Solved Exercises on Division Sharing and Grouping in Grade 3

Master division through sharing and grouping: equal distribution, grouping strategy, and problem-solving through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Equal Sharing
Exercise 1
Mia has 15 candies. She wants to share them equally among her 3 friends. How many candies does each friend get?
Definition:

Equal Sharing: Distributing a total amount equally among a specific number of people or groups.

Equal Sharing Method:
  1. Identify the total amount (dividend)
  2. Identify the number of people/groups (divisor)
  3. Share items one by one to each person/group
  4. Count how many each person/group receives (quotient)
Step 1: Identify the total and number of people

Total candies = 15, Number of friends = 3

Step 2: Share equally

Give 1 candy to each friend, then another, and so on...

Step 3: Count candies per friend

Each friend gets 5 candies

Step 4: Write the division equation

15 ÷ 3 = 5

15 ÷ 3 = 5 candies per friend
Final answer:

Each friend gets 5 candies.

Applied rules:

• Equal distribution: Every person gets the same amount

• Division as sharing: Total ÷ People = Amount per person

• Verification: 3 friends × 5 candies = 15 total candies

2 Grouping Strategy
Exercise 2
A teacher has 20 pencils. She puts them into groups of 4. How many groups can she make?
Definition:

Grouping: Making equal-sized groups from a total amount to find how many groups.

Step 1: Identify the total and group size

Total pencils = 20, Pencils per group = 4

Step 2: Make groups of 4

Keep making groups until all pencils are used

Step 3: Count the number of groups

Group 1, Group 2, Group 3, Group 4, Group 5 = 5 groups

Step 4: Write the division equation

20 ÷ 4 = 5

20 ÷ 4 = 5 groups
Final answer:

The teacher can make 5 groups.

Applied rules:

• Division as grouping: Total ÷ Group size = Number of groups

• Equal-sized groups: Each group has the same number of items

• Verification: 5 groups × 4 pencils = 20 total pencils

3 Mixed Sharing and Grouping
Exercise 3
A baker has 18 cupcakes. First, he shares them equally among 6 children. Then, he takes the same 18 cupcakes and makes groups of 3. Compare the results.
Definition:

Comparison Strategy: Understanding how changing the divisor affects the quotient in division.

Step 1: Analyze the sharing scenario

18 cupcakes ÷ 6 children = 3 cupcakes per child

Step 2: Analyze the grouping scenario

18 cupcakes ÷ 3 cupcakes per group = 6 groups

Step 3: Compare the results

Sharing: 6 people get 3 each, Grouping: 6 groups of 3 each

Step 4: Understand the relationship

Same total but different contexts lead to same numerical result

18 ÷ 6 = 3 (sharing) and 18 ÷ 3 = 6 (grouping)
Final answer:

In sharing: each child gets 3 cupcakes. In grouping: 6 groups of 3 cupcakes each.

Applied rules:

• Inverse relationship: Larger divisor → Smaller quotient

• Context matters: Same numbers, different interpretations

• Verification: 6 × 3 = 18 and 3 × 6 = 18

Rules and methods, laws,...
Total ÷ People = Each Person Gets
Sharing Formula
Total ÷ Group Size = Number of Groups
Grouping Formula
Sharing
12 ÷ 4 = 3
12 items shared among 4 people = 3 each
Grouping
12 ÷ 3 = 4
12 items in groups of 3 = 4 groups
Inverse
a ÷ b = c means b × c = a
Multiplication checks division
Key definitions:

Sharing: Distributing equally among people/groups

Grouping: Making equal-sized groups from a total

Dividend: The total amount being divided

Divisor: What we divide by (people or group size)

Quotient: The result of division

Complete methodology:
  1. Read carefully: Determine if it's sharing or grouping
  2. Identify parts: Find dividend, divisor, and unknown
  3. Visualize: Draw pictures or use objects
  4. Calculate: Perform the division
  5. Verify: Multiply to check your answer
Tip 1: Look for keywords: "shared equally" = sharing, "groups of" = grouping.
Tip 2: Always check: divisor × quotient = dividend.
Tip 3: Draw circles to represent groups or people.
Common errors: Confusing sharing with grouping, forgetting to check answers.
Memory aid: "Sharing is caring" - giving out equally.
Detailed Summary: Division Sharing and Grouping
a ÷ b = c if and only if b × c = a
Division-Multiplication Relationship
Core Concepts:

Division: The process of splitting a total amount into equal parts

Sharing: Distributing items equally among people/groups (finding amount per person)

Grouping: Creating equal-sized groups from a total (finding number of groups)

Remainder: Leftover items that cannot form a complete group

Step-by-Step Approach:
  1. Identify the type: Is it sharing or grouping?
  2. Find the numbers: What's the total? What's the divisor?
  3. Visualize: Draw representations or use physical objects
  4. Perform division: Calculate the quotient
  5. Verify: Multiply to confirm your answer
Strategy 1: Use skip counting to find division facts quickly.
Strategy 2: Think of division as repeated subtraction.
Strategy 3: Connect to multiplication tables you know.
Important Rules:

• Division Property: a ÷ b = c means b groups of c equals a

• Zero Property: 0 ÷ a = 0 (when a ≠ 0)

• One Property: a ÷ 1 = a

• Undefined: Cannot divide by zero (a ÷ 0 is undefined)

Key insight: Sharing and grouping are two ways to think about the same division fact.
Connection: Division connects to multiplication, fractions, and ratios.
Examples:
Practical Applications
Simple Example

Sharing: 8 apples ÷ 4 people = 2 apples per person

Grouping: 8 apples ÷ 2 apples per bag = 4 bags

Intermediate Example

Sharing: 24 cookies ÷ 6 children = 4 cookies per child

Grouping: 24 cookies ÷ 4 cookies per plate = 6 plates

Advanced Example

Word problem: 36 books in 9 equal stacks = 4 books per stack

Verification: 9 stacks × 4 books = 36 total books ✓

Questions & Answers

Question: How do I know if a word problem is about sharing or grouping? They seem similar to me.

Answer: Great question! Look for these clues:

  • Sharing keywords: "shared equally", "given to each", "divided among", "per person"
  • Grouping keywords: "groups of", "packs of", "sets of", "how many groups"

Examples:

  • "12 cookies shared among 4 friends" = Sharing (12 ÷ 4 = 3 each)
  • "12 cookies in groups of 4" = Grouping (12 ÷ 4 = 3 groups)

The math is the same, but the context changes what the answer represents!

Question: What happens if I can't divide evenly? Like 10 cookies shared among 3 friends?

Answer: When division doesn't come out evenly, we have a remainder!

For 10 ÷ 3:

  • Each friend gets 3 cookies (3 × 3 = 9)
  • There's 1 cookie left over (10 - 9 = 1)
  • We write: 10 ÷ 3 = 3 R1 (3 remainder 1)

The remainder tells us how many items are left after making equal shares. This is completely normal in division!

Question: How can I check if my division answer is correct? Sometimes I'm not sure.

Answer: There are two excellent ways to check your division:

  1. Multiplication check: Multiply your answer by the divisor
  2. Addition check: Add up all the equal parts

Example: If 15 ÷ 3 = 5

  • Multiplication: 5 × 3 = 15 ✓
  • Addition: 5 + 5 + 5 = 15 ✓

If you get back to your original number, your answer is correct!