card
Number on my friend's card Compare
1 4 3 4 > 3
2
3
4
5
27
3 dogs are sitting.3 dogs are standing.There are 6 dogs.
2 flowers are red. 4 flowers are yellow.There are 6 flowers.
Warm Up
3
2
3
4
6
6
Number Bonds2
28
3
14
Put and together. Make a .
Making Number Bonds
How many are there in each part?
3 and 1 make 4.This is a number bond.
part
wholepart
We can make number bonds by breaking 4 into two numbers.
3
14
part
wholepart
Tell children to draw two circles on their desk with chalk. Give 4 cubes to each child. Ask them to keep these cubes in the first circle. Record the number combination. Then move one cube to the second circle. Record the new combination. Do this activity until all the cubes are in the second circle.
Maths Fun
Now, break into and .
29
2
24
There are 2 balls.
There are 4 leaves.
There are 5 teddy bears.
1 and 1 make 2.
2 and 2 make 4.
1 and 4 make 5.
2 and 3 make 5.
Making 2
Making 4
Making 5
1
12
2
13
1
45
2
35
There are 3 handkerchiefs.
2 and 1 make 3.
Making 3
Think Smart
What numbers make 1? Can you find all the possible ways?
Which other number combinations
can be used to make 5?
28
3
14
Put and together. Make a .
Making Number Bonds
How many are there in each part?
3 and 1 make 4.This is a number bond.
part
wholepart
We can make number bonds by breaking 4 into two numbers.
3
14
part
wholepart
Tell children to draw two circles on their desk with chalk. Give 4 cubes to each child. Ask them to keep these cubes in the first circle. Record the number combination. Then move one cube to the second circle. Record the new combination. Do this activity until all the cubes are in the second circle.
Maths Fun
Now, break into and .
29
2
24
There are 2 balls.
There are 4 leaves.
There are 5 teddy bears.
1 and 1 make 2.
2 and 2 make 4.
1 and 4 make 5.
2 and 3 make 5.
Making 2
Making 4
Making 5
1
12
2
13
1
45
2
35
There are 3 handkerchiefs.
2 and 1 make 3.
Making 3
Think Smart
What numbers make 1? Can you find all the possible ways?
Which other number combinations
can be used to make 5?
30
There are 6 mangoes.
There are 7 cubes.
2 and 4 make 6.
2 and 5 make 7.
Making 6
Making 7
2
46
3
36
1
56
0
66
3
58
4
59
4
48
2
57
There are 8 kites.
3 and 5 make 8.
Making 8
4 and 4 make 8.
There are 9 shirts.
4 and 5 make 9.
Making 9
How many number bonds
can you make for 7 and 8?
31
1. What are the missing numbers in each number bond?
Exercise
a)
c)
b)
d)
2. Fill in the missing numbers to complete the number bonds.
a) b) c)
d) e) f)
g) h) i)
3. What numbers make 10? Draw all the possible number bonds.
1 4
2
4
4
1
1
4
5
2
6
3
1
9
0
6
3
5
5
0
1
2
7
30
There are 6 mangoes.
There are 7 cubes.
2 and 4 make 6.
2 and 5 make 7.
Making 6
Making 7
2
46
3
36
1
56
0
66
3
58
4
59
4
48
2
57
There are 8 kites.
3 and 5 make 8.
Making 8
4 and 4 make 8.
There are 9 shirts.
4 and 5 make 9.
Making 9
How many number bonds
can you make for 7 and 8?
31
1. What are the missing numbers in each number bond?
Exercise
a)
c)
b)
d)
2. Fill in the missing numbers to complete the number bonds.
a) b) c)
d) e) f)
g) h) i)
3. What numbers make 10? Draw all the possible number bonds.
1 4
2
4
4
1
1
4
5
2
6
3
1
9
0
6
3
5
5
0
1
2
7
32
4. Look at each picture carefully. Fill in the missing numbers. The
a)
b)
c)
d)
5. Complete the number bonds for each of the following.
a)
b)
c)
3
25
12
5
9
33
1. Complete the given number bonds.
2. Write the missing number in each number bond.
a) b) c)
a) b) c)
d) e) f)
d) e) f)
g) h) i)
g) h) i)
1
1 35
14
4
4
37
56
22
6
2 89
2 2 0
1 4
6 4
2
3 7
5 9
5 1
5 8
7 9
32
4. Look at each picture carefully. Fill in the missing numbers. The
a)
b)
c)
d)
5. Complete the number bonds for each of the following.
a)
b)
c)
3
25
12
5
9
33
1. Complete the given number bonds.
2. Write the missing number in each number bond.
a) b) c)
a) b) c)
d) e) f)
d) e) f)
g) h) i)
g) h) i)
1
1 35
14
4
4
37
56
22
6
2 89
2 2 0
1 4
6 4
2
3 7
5 9
5 1
5 8
7 9
34
Aim: To make number bonds using a number balance.Requirement: Number balanceSteps:1. Work in pairs.2. Take a number balance.3. Put a on one side of the number balance on any number, say 8. 4. Now, take two or more and place it on the numbers on the other
side such that the parts together make 8.
5. Explore and find all possible ways to make number bonds of 8 using .
6. Repeat the activity for other numbers.
10 9 8 7 6 5 4 3 2 1 109876543215
38
10 9 8 7 6 5 4 3 2 1 10987654321
3
4
1
8
MATHS LAB ACTIVITY
Maths Lab Activity
35
1. Count and add.
a)
a)
b)
c)
b)
2. Add the numbers.
+
+
+
+
=
=
=
=
+5 4
1 2 3 4
=
1 2 3 4 5 6 7 8 9 10
+
+
4
9
3
1
=
=
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
I Can
Addition to 103
Remember + means to put
together or add.It is read as
plus.
34
Aim: To make number bonds using a number balance.Requirement: Number balanceSteps:1. Work in pairs.2. Take a number balance.3. Put a on one side of the number balance on any number, say 8. 4. Now, take two or more and place it on the numbers on the other
side such that the parts together make 8.
5. Explore and find all possible ways to make number bonds of 8 using .
6. Repeat the activity for other numbers.
10 9 8 7 6 5 4 3 2 1 109876543215
38
10 9 8 7 6 5 4 3 2 1 10987654321
3
4
1
8
MATHS LAB ACTIVITY
Maths Lab Activity
35
1. Count and add.
a)
a)
b)
c)
b)
2. Add the numbers.
+
+
+
+
=
=
=
=
+5 4
1 2 3 4
=
1 2 3 4 5 6 7 8 9 10
+
+
4
9
3
1
=
=
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
I Can
Addition to 103
Remember + means to put
together or add.It is read as
plus.
36
Warm Up
There are 7 boys in the
party.
There are 3 girls in the party.
How many children are
there in total?
37
There are 5 girls in the party.
How many girls are there in all?
There are .
How many are there in all?
There are 6 cubes in all.
4 + 2 = 6 is an addition sentence.
Four plus two equals six.
4 + 2 = 6
+ =
There are more.
There are 7 girls in all.
The number we get on adding two or more numbers is called the ‘sum’ or the ‘total’.
5 + 2 = 7
5 and 2 make 7.
2 more girls join the party.
Five plus two equals seven.
‘=’ means ‘equal to’
Addition using Number Bonds
1
2
‘+’ is called plus. It means to put together. ‘4 + 2’ is the
same as 6.
Addition means putting
together.
part
partwhole
4
26
girls
girls
girls5
27
36
Warm Up
There are 7 boys in the
party.
There are 3 girls in the party.
How many children are
there in total?
37
There are 5 girls in the party.
How many girls are there in all?
There are .
How many are there in all?
There are 6 cubes in all.
4 + 2 = 6 is an addition sentence.
Four plus two equals six.
4 + 2 = 6
+ =
There are more.
There are 7 girls in all.
The number we get on adding two or more numbers is called the ‘sum’ or the ‘total’.
5 + 2 = 7
5 and 2 make 7.
2 more girls join the party.
Five plus two equals seven.
‘=’ means ‘equal to’
Addition using Number Bonds
1
2
‘+’ is called plus. It means to put together. ‘4 + 2’ is the
same as 6.
Addition means putting
together.
part
partwhole
4
26
girls
girls
girls5
27
38
Exercise 1
1. Find the total.
2. Write the given number bonds as addition sentences.
4
1
4 + 1 =
a)
d)
6
0
4
2
4 + 2 =
3
4
5
3
b)
e)
3
4
3 + 4 =
2
2
2 + 2 =
4
4
9
1
c)
f)
a)
d)
b)
e)
c)
f)
5
4
5 + 4 =
6
3
6 + 3 =
7
0
3. Count the objects and write the addition sentence.
+Addition sentence
a)
+ =
39
4. Look at each picture carefully. Complete the number bond and write the addition sentence.
+Addition sentence
+ =
Explain to the children that parts add up to give the whole (sum). These parts and wholes are written together as an addition sentence using ‘+’sign and ‘=’ sign.
TeachingTip
4
6
8
8
Maths FunPlay the game in pairs. Make two sets of number cards, from 0 to 9.Mix the cards and place them face down on the table.Take turns to flip over any two cards. Do they make up 8?If yes, keep the cards. If no, place them back facing down and let your partner play.Repeat. The child who gets the maximum cards, wins.
b)
a)
b)
c)
d)
38
Exercise 1
1. Find the total.
2. Write the given number bonds as addition sentences.
4
1
4 + 1 =
a)
d)
6
0
4
2
4 + 2 =
3
4
5
3
b)
e)
3
4
3 + 4 =
2
2
2 + 2 =
4
4
9
1
c)
f)
a)
d)
b)
e)
c)
f)
5
4
5 + 4 =
6
3
6 + 3 =
7
0
3. Count the objects and write the addition sentence.
+Addition sentence
a)
+ =
39
4. Look at each picture carefully. Complete the number bond and write the addition sentence.
+Addition sentence
+ =
Explain to the children that parts add up to give the whole (sum). These parts and wholes are written together as an addition sentence using ‘+’sign and ‘=’ sign.
TeachingTip
4
6
8
8
Maths FunPlay the game in pairs. Make two sets of number cards, from 0 to 9.Mix the cards and place them face down on the table.Take turns to flip over any two cards. Do they make up 8?If yes, keep the cards. If no, place them back facing down and let your partner play.Repeat. The child who gets the maximum cards, wins.
b)
a)
b)
c)
d)
40
Addition on Number Line
Exercise 2
1. Add the numbers on the number line.
2. Use the number line to count on and add.
1 2 3 4 5 6 7 8 90
1 2 3 4 5 6 7 8 90
2 + 3 = a)
b) 4 + 2 =
0 1 2 3 4 5 6 7 8 9 10
8 + 1 = a) b) c)6 + 2 = 4 + 5 =
2 + 8 = d) e) f)5 + 1 = 3 + 7 =
Add 3 and 1.
Start with the greater number 3. Move one
step: 3 4
Add 7 and 3. Start with the greater number 7. Count on 3 steps:
7 8 9 101 2 3
1
1
1 2 3 4 5 6 7 8 90 107 + 3 = 103 + 1 = 4
3 steps
41
Adding Two Numbers
3
3 2 5
2 5
5 50
Tina has 5 fish in her fish tank. She adds 0 fish to the tank. How many fish does she have in all?
Tina has 5 fish in all.
There are 3 birds sitting on a tree.
How many birds are now sitting on the tree?
This is same as
5 birds are now sitting on the tree.
+
+
=
=
2 more birds join in.
5
+ =
0
When zero is added to a number, the total remains the same.
Fact ZoneYou can add numbers in any order. The answer will be the same in all the cases.
Adding Zero
3
+ 2
5
5
+ 0
5
5
3 + 2 = 5
5 + 0 = 5
40
Addition on Number Line
Exercise 2
1. Add the numbers on the number line.
2. Use the number line to count on and add.
1 2 3 4 5 6 7 8 90
1 2 3 4 5 6 7 8 90
2 + 3 = a)
b) 4 + 2 =
0 1 2 3 4 5 6 7 8 9 10
8 + 1 = a) b) c)6 + 2 = 4 + 5 =
2 + 8 = d) e) f)5 + 1 = 3 + 7 =
Add 3 and 1.
Start with the greater number 3. Move one
step: 3 4
Add 7 and 3. Start with the greater number 7. Count on 3 steps:
7 8 9 101 2 3
1
1
1 2 3 4 5 6 7 8 90 107 + 3 = 103 + 1 = 4
3 steps
41
Adding Two Numbers
3
3 2 5
2 5
5 50
Tina has 5 fish in her fish tank. She adds 0 fish to the tank. How many fish does she have in all?
Tina has 5 fish in all.
There are 3 birds sitting on a tree.
How many birds are now sitting on the tree?
This is same as
5 birds are now sitting on the tree.
+
+
=
=
2 more birds join in.
5
+ =
0
When zero is added to a number, the total remains the same.
Fact ZoneYou can add numbers in any order. The answer will be the same in all the cases.
Adding Zero
3
+ 2
5
5
+ 0
5
5
3 + 2 = 5
5 + 0 = 5
42
a) b) c)
d) e) f)
Exercise 3
1. Add 0 and write the total in each box.
2. Add and write.
0 + 9 = 3 + 0 =
6 + 0 =
8 + 0 =
a) b) c) 4 + 0 = 3 + 1 = 2 + 5 =
d) e) f) 3 + 4 = 2 + 1 = 4 + 3 =
g) h) i) 5 + 1 = 4 + 4 = 5 + 3 =
j) k) l) 7 + 2 = 6 + 3 = 0 + 5 =
m) n) o) 2 + 6 = 8 + 1 = 1 + 9 =
0 + 1 = 7 + 0 =
a) b) c) d) e)
f) g) h) i) j)
3. Add the following.
6
3+
3
4+
5
2+
5
3+
0
9+
2
7+
4
5+
7
0+
2
8+
0
0+
Make students observe the fact that numbers can be added in any order by making them add with concrete objects like chalk pieces, pencils and other objects.
TeachingTip
43
Adding Three Numbers
There is 1 hen in a garden.
We write it as:
Now, there are 4 hens in the garden.
3 more hens join in.
1 + +
+
3
4
2
2
6
2 more hens join them.
Now, there are 6 hens in the garden.2
+
+ +
1 1
1
There are 6 hens in all.
= hens
= 132+
6
3
3
1 3 2
Think Smart
Make two addition sentences with 1, 2, 5, 7, 8 and 9. Use each number once.
+ = + =
42
a) b) c)
d) e) f)
Exercise 3
1. Add 0 and write the total in each box.
2. Add and write.
0 + 9 = 3 + 0 =
6 + 0 =
8 + 0 =
a) b) c) 4 + 0 = 3 + 1 = 2 + 5 =
d) e) f) 3 + 4 = 2 + 1 = 4 + 3 =
g) h) i) 5 + 1 = 4 + 4 = 5 + 3 =
j) k) l) 7 + 2 = 6 + 3 = 0 + 5 =
m) n) o) 2 + 6 = 8 + 1 = 1 + 9 =
0 + 1 = 7 + 0 =
a) b) c) d) e)
f) g) h) i) j)
3. Add the following.
6
3+
3
4+
5
2+
5
3+
0
9+
2
7+
4
5+
7
0+
2
8+
0
0+
Make students observe the fact that numbers can be added in any order by making them add with concrete objects like chalk pieces, pencils and other objects.
TeachingTip
43
Adding Three Numbers
There is 1 hen in a garden.
We write it as:
Now, there are 4 hens in the garden.
3 more hens join in.
1 + +
+
3
4
2
2
6
2 more hens join them.
Now, there are 6 hens in the garden.2
+
+ +
1 1
1
There are 6 hens in all.
= hens
= 132+
6
3
3
1 3 2
Think Smart
Make two addition sentences with 1, 2, 5, 7, 8 and 9. Use each number once.
+ = + =
44
+ +
+=
= caps
+ +
+=
= flowers
2. Add and write the answer in the boxes.
a) 3 + 1 + 2 = b) 1 + 1 + 1 =
c) 4 + 3 + 0 = d) 3 + 2 + 4 =
e) 6 + 2 + 1 = f) 7 + 1 + 2 =
g) 5 + 2 + 2 = h) 0 + 8 + 0 =
Exercise 4
1. Count each object and find the total.
+ +
+=
= cars
a)
b)
c)
45
3. Add the following.313+
422+
521+
631+
240+
4. Read and solve.
a) b) c) d) e)
Everyday Maths
Count the number of pencils you have in your pencil box.
Write the number of pencils.
Count the number of pencils your friend has in his/her pencil box.
Write the number of pencils.
How many pencils do both of you have altogether?
+ =
Gagan has 3 towels.a)
Meena has 2 towels.
Priya has 1 towel.
There are towels in all.
+=
?
3 2 1
+
Lata ate 3 apples.b)
Varun ate 2 apples.
Jatin ate 2 apples.
=
?
3 2 2There are apples in all.
44
+ +
+=
= caps
+ +
+=
= flowers
2. Add and write the answer in the boxes.
a) 3 + 1 + 2 = b) 1 + 1 + 1 =
c) 4 + 3 + 0 = d) 3 + 2 + 4 =
e) 6 + 2 + 1 = f) 7 + 1 + 2 =
g) 5 + 2 + 2 = h) 0 + 8 + 0 =
Exercise 4
1. Count each object and find the total.
+ +
+=
= cars
a)
b)
c)
45
3. Add the following.313+
422+
521+
631+
240+
4. Read and solve.
a) b) c) d) e)
Everyday Maths
Count the number of pencils you have in your pencil box.
Write the number of pencils.
Count the number of pencils your friend has in his/her pencil box.
Write the number of pencils.
How many pencils do both of you have altogether?
+ =
Gagan has 3 towels.a)
Meena has 2 towels.
Priya has 1 towel.
There are towels in all.
+=
?
3 2 1
+
Lata ate 3 apples.b)
Varun ate 2 apples.
Jatin ate 2 apples.
=
?
3 2 2There are apples in all.
46
Solving Word Problems
Irfan has 3 balloons.
Venu has 4 kites.
How many balloons do they have altogether?
How many kites does he have in all?
They have 7 balloons altogether.
Venu has 9 kites in all.
Venu has 4 balloons.
He buys 5 more kites.
3
4+
7
4
5+
9
37
4
49
5
Tina has 2 dolls.
She has dolls in all.
+ =
How many dolls does she have in all?
She buys 3 more dolls.
Exercise 5
Solve the given word problems.
+
1.
1
2
47
Mental Maths
Venu now has pencils in all.
+ =
4. Venu has no pencil in his pencil box.
Irfan gives 3 pencils to Venu.
How many pencils does Venu now have?
Solve the following.
2 + 0 =
2 + 1 = 3 + 5 =
4
2
2 3
6 + 3
0 1 2 3 4 5 6 7Start end
+ =
+
+
Irfan has 3 cats.
Siya baked 6 cakes.
He has animals in all.
She baked cakes in all.
+
+
=
=
How many animals he has in all?
How many cakes did she bake in all?
He also has 2 rabbits.
She baked 3 more cakes.
+
+
2.
3.
46
Solving Word Problems
Irfan has 3 balloons.
Venu has 4 kites.
How many balloons do they have altogether?
How many kites does he have in all?
They have 7 balloons altogether.
Venu has 9 kites in all.
Venu has 4 balloons.
He buys 5 more kites.
3
4+
7
4
5+
9
37
4
49
5
Tina has 2 dolls.
She has dolls in all.
+ =
How many dolls does she have in all?
She buys 3 more dolls.
Exercise 5
Solve the given word problems.
+
1.
1
2
47
Mental Maths
Venu now has pencils in all.
+ =
4. Venu has no pencil in his pencil box.
Irfan gives 3 pencils to Venu.
How many pencils does Venu now have?
Solve the following.
2 + 0 =
2 + 1 = 3 + 5 =
4
2
2 3
6 + 3
0 1 2 3 4 5 6 7Start end
+ =
+
+
Irfan has 3 cats.
Siya baked 6 cakes.
He has animals in all.
She baked cakes in all.
+
+
=
=
How many animals he has in all?
How many cakes did she bake in all?
He also has 2 rabbits.
She baked 3 more cakes.
+
+
2.
3.
48
Making Addition Stories
There are 3 pink .There are 4 .How many are there in all?
There are 4 blue dots.There are 6 red dots.How many dots are there in total?
1.
2.
____________________________________________________________________________________
3 + 4 = 7
4 + 6 = 10
Exercise 6
Look at the pictures below and write an addition story for each.
____________________________________________________________________________________
CLUES
flowers, pink, yellow, in all
red, blue,dots, total
red, green, balls, total
sharpeners, red, yellow, in all
1
2
CLUES
CLUES
CLUES
49
____________________________________________________________________________________
____________________________________________________________________________________
Think Smart
Look at the picture given below. Write an addition story, using the given words. a) Red and yellow flowers b) Brown and yellow birdsc) Yellow and blue balloons d) Boys, girls and children
3.
4.
apples, bananas, fruits, altogether
red, yellow, flowers, in all
CLUES
CLUES
48
Making Addition Stories
There are 3 pink .There are 4 .How many are there in all?
There are 4 blue dots.There are 6 red dots.How many dots are there in total?
1.
2.
____________________________________________________________________________________
3 + 4 = 7
4 + 6 = 10
Exercise 6
Look at the pictures below and write an addition story for each.
____________________________________________________________________________________
CLUES
flowers, pink, yellow, in all
red, blue,dots, total
red, green, balls, total
sharpeners, red, yellow, in all
1
2
CLUES
CLUES
CLUES
49
____________________________________________________________________________________
____________________________________________________________________________________
Think Smart
Look at the picture given below. Write an addition story, using the given words. a) Red and yellow flowers b) Brown and yellow birdsc) Yellow and blue balloons d) Boys, girls and children
3.
4.
apples, bananas, fruits, altogether
red, yellow, flowers, in all
CLUES
CLUES
50
1. Complete the number bonds. Write the addition sentence.
2. Add on the number line and write the sum.
3. Add the following.
4. Read the story and add.
2
7
5
4
1 2 3 4 5 6 7 8 9 100
a)
a)
c)
a) b) c) d) e)
b)
b)
d)
2 + 2 = 4 + 3 =
7 + 0 = 8 + 1 =
5
2+
3
3+
9
1+
8
0+
1
6+
Siya has no apples on her plate.
Siya has apples now.
+ =
How many apples does Siya now have?
Tina puts 6 apples on Siya’s plate.
51
Aim: To add different numbers and find their sum.Requirements: 1 dice, 2 sets of number cards (1 to 4)
Record Table
Number on my dice Number on the card Sum
Steps:1. Arrange the children in pairs.2. From the pair, one child rolls the dice and the
other picks a card.3. Next, they note down the numbers on the dice
and the card in the table given below and find the sum.
4. Reverse the roles and repeat steps 2 to 4.5. Continue the activity until the table gets filled.
1 2 3 4
MATHS LAB ACTIVITY
Maths Lab Activity
50
1. Complete the number bonds. Write the addition sentence.
2. Add on the number line and write the sum.
3. Add the following.
4. Read the story and add.
2
7
5
4
1 2 3 4 5 6 7 8 9 100
a)
a)
c)
a) b) c) d) e)
b)
b)
d)
2 + 2 = 4 + 3 =
7 + 0 = 8 + 1 =
5
2+
3
3+
9
1+
8
0+
1
6+
Siya has no apples on her plate.
Siya has apples now.
+ =
How many apples does Siya now have?
Tina puts 6 apples on Siya’s plate.
51
Aim: To add different numbers and find their sum.Requirements: 1 dice, 2 sets of number cards (1 to 4)
Record Table
Number on my dice Number on the card Sum
Steps:1. Arrange the children in pairs.2. From the pair, one child rolls the dice and the
other picks a card.3. Next, they note down the numbers on the dice
and the card in the table given below and find the sum.
4. Reverse the roles and repeat steps 2 to 4.5. Continue the activity until the table gets filled.
1 2 3 4
MATHS LAB ACTIVITY
Maths Lab Activity
52
I Can
Fill in the blanks. One has been done for you.
– =
– =
– =
– =
Subtraction to 104Remember – means
to take away.It is read as minus.
4 2 2
53
Warm Up
How many ducks are left in
the pond?
There were 5 ducks in the pond. 3 came
out.
52
I Can
Fill in the blanks. One has been done for you.
– =
– =
– =
– =
Subtraction to 104Remember – means
to take away.It is read as minus.
4 2 2
53
Warm Up
How many ducks are left in
the pond?
There were 5 ducks in the pond. 3 came
out.
54
Subtraction using Number Bonds
There are 7 birds.
Emphasise the use of words like ‘out’, ‘away’ (take away, gave away, run away, go away, fly away), ‘left’, ‘subtraction’, ‘minus’, ‘less than’ to build the concept of subtraction.
TeachingTip
4 birds are left.
Seven minus three equals four.7 – 3 = 4 is a subtraction sentence.
7 – 3 = 4
There are .
How many are left?
5 2 3
– =
Take away .
1
2
‘–’ is called minus.It means take away.
‘5 – 2’ is the same as 3.
part
partwhole
2
35
3
47
3 cubes are left.
5 – 2 = 3 is a subtraction sentence.
Five minus two equals three.
3 birds fly away.
How many birds are left?7
3–
4
55
Exercise 1
1. Subtract using number bonds.
2. Write each number bond as a subtraction sentence.
3. Look at the pictures. Complete the number bond for each. Then, write the subtraction sentence.
53
62
87
5 – 3 = 6 – 2 = 8 – 7 =
5
49
710
45
9 – 5 = 4
81
25
7
a)
a)
d)
a)
b)
b)
b)
e)
c)
c)
f)4
54
Subtraction using Number Bonds
There are 7 birds.
Emphasise the use of words like ‘out’, ‘away’ (take away, gave away, run away, go away, fly away), ‘left’, ‘subtraction’, ‘minus’, ‘less than’ to build the concept of subtraction.
TeachingTip
4 birds are left.
Seven minus three equals four.7 – 3 = 4 is a subtraction sentence.
7 – 3 = 4
There are .
How many are left?
5 2 3
– =
Take away .
1
2
‘–’ is called minus.It means take away.
‘5 – 2’ is the same as 3.
part
partwhole
2
35
3
47
3 cubes are left.
5 – 2 = 3 is a subtraction sentence.
Five minus two equals three.
3 birds fly away.
How many birds are left?7
3–
4
55
Exercise 1
1. Subtract using number bonds.
2. Write each number bond as a subtraction sentence.
3. Look at the pictures. Complete the number bond for each. Then, write the subtraction sentence.
53
62
87
5 – 3 = 6 – 2 = 8 – 7 =
5
49
710
45
9 – 5 = 4
81
25
7
a)
a)
d)
a)
b)
b)
b)
e)
c)
c)
f)4
56
1. Subtract the numbers on the number line.
2. Use the number line to count back and subtract.
1 2 3 4 5 6 7 8 90 10
6 – 3 =
7 – 6 =
4 – 1 = 9 – 3 = 3 – 3 =
8 – 2 = 6 – 4 = 5 – 4 =
Subtraction on a Number Line
a)
a) b) c)
d) e) f)
b)
Exercise 2
12
Subtract 2 from 8. Start with 8 and count
2 steps backwards.
6 7 8
Subtract 4 from 9. Start with 9 and count backwards, 4 steps. 5 6 7 8 9
1234
1 2 3 4 5 6 7 8 90 10
9 – 4 = 51234
1 2 3 4 5 6 7 8 90 10
1 2 3 4 5 6 7 8 90 10
12
57
1. Subtract by crossing out the boxes.
2. Subtract the following. Draw blocks and cross out.
6 – 1 =
9 – 5 =
5 – 2 = a) b)
7 – 4 = c) d)
8 – 2 = e) f)
3 – 2 = a) b)
7 – 2 = c) d)
5 – 4 = e) f)
7 – 1 = g) h)
6 – 4 = i) j) 8 – 4 =
4 – 3 =
Subtraction by Crossing Out
There are 6 apples. 4 apples are eaten. How many apples are left?
2 apples are left.
Cross out the number of
apples eaten.6
2
Exercise 3
7 – 5 =
4 – 1 =
5 – 3 =
6 – 6 =
6
4–
26 – 4 = 2
56
1. Subtract the numbers on the number line.
2. Use the number line to count back and subtract.
1 2 3 4 5 6 7 8 90 10
6 – 3 =
7 – 6 =
4 – 1 = 9 – 3 = 3 – 3 =
8 – 2 = 6 – 4 = 5 – 4 =
Subtraction on a Number Line
a)
a) b) c)
d) e) f)
b)
Exercise 2
12
Subtract 2 from 8. Start with 8 and count
2 steps backwards.
6 7 8
Subtract 4 from 9. Start with 9 and count backwards, 4 steps. 5 6 7 8 9
1234
1 2 3 4 5 6 7 8 90 10
9 – 4 = 51234
1 2 3 4 5 6 7 8 90 10
1 2 3 4 5 6 7 8 90 10
12
57
1. Subtract by crossing out the boxes.
2. Subtract the following. Draw blocks and cross out.
6 – 1 =
9 – 5 =
5 – 2 = a) b)
7 – 4 = c) d)
8 – 2 = e) f)
3 – 2 = a) b)
7 – 2 = c) d)
5 – 4 = e) f)
7 – 1 = g) h)
6 – 4 = i) j) 8 – 4 =
4 – 3 =
Subtraction by Crossing Out
There are 6 apples. 4 apples are eaten. How many apples are left?
2 apples are left.
Cross out the number of
apples eaten.6
2
Exercise 3
7 – 5 =
4 – 1 =
5 – 3 =
6 – 6 =
6
4–
26 – 4 = 2
58
Think Smart
3. Fill in the boxes. Subtract by crossing out.
glasses are empty. – =
There are 9 glasses. 5 are full of water. How many glasses are empty?
a)
bees were left around the hive.
– =
b) There were 8 bees around the hive. 3 bees flew away. How many bees were left?
Complete the subtraction wheel. Fill in the missing numbers.
42
1 5
59
7 2
8
2
8
37
37
4
6
59
Subtracting Zero
9 – 0 = a) b) c)2 – 0 = 3 – 0 =
4 – 0 = d) e) f)5 – 0 = 6 – 0 =
1. Subtract the following.
2. Subtract.
Exercise 4
a) 9
2–
b) 2
1–
c) 6
4–
d) 8
6–
e) 7
5–
Reinforce that we always subtract a smaller number from a greater number. When we subtract 0 from any number, the answer is the number itself.
TeachingTip
Subtracting Numbers
There are 7 butterflies.
How many are left?
3 fly away.
4 butterflies are left.
7
3–
44
7
7 – 3 = 4
4 cars are left.
There are 4 cars.
How many are left?
None goes away.
?
4 4
0–
44 – 0 = 4
58
Think Smart
3. Fill in the boxes. Subtract by crossing out.
glasses are empty. – =
There are 9 glasses. 5 are full of water. How many glasses are empty?
a)
bees were left around the hive.
– =
b) There were 8 bees around the hive. 3 bees flew away. How many bees were left?
Complete the subtraction wheel. Fill in the missing numbers.
42
1 5
59
7 2
8
2
8
37
37
4
6
59
Subtracting Zero
9 – 0 = a) b) c)2 – 0 = 3 – 0 =
4 – 0 = d) e) f)5 – 0 = 6 – 0 =
1. Subtract the following.
2. Subtract.
Exercise 4
a) 9
2–
b) 2
1–
c) 6
4–
d) 8
6–
e) 7
5–
Reinforce that we always subtract a smaller number from a greater number. When we subtract 0 from any number, the answer is the number itself.
TeachingTip
Subtracting Numbers
There are 7 butterflies.
How many are left?
3 fly away.
4 butterflies are left.
7
3–
44
7
7 – 3 = 4
4 cars are left.
There are 4 cars.
How many are left?
None goes away.
?
4 4
0–
44 – 0 = 4
60
Subtracting from 10
cross out.
Exercise 5
10 – 1 = 1. 2. 10 – 2 =
10 – 3 = 3. 4. 10 – 4 =
10 – 5 = 5. 6. 10 – 6 =
10 – 7 = 7. 8. 10 – 0 =
10 ants are standing in a row. 1 ant goes away.1
How many ants are left?
9 ants are left.
10 – 1 = 9
10
9
1
910
There are 10 leaves on a branch of a tree.
How many leaves are left?
4 are blown away.
6 leaves are left on the branch of the tree.
10 – 4 = 6
10
6
4
610
2
61
Solving Word Problems
frogs are left in the pond. – =
1. There were 7 frogs in the pond. 2 frogs came out. How many frogs are left in the pond?
Exercise 6
When we subtract 1 from a number, the answer is the
number just ‘before’.
Fact Zone
There are 6 gift boxes. 1 box is taken away. How many gift boxes are left?
6 – 1 = 5
5 boxes are left.
6
1–
5
6
?
1
There are 5 children. 3 of them are boys. How many girls are there?
5 – 3 = 2
There are 2 girls.
5
2 5
3–
2
2
60
Subtracting from 10
cross out.
Exercise 5
10 – 1 = 1. 2. 10 – 2 =
10 – 3 = 3. 4. 10 – 4 =
10 – 5 = 5. 6. 10 – 6 =
10 – 7 = 7. 8. 10 – 0 =
10 ants are standing in a row. 1 ant goes away.1
How many ants are left?
9 ants are left.
10 – 1 = 9
10
9
1
910
There are 10 leaves on a branch of a tree.
How many leaves are left?
4 are blown away.
6 leaves are left on the branch of the tree.
10 – 4 = 6
10
6
4
610
2
61
Solving Word Problems
frogs are left in the pond. – =
1. There were 7 frogs in the pond. 2 frogs came out. How many frogs are left in the pond?
Exercise 6
When we subtract 1 from a number, the answer is the
number just ‘before’.
Fact Zone
There are 6 gift boxes. 1 box is taken away. How many gift boxes are left?
6 – 1 = 5
5 boxes are left.
6
1–
5
6
?
1
There are 5 children. 3 of them are boys. How many girls are there?
5 – 3 = 2
There are 2 girls.
5
2 5
3–
2
2
62
2. Siya has 7 books. She opens 5 books. How many books are closed ?
books are closed.
– =
3. Irfan has 10 pencils. 2 pencils break. How many pencils are left with Irfan?
4. There are 5 candles. 3 candles are used. How many candles are not used?
candles are not used.
– =
Think SmartCan we subtract the greater number from the smaller number?
Explain why we always subtract the smaller number from the greater number.
TeachingTip
pencils are left with Irfan.
– =
63
Making Subtraction Stories
Ask the children to make subtraction stories from everyday situations around the classroom and home.
TeachingTip
Look at the pictures and complete the number bond family.
+ = 8 8 – =
+ = 8 8 – =
Mental Maths
There are 7 .3 are pink.How many are yellow?
4 flowers are yellow.
7 – 3 = 4
flowers, pink, yellow
CLUES
1
6 lollipops are left.
There are 10 lollipops.4 lollipops are eaten.How many lollipops are left?
10 – 4 = 6
CLUES
lollipops, eaten, left
2
62
2. Siya has 7 books. She opens 5 books. How many books are closed ?
books are closed.
– =
3. Irfan has 10 pencils. 2 pencils break. How many pencils are left with Irfan?
4. There are 5 candles. 3 candles are used. How many candles are not used?
candles are not used.
– =
Think SmartCan we subtract the greater number from the smaller number?
Explain why we always subtract the smaller number from the greater number.
TeachingTip
pencils are left with Irfan.
– =
63
Making Subtraction Stories
Ask the children to make subtraction stories from everyday situations around the classroom and home.
TeachingTip
Look at the pictures and complete the number bond family.
+ = 8 8 – =
+ = 8 8 – =
Mental Maths
There are 7 .3 are pink.How many are yellow?
4 flowers are yellow.
7 – 3 = 4
flowers, pink, yellow
CLUES
1
6 lollipops are left.
There are 10 lollipops.4 lollipops are eaten.How many lollipops are left?
10 – 4 = 6
CLUES
lollipops, eaten, left
2
64
Observe the pictures below and write a subtraction story for each.
Exercise 7
eaten
1.
Give playing cards, numbered from 1 to 9, to the children. Ask them to draw two cards from the pile. Subtract the smaller number from the greater number. Write the subtraction sentence. Repeat the same activity again.
Maths Fun
Subtraction Story________________________________________________________________________________________________________________
bananas, eaten, left
CLUES
fall
2.
Subtraction Story________________________________________________________________________________________________________________
mangoes, fall, left, tree
CLUES
65
1. Complete the number bond. Write the subtraction sentence.
310
36
a) b)
3. Subtract the following.
a) b) c) d) e)81–
97–
66–
40–
32–
4. Read the story and subtract.
1 0
3–
There were 10 eggs in the basket. 3 eggs broke. How many eggs are left unbroken?
eggs are left unbroken.
– =
1 2 3 4 5 6 7 8 9 100
9 – 3 = a) b) 6 – 1 =
8 – 0 = c) d) 4 – 2 =
64
Observe the pictures below and write a subtraction story for each.
Exercise 7
eaten
1.
Give playing cards, numbered from 1 to 9, to the children. Ask them to draw two cards from the pile. Subtract the smaller number from the greater number. Write the subtraction sentence. Repeat the same activity again.
Maths Fun
Subtraction Story________________________________________________________________________________________________________________
bananas, eaten, left
CLUES
fall
2.
Subtraction Story________________________________________________________________________________________________________________
mangoes, fall, left, tree
CLUES
65
1. Complete the number bond. Write the subtraction sentence.
310
36
a) b)
3. Subtract the following.
a) b) c) d) e)81–
97–
66–
40–
32–
4. Read the story and subtract.
1 0
3–
There were 10 eggs in the basket. 3 eggs broke. How many eggs are left unbroken?
eggs are left unbroken.
– =
1 2 3 4 5 6 7 8 9 100
9 – 3 = a) b) 6 – 1 =
8 – 0 = c) d) 4 – 2 =
66
Aim: To subtract numbers and find the difference.Requirement: 1 dice for each child.
Record Table
Greater number Smaller number Difference
6 2 6 – 2 = 4
Steps:
1. Arrange children in pairs.
2. Each child rolls a dice and writes the number shown on both the dice in the table given below.
3. Subtract the smaller number from the greater number to get the difference. Repeat the game until the given table is filled.
MATHS LAB ACTIVITY
Maths Lab Activity
67
I Can
1. Count the circle and write the number in the boxes. Draw lines to match the identical numbers.
2. Fill in the missing numbers from 1 to 20.
1 5 9
13 18
3. Find the missing numbers in the pattern.
8 10 12 14 16
Numbers 11 to 205