Solved Exercises on Understanding Division as Sharing in Grade 3

Master division as sharing: equal groups, fair distribution, and real-world applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Sharing
Exercise 1
Sarah has 12 cookies. She wants to share them equally among 4 friends. How many cookies does each friend get?
Definition:

Division as Sharing: Splitting a total number of items into equal groups. We divide the total number of items by the number of groups to find how many items each group gets.

Sharing Method:
  1. Identify the total: How many items are being shared?
  2. Identify the groups: How many people or groups will receive items?
  3. Divide: Total ÷ Number of groups = Items per group
  4. Verify: Multiply to check if the answer is correct
Total cookies
12
Number of friends
4
Cookies per friend
3
Step 1: Identify what needs to be shared

Sarah has 12 cookies to share

Step 2: Identify the number of groups

She has 4 friends to share with

Step 3: Divide to find equal shares

12 cookies ÷ 4 friends = 3 cookies per friend

Step 4: Verify the answer

3 cookies × 4 friends = 12 cookies total ✓

12 ÷ 4 = 3 cookies per friend
Final answer:

Each friend gets 3 cookies because 12 ÷ 4 = 3

Applied rules:

• Sharing Rule: Total ÷ Number of groups = Items per group

• Equal Distribution: Each group gets the same number of items

• Verification: Multiply back to check the division

2 Candy Sharing
Exercise 2
Tom has 20 candies. He wants to share them equally among his 5 sisters. How many candies does each sister get?
Definition:

Fair Distribution: The process of dividing items equally among a specified number of recipients, ensuring each person receives the same amount.

Sister 1
Sister 2
Sister 3
Sister 4
Sister 5
Total candies
20
Number of sisters
5
Candies per sister
4
Step 1: Identify the total amount

Tom has 20 candies

Step 2: Identify the number of recipients

He has 5 sisters

Step 3: Divide to find equal shares

20 candies ÷ 5 sisters = 4 candies per sister

Step 4: Verify the answer

4 candies × 5 sisters = 20 candies total ✓

20 ÷ 5 = 4 candies per sister
Final answer:

Each sister gets 4 candies because 20 ÷ 5 = 4

Applied rules:

• Fair Distribution: Each recipient gets an equal share

• Division Formula: Total ÷ Number of recipients = Share per recipient

• Verification: Multiply to confirm the division is correct

3 Apple Sharing
Exercise 3
There are 18 apples. They need to be shared equally among 6 baskets. How many apples go in each basket?
Definition:

Division as Sharing: Distributing a total quantity into equal portions among a specified number of containers or recipients.

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Total apples
18
Number of baskets
6
Apples per basket
3
Step 1: Identify the total number of items

There are 18 apples

Step 2: Identify the number of containers

There are 6 baskets

Step 3: Divide to find equal distribution

18 apples ÷ 6 baskets = 3 apples per basket

Step 4: Verify the answer

3 apples × 6 baskets = 18 apples total ✓

18 ÷ 6 = 3 apples per basket
Final answer:

Each basket gets 3 apples because 18 ÷ 6 = 3

Applied rules:

• Equal Distribution: Each container receives the same number of items

• Division Formula: Total ÷ Number of containers = Items per container

• Verification: Multiply back to confirm the division

Division as Sharing Concepts
Total ÷ Groups = Share per Group
Sharing Formula
Concept 1
Equal Groups
Same number in each group
Concept 2
Fair Share
Everyone gets the same amount
Concept 3
Division
Splitting into equal parts
Concept 4
Verification
Multiply to check answer
Division Sharing Interpretation Example 12 ÷ 3 12 items shared among 3 people Each gets 4 items 20 ÷ 5 20 items shared among 5 people Each gets 4 items 15 ÷ 3 15 items shared among 3 people Each gets 5 items 24 ÷ 6 24 items shared among 6 people Each gets 4 items
Key definitions:

Division: The operation of splitting a number into equal parts

Sharing: Distributing items equally among recipients

Equal Groups: Groups that contain the same number of items

Remainder: Leftover items that cannot be evenly distributed

Sharing Method Steps:
  1. Identify the total: How many items are there?
  2. Identify the groups: How many people/containers?
  3. Divide: Total ÷ Groups = Items per group
  4. Verify: Multiply back to check your answer
Key Principle: Division as sharing creates equal groups.
Fair Distribution: Each recipient gets the same amount.
Tip 1: Always make sure each group gets the same number of items.
Tip 2: Draw pictures or use objects to visualize the sharing.
Tip 3: Check your answer by multiplying back.
Solution: Exercises 4 to 5
4 Pizza Sharing
Exercise 4
Mom made 24 pizza slices for 8 children. If she wants to share them equally, how many slices does each child get?
Definition:

Real-World Sharing: Applying the concept of division as sharing to practical situations involving food, toys, or other everyday items.

Child 1
Child 2
Child 3
Child 4
Child 5
Child 6
Child 7
Child 8
Total slices
24
Number of children
8
Slices per child
3
Step 1: Identify the total number of items

Mom made 24 pizza slices

Step 2: Identify the number of recipients

There are 8 children

Step 3: Divide to find equal shares

24 slices ÷ 8 children = 3 slices per child

Step 4: Verify the answer

3 slices × 8 children = 24 slices total ✓

24 ÷ 8 = 3 slices per child
Final answer:

Each child gets 3 pizza slices because 24 ÷ 8 = 3

Applied rules:

• Real-World Application: Division applies to everyday sharing situations

• Equal Distribution: Each child receives the same number of slices

• Verification: Multiply back to confirm the division is correct

5 Book Sharing
Exercise 5
A teacher has 30 books to distribute equally among 5 reading groups. How many books does each group get?
Definition:

Educational Sharing: Using division as sharing in classroom contexts where materials need to be distributed equally among groups or students.

Total books
30
Number of groups
5
Books per group
6
Step 1: Identify the total number of items

The teacher has 30 books

Step 2: Identify the number of groups

There are 5 reading groups

Step 3: Divide to find equal distribution

30 books ÷ 5 groups = 6 books per group

Step 4: Verify the answer

6 books × 5 groups = 30 books total ✓

30 ÷ 5 = 6 books per group
Final answer:

Each reading group gets 6 books because 30 ÷ 5 = 6

Applied rules:

• Classroom Application: Division helps distribute materials fairly

• Equal Distribution: Each group receives the same number of books

• Verification: Multiply back to confirm the division is correct

Advanced Sharing Concepts
a ÷ b = c
Division Formula
Key definitions:

Dividend: The number being divided (a in a ÷ b = c)

Divisor: The number that divides the dividend (b in a ÷ b = c)

Quotient: The result of the division (c in a ÷ b = c)

Remainder: Leftover amount when division is not exact

Advanced Sharing Strategies:
  1. Estimate first: Predict the approximate answer before calculating
  2. Use known facts: Apply multiplication facts to help with division
  3. Check your work: Multiply the quotient by the divisor
  4. Visualize: Draw or model the sharing situation
  5. Verify: Ensure the answer makes sense in the context
Tip 1: Division as sharing always creates equal groups.
Tip 2: You can always check division by multiplying back.
Tip 3: Use visual models to understand the concept better.
Tip 4: Practice with different numbers to build confidence.
Key Pattern: Division as sharing ensures fairness by creating equal distributions.
Foundation: Understanding sharing helps with more complex division concepts.
Advanced rules:

• Division as Sharing: Total ÷ Number of groups = Items per group

• Verification: Quotient × Divisor = Dividend

• Equal Distribution: Each group receives the same number of items

• Real-World Application: Sharing applies to many practical situations

Example
Division
Sharing Result
Simple
12 ÷ 4
3 per group
Medium
20 ÷ 5
4 per group
Advanced
36 ÷ 6
6 per group

Questions & Answers

Question: Why do we need to learn division as sharing? Can't we just count?

Answer: Division as sharing is much more efficient than counting! Here's why:

  • Saves time: Instead of counting out 24 items one by one to 6 people, division tells us each person gets 4
  • Ensures fairness: Division guarantees everyone gets exactly the same amount
  • Works with big numbers: Try sharing 100 cookies among 10 people by counting!
  • Prepares for more math: Division is essential for advanced math concepts

Division is like a shortcut that helps us share fairly and quickly!

Question: How can I help my child understand division as sharing at home?

Answer: Here are some practical activities to try:

  • Use real objects: Share snacks, toys, or household items equally
  • Play sharing games: "We have 12 cookies for 4 people, how many each?"
  • Cook together: Divide ingredients equally for recipes
  • Draw pictures: Sketch groups and distribute items visually
  • Practice with money: Share coins or bills equally
  • Story problems: Create scenarios with friends, pets, or family members

The key is making it hands-on and fun!

Question: What happens if the items don't divide evenly? Like 13 cookies shared among 4 people?

Answer: Great question! When items don't divide evenly, we get a remainder:

  • 13 ÷ 4 = 3 remainder 1
  • Each person gets 3 cookies
  • There is 1 cookie left over (the remainder)

In real life, you might:

  • Cut the leftover cookie into pieces
  • Give the extra to someone special
  • Save it for later

The remainder tells us how many items are left after equal sharing!