Equal Shares Math

Visual Sharing Models: Problems 3 – 5

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3

Five friends share 4 cookies equally.

Division Expression: \( 4 \div 5 = \frac{4}{5} \) cookie

Model: 4 cookies each split into 5 equal wedges (1/5 each). Shaded pieces show 1 friend's share:

Cookie 1

1/5

Cookie 2

1/5

Cookie 3

1/5

Cookie 4

1/5

Each friend gets 1 fifth from each of the 4 cookies: \( \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{4}{5} \) cookie per friend.

4

Seven pizzas are shared between 3 friends.

Division Expression: \( 7 \div 3 = \frac{7}{3} = 2\frac{1}{3} \) pizzas

Model: Distribute whole pizzas first (6 wholes = 2 each), then divide the 7th pizza into 3 thirds:

Pizza 1

Friend 1

Pizza 2

Friend 2

Pizza 3

Friend 3

Pizza 4

Friend 1

Pizza 5

Friend 2

Pizza 6

Friend 3

Pizza 7 (1/3s)

1/3

1/3

1/3

Each friend gets 2 whole pizzas + 1 third of a pizza = \( 2\frac{1}{3} \) pizzas (or \( \frac{7}{3} \) pizzas).

5

Two jars of slime shared between 6 classmates.

Division Expression: \( 2 \div 6 = \frac{2}{6} = \frac{1}{3} \) jar

Model: Each jar partitioned into 6 equal sixths; each student takes 1 sixth from each jar:

Jar 1 (6 equal parts)

1/6

2

3

4

5

6

Jar 2 (6 equal parts)

1/6

2

3

4

5

6

Each classmate gets \( \frac{1}{6} + \frac{1}{6} = \frac{2}{6} \) of a jar, which simplifies to \( \frac{1}{3} \) of a jar of slime.

Grade 5 Math • U2, L1: Fractions as Quotients Equal Shares Diagram Guide • Page 2 (Black & White Edition)

Practice Set • Part 2 Models & Division Expressions

Visual Sharing Models: Problems 6 – 8

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6

Nine pounds of clay shared equally between four artists.

Division Expression: \( 9 \div 4 = \frac{9}{4} = 2\frac{1}{4} \) lbs

Model: 8 whole pounds (2 per artist) + 9th pound split into 4 equal fourths:

Artist 1

2 Whole Lbs

+ 1/4 Lb

Artist 2

2 Whole Lbs

+ 1/4 Lb

Artist 3

2 Whole Lbs

+ 1/4 Lb

Artist 4

2 Whole Lbs

+ 1/4 Lb

9th Pound

1/4

1/4

1/4

1/4

Each artist gets 2 whole pounds and 1 fourth of a pound = \( 2\frac{1}{4} \) pounds of clay (or \( \frac{9}{4} \) lbs).

7

Five liters of Gatorade shared equally among three teams.

Division Expression: \( 5 \div 3 = \frac{5}{3} = 1\frac{2}{3} \) liters

Model: 3 whole liters (1 per team) + remaining 2 liters split into thirds:

Liter 1

Team A

Liter 2

Team B

Liter 3

Team C

Liter 4 (Thirds)

A

B

C

Liter 5 (Thirds)

A

B

C

Each team receives 1 whole liter + \( \frac{1}{3} + \frac{1}{3} = \mathbf{1\frac{2}{3}} \) (or \( \frac{5}{3} \)) liters of Gatorade.

8

Seven granola bars shared equally among five campers.

Division Expression: \( 7 \div 5 = \frac{7}{5} = 1\frac{2}{5} \) bars

Model: 5 whole bars (1 per camper) + 2 bars each partitioned into fifths:

Bar 1

Camp 1

Bar 2

Camp 2

Bar 3

Camp 3

Bar 4

Camp 4

Bar 5

Camp 5

Bar 6 (1/5s)

1

2

3

4

5

Bar 7 (1/5s)

1

2

3

4

5

Each camper receives 1 whole bar + \( \frac{1}{5} + \frac{1}{5} = \mathbf{1\frac{2}{5}} \) (or \( \frac{7}{5} \)) granola bars.

Grade 5 Math • U2, L1: Fractions as Quotients Equal Shares Diagram Guide • Page 3 (Black & White Edition)

Uncommon Schools • LP U2, L1 Exit Ticket Solution & Modeling Guide

U2, L1: Share Sandwiches Exit Ticket

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Exit Ticket Task

3 sandwiches are equally shared by 4 people. How much sandwich does each person get?

Division Expression \( 3 \div 4 = \frac{3}{4} \)

1

Draw a diagram to show how much sandwich each person will get.

3 Authentic Lesson Plan Models

Model A: Square Fourths 1 quarter shaded on each sandwich

\( \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4} \)

Model B: Numbered Shares Labeling shares 1, 2, 3, 4

1

2

3

4

1

2

3

4

1

2

3

4

Person 1 gets three 1/4 pieces

Model C: Oval / Sub Rolls Concrete sub-roll representations

1 slice from each of 3 subs = \( \frac{3}{4} \)

2

Explain or show how you know that each person gets the same amount of sandwich.

Official Sample Responses from Teacher Lesson Plan:

•

Sample Response 1: “Each person gets one fourth of each sandwich.” (\( \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4} \) sandwich total)

•

Sample Response 2: “Each person gets one half plus one fourth of each sandwich.” (Divide 2 sandwiches into 4 halves: each gets \( \frac{1}{2} \). Divide 3rd sandwich into 4 fourths: each gets \( \frac{1}{4} \). Total = \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \))

•

Sample Response 3: “Each person gets \( \frac{3}{4} \) of a sandwich.” (Check: \( 4 \text{ people} \times \frac{3}{4} = \frac{12}{4} = 3 \) whole sandwiches shared with 0 leftover)

Lesson Mini-Stamp: “Sharing means splitting a total into equal groups. We can represent equal sharing situations with division expressions: dividend ÷ divisor.”

Teacher Monitoring Note: Our dividend (3 sandwiches) tells what is being shared. Our divisor (4 people) tells how many equal shares. Each share is \( \frac{3}{4} < 1 \) sandwich.

Uncommon Schools • Adapted from Illustrative Math • Grade 5 Math LP U2, L1 Exit Ticket Solution Guide • Page 4