Imagine_Maths_TM_Grade2,3 & 4_Sample

MATHEMATICS

Teacher Manual

Grades 2, 3 & 4

Teacher Manual

MATHEMATICS

Master Mathematical Thinking

Sales Sample

Mathematics is not just another subject. It is an integral part of our lives. It shapes the very foundation of our understanding, personality and interaction with the world around us.

However, due to the subject’s abstract nature, the stress of achieving high academic scores and complex teaching methods, most children develop a fear of mathematics from an early age. This fear not only hinders their mathematical thinking, logical reasoning and general problem solving abilities, but also negatively impacts their performance in other academic subjects. This creates a learning gap which widens over the years.

The NEP 2020 has distinctly recognised the value of mathematical thinking among young learners and the significance of fostering love for this subject by making its learning engaging and entertaining. Approaching maths with patience and relatable real-world examples can help nurture an inspiring relationship with the subject. It is in this spirit that Uolo has introduced the Imagine Mathematics product for elementary grades (1 to 8). This product’s key objective is to eliminate the fear of mathematics by making learning exciting, relatable and meaningful for children. This is achieved by making a clear connection between mathematical concepts and examples from daily life. This opens avenues for children to connect with and explore maths in pleasant, relatable, creative and fun ways.

This product, as recommended by the NEP 2020 and the recent NCF draft, gives paramount importance to the development of computational and mathematical thinking, logical reasoning, problem solving and mathematical communication, with the help of carefully curated content and learning activities.

IMAGINE Mathematics strongly positions itself on the curricular and pedagogical approach of the Gradual Release of Responsibility (GRR), which has been highly recommended by the NEP 2020, the latest NCF Draft and other international educational policies. In this approach, while learning any new mathematical concept, learners first receive sufficient modelling, and then are supported to solve problems in a guided manner before eventually taking complete control of the learning and application of the concept on their own. In addition, the book is technologically empowered and works in sync with a parallel digital world which contains immersive gamified experiences, video solutions and practice exercises among other things. Interactive exercises on the digital platform make learning experiential and help in concrete visualisation of abstract mathematical concepts.

In IMAGINE Mathematics, we are striving to make high quality maths learning available for all children across the country. The product maximizes the opportunities for self-learning while minimising the need for paid external interventions, like after-school or private tutorial classes.

The book adapts some of the most-acclaimed, learner-friendly pedagogical strategies. Each concept in every chapter is introduced with the help of real-life situations and integrated with children’s experiences, making learning flow seamlessly from abstract to concrete. Clear explanations and simple steps are provided to solve problems in each concept. Interesting facts, error alerts and enjoyable activities are smartly sprinkled throughout the content to break the monotony and make learning holistic. Most importantly, concepts are not presented in a disconnected fashion, but are interlinked and interwoven in a sophisticated manner across strands and grades to make learning scaffolded, comprehensive and meaningful.

As we know, no single content book can resolve all learning challenges, and human intervention and support tools are required to ensure its success. Thus, Imagine Mathematics not only offers the content books, but also comes with teacher manuals that guide the pedagogical transactions that happen in the classroom; and a vast parallel digital world with lots of exciting materials for learning, practice and assessment. In a nutshell, Imagine Mathematics is a comprehensive and unique learning experience for children.

On this note, we welcome you to the wonderful world of Imagine Mathematics. In the pages that follow, we will embark on a thrilling journey to discover wonderful secrets of mathematics—numbers, operations, geometry and measurements, data and probability, patterns and symmetry, algebra and so on and so forth. Wishing all the learners, teachers and parents lots of fun-filled learning as you embark upon this exciting journey with Uolo.

Key Elements of a Lesson—A Quick Glance

Multiplication 4

Clear and concise lesson titles that can be implemented through the academic year. Each lesson is perfectly aligned to the topics covered in the Imagine Mathematics learners’ content book.

Multiplication 4

1.

2.

Multiplication 4

● make equal groups and find the total.

Learning Outcomes

Clear, specific and measurable learning outcomes of what students should know, understand, or do by the end of the lesson.

1. Forming Groups Grouping

3.

Multiplication 4

2. Repeated Addition Repeated Addition

Learning Outcomes

3. The Multiplication Symbol What is Multiplication

Students will be able to:

● make equal groups and find the total.

● find the total using repeated addition.

Learning Outcomes

● write a multiplication sentence using the symbols (×) and (=) for a given group of things.

1.

Students will be able to:

Alignment to NCF

● make equal groups and find the total.

2.

● Uses repeated adding to solve simple multiplication problems up to 99.

● find the total using repeated addition.

3.

● find the total using repeated addition.

Students will be able to:

● write a multiplication sentence using the symbols (×) and (=) for a given group of things.

Learning Outcomes as recommended by the NEP 2020 and the recent National Curricular Framework (NCF).

Alignment to NCF

● make equal groups and find the total.

● find the total using repeated addition.

● Uses repeated adding to solve simple multiplication problems up to 99.

● write a multiplication sentence using the symbols × and = for a given group of things.

Let’s Recall

Learning Outcomes

● Recap to check if students know how to add two numbers using pictures.

Students will be able to:

● Ask students to solve the questions given in the Let’s Warm-up section. Vocabulary

●

Alignment to NCF

● make equal groups and find the total.

● Uses repeated adding to solve simple multiplication problems up to 99.

● find the total using repeated addition.

● write a multiplication sentence using the symbols × and = for a given group of things.

Let’s Recall

● Recap to check if students know how to add two numbers using pictures.

Alignment to NCF

● Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary to help recap the important terms that are introduced, defined or emphasized in the chapter.

● Uses repeated adding to solve simple multiplication problems up to 99.

Vocabulary

Let’s Recall

● equal group; unequal group; repeated addition; skip count; multiplication fact

● Recap to check if students know how to add two numbers using pictures.

● Ask students to solve the questions given in the Let’s Warm-up section.

Teaching Aids

Vocabulary

● Imagine Mathematics book, notebook

● Circular plates made out of paper (5 per group of 3); counters (30 per group of 3)

● equal group; unequal group; repeated addition; skip count; multiplication fact

● QR codes to go to the Do It Yourself pages.

Teaching Aids

● Imagine Mathematics book, notebook

● Circular plates made out of paper (5 per group of 3); counters (30 per group of 3)

● QR codes to go to the Do It Yourself pages.

QR Code: Access to digital solutions and other interactive resources

● write a multiplication sentence using the symbols × and = for a given group of things.

Let’s Recall

● Recap to check if students know how to add two numbers using pictures.

Learning Outcomes

Recap exercises to check the understanding of prerequisite concepts before starting a topic and establishing familiarity towards it.

Alignment to NCF

● Ask students to solve the questions given in the Let’s Warm-up section.

Students will be able to:

● Uses repeated adding to solve simple multiplication problems up to 99.

Vocabulary

● make equal groups and find the total.

● equal group; unequal group; repeated addition; skip count; multiplication fact

● find the total using repeated addition.

Let’s Recall

● write a multiplication sentence using the symbols × and = for a given group of things.

Teaching Aids

● Recap to check if students know how to add two numbers using pictures.

● Imagine Mathematics book, notebook

● Ask students to solve the questions given in the Let’s Warm-up section.

Alignment to NCF

● Circular plates made out of paper (5 per group of 3); counters (30 per group of 3)

● QR codes to go to the Do It Yourself pages.

● Uses repeated adding to solve simple multiplication problems up to 99.

Vocabulary

Let’s Recall

● equal group; unequal group; repeated addition; skip count; multiplication fact

● Recap to check if students know how to add two numbers using pictures.

Teaching Aids

● Ask students to solve the questions given in the Let’s Warm-up section.

Aids and resources that the teachers can use to significantly improve the teaching and learning process for the students.

● Imagine Mathematics book, notebook

Vocabulary

● Circular plates made out of paper (5 per group of 3); counters (30 per group of 3)

● equal group; unequal group; repeated addition; skip count; multiplication fact

● QR codes to go to the Do It Yourself pages.

Teaching Aids

● Imagine Mathematics book, notebook

● Circular plates made out of paper (5 per group of 3); counters (30 per group of 3)

● QR codes to go to the Do It Yourself pages.

Answers, provided after each chapter, for the questions given in Do It Together and Think and Tell sections of the Imagine Mathematics book.

A detailed and organized lesson plan for the teachers that outlines what will be taught, how it will be taught, and what activities and assessments are to be used to facilitate learning.

Learning Outcomes

Students will be able to:

● make equal groups and find the total.

● find the total using repeated addition.

● write a multiplication sentence using the symbols (×) and (=) for a given group of things.

Alignment to NCF

● Uses repeated adding to solve simple multiplication problems up to 99.

Let’s Recall

● Recap to check if students know how to add two numbers using pictures.

● Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

● equal group; unequal group; repeated addition; skip count; multiplication fact

Teaching Aids

● Imagine Mathematics book, notebook

● Circular plates made out of paper (5 per group of 3); counters (30 per group of 3)

1 Forming Groups

Learning Outcomes

● Students will be able to make equal groups and find the total.

Concept I Do

Instruct: Go to the second page of chapter 4.

Ask: How many groups of balloons does Raghu have? How many balloons are there in each group? What is the total number of balloons?

Write: Raghu’s balloons = 5 groups of 3 = 15.

Say: Raghu bought 5 groups of 3 balloons, which is 15 balloons in all.

Draw pictures to show some more examples of equal groups.

Discuss the examples with the students. Show some more examples on equal and unequal groups to the students.

Do It Together

Instruct students to refer to the problem given in Do It Together.

Distribute the plates and the counters to the students.

Instruct: Work in groups of 3. Imagine that the counters are guavas. Show the problem using the plates and the counters. Then, in your notebook, first write the number of plates; then the number of counters on each plate; and finally, the total number of counters.

Write: A. 3 groups of 9;  B. 4 groups of 8.

Ask the students to read each new problem written on the board and show them using the plates and the counters. They will then write the total number in their notebooks.

Draw the given set of balloons on the board.

Ask: Now, look at the set of balloons shown on the board. How are they different from Raghu’s?

Read the question from the Think and Tell section aloud to the students. Discuss the difference between equal and unequal groups.

We Do

Teacher Tip: If resources are unavailable, you can ask them to make groups using things around them like pencils, crayons, etc.

Do It Yourself You Do

Say: Go to the Do It Yourself 4A exercise. Solve Q1 and Q3 on your own.

Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Which is more: 3 groups of 9 or 6 groups of 7?

Say: 3 groups of 9 is 27 and 6 groups of 7 is 42. Since 42 > 27, 6 groups of 7 is more than 3 groups of 9.

Instruct: Solve Q2, 4 and 5 from Do it Yourself 4A for homework.

2 Repeated Addition

Learning Outcomes

● Students will be able to find the total using repeated addition.

Concept I Do

Instruct: Go to the section Repeated Addition of chapter 4.

Say: Let us again look at the pictures of Raghu’s balloons. We know that there are 3 balloons in each group. Let us now add all the balloons to find the total.

Ask: What is the total?

Write: 3 + 3 + 3 + 3 + 3 = 15.

Say: We write 3 below each group of balloons. So, when 3 is added 5 times, we get 15 balloons in total. When we add the same number again and again, it is called repeated addition.

Ask: Can we write a repeated addition sentence for Gary’s balloons? Discuss.

Balloons

Do It Together We Do

Instruct students to refer to the problem given in Do

It Together

Distribute the plates and the counters to the students.

Instruct: Work in groups of 3. Imagine that the counters are flowers. Show the problem using the plates and the counters. Then, in your notebook, first write the grouping shown by the flowers, and the repeated addition sentence.

Write: A. B. 6 groups of 4.

Instruct: Look at the pictures given on the board. Show them using the plates and the counters. Write the equal grouping and repeated addition sentences, in your notebooks.

Teacher Tip: Help students put the counters into equal groups and write the number of items repeatedly to find the answer.

Do It Yourself You Do

Say: Go to the Do It Yourself 4B exercise. Solve Q1 and Q2 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Which of these is the correct way of writing 8 groups of 4: 8 + 8 + 8 + 8 or 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4?

Say: We write the groups first and then the number of things in each group. 8 groups of 4 shows 8 groups with 4 things in each group. So, 8 groups of 4 will be written as 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4.

Instruct: Solve Q3, 4, and 5 from Do It Yourself 4B for homework.

Gary's

4  +  3  +  2

3 Multiplication Symbol

Learning Outcomes

● Students will be able to write a multiplication sentence using the symbols (×) and (=) for a given group of things.

Concept I Do

Instruct: Go to the section What is Multiplication of chapter 4.

Say: We know that Raghu has 5 groups of 3 balloons which is 15 balloons. Let us write it in different ways. Write the multiplication sentence on the board.

Say: A multiplication sentence is written as the number of equal groups first, then the multiplication symbol (×), the number of things in each group, followed by the equal-to (=) symbol, and finally, the total number of things.

Read the question from the Think and Tell section aloud to the students. Discuss their responses, guiding them wherever needed.

Do It Together We Do

Instruct students to refer the problem given in Do

It Together

Distribute the plates and the counters to the students.

Instruct: Work in groups of 3. Imagine that the counters are crayons. Show the problem using the plates and the counters. Then, in your notebook, first write the grouping shown by the crayons and the multiplication sentence.

Draw: A. B.

Instruct: Look at the pictures given on the board. Show them using the plates and the counters. Write the multiplication sentences, in your notebooks.

Teacher Tip: Make sure that each member of the group gets to solve one problem.

Do It Yourself You Do

Say: Go to the Do It Yourself 4C exercise. Solve Q1 and Q4 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: How is 9 × 4 different from 4 × 9? How are they similar?

Say: 9 × 4 shows 9 groups with 4 things in each group. 4 × 9 shows 4 groups with 9 things in each group. Both multiplications give the same answer, which is 36.

Instruct: Solve Q2, 3, and 5 from the Do It Yourself 4C for homework.

1. Grouping

Think and Tell

No, it will not be easy to find the total for unequal groups. Skip counting by the same number is easier.

Do It Together

There are 3 plates. Each plate has 4 guavas.

3 groups of 4 guavas.

2. Repeated Addition

Do It Together

There are 3 bunches of flowers with 5 flowers in each. How many flowers are there in all?

3 groups of 5 flowers.

5 + 5 + 5 = 15

There are 5 flowers.

3. What is Multiplication

Think and Tell

If there are 3 groups and 5 stars in each group, there will be a total of 15 stars.

Do It Together

There are 5 boxes of crayons. Each box has 5 crayons. How many crayons are there in all?

3 groups of 5

5 + 5 + 5 = 15

3 × 5 = 15

There are 15 crayons in all.

Learning Outcomes

Students will be able to:

● read the time to the half hour on a clock.

● recall the days of the week and use today, tomorrow and yesterday.

● name the months of the year and arrange them in order.

● recall the days of the week and months of the year and use today, tomorrow and yesterday.

● read a calendar and identify the different seasons and festivals in a year.

● solve problems on reading a timetable.

Alignment to NCF

● Identifies the days of the week and months of the year.

● Sequences the events occurring according to their duration in terms of hours/days; for example, does a child remain in school for a longer period than at home?

Let’s Recall

Recap to check if students know the different parts of a day as morning, afternoon, evening and night; and the activities that they do in each part of the day.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● clock, days, week, year, months, time, seasons, festivals, timetable, departure

Teaching Aids

● Imagine Mathematics book, notebook

● Clock with movable hour and minute hands (1 for class); chart paper (1 per group); sketch pens (1 set per group); Colour pencils (1 set per group)

Time on a Clock

Learning Outcomes

● Students will be able to read the time to the half hour on a clock.

Concept I Do

Instruct: Go to the section Time on a Clock in chapter 13.

Ask: What time does Mia have to go for her drawing class? How will you know that it is 5 o’clock?

Say: Mia has to go for her drawing class at 5 o’clock. When the minute hand is on 12 and the hour hand is on 5, the time will be 5 o’clock. The time to the hour is read by looking at the minute and hour hand. The minute hand will always be on 12 and the hour hand on the number of the hour.

Ask: What time does the clock show?

Say: The time on the clock shows half past 4. Let’s see how we can read time to the half hour.

Discuss how to read time to the half hour on a clock.

Say: When the time is to the half hour, the minute hand is always on 6. The hour hand is between 2 numbers. The number before the hour hand tells us the hour that has passed. For example, if the hour hand is between 7 and 8, the time is 7:30 or half past 7.

Do It Together We Do

Instruct Work in pairs. Look at the time on my clock. I will show you 2–3 times. Read the time on the clock each time. Discuss with your partner what all the clocks have in common and what is different.

Move the hands of the clock to show the time 1:30, 6:30, and 10:30.

Ask: What time do you see on these clocks.? What is the same and different in these clocks?

Discuss student responses.

Say: The minute hand on the clock was not moved—it was on 6 for all the times shown. The hour hand moved. Instruct students to refer to the problem given in Do It Together.

Instruct: Read the time given on the clocks. Write the time in 2 different ways.

Discuss how the time on the first 2 clocks is different from the last clock.

Teacher Tip: Discuss the Error Alert section here, where they need to remember that the long hand is the minute hand and the short hand is the hour hand.

Do It Yourself You Do

Say: Go to the Do It Yourself 13A exercise. Solve Q1, Q2 and Q4 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: A train takes 2 hours to reach Station B from Station A. If the train starts from Station A at 9:30, what will be the time on the clock when the train reaches Station B?

Say: The train will reach Station B at 11:30.

Instruct: Solve Q3 and Q5 from Do It Yourself 13A for homework.

Learning Outcomes

● Students will be able to recall the days of the week and use today, tomorrow and yesterday.

Concept I Do

Instruct: Go to the section Days of the Week in chapter 13. Show the monthly calendar to the students. Let them recite the days of the week, in chorus twice.

Ask: What day is it today? What day was it yesterday? What day will it be tomorrow?

Discuss their responses, guiding them wherever needed.

Ask: How many days are there in a week?

Say: There are 7 days in a week.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Instruct: Read the names of the sweets available in a shop each day. Fill in the blanks. Discuss the answers with the students.

Distribute the chart paper and sketch pens among the groups.

Instruct: In groups, make a display board for the shopkeeper to put in his shop to show the different days and the sweets that he sells each day.

Allow students to display their charts on the board.

Ask: What day is it today? What sweet is the shopkeeper selling today? What sweet did he sell yesterday? What sweet will he sell tomorrow?

Accept student responses.

Teacher Tip: Instruct students to put their Imagine Mathematics books aside before they start working on the chart.

Do It Yourself You Do

Say: Go to the Do It Yourself 13B exercise. Solve Q1 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Surbhi attends night school every Tuesday, Thursday and Saturday. Which are the days when Surbhi does not have school?

Say: Surbhi does not have school on Monday, Wednesday, Friday and Sunday.

Instruct: Solve Q2 from Do it Yourself 13B for homework.

Learning Outcomes

● Students will be able to name the months of the year and arrange them in order.

Concept I Do

Instruct: Go to the section Months of the Year in chapter 13. Show the monthly calendar to the students. Let them recite the months of the year, in chorus twice.

Ask: What month is it now? What is the next month?

Discuss their responses, guiding them wherever needed.

Ask: How many months are there in a year?

Say: There are 12 months in a year. Different months have different numbers of days.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Instruct: Read the calendar in the Do It Together and check the number of days in each month. Colour the months with only 30 days in yellow and the months with 31 days in green.

Ask: What months did you colour in yellow? What months did you colour in green?

Say: April and June were coloured in yellow since they have 30 days. January, March, May, July and August were coloured in green since they have 31 days.

Distribute the chart paper, sketch pens and colour pencils among the students.

Instruct: Work in groups of 6. Each group makes the calendar for the complete year. Each student makes the calendar for 2 months. Colour them in the same colour as done in the Do It Together section. Paste them on the chart to form a complete calendar.

Allow students to display their charts on the board.

Teacher Tip: Distribute squared paper to the students if they are facing an issue with making a calendar.

Do It Yourself You Do

Say: Go to the Do It Yourself 13B exercise. Solve Q3 and Q5 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Say: Rahul’s birthday comes in a month that has 31 days. The name of the month starts with the letter ‘J’ and it is not the first month of the year.

Ask: In which month does Rahul’s birthday fall?

Say: The months that have 31 days are January, March, May, July, August, October and December. January and July start with the letter ‘J’. Since, Rahul’s birthday is not in the first month of the year, his birthday comes in July.

Instruct: Solve Q4 from Do It Yourself 13B for homework.

4 Seasons and Festivals

Learning Outcomes

● Students will be able to read a calendar and identify the different seasons and festivals in a year.

Concept I Do

Instruct: Go to the section Seasons and Festivals in chapter 13.

Ask: What season is it now? Are you wearing your winter clothes or summer clothes? What festival comes in this season?

Discuss student responses.

Say: There are 5 seasons—Winter, Spring, Summer, Monsoon and Autumn. Different festivals come in different seasons.

Read the section on Seasons and Festivals of chapter 13.

Do It Together We Do

Distribute the chart paper and the sketch pens.

Instruct: Work in groups of 5. Each member of the group chooses one season. He/she will then draw a picture of that season and write the festivals that come in that season. Each group will then come up and present their charts.

Read the question from the Think and Tell section aloud to the students. Discuss their work, guiding them wherever needed.

Instruct students to refer to the problem given in Do It Together.

Instruct: Discuss the questions in your groups. Write the answers.

Teacher Tip: Remind students that some seasons may overlap and some festivals fall on the same date every year and some might fall in different months.

Do It Yourself You Do

Say: Go to the Do It Yourself 13C exercise. Solve Q1, Q2a, Q2b, and Q4a. to b. on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Richa visited her grandparents after April and came back before monsoon. In which season did she visit her grandparents? For how many months did she stay there?

Say: Richa visited her grandparents in the month of May and came back before July. So, she visited her grandparents in the summer season. She visited them for 2 months.

Instruct: Solve Q2c, Q2d, Q2e, Q3, Q4c, Q4d, Q4e and 5 from Do It Yourself 13C for homework.

Learning Outcomes

● Students will be able to solve problems on reading a timetable.

Concept I Do

Instruct: Go to the section Story Problems on Time in chapter 13. Look at Noni’s timetable.

Ask: On which day does Noni have her first Art class of the week? What period is the Art class? What does a timetable tell us?

Say: Noni has her first Art class of the week on Wednesday in the 2nd period. We look for Art in each row that shows the day. Once we have found it, we look for the period it is in. A timetable tells us the daily routine of a student in school. It tells us the number of days the school is open, the number of periods, the subjects that will be taught on each day. It also tells us after which period the students will have their lunch break. Discuss the different features of the timetable with the students.

Do It Together We Do

Instruct students to refer to the problem given in Do It

Together

Instruct: Work in groups of 4. Discuss Manoj’s daily timetable and fill in the blanks. Discuss student responses.

Instruct: Work in your groups of 4. In your notebooks, make a new timetable with your daily routine for tasks given below: 1. Wake up; 2. School start time; 3. Lunch break; 4. School end time; 5. Homework time; 6. Play time; 7. Dinner time; 8. Bedtime. Discuss the timetable of the other group members.

Ask: How is your timetable different from the timetable made by the other members of your group? How is it the same?

Say: Some activities like school start time, school end time, lunch break is the same for all students. But activities like waking up, homework time, play time, dinner time and bedtime might be different for different students.

Teacher Tip: Ask students if there are other places where they might have seen a timetable and how is it helpful.

Do It Yourself You Do

Say: Go to the Do It Yourself 13D exercise. Solve Q3 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: A timetable shows that Train A leaves at 3:30 and Train B leaves 3 hours later. What is the time written on the timetable for Train B?

Say: The time of departure written on the timetable B is 6:30.

Instruct: Solve Q1, 2, 4, and 5 from Do It Yourself 13D for homework.

1. Time on a Clock

Do It Together

12:30 2:30 12:00

2. Days of the Week

Do It Together

1. Pudding

2. Wednesday

3. Monday

4. Thursday

3. Months of the Year

Do It Together

1. Months coloured yellow: April, June

2. Months coloured green: January, March, May, July, August

3. January—31 days and February—28 days

4. Hours—Going to school, watching television Days—exams, camping Months—summer vacations, seasons

4. Seasons and Festivals

Do It Together

1. July and August

2. 3

3. Spring

4. Spring

5. Monsoon

Think and Tell

Different people celebrate different festivals. For example, the Sikhs celebrate Guru Nanak Jayanthi that falls in the spring. Christians celebrate Easter that falls in the spring.

5. Story problems in Time

Do It Together

1. 8:00 2. swimming

3. Friday 4. art

Learning Outcomes

Students will be able to:

● identify different coins and notes (up to ₹500).

● count money to find the notes and coins needed to pay for something that they buy (up to ₹50).

● solve problems on adding and subtracting money.

Alignment to NCF

● Represents an amount up to ₹100 using 3–4 notes and coins (of same/different denominations of play money).

Let’s Recall

● Recap to check if students know where to use money and its value.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● notes, coins, rupees, paise, total cost

Teaching Aids

● Imagine Mathematics book, notebook

● Play money (1 note of ₹500, ₹100, ₹50, ₹20, ₹10, ₹5, ₹2, ₹1 – 1 set per group)

1 Indian Coins and Notes

Learning Outcomes

● Students will be able to identify different coins and notes (up to ₹500).

Concept I Do

Instruct: Go to the second page of chapter 14. Look at the pictures of the coins and notes given.

Ask: Which type of coins have you seen in your daily life? What type of notes have you seen?

Say: Coins that we see in our daily lives are ₹1, ₹2, ₹5, ₹10 and ₹20. The notes that we usually see are ₹10, ₹20, ₹50, ₹100 and ₹500.

Ask: Has anyone seen ₹5 note or 50 paise coin? What are the coins that you have never seen? Why? Discuss their responses, guiding them wherever needed.

Say: The 5p, 10 p, 20 p, 25 p or 50 p coins are not used anymore. Show them different notes and coins.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Distribute the play money to the students.

Instruct: Work in groups of 4. Look at the play money and sort them into notes and coins. Discuss in your groups the difference between the different notes and coins. Compare the money values with the notes and coins given in your book. Now, fill in the boxes in the Do It Together section.

Discuss the different elements in each note and coin.

Teacher Tip: If possible, arrange for notes and coins that are not used anymore to show the students.

Do It Yourself You Do

Say: Go to the Do It Yourself 14A exercise. Solve Q3, Q4 and Q5 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Which is costlier – a chocolate costing ₹50 or a toy costing ₹200? How do you know?

Say: The cost of the toy is ₹200 and the chocolate is ₹50. ₹200 > ₹50 so the toy is costlier.

Instruct: Solve Q1 and 2 from Do it Yourself 14A for homework.

How to Pay

Learning Outcomes

● Students will be able to count money to find the notes and coins needed to pay for something that they buy (up to ₹100).

Concept I Do

Instruct: Go to the section Exchange of Money in chapter 14.

Ask: So, Riya goes to the market and purchases a lunch box. What is the cost of the lunch box? Read the different ways that Riya can pay for the lunch box.

Ask: What is the cost of the lunch box? Can you give one more way that is not in the book to pay for the lunch box? How do you know?

Say: The cost of the lunch box is ₹50. Riya can pay using ten ₹5 coins or fifty ₹1 coins.

Ask: How will you pay for a pen that costs ₹60? Discuss the answers. Write the amounts on the board. Discuss their responses, guiding them wherever needed.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together. Distribute the play money among the students.

Instruct: Work in groups of 4. Read the cost of each item. Use the notes and coins to make up the amount. Circle the notes and coins needed to buy these things in your books. Write the amounts in your notebooks as given on the board.

Write: ₹40 = ₹20 + ₹10 + ₹10

Teacher Tip: Help students put the play money in such a way that they make up the required amount of money and find the answer.

Do It Yourself You Do

Say: Go to the Do It Yourself 14B exercise. Solve Q1 and Q3 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: We have many notes of ₹50, ₹10 and ₹5. What is the minimum number of notes needed to make ₹75? Say: We can make ₹75 in different ways. ₹50 + ₹10 + ₹10 + ₹5 = ₹75. So, the minimum number of notes required is 4.

Instruct: Solve Q2, Q4 and Q5 from Do it Yourself 14B for homework.

Adding and Subtracting Money

Learning Outcomes

● Students will be able to solve problems on adding and subtracting money.

Concept I Do

Instruct: Go to the section Adding and Subtracting Money in chapter 14.

Say: We know that the cost of the lunch box is ₹50 and the cost of the bottle is ₹90.

Ask: How can we find out how much does Riya needs to pay for both the items?

Say: We add the cost of the lunch box and the bottle to find the total cost. ₹50 + ₹90 = ₹140

Read the question from the Think and Tell section aloud to the students. Discuss their responses, guiding them wherever needed. Write the different notes that Riya can use to pay ₹140.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Distribute the play money to the students.

Instruct: Work in groups of 4. Read the cost of each item. Use the notes and coins to make up the amount. Then find the total amount of money paid for the items or the amount of money that will be returned to them. Add or subtract using the column method in your notebooks. Write the answers in the Do It Together section.

Teacher Tip: Make sure that each member of the group gets to solve one problem.

Do It Yourself You Do

Say: Go to the Do It Yourself 14C exercise. Solve Q1, Q3 and word problems on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to the relevant questions in the Chapter Checkup section.

Ask: Anna buys a book for ₹85. Anna pays with a ₹100 note. Which coins can be used by the shopkeeper to give her change?

Say: To find the amount of money that the shopkeeper will return, we subtract. ₹100 – ₹85 = ₹15

The shopkeeper can pay in different ways. He can pay with one ₹10 and one ₹5 coin. He can also pay with three ₹5 coins.

Instruct: Solve Q2, Q4 and Q5 from Do it Yourself 14C for homework.

1. Indian Coins and Notes

Do It Together

`200  `2  `50  `10  `20  `5

2. How to Pay

Do It Together

`25 = `20, `5

`40 = `20, `10, `10

`65 = `50, `10, `5

`24 = `20, `2, `2

`7 = `5, `2

3. Adding and Subtracting Money

Think and Tell

She can give one ₹100 note and two ₹20 notes or she can give one ₹100 note and four ₹10 notes.

Do It Together

Total cost of 1 bag and 1 toy train = ₹102

Total cost of 1 hat and 1 bag = ₹105

Change amount after buying a bag = ₹25

Change amount after buying a box of crayons = ₹33

Place Value 1

Learning Outcomes

Students will be able to:

● write the place value and expanded form for 4-digit numbers.

● read and show a 4-digit number using the abacus and place value blocks.

● compare 2 or more 4-digit numbers and arrange them in ascending and descending order.

● form 4-digit numbers using the given 4 digits.

● round off numbers up to 3 digits to the nearest 10 using a number line.

Alignment to NCF

● Works with three-digit numbers a) reads and writes numbers up to 999 using place value b) compares numbers up to 999 for their value based on their place value.

Let’s Recall

● Recap to check if students know about place values of 2-digit and 3-digit numbers.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● place value, abacus, expanded form, comparison, ascending order, descending order, rounding off

Teaching Aids

● Imagine Mathematics book, notebook

● Place value chart showing 1000s, 100s, 10s, and 1s (1 each per student); place value blocks of 1000s, 100s, 10s, and 1s (10 of each per group of 4); 4-rod abacus (1 per group of 4)

1 Place Value and Expanded Form of 4-digit Numbers

Learning Outcomes

● Students will be able to write the place value and expanded form of 4-digit numbers.

Concept I Do

Instruct: Go to the second page of chapter 1.

Ask: How many coins does Ajay have? How many more coins did Ajay’s father give him? How many ones are added?

Say: Ajay had 999 coins. His father gave him 1 more. 999 is 9 hundreds, 9 tens, and 9 ones. 1 coin is added to 999 coins. So, 1 one is added. 1 more than 999 is 1000. So, Ajay has 1000 coins.

Ask: What is the place value and the expanded form of a number? How will you write 3459 using the place value and the expanded form?

Discuss student responses, guiding them wherever needed.

Say: The place value of a digit is the value of its position in a number. A 3-digit number has 3 places— hundreds, tens and ones. A 4-digit number has 4 places—thousands, hundreds, tens, and ones. So, 3459 has 3 thousands, 4 hundreds, 5 tens and 9 ones. The place value is formed by multiplying the digit by the value of the place. For example, 3 × 1000 = 3000. So, the place value of 3 is 3000. The expanded form is the sum of the place values of its digits. The expanded form of 3459 is 3000 + 400 + 50 + 9.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together

Distribute the place value charts to the students.

Instruct: Work in groups of 4. Show the 4-digit number 4319 on the place value chart by writing each digit in its correct place. In your notebooks, write the number of thousands, hundreds, tens, and ones. Also, write the number using place values and in its expanded form. Then, fill in the blanks in the Do It Together section.

Ask: How many thousands, hundreds, tens and ones are there in the number? How did you write the number using the place value and the expanded form?

Say: There are 4 thousands, 3 hundreds, 1 ten and 9 ones in 4319. The place value of the digits are 4000, 300, 10, 9. The number in its expanded form can be written as 4000 + 300 + 10 + 9.

Instruct: Now repeat the activity for the number 1943.

Teacher Tip: If place value charts are not available, the students can draw the chart in their notebook to show the 4-digit number.

Do It Yourself You Do

Say: Go to the Do It Yourself 1A exercise. Solve Q6 a. to c., Q7 a. to c., and Q8 a. to d. on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice, refer to relevant questions in the Chapter Checkup section.

Ask: How will you write the expanded form for a number which has 3 hundreds more than 8823?

Say: 3 hundreds more than 8823 = 8823 + 300 = 9123. So, the expanded form of 9123 = 9 thousands + 1 hundred + 2 tens + 3 ones = 9000 + 100 + 20 + 3.

Instruct: Solve Q6 d. to h., Q7 d. to h., Q8 d. to j. and Q9 from Do it Yourself 1A for homework.

2 Reading 4-digit Numbers

Learning Outcomes

● Students will be able to read and show a 4-digit number using the abacus and place value blocks.

Concept I Do

Instruct: Go to the section Reading 4-Digit Numbers of chapter 1. Look at the place value blocks.

Ask: How many place value blocks do you see? How will you read the number?

Say: There are 2 thousands, 2 hundreds, 3 tens and 8 ones blocks. We can write their place values as: 2000, 200, 30 and 8. We can write them in expanded form as 2000 + 200 + 30 + 8 which is equal to 2238. We can read the number as two thousand two hundred thirty-eight.

Discuss how to read 4-digit numbers.

Do It Together We Do

Instruct students to refer to the problem given in Do

It Together.

Distribute the place value blocks and the abacus to the students.

Instruct: Work in groups of 4. Use the same number of blocks, as given in the question, to show the number. In your notebooks, write the number of thousands, hundreds, tens and ones. Also write the place value of each digit of the number, its expanded form and in words. Then, fill in the blanks in the Do It Together section.

Ask: How many thousands, hundreds, tens and ones are there in the number? How will you write the place value, expanded form and number name?

Say: There are 6 thousands, 4 hundreds, 3 tens and 4 ones in 6434. The place value of each digit in 6434 is 6000, 400, 30, 4. The expanded form is 6000 + 400 + 30 + 4. The number name is six thousand four hundred thirty-four.

Instruct: Now, show the same number on the abacus.

Ask: Do you get the same number of thousands, hundreds, tens and ones?

Discuss student responses, guiding them wherever necessary.

Teacher Tip: If time permits, let students solve the problem given in the Do It Together section of 4-digit Numbers on Abacus.

Do It Yourself You Do

Say: Go to the Do It Yourself 1A exercise. Solve Q1 a. to b., Q2 a. to b., Q3 a., Q4 a. to c. and Q5 a. to c. on your own.

Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: How will you show the number five thousand six hundred forty using place value blocks and the abacus?

Say: To show the number 5640, we use 5 thousands, 6 hundreds, 4 tens blocks. To show the number on the abacus we put 5 beads in the thousands rod, 6 beads in the hundreds rod, and 4 beads in the tens rod.

Instruct: Solve Q1 c. to d., Q2 c. to d., Q3 b. to f., Q4 a. to c. and Q5 a. to c. from Do it Yourself 1A for homework.

3 Comparing Numbers

Learning Outcomes

● Students will be able to compare 2 or more 4-digit numbers and arrange them in ascending and descending order.

Concept I Do

Instruct: Go to the section Comparing Numbers of chapter 1.

Ask: How can we compare two 4-digit numbers? Which is bigger, 1235 or 1145? How will you compare 3 or more numbers?

Say: Two 4-digit numbers can be compared by comparing the thousands, hundreds, tens and ones in them. Since 1235 has more hundreds, the number is bigger. More than 2 numbers can be compared in the same way. We can also compare numbers by starting to compare the digits from the left and move to the right. When we arrange numbers from smallest to greatest, it is called ascending order. When we arrange numbers from greatest to smallest, it is called descending order.

Do It Together We Do

Distribute the place value blocks to the students.

Instruct: Work in groups of 4. Show two numbers, 1234 and 1252, using the place value blocks. First compare the number of thousands blocks in both numbers, then compare the hundreds, tens, and finally the ones blocks. In your notebooks, write the numbers and write which is bigger.

Ask: Which is bigger—1234 or 1252?

Say: 1252 is bigger. Both 1234 and 1252 have an equal number of thousands and hundreds but 1252 has 5 tens and 1234 has 3 tens. So, 1252 is bigger. On comparing the digits, we see that the digit in the tens place of 1252 is bigger than the digit in the tens place of 1234.

Instruct students to refer to the problem given in Do It Together. Ask them to compare the numbers and fill in the blanks.

Teacher Tip: If place value blocks aren’t available, students can draw blocks in their notebook for the activity.

Do It Yourself You Do

Say: Go to the Do It Yourself 1B exercise. Solve Q1 a. to b., Q2 a. to b., Q3 a. to b. and Q4 a. to b. on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice, refer to the relevant questions in the Chapter Checkup section.

Ask: Which is a smaller number: 5000 + 300 + 20 or five thousand three hundred two?

Say: 5000 + 300 + 20 is 5320 and five thousand three hundred two is 5302. On comparing 5320 and 5302, we see that 5320 has 2 tens and 5302 has 0 tens. So, 5302 is smaller.

Instruct: Solve Q1 c. to g., Q2 c. to f., Q3 c. to f. and Q4 c. to g. from Do it Yourself 1B for homework.

4 Forming 4-digit Numbers

Learning Outcomes

● Students will be able to form 4-digit numbers using the given 4 digits.

Concept I Do

Instruct: Go to the section Forming 4-digit Numbers of chapter 1.

Ask: How can you form the smallest 4-digit number using the digits 1, 8, 5, 4 only once?

Say: Place the digits in ascending order. Here, we place the digits in this order: 1, 4, 5, 8 to get the smallest 4-digit number, 1458, using the given digits.

Ask: How will you form the smallest 4-digit number using the digits 5, 0, 8, 2 only once?

Discuss student responses.

Read the question from the Think and Tell section aloud to the students.

Say: The smallest number will be 2058. We will not place 0 in the thousands place since 0258 will be a 3-digit number. To make it a 4-digit number, we have to place 0 in the hundreds place.

Do It Together We Do

Distribute the abacus to the students.

Instruct: Work in groups of 4. Refer to the problem given in Do It Together. Then, use the abacus to first show the smallest and then the largest 4-digit numbers using each of the given digits only once. Finally, fill in the blanks.

Ask: What is the smallest number formed? What is the largest number formed?

Say: The smallest number is 3059 and the largest number is 9530.

Teacher Tip: If abacus isn’t available, the students can draw the abacus in their notebooks and draw circles for beads.

Do It Yourself You Do

Say: Go to the Do It Yourself 1C exercise. Solve Q1, Q2 and Q3 a. to b. on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice, refer to the relevant questions in the Chapter Checkup section.

Ask: How many 3-digit numbers can be formed using the digits 1, 2, and 3 only once, making the number divisible by 2?

Say: The possible 3-digit numbers using each of the digits 1, 2, and 3 only once are: 123, 132, 231, 231, 312, and 321. Out of these, the numbers that are divisible by 2 are 132 and 312. So, only two 3-digit number can be formed using the given rule.

Instruct: Solve Q3 c. to h., Q4 and Q5 from Do it Yourself 1C for homework.

5 Rounding off 3-digit Numbers

Learning Outcomes

● Students will be able to round off numbers up to 3-digits to the nearest 10 using a number line.

Concept I Do

Instruct: Go to the section Rounding off 3-digit Numbers of chapter 1.

Ask: Why did Lina’s mother say that there were about 30 names in the list? What does it mean?

Say: “About 30” means that this was not the exact number but a number closer to the actual number. When we round off 27 we get 30. To round off a number to the nearest 10, we find the nearest 10. The nearest 10 for 27 is 30 so 27 gets rounded off to 30. If the number was 22, it would have got rounded off to 20. We can draw a number line to check which is the closer ten for a 2-digit number.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together. Look at the number line. Find the nearest 10 of 286 and fill in the blanks.

Ask: How can we round off the numbers using a number line? Which is the nearest ten of 286: 280 or 290?

Say: We plot 280 and 290 on the number line between which the number 286 lies. Draw 9 divisions between the two tens. Plot the remaining numbers 281, 282, 283, 284, 285, 286, 287, 288, 289 on the 9 divisions. 286 is closest to 290. So, 286 when rounded off to the nearest 10 is 290.

Instruct: Now, draw a number line in your notebooks to round off 353 and 358 to the nearest 10.

Ask: What is the nearest 10 that 353 and 358 are rounded off to?

Say: 353 is rounded off to 350 and 358 is rounded off to 360. We looked at the digit in the ones place. If the digit in the ones place is 5 or more, we round up to the higher ten, else we round down to the lower ten.

Teacher Tip: Draw a number line on the board for help.

Do It Yourself You Do

Say: Go to the Do It Yourself 1D exercise. Solve Q1 and Q2 a. to c. on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: A number rounded off to the nearest 10 is 80. The number was an even number less than 80 and more than 77. What is the number?

Say: The numbers that can be rounded off to 80 are: 75, 76, 77, 78, 79, and 80, 81, 82, 83, 84. But the number is an even number so the number can be 76, 78, 80, 82 or 84. Since the number is less than 80 and more than 77, the number is 78.

Instruct: Solve Q2 d. to h. from Do it Yourself 1D for homework.

1. Place Value and Expanded Form of 4-digit Numbers

Do It Together

3, 9

9 ones or 9

1 ten or 10

3 hundreds or 300

4 thousands or 4000

9 × 1 = 9 or 9 ones

1 × 1 = 1 or 1 ten

9 × 1 = 9 or 9 hundred

9 × 1 = 9 or 9 thousands

2. Reading 4-digit Numbers

Do It Together

6 thousands 4 hundreds 3 tens 4 ones

6434 = 6000 + 400 + 30 + 4

six thousand thirty

The number 6434 can be read as six thousand four hundred thirty-four. Do It Together

5; hundreds; 4; ones

5; 4

5241

two; forty

3. Comparing Numbers

Do It Together

6 > 4 > 1

4538 > 4372

The ascending order is: 1765, 4372, 4538, 6145.

The descending order is: 6145, 4538, 4372, 1765.

4. Forming 4-digit Numbers

Think and Tell

0 cannot be placed in the thousands place since that will make the number a 3-digit number instead of a 4-digit number. Do It Together

ascending; 3, 0, 9; descending 5, 3; 3059; 9530

5. Rounding off 3-digit Numbers

Do It Together

286 is in between 280 and 290 but is closer to 290. Therefore, it is rounded off to 290.

Learning Outcomes

Students will be able to:

● identify halves, thirds, and fourths of a whole and shade pictures to show them.

● find the fraction of a collection of objects and shade to show the fraction.

● identify fractions of a whole and write them in their fraction form.

● solve word problems on fractions of a whole and collection.

Alignment to NCF

● Explains the meaning of division facts by equal grouping/sharing and finds it by repeated subtraction. For example, 12 ÷ 3 can be explained as number of groups of 3 to make 12 and finds it as 4 by repeatedly subtracting 3 from 12.

Let’s Recall

● Recap to check if students know, that a whole can be divided into equal parts and that a fraction is a part of a whole.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● fraction, numerator, denominator

Teaching Aids

● Imagine Mathematics book, notebook

● strip of coloured paper of size 6 cm × 10 cm (4 strips per group); 20 yellow and 20 green buttons (1 set for a group); bangles (5 per group); colour pencils (1 box per group)

Learning Outcomes

● Students will be able to identify halves, thirds, and fourths of a whole; and shade pictures to show them.

Concept I Do

Instruct: Go to the second page of chapter 12.

Ask: How is a whole different from a fraction?

Say: A full or complete object is called a whole. For example, a whole pizza, and a whole chocolate. When a whole is divided into equal parts, fractions are formed. Let’s say a chocolate is divided into 2 equal parts, each part is one-half.

Discuss the basic fractions given in the book. Let them identify halves, thirds and fourths. Read the question from the Think and Tell section aloud to the students. Discuss their responses, guiding them wherever needed.

Do It Together We Do

Instruct students to refer to the problem given in

Do It Together.

Instruct: Look at the figure. Count the total number of parts, and the shaded and unshaded parts as well. After that, fill in the blanks.

Ask: What were the answers?

Say: The figure is divided into 4 equal parts. 3 parts are shaded and 1 part is unshaded. The fraction for the shaded part is 3 4 and the fraction for the unshaded part is 1 4

Distribute the strips of paper and colour pencils to the students.

Instruct: Work in groups of 4. Fold the strips into halves, fourths, and thirds. Shade to show the fractions one-half, one-fourth, one-third and two-thirds. Each of you must show one fraction.

Ask: How did you show the fractions?

Say: We showed the fraction by folding the strip into the same number of equal parts as the denominator, and shaded the same number of equal parts as the numerator.

Teacher Tip: Help students in folding the strips into 3 equal parts.

Do It Yourself You Do

Say: Go to the Do It Yourself 12A exercise. Solve Q1 and Q3 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice, refer to the relevant questions in the Chapter Checkup section.

Ask: A circle is divided into 2 equal parts with 1 part shaded. Another circle is divided into 4 equal parts with 2 parts shaded. What do you notice?

Say: We see that the shaded part in both the circles are the same, and that one-half is equal to two-fourths.

Homework: Solve Q2, Q4, Q5 and Q6 from Do It Yourself 12A for homework.

Learning Outcomes

● Students will be able to find the fraction of a collection of objects; and shade to show the fraction.

Concept I Do

Instruct: Go to the section Fraction of a Collection in chapter 12.

Ask: I have 6 apples. I want to divide them equally among 2 students. How may apples will each student get? What part of the apples were shared with each student?

Say: Each child will get 3 apples. On dividing 6 apples into 2 equal groups, each student will get 1 part of the 2 groups. This means that each student will get one half of the set of apples. The set of 6 apples is called collection. Draw 6 apples on the board and make 2 equal groups to explain one half of a collection.

Do It Together We Do

Instruct students to refer to the problem given in Do

It Together

Distribute the yellow buttons and the bangles to the students.

.

Instruct: Work in groups of 4. Imagine that the buttons are balls. Show the problem using the buttons and the bangles. Put the buttons inside the bangles to show equal groups. Then, show one-fourth of the collection of the buttons. Colour the same number of balls as the buttons that come in one-fourth of the collection. Then, fill in the blanks in the Do It Together section.

Ask: How many balls are there? How many balls will you colour? What is one-fourth of 8?

Say: There are 8 balls. We will colour 2 balls. One-fourth of 8 is 2.

Write: A. One-third of 15 buttons; B. Three-fourths of 20 buttons

Ask the students to read each new problem written on the board and show them using the buttons and bangles. They will then write the number of buttons in each collection.

Teacher Tip: If buttons are unavailable, students can be asked to use things around them like pencils, colour pencils, crayons, etc.

Do It Yourself You Do

Say: Go to the Do It Yourself 12B exercise. Solve Q1a. to b., Q2a. to b., Q3a. to b., Q4, Q5a. to c. on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice, refer to the relevant questions in the Chapter Checkup section.

Ask: Phoebe has 16 marbles. She gives one-half of the marbles to her sister Jean. She then gives one-fourth of the remaining marbles to her friend Roshni. How many marbles are left with Phoebe?

Say: One-half of 16 is 8. So, Phoebe gives 8 marbles to her sister Jean. Phoebe is left with 16 – 8 = 8 marbles. She then gives one-fourth of the remaining marbles to Roshni. So, one-fourth of 8 is 2. So, 8 – 2 = 6 marbles are left with Phoebe.

Draw the marbles into groups and show it to the students.

Instruct: Solve Q1c. to d., Q2c. to d., Q3c. to d., and Q5d. to h. from Do it Yourself 12B for homework.

Learning Outcomes

● Students will be able to identify fractions of a whole and write them in their fraction form.

Concept I Do

Draw this figure on the board.

Instruct: Look at the figure given on the board.

Ask: What do you notice about the fractions and the shaded parts?

Say: We see that in the fraction, the top part is the parts shaded. The bottom part shows the total number of equal parts. So, we can say that the numerator shows the total parts shaded. The denominator shows the total number of equal parts.

Instruct: Go to the section Writing a Fraction of chapter 12. Look at the figure shown. Compare the figure with the fraction 5 8 .

Do It Together We Do

Instruct students to refer to the problem given in Do

It Together

Distribute the yellow and the green buttons to the students.

Instruct: Work in groups of 4. Imagine that the buttons are balloons. Show the balloons using the buttons. Then, fill in the blanks in the Do It Together section.

Ask: What is the fraction for the yellow and the green balloons?

Say: The fraction of yellow balloons is 3 7 and the fraction of green balloons is 4 7 .

Write: 9 yellow and 8 green balloons

Instruct: Look at the number of balloons written on the board. Show them using the yellow and the green buttons. Write the fraction of the yellow and the green balloons, in your notebooks.

Ask: What is the fraction for the yellow and green balloons?

Say: The fraction of yellow balloons is 9 17 and the fraction of green balloons is 8 17

Teacher Tip: If buttons are unavailable, students can be given small chits of coloured paper.

Do It Yourself You Do

Say: Go to the Do It Yourself 12C exercise. Solve Q1a. to c., Q2a. to c., Q3a. to b. and Q4a. to b. on your own . Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice, refer to the relevant questions in the Chapter Checkup section.

Ask: A circle is divided into 11 equal parts with 8 parts shaded. How many more parts need to be shaded to make the fraction 9 11 ?

Say: 1 more part needs to be shaded.

Instruct: Solve Q1d. to e., Q2c. to f., Q3c. to d., Q4c. to d. and Q5 from the Do It Yourself 12C for homework.

Learning Outcomes

● Students will be able to solve word problems on fractions of a whole and collection.

Concept I Do

Instruct: Go to the section Word Problems of chapter 12. Read the word problem.

Ask: How many slices was the pizza cut into? How many slices was eaten by Manya? How will you write the fraction of the pizza eaten by Manya?

Say: The pizza is cut into 8 slices and Manya ate 3 slices. The fraction can be written as 3 8 . So, Manya ate three-eighths of the pizza.

Ask: How can we solve word problems on fractions?

Say: We need to read the problem and identify what is given and what is asked. We then write what needs to be done and finally find the answer.

Do It Together We Do

Instruct students to refer to the problem given in Do

Distribute the green buttons to the students.

It Together

.

Instruct: Work in groups of 4. Imagine that the buttons are flowers. Show the flowers in the problem using the buttons. Find one-third of the total flowers by making equal groups of the buttons. Then, in your notebook, first write the total number of buttons, then the buttons that form one-third of the collection. Show the solution in your notebooks.

Invite 1–2 students to come up on the board to solve the problem.

Write: Mohit travels a distance of 8 miles to reach home. The bus ride covers 5 miles. He hires an auto rickshaw to cover the rest of the distance. What fraction of distance was covered by auto rickshaw?

Instruct: In your groups, solve the problem using the buttons. Write the answer in your notebooks. Discuss the answer with the students.

Teacher Tip: Guide the students to circle what is given and underline the question. That would make it easier for them to solve the problem.

Do It Yourself You Do

Say: Go to the Do It Yourself 12D exercise. Solve Q1, Q4 and Q7 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: One-fourth of the students of a class play cricket whereas the rest play football. If the number of students playing football is 15, how many students play cricket?

Discuss student responses.

Say: One-fourth of the students play cricket and three-fourths play football. Three-fourths of the total students is 15. So, the total number of students is 20. One-fourth of 20 is 5. So, 5 students play cricket.

Instruct: Solve Q2, Q3, Q5, Q6 and Q8 from Do It Yourself 12D for homework.

1. Parts of a Whole

Think and Tell

An object can be divided into any number of equal parts. When a pizza is divided into 5 equal parts, each part is termed as one-fifth.

Do It Together

What fraction of the given shape is

What fraction of the given shape is

1  shaded     2  not shaded

1. shaded     2. not shaded

Total number of equal parts = 4

Total number of equal parts = 4

Number of parts shaded = 3

Number of parts shaded = out of 4 parts are shaded, hence fraction is shaded.

3 out of 4 parts are shaded, hence 3 4 fraction is shaded.

Number of parts not shaded = 1

Number of parts not shaded = 1

1 out of parts are not shaded, hence fraction is not shaded.

1 out of 4 parts are not shaded, hence 1 4 fraction is not shaded.

2. Fraction of a Collection

Do It Together

Colour one-fourth of the collection of balls.

Total number of balls = 8

Colour one-fourth of the collection of balls. Total number of balls = 8

Collection of balls we want to colour = 2

2 balls can be coloured as:

Collection of balls we want to colour = balls can be coloured as:

3. Writing a Fraction

Do It Together

What fraction of the balloons are:

a. Yellow

b. Green

Number of yellow balloons = 3

Total number of balloons = 7

Fraction of yellow balloons = Number of yellow balloons

Total number of balloons = 3 7

Number of green balloons = 4

Total number of balloons = 7

Fraction of green balloons = Number of green balloons

Total number of balloons = 4 7

4. Word Problems

Do It Together

Total roses = 15

Fraction of roses in the vase = 1 3

Number of roses he put in the vase = 1 3 of 15 = 5 roses

Data Handling

Learning Outcomes

Students will be able to:

● organise the given data in a table.

● draw a pictograph using a scale for the given data.

● read a pictograph and answer questions on it.

● draw a bar graph using the given data.

● read a bar graph and answer questions on it.

Alignment to NCF

● Records data using tally marks, represents pictorially and draws conclusions.

Let’s Recall

● Recap to check if students know how to read data in a table.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● table, data, pictograph, key, bar graph, title, label, scale

Teaching Aids

● Imagine Mathematics book, notebook

● Crayons (4 per group of 4)

Learning Outcomes

● Students will be able to organise the given data in a table.

Concept I Do

Instruct: Go to the second page of chapter 13.

Ask: How many wickets are taken by each player? What is an easier way to represent data?

Say: Amir took 8 wickets, Vihan took 7, Avyaan took 8, Deepak took 9, Prabhakar took 6, and Shreshth took 7. This answer is difficult to understand, but presenting the same information in a table can make it much easier to understand.

Instruct: Read the table given in the second page that lists the wickets taken by each player.

Ask: Who took more wickets—Prabhakar or Vihan? Was it easier to understand the data when it was written in the table?

Say: Vihan took more wickets. It was very easy to read the data given in the table.

Do It Together We Do

Instruct students to read the data given in Do It Together Complete the data table by writing the name of the favorite sport and the number of students who like it. Finally, answer the questions written on the board in their notebooks.

Write on the board: 1. Which is the most favourite sport? 2. Which sport is liked more—cricket or badminton?

Ask: Which is the most favourite sport? Which sport is liked more—tennis or badminton?

Say: The most favourite sport is cricket. Badminton is liked more than tennis.

Teacher Tip: If time permits, ask more questions on reading the data table.

Do It Yourself You Do

Say: Go to the Do It Yourself 13A exercise. Solve Q1, Q3 and word problems on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: In the data table given in the Do It Together section, 4 students changed their favourite sport from cricket to badminton. How many people liked both cricket and tennis?

Say: The total number of people who liked cricket was 11 and those who liked badminton were 7. On 4 students changing their favourite sport from cricket to badminton, the number of students who now like cricket is 7 and those who like badminton is 11. So, the total number of students who like both cricket and tennis is 7 + 5 = 12 students.

Instruct: Solve Q2, Q4 and Q5 from Do it Yourself 13A for homework.

2 Drawing a Pictograph

Learning Outcomes

● Students will be able to draw a pictograph using a scale for the given data.

Concept I Do

Instruct: Go to the section Drawing a Pictograph in chapter 13. Read how the same data of the players can be represented differently.

Ask: Will it be easier to understand data if we draw pictures to show data? Why?

Say: Sometimes data given as pictures is easier to understand. A pictograph helps us show data using pictures or symbols.

Read the question from the Think and Tell section aloud to the students. Discuss student responses.

Say: We use a key to find the number of units that represent one picture. It is important to select a key so that we know how many pictures are to be drawn for each data. For example, if Amir took 8 wickets, and we show 1 picture for 2 wickets, we will show Amir’s data using 8 ÷ 2 = 4 pictures.

Do It Together We Do

Instruct students to read the problem given in Do It Together. Read the data given in the table and complete the pictograph.

Ask: How many students are represented by one symbol? How many symbols did you draw for section B and section D?

Say: 1 student is represented by 1 symbol. Since 8 students went on the trip from section B, 8 symbols were used to show the data. 9 students went on a trip from section D so 9 pictures were drawn to show the data.

Instruct: Now in your notebooks draw a pictograph using the same data. Take the key as 1 symbol = 2 students.

Ask: How many symbols will you draw for odd number of students? Since 1 symbol = 2 students, we will draw half a picture to show 1 student.

Teacher Tip: Allow students to draw simple pictures if they are unable to draw the given symbol. The data table can also be drawn on the board to help students look at it and draw the pictograph in their notebooks.

Do It Yourself You Do

Say: Go to the Do It Yourself 13B exercise. Solve Q2 and Q4 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Ramya drew 3 and a half pictures to show the number of students who went to art class. If the key used in the pictograph is 1 picture = 10 students, what is the total number of students who went for the art class?

Say: When 1 picture = 10 students, 3 and half pictures = 30 + 5 = 35 students.

Instruct: Solve Q1 and Q5 from Do it Yourself 13B for homework.

3 Reading a Pictograph

Learning Outcomes

● Students will be able to read a pictograph and answer questions on it.

Concept I Do

Instruct: Go to the section Reading a Pictograph in chapter 14. Read the weather data pictograph.

Ask: What is the key for the pictograph? How many symbols represent the rainfall for the month of July? What is the total rainfall for the month of August?

Say: The key shows 1 picture = 5 cm. August shows rainfall using 3 pictures. Since 1 picture shows 3 cm of rainfall, August will have 3 × 5 = 15 cm of rainfall.

Read the question from the Think and Tell section aloud to the students.

Say: In the pictograph, 1 picture = 5 cm. If we change the key to 1 picture = 1 cm, we will have to draw the 15 pictures which will make the pictograph difficult to read.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together. Read the pictograph showing the number of chocolates purchased by 7 friends.

Ask: What is the key used in the pictograph? Are there half pictures drawn for any student? How did you find the number of chocolates for that student?

Say: The key used in the pictograph is 1 picture = 2 chocolates. Half pictures are drawn for Shubh, Aahan and Param. A half picture represents half of 2 chocolates which is 1 chocolate. For example, the pictograph shows 3 and half pictures for Shubh which means he bought 6 + 1 = 7 chocolates.

Instruct: Answer the questions given in Do It Together. Write your answers.

Teacher Tip: If time permits, give them some more questions on reading the pictograph. Let them discuss the answers with their partners.

Do It Yourself You Do

Say: Go to the Do It Yourself 13B exercise. Solve Q3, Q6 and Word Problem 2 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: In the pictograph showing the chocolates bought by 7 students, the key changes to 1 picture = 4 chocolates. How many pictures will you draw for Jennifer who buys 8 chocolates? How many pictures will you draw if a student buys 2 chocolates for the key 1 picture = 4 chocolates?

Say: Jennifer buys 8 chocolates. When the key is 1 picture = 4 chocolates, we will draw 8 ÷ 4 = 2 pictures to show her data. If a student buys 2 chocolates, we will draw half a picture.

Instruct: Solve Q7 and Word Problem 1 from Do it Yourself 13B for homework.

Learning Outcomes

● Students will be able to draw a bar graph using the given data.

Concept I Do

Instruct: Go to the section Drawing a Bar Graph in chapter 13. Read the different steps of drawing a bar graph.

Ask: How is a bar graph different from a pictograph? How will you draw a bar graph?

Discuss student responses.

Say: A bar graph is also a pictorial representation of data. A pictograph uses symbols and pictures whereas a bar graph uses rectangular bars to show the data. We can draw a bar graph by first drawing the x-axis and y-axis. Then, we label the x-axis by the categories and y-axis by number for the categories. Finally, bars are drawn to show each data.

Do It Together We Do

Instruct students to refer to the problem given in Do

Distribute the crayons to the students.

It Together

Instruct: Work in groups of 4. Read the data in the table. Complete the bar graph by drawing the bars using different coloured crayons.

Ask: How many boxes did you colour to show the number of pencils for Akram, Vinay and Atif?

Say: Akram has 6 pencils so 6 boxes were coloured vertically. Vinay has 4 pencils so 4 boxes were coloured. Atif has 9 pencils so 9 boxes were coloured.

Ask: Why were the same number of boxes coloured for the number of pencils with each student?

Say: The key used is 1 division = 1 pencil so for each pencil with a student the same number of divisions or boxes were shaded.

Teacher Tip: Instruct students to make sure that the boxes are coloured one above the other to show the data for 1 student.

Do It Yourself You Do

Say: Go to the Do It Yourself 13C exercise. Solve Q1 on your own.

Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: How many boxes will you colour for 1 picture = 2 pencils for a student who has 8 pencils?

Say: We can change the scale in a bar graph just as we do in a pictograph. To show 8 pencils when the key is 1 picture = 2 pencils, we will colour 8 ÷ 2 = 4 boxes.

Instruct: Solve Q2 and the first part of the word problem from Do It Yourself 13C for homework.

5 Reading a Bar Graph

Learning Outcomes

● Students will be able to read a bar graph and answer questions on it.

Concept I Do

Instruct: Go to the section Reading a Bar Graph in chapter 13. Read the bar graph showing the marks scored by 6 students.

Ask: The data for how many students is shown on the bar graph? What is the scale used? Who scored the least marks? How do you read the data in a bar graph?

Say: The bar graph shows the marks for 6 students. The scale is 1 division = 1 mark. The length of the rectangular bar for Prabhakar is the least. So, Prabhakar scored the least marks. To read data on a bar graph, we first find the bar for the category asked on the x-axis. We then see the height of the bar and match it to the number of students on the y-axis. The corresponding number gives us the answer.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together. Read the given bar graph.

Ask: What data is shown on the bar graph? What is the scale used?

Say: The bar graph shows the time spent on homework for different subjects in a month. The scale for the bar graph is 1 division = 1 hour.

Instruct: Work in groups of 4. Discuss the answers of the question given. Write the answers in your notebooks.

Ask: What were the answers?

Discuss student responses, guiding them wherever needed.

Teacher Tip: If time permits ask more questions on reading the bar graph.

Do It Yourself You Do

Say: Go to the Do It Yourself 13C exercise. Solve Q3 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: In the bar graph given in the Do It Together section, if the scale changes to 1 division = 2 hours, how would the height of the bars change?

Say: If the scale changes to 1 division = 2 hours, the height of the bars will reduce to half for all subjects since the numbers on the y-axis will change to 2, 4, 6, 8, 10.

Instruct: Solve Q4 and the subparts of the word problem from Do it Yourself 13C for homework.

1. Data Tables

2. Drawing a Pictograph

Think and Tell

It is important to select a key so that we know how many pictures are to be drawn for each unit of data. Do It Together

Sections Number of Students

Section A

Section B

Section C

Section D

3. Reading a Pictograph

Think and Tell

If we change the key to 1 picture = 1 cm, we will have to draw 15 pictures which will make the pictograph difficult to read.

Do It Together

1. 2 and a half

Thus, Ahaan purchased 5 chocolates.

2. Jennifer purchased the maximum number of chocolates since the greatest number of pictures are drawn for Jennifer.

2 + 2 + 2 + 2 = 8 chocolates

4. Drawing a Bar Graph

Do It Together

Key:

2 chocolates

2    4   1

5. Reading a Bar Graph

Do It Together

Number of hours spent on Maths homework = 9 hours

Number of hours spent on English homework = 6 hours

Difference between the hours spent on Math homework and English homework = 9 – 6 = 3 hours.

Maths—9 hours; Science—8 hours; English—6 hours; Hindi—7 hours

Ascending order

6 < 7 < 8 < 9

English < Hindi < Science < Maths

Multiples and Factors 5

Learning Outcomes

Students will be able to:

● find the multiples of a number using the multiplication tables.

● find the common multiples of two or more numbers.

● find the factors of 2 numbers using square tiles and multiplication.

● find the factors of 2 numbers using division.

● find the common factors of 2 numbers and then their highest common factor.

Alignment to NCF

Applies operations of numbers in daily life.

● Multiplies 2- and 3-digit numbers.

● Divides a number by another number using different methods like pictorially (by drawing dots), equal grouping or repeated subtraction and by using inter-relationship between division and multiplication.

Let’s Recall

● Recap to check if students are able to understand that multiplication and division are closely related to one another.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● multiples, common multiples, factors, common factors

Teaching Aids

● Imagine Mathematics book, notebook

● Number grid 1–50 (1 per pair), counters (40 per group of 4), crayons

Learning Outcomes

● Students will be able to find the multiples of a number using the multiplication tables.

Concept I Do

Instruct: Go to the second page of chapter 5.

Ask: What are the dates when Sahil can take the train to Ooty?

Say: The train departs every second day which means on the 2nd, 4th, 6th, and so on. So, Sahil can take the train only on those dates when the train departs.

Read the question from the Think and Tell section aloud to the students.

Discuss the pattern that they see in the numbers.

Say: We see a pattern in the numbers. These numbers are increasing in 2s. These numbers also appear in the multiplication table of 2 and are called multiples. The multiples of a number are the products we get by multiplying the number by 1, 2, 3,... and so on.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Instruct: Show jumps of 6 on the number line to find the multiples of 6. Complete the multiplication sentences. Then use the long division method to divide 92 and 96 by 6.

Ask: What are the first 5 multiples of 6? What did you see when you divided 92 and 96 by 6?

Say: The first 5 multiples of 6 are 6, 12, 18, 24 and 30. On dividing 92 by 6, we get 2 as remainder. So, 92 is not divisible by 6. On dividing 96, we get 0 as the remainder. So, 96 is divisible by 6.

Distribute the number grid and crayons among the students.

Write on board: A: First 8 multiples of 5 B: First 6 multiples of 7

Instruct: Work in pairs. One student to colour every 5th number on the number grid. The second student to colour every 7th number on the number grid. Write the numbers each of you have coloured on your grids.

Ask: What are the numbers you shaded? What do you notice?

Discuss student responses.

Say: One student in the pair must have coloured the numbers 5, 10, 15, 20, 25, 30, 35 and 40. The other student must have coloured the numbers 7, 14, 21, 28, 35 and 42.

Teacher Tip: If number grids are unavailable, students can be asked to write the numbers 1–50 in their notebooks, and then circle the numbers as asked in the question.

Do It Yourself You Do

Say: Go to the Do It Yourself 5A exercise. Solve Q1, Q2a–Q2c, Q4, Q6a–Q6c on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: How many multiples does a number have? Is 1 a multiple of every number?

Say: Every number has an infinite number of multiples. No, 1 is not a multiple of every number.

Instruct: Solve Q2d–Q2o, Q3, Q5, Q6d–Q6f and Q7 from Do It Yourself 5A for homework.

Learning Outcomes

● Students will be able to find the common multiples of two or more numbers.

Concept I Do

Instruct: Go to the section Common Multiples of chapter 5.

Ask: On which dates can Ashima travel to Ooty? What are the common dates on which both Ashima and Sahil can go to Ooty?

Say: Since the train from Ashima’s city leaves on every third day, Ashima can leave on the 3rd, 6th, 9th, 12th,… of the month. Sahil and Ashima can visit to Ooty together on the 6th, 12th, 18th, 24th and 30th. A number that is a multiple of two or more numbers is a common multiple of those numbers.

Instruct: Now look at the number line showing jumps of 3 and 4.

Ask: What are the common multiples of 3 and 4?

Discuss their responses, guiding them wherever needed.

Say: The common multiples of 3 and 4 are 12 and 24.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together. Distribute the number grid and crayons among the students.

Instruct: Work in pairs. Imagine that the number grid shows a building and each of you run the canteen and the party hall. To show that every second floor has a canteen, write ‘C’ on every second number on the grid. To show that every fifth floor has a party hall, write ‘P’ on every fifth number on the grid. In your notebooks, write down the numbers on which you wrote C and P. Circle the numbers that had both C and P written on them.

Ask: What are the numbers that have both C and P written on them?

Say: The numbers that have both C and P written are 10 and 20.

Instruct: In the Do It Together section, fill in the blanks. Compare the answers with the common multiples found above.

Read the question from the Think and Tell section aloud to the students. Discuss their responses.

Teacher Tip: If time permits, let students find the common multiples of 2 more numbers on the number grid.

Do It Yourself You Do

Say: Go to the Do It Yourself 5B exercise. Solve Q1a–Q1c, Q2a, Q2b, Q4 and word problem on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: What are the common multiples of 6 and 7 that are less than 40?

Show the multiples of 6 and 7 on the number grid. Circle the common multiples less than 40, if any.

Say: 6 and 7 have no common multiples which are less than 40.

Instruct: Solve Q1d–Q1h, Q2c–Q2d, Q3, and Q5 from Do It Yourself 5B for homework.

HW

Finding Factors Using Multiplication

Learning Outcomes

● Students will be able to find the factors of 2 numbers using square tiles and multiplication.

Concept I Do

Instruct: Go to the section Finding Factors Using Multiplication of chapter 5.

Ask: How many apples does Sheela’s aunty have? What arrangements can she make to distribute the apples? Discuss the different arrangements.

Say: The different arrangements are: 8 = 1 × 8; 8 = 2 × 4; 8 = 4 × 2; 8 = 8 × 1. To find the factors of a number using multiplication, we look for numbers whose product is the given number.

Read the question from the Think and Tell section aloud to the students.

Discuss in which case maximum number of students get an apple.

Say: To distribute apples to the maximum number of children, each child will get one apple. So, there will be 8 plates. Thus, there will be 8 plates with 1 apple each.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together

Distribute the counters among the students.

Instruct: Work in groups of 4. Take 20 counters and arrange them in different ways so that they are placed in equal rows and columns. Write multiplication sentences for each arrangement having an equal number of counters. Then, fill in the blanks in the Do It Together section.

Discuss the answers.

Say: The factors of 20 are 1, 2, 4, 5, 10 and 20.

Instruct: Now, find the factors of 6 by showing them using the counters in equal numbers of rows and columns. Write the multiplication sentence in your notebooks.

Ask: What are the arrangements of counters and the multiplication sentences? What are the factors of 6?

Say: We can arrange the 6 counters as 6 rows of 1, 3 rows of 2, 2 rows of 3, 1 row of 6. The multiplication sentences are 6 = 6 × 1; 6 = 3 × 2; 6 = 2 × 3; 6 = 1 × 6. The factors of 6 are 1, 2, 3, and 6.

Read the question from the Think and Tell section aloud to the students. Discuss student responses, guiding them wherever needed.

Teacher Tip: If the resources are not available, ask the students to use rajma beans or pebbles.

Do It Yourself You Do

Say: Go to the Do It Yourself 5C exercise. Solve Q1, Q4a–Q4c, and Q7 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Are there any numbers that have only 2 factors? Which are those numbers?

Say: Yes, some numbers have only 2 factors which are only divisible by 1 and themselves. For example, 2 = 1 × 2; 5 = 1 × 5. Such numbers are called prime numbers.

Instruct: Solve Q2, Q3 and 4d–4i from Do It Yourself 5C for homework.

4

Finding Factors Using Division

Learning Outcomes

● Students will be able to find the factors of 2 numbers using division.

Concept I Do

Instruct: Go to the section Finding Factors Using Division of chapter 5.

Ask: If I divide 15 apples into 3 groups and get 5 apples in each group, are 3 and 5 factors of 15? Why?

Say: Yes, 3 and 5 are factors of 15 since on dividing 15 by 3 or 5 we get no remainder. For example, on dividing 15 by 4, we get 3 as the remainder. So, 4 is not a factor of 15. So, to find the factors of a number, we can look for numbers that divide it exactly without leaving a remainder.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together

Distribute the counters among the students.

Instruct: Work in groups of 4. Pick up 36 counters. Work in groups to divide 36 counters into as many equal groups as you can. Write the division sentences. Now, fill in the table given in the Do It Together to find the answers. List the numbers that leave no remainder.

Ask: What is similar to the arrangement that you made and the numbers that did not leave a remainder, on dividing?

Say: The number of equal rows and columns that the counters are arranged in, are the same as the divisor and the quotient in the division statement.

Read the question from the Think and Tell section aloud to the students. Discuss student responses, guiding them wherever needed.

6 rows and 6 columns

Teacher Tip: If time permits, give students one more number and let them find its factors using division and counters.

Do It Yourself You Do

Say: Go to the Do It Yourself 5C exercise. Solve Q5a–Q5c, Q6, Q9 and word problem 1 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Say: Go to the Do It Yourself 5C exercise. Solve Q8 on your own.

Ask: What is the smallest number which has exactly 3 factors?

Say: The smallest number that has exactly 3 factors is 4.

Instruct: Solve Q5d–Q5f, Q10 and word problem 2 from Do It Yourself 5C for homework.

Learning Outcomes

● Students will be able to find the common factors of 2 numbers and then their highest common factor.

Concept I Do

Instruct: Go to the section Common Factors of chapter 5. Look at the table showing the factors of 4 and 8.

Ask: What do you notice about the factors of 4 and 8?

Read the question from the Think and Tell section aloud to the students.

Say: The factors of 4 are 1, 2 and 4. The factors of 8 are 1, 2, 4 and 8. We see that there are 3 factors that are common to the two numbers 4 and 8 which are 1, 2 and 4. Common factors of two or more numbers are the numbers that divide the numbers completely, leaving no remainder. Here, the lowest common factor is 1 and the highest common factor is 4.

Read the question from the Think and Tell section aloud to the students. Discuss student responses, guiding them wherever needed.

Do It Together We Do

Instruct students to refer to the problem given in Do

Distribute the counters among the students.

It Together

Instruct: Work in groups of 4. Find the factors of 20 and 30 by arranging the counters in equal rows and columns, until there are no arrangements left. Then, fill in the blanks in the Do It Together section.

Ask: What are the factors of 20 and 30, their common factors and the highest common factor?

Say: The factors of 20 are 1, 2, 4, 5, 10 and 20. The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. The common factors of 20 and 30 are 1, 2, 5 and 10. The highest common factor is 10.

Teacher Tip: Help students understand that the duplicate factors should not be listed while filling in the table. For example, the arrangement 4 × 5 and 5 × 4 have repeated numbers but 4 and 5 should each be listed only once.

Do It Yourself You Do

Say: Go to the Do It Yourself 5D exercise. Solve Q1a. to c., Q2a. to b., Q3a. to b. and word problem on your own.

Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: When finding common factors of 2 numbers, can one of the numbers be the common factor of itself and the other number?

Say: Yes, a number can be a common factor of itself and the other number. For example, for numbers 5 and 15, the number 5 is a common factor of 5 and 15.

Instruct: Solve Q1d. to j., Q2c. to f., Q3c. to e., Q4, and Q5 from Do It Yourself 5D for homework.

Answers

1. Finding Multiples

Think and Tell

Yes, multiples of an even number are always even numbers.

Do It Together

Show jumps on numbers 18, 24, 30

6 × 2 = 12; 6 × 3 = 18; 6 × 4 = 24; 6 × 5 = 30

The first 5 multiples are 6 are 6, 12, 18, 24, 30. On dividing 96 by 6, we get 0 remainder.

So, 92 is not a multiple of 6. 96 is a multiple of 6.

3. Finding Factors Using Multiplication

Think and Tell

She should go with 8 plates with 1 apple in each.

Think and Tell

2. Common Multiples

Think and Tell

We stopped at 20 since there were only 20 floors in the building.

Do It Together

2 × 2 = 4; 2 × 3 = 6; 2 × 4 = 8; 2 × 7 = 14

2 × 8 = 16; 2 × 9 = 18; 2 × 10 = 20

5 × 1 = 5; 5 × 2 = 10; 5 × 3 = 15; 5 × 4 = 20

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Multiples of 5 = 5, 10, 15, 20

We can find the canteen and party hall together on floors 10 and 20.

When finding factors by multiplication we always start with multiplying by 1 and stop when any factor starts repeating. This may be time consuming. The quicker method to find factors is division.

Do It Together

Multiply by 2 2 × 10 = 20; Multiply by 4 4 × 5 = 20; Multiply by 5 5 × 4 = 20; Multiply by 6 Not possible

Should we multiply further? No

So, the factors of 20 are 1, 2, 5, 10 and 20.

4. Finding Factors Using Division

Think and Tell

No, we do not need to go beyond 6 to find more factors of 36.

Do It Together

So, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

5. Common Factors

Think and Tell

Sheela aunty stopped after making 4 plates as 4 children received an equal number of each type of fruit and there were no other combinations left.

Think and Tell

The lowest common factor of 4 and 8 is 1. The highest common factor of 4 and 8 is 4.

Do It Together

Factors of 20 = 1, 2, 4, 5, 10, 20

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

The common factors of 20 and 30 = 1, 2, 5 and 10.

The highest common factor of 20 and 30 is 10.

Representing 3-D Shapes 8

Learning Outcomes

Students will be able to:

● draw different views of objects.

● identify the nets of a cube and a cuboid and draw them.

● read a map and answer questions on it.

Alignment to NCF

● Makes cubes/cuboids using the given nets.

● Draws top view, front view and side view of simple objects.

Let’s Recall

● Recap to check if students can identify 2-D and 3-D shapes and differentiate between them.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● views, nets, maps

Teaching Aids

● Imagine Mathematics book, notebook

● cardstock paper, ruler, marker pen, a pair of scissors, tape or glue (1 per group of 3); sheet with nets drawn and lengths of sides written (1 per group of 3)

1 Views of Objects

Learning Outcomes

● Students will be able to draw different views of objects.

Concept I Do

Instruct: Go to the second page of chapter 8.

Ask: Why is Riya’s drawing different from Pooja’s drawing?

Say: Riya drew the car while sitting by the window whereas Pooja drew the car while standing on the roof. So, both drew different views. Riya gets to see the side view and Pooja the top view. Read the question from the Think and Tell section aloud to the students. Discuss their responses, guiding them wherever needed.

Say: The view of an object depends on the position of the eye. When we see things from the top, we draw only the top view. To draw the side view, we need to see the object from the side. The object when seen from the front helps us draw the front view. But all objects do not look different from different views. Some look the same from 2 or more views.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Distribute the cardstock paper, a pencil and a pair of scissors to the students.

Instruct: Work in groups of 3. Look at your desks. Each of you will draw the front, side and top view of the desk. Compare the views within your groups to see if they match. Note down your observations. Discuss the observation of the students in class.

Instruct: Now, look at the other 3 images of the house, the pie and the speakers in the Do It Together section. Draw the front view of the house, the top view of the pie, and the side view of the speakers. Compare the views within your groups.

Teacher Tip: If students want to discuss the back and bottom view of objects and why these are not drawn, discuss in class.

Do It Yourself You Do

Say: Go to the Do It Yourself 8A exercise. Solve Q1 and Q3 on your own.

Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: Can you name a 3-D shape where 2 or more views are the same?

Say: All the views of a cube are the same. They are all squares. A cone has the same front and side view and a different top view. A cone has triangles as its side and front view and a circle as its top view.

Instruct: Solve Q2, 4 and 5 from Do it Yourself 8A for homework.

2 Nets of 3-D Shapes

Learning Outcomes

● Students will be able to identify the nets of a cube and a cuboid and draw them.

Concept I Do

Instruct: Go to the section Nets of 3-D Shapes of chapter 8.

Ask: Have you ever seen shopkeepers folding a cutout to form a box? Have you also wondered how quickly they do that and how?

Say: Yes, most shopkeepers keep 3-D boxes unfolded as 2-D shapes. This is called the net of a 3-D shape. On folding these nets drawn on flat paper, we can form 3-D shapes. These help in packing stuff. It also saves them a lot of space. Storing boxes takes up a lot more space than flat shapes. Show the students by folding a cutout to form a box.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Distribute the cardstock paper, marker pen, glue, colour pencils and the pair of scissors among the students.

Instruct: Work in groups of 3. Look at the net of the cube. Discuss and draw the net on the cardstock paper with the help of a marker pen. Colour as given. Now cut out the net and fold to form a box. Use the glue to stick the edges.

Ask: What shape did you get on folding the net? How do you know?

Say: When we fold the net, we get a cube since all sides are squares.

Teacher Tip: Help the students identify the faces which will come opposite to each other in a cube.

Do It Yourself You Do

Say: Go to the Do It Yourself 8B exercise. Solve Q1 and Q4 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: When 2 cubes are joined on one side, will its net remain the same? Why?

Say: When 2 cubes are joined on one side, the shape changes to a cuboid. So, the net will also change to a cuboid net.

Instruct: Draw the net of the new shape formed.

Instruct: Solve Q2, 3 and 5 from Do it Yourself 8B for homework.

Learning Outcomes

● Students will be able to read a map and answer questions on it.

Concept I Do

Instruct: Go to the section Maps of chapter 8.

Ask: What can help Riya find her way easily from the sweet shop to the hospital? How will she reach the hospital if she follows the route given in the map?

Say: A route map can help Riya find her way easily. A map is a drawing of an area made on a flat surface. It helps us go from one place to another by following the path defined in it. To reach the hospital Riya will take a left turn, then move straight. She will then take the first right-hand turn and move straight. She will again take the first right-hand turn and move straight. The hospital will be in front of her. Read the question from the Think and Tell section aloud to the students.

Say: No. To reach the hospital from the super market, Riya will first take a right-hand turn and then walk straight. She will then take the first right-hand turn and walk straight. Finally, she will take a right-hand turn to reach the hospital which will be in front of her.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Distribute the colour pencils to the students.

Instruct: Look at the map showing the routes from Mohan’s house to Neerja’s house. Mark 2 more routes from Mohan’s house to Neerja’s house. Write the route in your notebooks.

Ask: Which is the shortest route? Which is the longest route? Discuss their responses, guiding them wherever needed.

Teacher Tip: Instruct students to draw the routes using different colour pencils to be able to differentiate.

Do It Yourself You Do

Say: Go to the Do It Yourself 8C exercise. Solve Q2 and Q4 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Instruct: Solve Q5 from the Do It Yourself 8C exercise. Draw the routes in different colours. Write the answers in your notebooks.

Ask: Which road will the truck NOT cross to reach the burning house?

Say: One of the roads that the truck will not cross is the Farm road since it is a deadend and does not lead to any other road from where the truck can go to the burning house.

Instruct: Solve Q1 and Q3 from Do it Yourself 8C for homework.

Answers

1. Views of Objects

Think and Tell

All objects do not look different from different views. Some look the same from 2 or more views. For example, an ice-cream cone looks the same from the front and the side view but different from the top view.

Do It Together

2. Nets of 3-D Shapes

Do It Together

3. Maps

Think and Tell

No. To reach the hospital from the supermarket, Riya will first take a right-hand turn and then walk straight. She will then take the first right-hand turn and walk straight. Finally, she will take a right-hand turn to reach the hospital which will be in front of her.

Do It Together

The blue arrows show the third route and the red arrows show the fourth route.

Mohan's House

Mohan's House

Neerja's House

Neerja's House

Perimeter and Area 11

Learning Outcomes

Students will be able to:

● find the perimeter of different shapes.

● find the length of the missing side of a polygon, when the perimeter and length of the other sides are given.

● find the area of irregular shapes on squared paper.

Alignment to NCF

● Recognises the total length of the boundary as the perimeter of a plane figure and calculates the perimeter of simple shapes.

● Estimates and compares the perimeter of various figures.

● Solves real-life problems involving the perimeter of simple shapes.

● Determines the size of a shape by using a smaller shape as a unit.

● Determines the size (or area) of simple geometrical shapes and irregular figures given on a square grid.

● Solves real-life problems based on the area of plane figures.

Let’s Recall

● Recap to check if students know how to measure length in different units of measurement.

● Ask them to solve the questions given in the Let’s Warm-Up section.

Vocabulary

● perimeter, boundary, area, inside boundary, length, units, sq. units

Teaching Aids

● Imagine Mathematics book, notebook

● Squared paper, thread, dot grid paper, pencils

1 Finding Perimeter on Squared paper

Learning Outcomes

● Students will be able to find the perimeter of different shapes.

Concept I Do

Instruct: Go to the second page of chapter 11. Observe the photo frame given.

Ask: How will you find the length of the ribbon needed for the photo frame?

Say: Imagine your mathematics book as Rita’s photo frame and your finger as the ribbon. Move your finger around the sides of the book.

Say: This is the boundary of the book (photo frame). The total length of this boundary is called the perimeter of the book. We can measure it using different methods—like a piece of string or a ruler.

Ask: Look at the 3 figures on page 197. How is finding the perimeter of figure A different from figures B and C?

Read the question from the Think and Tell section aloud to the students.

Say: When we are given the measures of the sides, we can find the perimeter by simply adding the lengths. The perimeter of the triangle can be found by adding the lengths of the 3 sides. When we are not given the lengths of the sides, we can still find the perimeter using a squared or dot grid paper. The perimeter of the rectangle can be found by counting the number of units around it.

Do It Together We Do

Instruct students to refer to the problem given in Do It Together.

Distribute the piece of thread and a ruler among the students.

Instruct: Work in pairs. Measure the perimeter of the figures using the thread and the ruler. Write the measure in your notebooks. Then find the perimeter of the first 2 figures by counting each unit on the dot grid and squared paper. To find the perimeter of the third figure, add the lengths of the sides of the polygon. Write in your notebooks and compare the perimeters found using both methods. Discuss how close their measurements were to the actual perimeter.

Teacher Tip: If resources are unavailable, students can be asked to use their fingers or other smaller objects to measure the lengths of the sides.

Do It Yourself You Do

Say: Go to the Do It Yourself 11A exercise. Solve Q1, Q2a, Q2d, Q3a, Q3b and word problem 1 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Instruct: Draw a shape on squared paper with perimeter of 10 units.

Show one figure on the board, with perimeter measuring 10 units.

Instruct: Solve Q2b, Q2c, Q2e, Q2f, Q3c. to f. and Q6 from Do it Yourself 11A for homework.

Figure C

Figure B

5cm 5cm

cm

unit

2 Finding the Missing Side

Learning Outcomes

● Students will be able to find the length of the missing side of a polygon, when the perimeter and length of other sides are given.

Concept I Do

Draw the figure the board.

Say: We know that the perimeter of a shape is the sum of the lengths of all sides.

Ask: How will you find the length of a missing side, when the length of remaining sides and the perimeter is given?

Say: We first add the lengths of the given sides and subtract the sum from the given perimeter.

Do It Together We Do

Instruct students to refer to the figure given in Do It Together.

Instruct: Work in groups of 3. Find the length of the missing side in the figure. Add the given lengths and subtract the sum from the perimeter. Write in your notebooks. Compare your answers with your group.

Draw the figure given on the side, on the board.

Instruct: Look at the figure on the board. Find the missing length.

Ask: What is the missing length?

Discuss: The sum of the given length of sides is 12 + 6 + 5 + 2 + 7 = 32 cm. On subtracting the sum of the lengths from the perimeter, which is 41 cm, we get 41 – 32 = 9 cm.

Do It Yourself You Do

Say: Go to the Do It Yourself 11A exercise. Solve Q4a and Q5a on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Ask: How will you find the perimeter and the length of missing sides in a square if one side measures 5 cm?

Say: We will use the properties of a square that states that the length of all the sides in a square are equal. So, the length of the missing sides will be 3 cm each. The perimeter will be 4 × 3 = 12 cm.

Instruct: Solve Q4b, Q4c and Q5b from Do It Yourself 11A for homework.

3 Area of Irregular Shapes

Learning Outcomes

● Students will be able to find the area of irregular shapes on squared paper.

Concept I Do

Instruct: Go to the section Area of Irregular Shapes of chapter 11.

Ask: How will you find the area of the two figures given? How is finding the perimeter of the first figure different from the second?

Say: We count the shaded squares to find the areas. The first figure has only straight sides and have only full and half parts shaded. We will count the full square as 1 and two halves as 1. The second figure is of irregular shapes. Here we take full and more than full shaded squares as 1. We take 2 halves as 1 and ignore the less than half shaded squares.

Discuss the areas of shape A and B and compare.

Read the question from the Think and Tell section aloud to the students.

Discuss how the area of any irregular shape can be calculated by counting the squares inside the shape.

Do It Together We Do

Instruct students to refer to the problem given in Do

It Together

.

Instruct: Work in groups of 3. Mark the full and incomplete squares in the figure using different coloured dots and using the rule given in the table. Count each coloured square and fill in the table. Add the total squares to find the total area of the figures. Write the area in your notebooks. Compare your answers within your groups.

Do It Yourself You Do

Say: Go to the Do It Yourself 11B exercise. Solve Q1a, Q2a, Q2b, and Q4 on your own. Go around the class to check the students’ answers. Help them correct their work, wherever required. For more practice refer to relevant questions in the Chapter Checkup section.

Say: Go to the Do It Yourself 11B exercise. Solve Q4 on your own.

Ask: Are the area and perimeter of all shapes with an area of 12 sq. units the same?

Say: The area always remains the same. The perimeter can be the same, more or less.

Instruct: Solve Q1b. to f., Q2c. to f., Q3 and Q5 from Do It Yourself 11B for homework.

1. Finding Perimeter on Squared paper

Think and Tell

Yes, we can find the perimeter of a shape with straight sides using a ruler. We can first measure the length of sides using the ruler and then add the lengths to find the perimeter. But we can also find the perimeter of these shapes using a piece of thread. If the lengths of the sides are given, we can add the lengths to find the perimeter.

Do It Together

A = 12 units, B = 16 units, C = 36 m

2. Finding the Missing Side

Do It Together

3 cm + 5 cm + 2 cm + 2 cm + 2 cm + 5 cm + 3 cm + ? = 34 cm

22 cm + ? = 34 cm

? = 34 cm – 22 cm = 12 cm

3. Area of Irregular Shapes

Think and Tell

Yes, we can trace any small shape on the grid, and find its area by counting squares inside the shape.

Do It Together

1. 18 sq. units

2. 15 sq. units

About This Book

Imagine Mathematics seamlessly bridges the gap between abstract mathematics and realworld relevance, offering engaging narratives, examples and illustrations that inspire young minds to explore the beauty and power of mathematical thinking. Aligned with the NEP 2020, this book is tailored to make mathematics anxiety-free, encouraging learners to envision mathematical concepts rather than memorize them. The ultimate objective is to cultivate in learners a lifelong appreciation for this vital discipline.

Key Features

• Let’s Recall: Helps to revisit students’ prior knowledge to facilitate learning the new chapter

• Real Life Connect: Introduces a new concept by relating it to day-to-day life

• Examples: Provides the complete solution in a step-by-step manner

• Do It Together: Guides learners to solve a problem by giving clues and hints

• Think and Tell: Probing questions to stimulate Higher Order Thinking Skills (HOTS)

• Error Alert: A simple tip off to help avoid misconceptions and common mistakes

• Remember: Key points for easy recollection

• Did You Know? Interesting facts related to the application of concept

• Math Lab: Fun cross-curricular activities

• QR Codes: Digital integration through the app to promote self-learning and practice

About Uolo

Uolo partners with K-12 schools to provide technology-based learning programs. We believe pedagogy and technology must come together to deliver scalable learning experiences that generate measurable outcomes. Uolo is trusted by over 10,000 schools across India, South East Asia, and the Middle East.

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