Division as Sharing

Complete curriculum on division as sharing for grade 3 students. Comprehensive exercises, step-by-step solutions, and detailed explanations for mastering division concepts.

Division as Sharing: Grade 3 Curriculum
1 Basic Sharing
Sharing Exercise 1
Problem: Sarah has 12 cookies and wants to share them equally among 4 friends. How many cookies does each friend get?
What is Division as Sharing?

Division as sharing: The process of distributing a total amount equally among a certain number of recipients. Each recipient gets the same amount.

Method: Sharing Equally
  1. Count the total items (12 cookies)
  2. Count the number of people to share with (4 friends)
  3. Distribute items one at a time to each person
  4. Continue until all items are distributed
  5. Count how many each person received
Step 1: Identify the problem

We need to share 12 cookies equally among 4 friends: 12 ÷ 4 = ?

Step 2: Distribute equally

Round 1: Each friend gets 1 cookie → 4 cookies given out, 8 left
Round 2: Each friend gets 1 cookie → 4 more cookies given out, 4 left
Round 3: Each friend gets 1 cookie → 4 more cookies given out, 0 left

Step 3: Count and conclude

Each friend received 3 cookies.

12 ÷ 4 = 3 cookies per friend
Final answer:

Each friend gets 3 cookies because 12 shared equally among 4 people gives 3 to each person.

Key Rule:

• Equal sharing: Every person gets the same number of items

• Verification: 3 × 4 = 12 ✓

2 Group Sharing
Sharing Exercise 2
Problem: A teacher has 20 pencils to share equally among 5 students. How many pencils does each student get?
Important Terms:

Dividend: The total number being shared (20 pencils)

Divisor: The number of people sharing (5 students)

Quotient: The answer (number of pencils per student)

Step 1: Set up the sharing

20 pencils ÷ 5 students = ? pencils per student

Step 2: Distribute equally

Round 1: Each student gets 1 pencil → 5 pencils given out, 15 left
Round 2: Each student gets 1 pencil → 5 more pencils given out, 10 left
Round 3: Each student gets 1 pencil → 5 more pencils given out, 5 left
Round 4: Each student gets 1 pencil → 5 more pencils given out, 0 left

Step 3: Determine the answer

Each student gets 4 pencils.

20 ÷ 5 = 4 pencils per student
Final answer:

Each student gets 4 pencils because 20 shared equally among 5 students gives 4 to each student

Sharing Rule:

• Equal distribution: Each person receives the same amount

• Verification: 4 × 5 = 20 ✓

3 Real World Sharing
Sharing Exercise 3
Problem: A family has 36 stickers to share equally among 6 children. How many stickers does each child get?
Sharing Concept:

Equal sharing: Distributing items so that every recipient gets the same amount, with no one getting more or less than anyone else.

Step 1: Analyze the problem

We have 36 stickers and 6 children. We need to find how many stickers each child gets.

Step 2: Apply equal sharing

We distribute stickers so each child gets the same amount:
36 ÷ 6 = 6 stickers per child

Step 3: State the answer

Each child gets 6 stickers.

36 ÷ 6 = 6 stickers per child
Final answer:

Each child gets 6 stickers because 36 shared equally among 6 children gives 6 to each child

Applied Rules:

• Grouping principle: How many groups of 6 can we make from 36?

• Verification: 6 × 6 = 36 ✓

Complete Summary: Division as Sharing
Key Concepts and Definitions:

Division as sharing: The mathematical operation that distributes a total amount equally among a certain number of recipients. It helps us determine how many items each person gets when sharing fairly.

Sharing: Distributing items so that every recipient gets the same amount.

Dividend: The number being divided (the total amount to be shared).

Divisor: The number we divide by (how many people to share with).

Quotient: The result of division (how many each person gets).

Fact Family: A set of related multiplication and division facts that use the same numbers.

Step-by-Step Sharing Method:
  1. Read the problem carefully: Identify what needs to be shared and how many people to share with.
  2. Identify the dividend and divisor: The total amount and the number of recipients.
  3. Distribute equally: Give one item to each person at a time.
  4. Continue distributing: Keep giving items until they're all distributed.
  5. Count per person: See how many each person received.
  6. Write the answer: This count is your quotient.
  7. Verify your answer: Multiply the quotient by the divisor to check if you get the dividend.
Tip 1: Always make sure each person gets the same amount.
Tip 2: Count carefully to make sure sharing is fair.
Tip 3: Use drawings or objects to visualize the sharing.
Tip 4: Always check your answer: quotient × divisor = dividend.
Tip 5: Fair sharing means everyone gets exactly the same amount.
Examples from Simple to Advanced:

Simple Example: 8 ÷ 2 = ?
Share 8 items between 2 people → Each gets 4 items
Answer: 4

Intermediate Example: 15 ÷ 3 = ?
Share 15 items between 3 people → Each gets 5 items
Answer: 5

Advanced Example: 36 ÷ 6 = ?
Share 36 items between 6 people → Each gets 6 items
Answer: 6

Connection to Multiplication: Division is the inverse of multiplication. If 6 × 4 = 24, then 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
Word Problem Strategy: Look for key words like "share," "equally," "between," "each," or "per" to identify sharing problems.
Real-World Applications: Sharing helps solve practical problems like distributing resources, splitting costs, or organizing items fairly.
Important Rules to Remember:

• Fair Sharing: Everyone gets the same amount.

• Verification: Always multiply your answer by the divisor to check your work.

• Zero Property: Any number divided by itself equals 1 (e.g., 8 ÷ 8 = 1).

• One Property: Any number divided by 1 equals itself (e.g., 12 ÷ 1 = 12).

• Division by Zero: Division by zero is undefined (you cannot divide by zero).

Division as Sharing Concepts
Total Items ÷ Number of People = Items Per Person
Basic Sharing Formula
Sharing
12 ÷ 4 = 3
12 shared among 4 = 3 each
Multiplication Check
3 × 4 = 12
Inverse operation
Word Problem
20 items, 5 people
20 ÷ 5 = 4 each
Key Definitions:

Dividend: The number being shared (the total amount)

Divisor: The number of people sharing (number of recipients)

Quotient: The result of sharing (items per person)

Fair Share: Each person receiving the same amount

Sharing Process:
  1. Identify: Find the total items and number of people
  2. Distribute: Give one item to each person at a time
  3. Count: Keep track of how many each person gets
  4. Answer: The count is items per person
  5. Check: Multiply items per person × number of people
Tip 1: Use drawings to visualize the sharing.
Tip 2: Make sure sharing is fair and equal.
Tip 3: Practice with smaller numbers first.
Tip 4: Always verify your answer by multiplication.
Sharing Relationships: Sharing and multiplication are inverse operations that undo each other.
Problem Solving: Identify key words that indicate sharing is needed.
Real-World Connection: Sharing helps solve everyday problems involving fair distribution.
Advanced Sharing and Questions
4 Classroom Sharing
Sharing Exercise 4
Problem: There are 40 markers to share equally among 8 students. How many markers does each student get?
Step 1: Identify the components

Total markers = 40, students = 8, so 40 ÷ 8 = ?

Step 2: Distribute equally

Each student gets 5 markers (40 ÷ 8 = 5)

40 ÷ 8 = 5 markers per student
5 Party Planning
Sharing Exercise 5
Problem: A party planner has 56 balloons to share equally among 7 tables. How many balloons does each table get?
Step 1: Set up the problem

56 balloons ÷ 7 tables = ? balloons per table

Step 2: Apply equal sharing

56 ÷ 7 = 8 balloons per table

Step 3: Verify the answer

Check: 8 × 7 = 56 ✓

56 ÷ 7 = 8 balloons per table

Questions & Answers

Question: What happens if I can't share everything equally? Like if I have 10 cookies and 3 friends?

Answer: Great question! Sometimes sharing doesn't work out perfectly:

With 10 cookies and 3 friends:

  • Each friend gets 3 cookies (3 × 3 = 9)
  • That uses 9 cookies
  • 1 cookie is left over

This is called having a "remainder." Each friend gets 3 cookies with 1 left over!

Question: How can I help my child understand the concept of sharing in division?

Answer: Here are effective ways to teach sharing:

  • Use real objects: Counters, toys, or snacks to physically share
  • Draw pictures: Sketch circles to represent people and dots for items
  • Create scenarios: "If you have 12 cookies for 4 friends..."
  • Practice regularly: Start with small numbers and build up
  • Emphasize fairness: Everyone must get the same amount

Hands-on activities make the concept tangible and memorable!

Question: How do I know if a sharing problem is fair?

Answer: A sharing problem is fair when:

  • Every person gets the exact same number of items
  • No one gets more or less than anyone else
  • All items are distributed (no remainders, unless specified)

Think of it like cutting a pizza - each slice should be the same size!