MATHEMATICS
Master Mathematical Thinking
Numbers up to 200 1
Learning Outcomes
Students will be able to: write numbers up to 200 using numerals and number names. identify the place value for numbers up to 200 and write them in expanded form. compare and order numbers up to 200. read and write ordinal numbers from 1st to 10th. identify odd and even numbers.
Alignment to NCF
C-8.3: Reads and writes Indian numerals for numbers up to ninety-nine using place value in groups of tens and ones
C-8.4: Arranges numbers from a given set of numbers in ascending and descending order
C-8.5: Compares and forms the greatest and smallest two-digit numbers (with and without repetition of given digits). Recognises, reads, writes number names and numerals up to 99 using place value concept
Let’s Recall
Recap to check if students know how to count numbers from 1 to 9. Ask students to solve the questions given in the Let’s Warm-up section.
Vocabulary
counting forward: counting by adding 1 every time counting backward: counting by subtracting 1 every time place value: value of a digit based on its position in the number expanded form: the way to write a number by adding the value of its digits ordinal numbers: numbers that are used to show the positions of objects in a line
Teaching Aids
Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200; Strip with 8 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, I in purple, N in pink, G in grey; 2 groups of small straws—6 small straws and 9 small straws; 6 bangles
Chapter: Numbers up to 200
Building Numbers
Learning Outcomes
Students will be able to write numbers up to 200 using numerals and number names.
Teaching Aids
Place value blocks of 100s, 10s and 1s
Activity
Imagine Maths Page 3
Instruct the students to work in groups. Distribute the place value blocks to each group. Instruct the students to show the numbers 115 and 148 using the blocks. Ask them to count the number of hundreds, tens and ones shown by the blocks. Then, in their notebooks, they will write that number, and the number of hundreds, tens and ones in words to get the number name. Ask questions like: If I have place value blocks for the number 234, which place value blocks will we add to get the next 3 numbers?
Extension Idea
Ask: How many 1s blocks will you use to show the number one hundred fifty?
Say: The number one hundred fifty can be written as 150. Number of 1s blocks used = 0.
Place Value and Expanded Form
Learning
Outcomes
Imagine Maths Page 4
Students will be able to identify the place value for numbers up to 200 and write them in expanded form.
Teaching Aids
Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s
Activity
Distribute the place value blocks and place value charts among the students. Ask them to show the number 182 using place value blocks. Instruct the students to identify and write the same number in the place value chart by writing each digit in its correct place. Then, in their notebooks, they will write the number of hundreds, tens and ones as 100 + 80 + 2 to write the expanded form of the number and the place value of each digit. Ask questions like: What is the place value of 5 in the number 159?
Extension Idea
Ask: What would be the expanded form of the number 157 if the digits in the ones and tens places are interchanged?
Say: The digit in the ones place in 157 is 7, and the digit in the tens place is 5. On interchanging the places, the number that we get is 175. So, the expanded form of 175 = 100 + 70 + 5.
Learning Outcomes
Students will be able to compare and order numbers up to 200.
Teaching Aids
Place value blocks of 100s, 10s and 1s; Number cards for 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200
Activity
Ask the students to work in groups. Distribute the number cards for 8 numbers to each group. Instruct them to pick any 2 number cards, show the numbers using the place value blocks and then compare them. They will first compare the hundreds blocks in both numbers, then the tens and finally the ones. They will then shade the 2 numbers on the number chart. Ask them to write the comparison using the symbol <, > or =, in their notebooks. Discuss how the bigger number will appear after the smaller number on the number chart. Then, ask them to use the remaining number cards, locate the numbers on the number chart and shade them. Ask them to arrange the number cards in increasing and decreasing orders and write them in the same order, in their notebooks.
Ask questions like: Can a 2-digit number be greater than a 3-digit number?
Extension Idea
Ask: Find a number that lies between 95 and 107. There should be 4 numbers between 95 and this number. Say: The number is 100 since it lies between 95 and 107, and has 4 numbers between 95 and itself.
Ordinal Numbers
Learning Outcomes
Students will be able to read and write ordinal numbers from 1st to 10th.
Teaching Aids
Imagine Maths Page 8
Strip with 8 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, I in purple, N in pink, G in grey
Activity
Call 10 students to the front of the class and ask them to stand in a line.
Ask questions like: Who is second in the line? Who is tenth?
Ask the students to work in groups. Distribute the strips and cut-outs to each group.
Ask them to place the cut-outs on the square strip as per the instructions to get the word LEARNING. Use ordinal words for the positions of the letters. For example, ask them to place the orange cut-out in the first square and the green cut-out in the fifth square.
Ask them to write the letters in their notebooks with the correct position of each letter.
Learning Outcomes
Students will be able to identify odd and even numbers.
Teaching Aids
2 groups of small straws—6 small straws and 9 small straws; 6 bangles
Activity
Discuss some real-life things that come in pairs like socks, gloves, etc. Instruct the students to form groups of 4. Distribute a set of 6 straws, 9 straws and 6 bangles to each group. Ask them to first use 6 straws and 3 bangles and put pairs of straws inside the bangles. They will then use 9 straws and 5 bangles to make pairs.
Discuss that any number that forms pairs with no leftover is an even number and that a number that has a leftover is an odd number.
Instruct the students to draw 6 lines and 9 lines to show the straws in their notebooks, circle pairs of lines and then write the number and whether it is odd or even.
Ask questions like: What type of number will you get if you add 1 more straw to 9 straws?
Extension Idea
Ask: If we add 2 even numbers, do we get an odd number or an even number?
Say: If we add 2 even numbers, we will get an even number because the 2 numbers already form pairs without any leftovers.
Answers
1. Building Numbers
Think and Tell
20 boxes with 10 sweets in each = 20 tens = 200. It has 20 tens or 2 hundreds.
We write this as 2 hundreds 0 tens.
Do It Together
1. 1 hundred, 1 tens and 4 ones – one hundred fourteen 2. 1 hundred, 1 tens and 2 ones – one hundred twelve
2. Place Value and Expanded Form
Do It Together
Expanded form of 196 is
+ 90 + 6.
3. Increasing and Decreasing Order
Do It Together
Increasing order: 109, 111, 123, 132, 143
Decreasing order: 143, 132, 123, 111, 109
4. Ordinal Numbers
Do It Together 1. B 2. A 3. T 4. No
5. Odd and Even Numbers
Think and Tell
If we add 2 odd numbers, we will get an even number because the 2 leftovers without a pair will be paired together. Do It Together
Addition of 2-digit Numbers 2
Learning Outcomes
Students will be able to: add 2-digit numbers without regrouping. add 2-digit numbers by counting up. add 2-digit numbers with regrouping (sums up to 200). solve story problems on adding numbers (sums up to 200).
Alignment to NCF
C-8.6: Adds two numbers using place value concept (sum not exceeding 99) and applies them to solve simple daily life problems
C-8.6: Identifies appropriate operation (addition or subtraction) to solve problems in a familiar situation/ context
C-8.6: Comprehends and solves simple word problems
C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text
Let’s Recall
Recap to check if students know how to add two 1-digit numbers. Ask students to solve the questions given in the Let’s Warm-up section.
Vocabulary
regrouping: rearranging numbers into groups according to their place values number line: a line showing numbers at equal distances
Teaching Aids
Place value blocks of 100s, 10s and 1s; Number grid (numbers 41 to 70 written on them); Word problem written on a sheet of paper with space given for each element of the CUBES strategy
Chapter: Addition of 2-digit Numbers
Vertical Method; Horizontal Method
Learning Outcomes
Students will be able to add 2-digit numbers without regrouping.
Teaching Aids
Place value blocks of 10s and 1s
Activity
Ask the students to work in groups. Distribute the place value blocks to each group. Instruct them to show 42 and 36 using the place value blocks by placing them side by side. Ask them to put together or add the 1s blocks, count the total number of 1s blocks and write the number of 1s in their notebooks. Ask them to repeat this with the 10s blocks. Then, in their notebooks, they will add the numbers using the vertical method by first adding the digits in the 1s place, then the digits in the 10s place. Ask them to compare the answers that they got using the place value blocks and the vertical method.
Give them 2 more numbers and ask them to find the total using the place value blocks and the vertical method.
Extension Idea
Ask: What is the total number of 10s blocks that you will use to show the sum of five 10s blocks and six 1s blocks with 31?
Say: Five 10s blocks and six 1s blocks make the number 56. 56 + 31 = 87; hence, we need eight 10s blocks to show the sum. Mental Addition
Learning Outcomes
Students will be able to add 2-digit numbers by counting up.
Teaching Aids
Number grid (numbers 41 to 70 written on them)
Activity
Distribute the number grid to each student. Give them 2 numbers such as 43 and 25.
Say: We know 25 has two 10s and five 1s, so we can write it as: 43 + 25 = 43 + 20 + 5. Now in the number grid, jump two 10s from 43 to reach 63. Then jump five 1s to reach 68.
Give 2 more numbers like 52 and 15 to solve using the same number grid, and ask them to note down the answers in their notebooks.
Extension Idea
Ask: How can we quickly add 50 and 20?
Say: Look at the 10s digits. In 50, the 10s digit is 5, and in 20, the 10s digit is 2. Add the 10s digits together: 5 + 2 = 7. Now, add a zero to the end of 7, so it becomes 70.
Addition with Regrouping; Adding More Than 2 Numbers Imagine Maths Page 19
Learning Outcomes
Students will be able to add 2-digit numbers with regrouping (sums up to 200).
Teaching Aids
Place value blocks of 100s, 10s and 1s
Activity
Ask the students to work in groups. Distribute the place value blocks to each group. Instruct them to show 87 and 25 using the blocks by placing them side by side. Ask them to put together or add the 1s blocks. Ask how many blocks they have got on adding the 1s blocks. Discuss how ten 1s blocks become one 10s block, so we need to replace ten 1s blocks with one 10s block. Ask them to repeat the process with the 10s blocks and discuss how ten 10s become one 100s block. Then, in their notebooks, they will add the numbers using the vertical method by first adding the digits in the 1s place, then the digits in the 10s place and finally the digits in the 100s place. Ask them to check if the sums that they got using the place value blocks and the vertical method match. Ask questions like: What is thirty 10s? How will you show this using the 100s blocks?
Story Sums
Learning
Outcomes
Students will be able to solve story problems on adding numbers (sums up to 200).
Teaching Aids
Imagine Maths Page 25
Word problem written on a sheet of paper with space given for each element of the CUBES strategy
Activity
Distribute the sheet with the word problem to the students. Instruct them to circle the numbers, underline the question and box the key words. Discuss what they need to find. Ask them to evaluate the problem, solve it and write the answer using the vertical method.
Ask questions like: How will you find out if your answer is correct?
Extension Idea
Rhea sold 15 red roses, 12 white roses and 28 pink roses. How many roses did she sell altogether?
Ask: Create your own word problem where you need to add the numbers 118 and 56.
Say: Multiple story problems can be created based on adding 2 numbers. One such word problem could be: Kamal sold 118 oranges and 56 apples in a day. What is the total number of fruits that Kamal sold?
1. Vertical Method Do
Answers
6.
Adding More Than 2 Numbers
2. Horizontal Method Do It Together 34 + 42 = 76
3. Mental Addition
Do It Together
+ 43 = 24 + 40 + 3
64 + 3 = 67
4. Addition with Regrouping to 10 Do It Together
We get 0 in the ones place if we add 34 and 16. Do It Together
The sum of 48 and 22 is 70
5. Regrouping When the Sum is More
Are all the answers the same? Yes/ No
7. Story Sums
Do It Together
Rohan solved 15 sums on Monday, 23 sums on Tuesday, and 17 sums on Wednesday. How many sums did he solve in total? Solve using the CUBES method, given above.
Sums solved by Rohan on Monday = 15
Sums solved by Rohan on Tuesday = 23
Sums solved by Rohan on Wednesday = 17
Total sums solved = 55
Rohan solved 55 sums in total.
Subtraction of 2-digit Numbers 3
Learning Outcomes
Students will be able to: subtract 2-digit numbers without regrouping. subtract 2-digit numbers by counting backwards. subtract 2-digit numbers with regrouping. solve story problems on subtracting 2-digit numbers.
Alignment to NCF
C-8.6: Subtracts two numbers up to 99 using place value and applies them to solve simple daily life problems/situations
C-8.6: Appreciates and applies relationship between addition and subtraction of numbers
C-8.6: Identifies appropriate operation (addition or subtraction) to solve problems in a familiar situation/ context
C-8.6: Comprehends and solves simple word problems
C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text
Let’s Recall
Recap to check if students know how to subtract 1-digit numbers. Ask students to solve the questions given in the Let’s Warm-up section.
Vocabulary
regrouping: rearranging numbers into groups according to their place values addition fact: showing 2 numbers with a (+) sign in between them followed by the (=) sign and the sum of the 2 numbers
subtraction fact: showing 2 numbers with a (−) sign between them followed by the (=) sign and the difference of the 2 numbers
Teaching Aids
Places value blocks of 10s and 1s; Number strips; Rabbit toy; Pencils; Ice-cream sticks; Word problem sheets with a word problem written on each sheet of paper and space given for What is given? What do we need to find out? and How do we find out?
Chapter: Subtraction of 2-digit Numbers
Vertical Method
Learning Outcomes
Students will be able to subtract 2-digit numbers without regrouping.
Teaching Aids
Places value blocks of 10s and 1s
Activity
Ask the students to work in groups. Distribute the place value blocks to each group.
Imagine Maths Page 30
Instruct the students to subtract 17 from 39 by first showing the bigger number using place value blocks and then taking away or removing as many blocks as the smaller number. For example, to solve 39 − 17, they will take three 10s blocks and nine 1s blocks to show 39. They will then remove one 10s block and seven 1s blocks to subtract 17. Ask them to count the number of 10s and 1s blocks left to get the answer.
Then, in their notebooks, they will subtract using the vertical method by first subtracting the digit in the 1s place and then the digit in the 10s place.
Ask them to compare the answers they got using both the methods.
Instruct them to subtract 33 from 45 using the place value blocks and the vertical method.
Mental Subtraction
Imagine Maths Page 31 Learning Outcomes
Students will be able to subtract 2-digit numbers by counting backwards.
Teaching Aids
Number strips; Rabbit toy; Pencils Activity
Discuss how 2 numbers can be subtracted mentally.
Divide the class into groups. Distribute the number strips and rabbit toy to each group.
Give a subtraction problem 45 – 21. Ask the students to circle the numbers 45 and 21 on the number strip. Ask the group to help the rabbit hop two 10s backwards from 40 by drawing arrows on the number strip. They will then jump one 1s backwards to reach the answer. The group to place the rabbit correctly on the answer on the number strip will get a point.
Ask question such as: How many ones did the rabbit jump to get the answer?
Subtraction with Regrouping
Imagine Maths Page 33 Learning Outcomes
Students will be able to subtract 2-digit numbers with regrouping.
Teaching Aids
Place value blocks of 10s and 1s
Activity
Ask the students to work in groups. Distribute the place value blocks to each group.
Instruct them to solve 58 − 29. Ask them to first show the bigger number using the place value blocks and then take away as many blocks as the smaller number. As 9 ones is less than 8 ones, they will need to replace a 10s block with ten 1s blocks, and then subtract the ones and the tens.
Then, in their notebooks, they will subtract using the vertical method by first subtracting the digit in the 1s place, then the digit in the 10s place and regrouping wherever needed.
Ask questions like: What will you get if you add the ice-cream sticks and the smaller number?
Extension Idea
Ask: Can you think of two 2-digit numbers that give 15 after subtracting one from the other? What could the possible numbers be?
Say: Think of any two-digit number, say 52, and subtract 15 from it. 52 – 15 = 37. So, 52 and 37 are two such numbers that give 15 after subtraction.
Story Sums
Learning Outcomes
Students will be able to solve story problems on subtracting 2-digit numbers.
Teaching Aids
Ice-cream sticks; Word problem sheets with a word problem written on each sheet of paper and space given for What is given? What do we need to find out? and How do we find out?
Activity
Invite 2 students to the front of the class. Give 12 ice-cream sticks to one student and 15 ice-cream sticks to the other.
Ask questions to help the students understand the keywords: Who has more ice-cream sticks? Who has fewer ice-cream sticks? How many more ice-cream sticks does the second student have? How many fewer ice-cream sticks does the first student have?
Distribute the word problem sheet to the students with the problem written as: Priya has 25 toys and Satish has 18 toys. How many fewer toys does Satish have than Priya?
Priya has 25 toys and Satish has 18 toys. How many fewer toys does Satish have than Priya? What is given?
What do we need to find out?
How do we find out?
Solve to find the answer.
Instruct them to read the problem. Ask them to write what is given, what they need to find out and how to find the answer. Ask them to solve and write the final answer. Discuss the answers.
Extension Idea
Ask: Create your own word problem where you need to subtract 39 from 58.
Say: There can be multiple word problems on subtracting 39 from 58. One such problem could be: Richa read 58 pages of a book and Shalini read 39 pages of the book. How many more pages did Richa read than Shalini?
1. Subtraction without Regrouping
Do
Answers
4. Story Sums Do It Together
Number of toy cars = 33
Number of toy cars sold = 13
Number of toy cars left = 33 – 13 = 20
2. Mental Subtraction
Go back by 4 tens from 99 to reach 59.
Then move back by 9 ones to reach 50
So, 99 – 49 = 50.
3. Subtraction with Regrouping
Do It Together