MATHEMATICS
Master Mathematical Thinking
Grade 1
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Students will be able to: find where things are using the words behind–in front of, inside–outside, before–after–between, top–bottom, on–under, above–below, High–Low find the position of things using words like near, far, nearer, farther, nearest or farthest. read simple maps and layouts using words like left–right or up–down. compare the size of things using words like big–small, long–short, tall–short, thick–thin. compare the weight of things using words like heavy or light.
C-8.4: Arranges the same set of objects in different sequences based on different properties of objects (e.g., by size/length/weight/colour)
C-8.8: Develops and uses vocabulary of spatial relationship (e.g., top, bottom, on, under, inside, outside, above, below, near, far, before, after)
C-8.9: Distinguishes between near, far, thin, thick, longer/taller, shorter, high, low Let’s Recall
Recap to check if students know how to identify big and small things. Ask students to solve the questions given in the Let’s Warm-up section.
Vocabulary
position: the place of an object or thing in relation to other objects space: the area around us
map: a picture of a place printed on a flat surface
Three boxes of different sizes; Multiple toys; Sentence cards like The teddy bear is on the of Box A. Box B is Box A and Box C; Objects available in the classroom like chalk, pen, pencil, box, bag; 4 × 4 square grid drawn on the floor; 4 × 4 square grid drawn on paper; Counters; Playdough of red, blue and green colours; Picture cards of pairs of objects—papaya–balloon, feather–toy car, a bottle of water–orange; Objects like feathers, balloons, toy cars, a bottle of water, orange and papaya
Behind–In Front of, Inside–Outside; Before–After–Between; Top–Bottom, On–Under, Above–Below, High–Low
Learning Outcomes
Imagine Maths Page 2
Students will be able to find where things are using the words behind–in front of, inside–outside, before–after–between, top–bottom, on–under, above–below.
Teaching Aids
Three boxes of different sizes; Multiple toys; Sentence cards like The teddy bear is on the of Box A. Box B is Box A and Box C.
Activity
Instruct the students to form groups and take the sentence cards. Place 3 boxes of different sizes side by side. Place a toy/object over Box A, 2 toys/objects inside Box B and 1 toy/object in front of Box C. Instruct the students to look at the boxes and the placement of the toys. They will then fill in the blanks in the sentence cards. Discuss the answers.
Extension Idea
Ask: Can there be a toy that can be both on the top and at the bottom? Say: Yes, if we place 3 boxes, one on top of the other, and a toy in the middle box, then the toy will be on top of one box and at the bottom of the other.
Learning Outcomes
Imagine Maths Page 5
Students will be able to find the position of things using words like near, far, nearer, farther, nearest or farthest.
Teaching Aids
Objects available in the classroom like chalk, pen, pencil, box, bag Activity
Instruct the students to form groups of 5. Scatter the objects around the classroom and draw a start line for the students. Call 1 student from each group and make him/her stand behind the line. Give instructions like: Pick the thing that is the farthest. Pick the thing that is near you. Allow 2 students to follow each instruction and bring the things to you. Discuss with the class if each instruction is followed correctly. Try giving each student a chance. Repeat this process for each student from each group, one by one.
Extension Idea
Ask: Was there anything that was near to one student but far from the other student? How is this possible? Say: It is possible that one toy, which is near one student, can be far from the other student since the 2 students might be standing far from each other and the toy is kept close to one of the students.
Students will be able to read simple maps and layouts using words like left–right or up–down.
4 × 4 square grid drawn on the floor; 4 × 4 square grid drawn on paper; Counters
Activity
Draw a 4 × 4 square grid on the floor. Invite 2–3 students to come and stand in one corner. Give instructions like ‘Move 2 steps up. Move 2 steps left’. Instruct the students to follow the instructions and move on the grid. This will help the students understand how to perform the activity.
Instruct the students to form groups of 4. Distribute the 4 × 4 square grid, drawn on paper, and 1 counter to each group. Instruct the students to place their counters on M and write the letter M in their notebooks. Ask them to move their counter in different directions with each instruction. They will write the letter they land on, in their notebooks. Give them instructions in a way that will lead them to the cells with letters that form the word MATHS. For example, the instruction Move 1 step up and 1 step left will bring them to the letter A. The group that finds the word first is the winner.
Extension Idea
Ask: Can you write the directions for forming the word PURE?
Say: Start by standing on the letter ‘P’. Move 1 step up to reach ‘U’. Move 1 step right and 1 step down to reach ‘R’. Move 2 steps right to reach the letter ‘E’.
Students will be able to compare the size of things using words like big–small, long–short, tall–short, thick–thin.
Playdough of red, blue and green colours
Activity
Make groups of 5 students and distribute the playdough to each group.
Instruct the students to create big and small balls using the red playdough, short and tall towers using the blue playdough and thick and thin books using the green playdough.
Ask the students to compare the shapes.
Discuss the difference between the words and what they mean.
Extension Idea
Ask: How is tall different from long?
Say: Tall refers to the height of an object, that is, when the object is vertical or upright. Long refers to the length of objects, that is, when the object is lying down horizontally.
Students will be able to compare the weight of things using words like heavy or light.
Teaching Aids
Picture cards of pairs of objects—papaya–balloon, feather–toy car, a bottle of water–orange; Objects like feathers, balloons, toy cars, a bottle of water, orange and papaya
Activity
Ask the students to lift a pencil in one hand and the school bag in the other hand. Discuss how the bag is heavy and the pencil is light.
Instruct the students to look at the picture cards, and then pick up each object in each hand to decide which is heavy and which is light. Ask them to write ‘Heavy’ or ‘Light’ under each object.
Papaya Balloon
Discuss how things that seem the same size can be light or heavy and that the size of the object does not determine its weight.
Extension Idea
Ask: If you have 2 jars of the same size with sand filled in one jar and cotton in another, which jar will be heavy?
Say: The jar with sand will be heavy. The jar with cotton will be light.
1. Behind–In Front of, Inside–Outside Do It Together
The boy is the rocket. The boy is the rocket. outside
2. Before–After–Between Do It Together
The bear is before the rabbit.
The rabbit is between the bear and the lion.
The lion is after the rabbit.
3. Top–Bottom, On–Under, Above–Below, High–Low Do It Together
The vase is on the table.
The slippers are under the table.
4. Near–Far Do It Together
1. The boy is near the shop.
2. The mother is nearer to the shop.
3. The father is nearest to the shop.
5. Maps
Think and Tell
We will go 2 steps to the right from purple to reach blue. Do It Together
1. Sam is on C. He goes 1 step left. He reaches A
2. Sam is on X. He goes 1 step up. He reaches D.
6. Big and Small Do It Together
Students will be able to: match things one-to-one by drawing lines. count up to 9 things and write the number. write the number names for numbers up to 9. identify 0 as a number and in words and relate it to things. count things to make 10 and write the number and number name. count up to 20 things and write the number. write numbers from 11 to 20 as tens and ones. write the number names for numbers from 11 to 20. count forward or backwards to find the missing numbers for numbers up to 20. find numbers that come before, after and between for numbers up to 20. compare numbers up to 20 to find the smaller or greater number. order numbers up to 20 from smallest to greatest and greatest to smallest.
C-8.3: Counts forward and backward from a specific number (between 0 and 99)
C-8.5: Recognizes the symbol zero to represent absence of object/thing; Recognizes and writes numerals up to 20 and in words up to 10; Compares two numbers up to 20 and uses vocabulary like bigger than or smaller than
Recap to check if students know how to count things up to 5. Ask students to solve the questions given in the Let’s Warm-up section.
Vocabulary
number names: a way to express numbers in word form
Pictures of dog houses and dogs; Glue sticks; Classroom supplies such as pencils, books, erasers, crayons; Paper cards with simple drawings; Ice cream sticks; Rubber bands; Number mats (11 to 20); Flags with numbers from 11 to 20 and corresponding flags with number names; Paper cups; Marker; Large number cards from 1 to 20; Number strips with numbers from 1 to 20; Question cards with random numbers and blanks before, after or between the numbers; Sheets with a number line drawn from 1 to 20; Crayons; Pebbles, dried twigs, fallen leaves, flowers
Learning Outcomes
Students will be able to match things one-to-one by drawing lines.
Teaching Aids
Pictures of dog houses and dogs; Glue sticks
Activity
Imagine Maths Page 19
Instruct the students to work in groups. Distribute pictures of dog houses, dogs and glue sticks to each group. Give 1 extra house picture or extra dog picture to the groups. Instruct the students to match each dog to its house by gluing the dogs outside the kennels. This activity helps them practise matching one-to-one. Ask questions like: Could you give a house to each dog? Why?
Extension Idea
Ask: What will you need to match all the remaining dogs/dog houses?
Say: We will need more dog house/dog pictures to match the remaining dogs/dog houses.
Learning Outcomes
Students will be able to count up to 9 things and write the number.
Teaching Aids
Classroom supplies such as pencils, books, erasers, crayons
Activity
Imagine Maths Page 19
Scatter a variety of classroom supplies on a table ensuring that none of them exceed 9 items. For example, include 7 pencils, 8 books, 7 erasers and 9 crayons.
Instruct the students to form groups for the activity. Provide each group with a sheet of paper and a pencil.
Instruct the groups to take turns and explore the table. Ask them to count the number of each item they find and write down the corresponding numbers in their sheets. Repeat the activity for all the groups formed. After a set amount of time, gather the students and discuss the various supplies they discovered.
Extension Idea
Ask: Can you split into groups of 4 and count the total number of legs your group has?
Say: If there are 4 people in the group and each person has 2 legs, then you can count by saying: “1, 2, 3, 4”, for the number of people, and then count the legs as “1, 2, 3, 4, 5, 6, 7, 8” to find the total number of legs in the group. So, the answer is 8 legs.
Learning Outcomes
Students will be able to write the number names for numbers up to 9.
Teaching Aids
Paper cards with simple drawings
Activity
Discuss the number names for numbers up to 9 in the class. Instruct the students to work in groups. Distribute the paper cards with simple drawings among the groups. Ask the students to count the objects and write the number name below it. Encourage group discussions for deciding the right number names.
Extension Idea
Ask: Draw “three” stars and write the number.
Say: The number will be written as 3.
Learning Outcomes
Students will be able to identify 0 as a number and in words and relate it to things.
Teaching Aids
Ice cream sticks; Paper plates
Activity
Introduce the concept of “nothing” by explaining the use of the number 0. Write the word “Zero” on the board and discuss its meaning. Instruct the students to form groups for the activity. Distribute 9 ice cream sticks and 1 paper plate to each group.
Instruct the students to place as many sticks on the plate as the number called out. Start the game by calling out random numbers between 0 and 9. When they hear “Zero,” the students should refrain from placing any sticks on the paper plate. If a group puts sticks during a “Zero” call or places an incorrect number of sticks, they are out.
Continue the game for a set period. The group that survives till the end, without placing any sticks during “Zero” calls or making any mistakes, wins.
Extension Idea
Ask: Do you know who discovered the number zero?
Say: The Indian mathematician, Aryabhatta, discovered zero, long ago.
Students will be able to count things to make 10 and write the number and number name.
Teaching Aids
Ice cream sticks; Rubber bands
Activity
Instruct the students to form groups for the activity.
Distribute some ice cream sticks and rubber bands to each group of students. Ask them to count the ice cream sticks as 1, 2, 3... up to the number 9. Ask them to add 1 more ice cream stick. Discuss that the number that comes after 9 is 10. Instruct them to bundle those 10 sticks using rubber bands. Teach them the number name for 10 as “ten”.
Finally, ask them to write the number “10” and the corresponding number name “ten” in their notebooks.
Extension Idea
Ask: If you have 7 ice cream sticks, how many more do you need to make 10 sticks?
Say: The numbers that come after 7 are 8, 9 and 10. So, we will need 3 more sticks to make 10.
Students will be able to count up to 20 things and write the number.
Teaching Aids
Number mats (11 to 20); Ice cream sticks
Activity
Introduce numbers from 11 to 20 in the class.
Instruct the students to work in groups. Distribute number mats and ice cream sticks among the groups. Ask the students to place the number mats in front of them. Start by calling out random numbers. Ask the students to count as many ice cream sticks as the number being called out and place it on the corresponding number mat. Encourage the students to say the number aloud as they identify and place the ice cream sticks. Continue calling out numbers, allowing the students to swiftly count and cover the correct numbers on their mats. Check the ice cream sticks placed by the groups on the mats at the end.
Extension Idea
Ask: How many ice cream sticks would you have in all if we added 1 more ice cream stick to the number 14?
Say: We would have a total of 15 ice cream sticks.
Students will be able to write numbers from 11 to 20 as tens and ones.
Teaching Aids
Ice cream sticks; Rubber bands
Activity
Divide the class into small groups.
Distribute ice cream sticks (between 11–20) and rubber bands among the groups.
Ask the students to count 10 ice cream sticks and bundle them using rubber bands. Guide them in counting the bundled sticks as sets of 10 and the remaining ones separately. Assist them in grasping the concept of grouping with tens and ones, for example, 1 set of 10 and 2 ones make 12. Help them if needed.
Later, encourage the groups to share their counting methods and ways of bundling, using ice cream sticks and rubber bands.
Extension Idea
Ask: If you have 16 crayons, how many more crayons would you need to complete 2 sets of 10?
Say: We would need 4 more crayons to make 2 sets of 10 crayons each.
Names Imagine Maths Page 25
Students will be able to write the number names for numbers from 11 to 20.
Teaching Aids
Flags with numbers from 11 to 20 and corresponding flags with number names; Paper cups; Marker
Activity
Introduce number names from 11 to 20 in the class.
Instruct the students to work in groups.
Distribute the flags with numbers, corresponding flags with number names and empty cups among the groups.
Ask the groups to place the number flag, along with its name flag, in 1 cup. Encourage them to match each number with its name and place the flags in different cups and then write the number on the cup.
Instruct the students to write down the numbers and their corresponding number names in their notebooks.
Learning Outcomes
Students will be able to count forward or backwards to find the missing numbers for numbers up to 20.
Teaching Aids
Large number cards from 1 to 20
Activity
Take the students outdoors for the activity. Create 2 sets of number cards from 1 to 20 with a few numbers missing.
Split the students into 2 groups, assigning some students a number card from 1 to 20. Arrange each group in a line, forming a human number chain. Ask the students with no number cards from each group to stand on one side.
Place the pile of the missing number cards on a table. Ask the students with no number cards to race and pick a missing number card, and run to find their place in the number chain. The remaining students from their groups should assist in determining the correct place for the missing numbers in the chain. The first group to successfully form the complete number chain wins the relay challenge.
Extension Idea
Ask: What number comes 2 steps from the number 11 when counting forward?
Say: The number that comes 2 steps forward from the number 11 is 13.
Before, Between and After
Learning Outcomes
Students will be able to find numbers that come before, after and between for numbers up to 20.
Teaching Aids
Number strips with numbers from 1 to 20; Question cards with random numbers and blanks before, after or between the numbers; Ice cream sticks; Rubber bands
Activity
Ask the students to form groups. Distribute the number strips, question cards, ice cream sticks and rubber bands to each group. Instruct the students to examine the number strip provided to them. Using the number strips, guide them to identify numbers that come before, after or between the specific numbers mentioned on the question card. Encourage the students to count and bundle up the corresponding number of ice cream sticks to check if their answer is correct. Prompt them to write the identified numbers in their appropriate places on the question cards.
Extension Idea
Ask: What is the number name of the number that comes before sixteen?
Say: The number name of the number that comes before sixteen is fifteen.
Learning Outcomes
Students will be able to compare numbers up to 20 to find the smaller or greater number.
Teaching Aids
Sheets with a number line drawn from 1 to 20; Crayons
Activity
Instruct the students to work in groups. Distribute the sheets with a number line drawn to each group. Call out 2 numbers between 1–20.
Ask the students to shade the numbers called out on the number line using the crayons. Ask them to identify the number which is on the right. Discuss that the number which is on the right on the number line is always greater than the number on the left. Ask them to note down the comparison using the words ‘more than’ or ‘less than’ in their notebooks. Repeat the activity with 3 more sets of numbers.
Extension Idea
Ask: If Suresh has 10 pencils and 2 erasers, and his friend has 9 pencils and 2 erasers, which of them has a greater number of items?
Say: Both of them have 2 erasers each, but Suresh has 1 pencil more than his friend. Hence, Suresh has a greater number of items. Ordering Smallest
Learning Outcomes
Students will be able to order numbers up to 20 from smallest to greatest and greatest to smallest.
Teaching Aids
Pebbles, dried twigs, fallen leaves, flowers
Activity
Take the students outside to an open area with trees. Divide them into groups and instruct them to explore and find pebbles, dried twigs, fallen leaves, flowers and other items in their surroundings. After collecting their nature treasures, have the students count and group the items. Then, guide them to arrange the groups in either increasing or decreasing order, based on the item count. For example, if they have pebbles, they can organise the groups from the fewest to the most, or vice versa for decreasing order. Finally, help them record their findings in their notebooks.
Extension Idea
Ask: Can you give one number that can be both the smallest and the biggest?
Say: Yes, when we compare 6 and 7, 6 is the smallest number. But, when we compare 5 and 6, we notice that 6 becomes the biggest number.
1. One-to-one Matching Do It Together
2. Counting Things Up to 9 Do It
5. The Number 10 Do It Together
10. Before, Between and After Do It Together
12. Ordering Smallest to Biggest Do It Together 9, , , 20
13. Ordering Biggest to Smallest Do It Together 19, , , 10
11. Using the Number Strip Do It Together
Students will be able to: count forward to find the total number of things up to 10. add 0 to a number up to 10 and find the total number of things. find the sum when the order of the numbers is changed. write all the addition facts for numbers up to 10. add 2 or more numbers by writing them one below the other. solve word problems on adding 2 or 3 numbers (sum up to 10).
Alignment to NCF
C-8.3: Counts forward and backward from a specific number (between 0 and 99)
C-8.3: Counts objects greater than 20 using number names till 99 and observe the pattern as groups of 10, up to 99
C-8.5: Recognises and writes numerals up to 20 and in words up to 10
C-8.5: Compares two numbers up to 20 and uses vocabulary like bigger than or smaller than Let’s Recall
Recap to check if students know how to count the number of things. Ask students to solve the questions given in the Let’s Warm-up section.
Vocabulary
counting forward: counting by adding 1 every time addition fact: showing 2 numbers with a (+) sign between them, followed by the (=) sign and the sum of the 2 numbers
vertical addition: adding numbers by writing them one below the other
Bags containing ice cream sticks; Empty bags; Red and blue straws; Paper cups; Small pieces of red and blue straws; Sheet of paper with the column table drawn, with space to paste the straws; Sheets with a word problem written and space given for What do we know? What do we need to know? and Solve to find the answer.
Learning
Students will be able to count forward to find the total number of things up to 10.
Teaching Aids
Bags containing ice cream sticks; Paper cups
Activity
Instruct the students to work in pairs.
Distribute bags containing 10 ice cream sticks to each student. Ask 1 student to put 3 ice cream sticks in the paper cup. Ask the second student to put 4 ice cream sticks in the paper cup. Then will then together count forward to find the total number of ice cream sticks in the paper cup.
Discuss how the ice cream sticks added and can be written as: 3 + 4 = 7.
Repeat the activity with other 1-digit numbers. Ask the students to first use the ice cream sticks to find the total and then write the addition sentence in their notebooks.
Extension Idea
Ask: If you have 3 bags of ice cream sticks and each bag has 2 ice cream sticks, how many ice cream sticks are there in all?
Say: 2 + 2 = 4 and 4 + 2 = 6. So, we will have 6 ice cream sticks.
Learning
Students will be able to add 0 to a number up to 10 and find the total number of things.
Teaching Aids
Empty bags; Bags containing ice cream sticks
Activity
Instruct the students to work in pairs.
Distribute a bag containing 4 ice cream sticks to one student and an empty bag to another student in each pair. Ask the students to take out the ice cream sticks from their bags and place them together and count the total number of ice cream sticks. Explain that when we do not have anything, we show it with the number 0.
Discuss that the ice cream sticks taken by the pairs are added and can be written as: 4 + 0 = 4.
Repeat the activity once more to add the numbers 6 and 0. Ask the students to write the addition sentence in their notebooks.
Extension Idea
Ask: Do 5 + 0 and 0 + 5 give the same answer?
Say: Yes. 5 + 0 = 5 and 0 + 5 = 5. The total number of things will remain 5.
Learning Outcomes
Students will be able to find the sum when the order of the numbers is changed.
Teaching Aids
Red and blue straws
Activity
Instruct the students to work in groups.
Distribute 2 bags of straws with 3 red and 5 blue straws in one bag and 5 red and 3 blue straws in another bag, to each group.
Ask the students to take out the straws from the first bag. Ask them to count the number of red straws, then blue straws and finally the total number of straws. Help them to write the addition sentence in their notebooks.
Ask the students to now take out the straws from the second bag. Ask them to again count the number of red, blue and total straws, and write the addition sentence in their notebooks.
Ask questions like: What is different about 3 + 5 and 5 + 3? What is same?
Explain that, in both the cases, the number of straws remains the same. So, we can add 2 numbers in any order.
Extension Idea
Ask: Is 2 + 3 + 5 the same as 5 + 3 + 2? Why?
Say: 2 + 3 + 5 is the same as 5 + 3 + 2. Both give the same answer since the 3 numbers being added are the same, although their order is changed.
Addition Facts
Learning Outcomes
Students will be able to write all the addition facts for numbers up to 10.
Red and blue straws; Paper cups
Activity
Instruct the students to work in pairs.
Distribute the paper cups, red straws and blue straws to each pair.
Imagine Maths Page 41
Ask them to put 4 red straws in the first cup and keep the second cup empty. Show them how to write the addition sentence as 4 + 0 = 4. Let the students note down the addition sentence in their notebook. Now, ask the pairs to keep 3 red straws in the first cup and 1 blue straw in the second cup. Ask them to note down the addition sentence for the same.
Repeat the activity for all the addition sentences of the number 4 and make the students write the addition sentences. Ask questions like: In how many ways did you add 2 numbers to make 4?
Repeat the activity for the addition facts of 6.
Extension Idea
Ask: How will you show the addition facts of 5 by drawing red and blue lines?
Say: To show the addition facts of 5, we can draw 5 red–0 blue, 4 red–1 blue, 3 red–2 blue, 2 red–3 blue, 1 red–4 blue and 0 red–5 blue lines. Draw lines on the board to show.
Learning Outcomes
Students will be able to add 2 or more numbers by writing them one below the other.
Teaching Aids
Imagine Maths Page 43
Small pieces of red and blue straws; Sheet of paper with the column table drawn, with space to paste the straws
Activity
Distribute 2 pieces of red and 4 pieces of blue straws and a sheet of paper to the students. Instruct the students to count the number of red and blue straws and write the numbers in the table. Then, they will paste the straw pieces next to each number. Ask them to add the 2 numbers and write the answer in the table. Finally, ask them to count the total number of straws and match the answers.
Ask questions like: Could you add 2 or more numbers if there were no straws?
Learning Outcomes
Students will be able to solve word problems on adding 2 or 3 numbers (sum up to 10).
Teaching Aids
Imagine Maths Page 44
Sheets with a word problem written and space given for What do we know? What do we need to know? and Solve to find the answer.
Activity
Instruct the students to work in groups. Distribute the word problem sheets among the groups.
Read the word problem: Suman has 2 crayons. Ann has 3 crayons. Sia has 4 crayons. How many crayons do they have in all?
Suman has 2 crayons. Ann has 3 crayons. Sia has 4 crayons. How many crayons do they have in all? What do we know? What do we need to know? Solve to find the answer.
Discuss what is given and what we need to know. Ask the students to write the numbers to be added, draw the same number of lines as the number of crayons and find the sum. Discuss the answer in the class.
1. Adding One
8. Story Problems on Adding Numbers Do It Together