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Hanger Diagram
Distributive property
What is X?
Fractions and Percents
100

Your third grade neighbor wants to know what a hanger diagram is  and what they have to do with math- explain it to them

A hanger diagram needs to be balanced just like an equation. One side of the equal sign must equal the other side. 

100

What does it mean to distribute?

to pass out

100
What is the  name for a letter or symbol that is used to represent a number?

Variable

100

x is 25% of 60
Write an equation that represents this problem and solve for x

15

200
  1. Write an equation to represent the hanger.
     
  2. Explain how to reason with the hanger to find the value of x.
     
  3. Explain how to reason with the equation to find the value of x.

L3, P3

1.  2x=14.62

2. Each x can be grouped with half of the other side, so that means x is half of 14.62 or 7.31.

3. 14.62 is twice x, so x must be 7.31, since 2(7.31)=14.62.

200

Select all the expressions that represent the area of the large, outer rectangle
L9, P1

a: 5(2+4)

b: 5x2+4

c: 5x2 + 5x4

d: 5x2x4

e: 5+2+4

f: 5x6

A, C, F

200

Solve the following equations:

1. 2x = 7

2. y + 1.8 = 14.7

1.     3.5

2.      12.9

200

40% of x is 35.

Write an equation that shows the relationship of 40%, x, and 35

Use your equation to solve for x

0.4x=35
x=87.5

300

Select all of the equations that represent the hanger 

a: x+x+x=1+1+1+1+1+1

b: x*x*x = 6

c: 3x = 6

d: x+3 = 6

e: x*x*x= 1+1+1+1+1+1

L3, P1

A, C

300

Here is a rectangle.


  1. Explain why the area of the large rectangle is 2a + 3a +4a .
  2. Explain why the area of the large rectangle is  a(2+3+4).
  • The large rectangle is made up of three smaller rectangles whose areas are 2a,3a , and 4a.
  • The large rectangle has height a and length 2+3+4, so its area is a(2+3+4)
300

Solve the following equations:

1.      6 = 1/2z

2.      3 1/4 = 1/2 + w

3.       2.5t = 10

1.    z = 12

2.    w = 2 3/4  or 2.75

3.     t = 4

300

Brian has completed 9 exam questions. This is 60% of the questions on the exam.

  1. Write an equation representing this situation. Explain the meaning of any variables you use.

  2. How many questions are on the exam? Show your reasoning.

9 = 0.6x

15 because 9/0.6=15

400

Write an equation to represent each hanger. (L3, P2)


1.     2x = 3

2.      w + 1.3 = 2.7

3.      3y=5.1

4.       z + 1/3 = 1/2

400

Use the distributive property to write an equivalent expression- then solve


15(22-6)

15x22 - 15x6

330-90= 240

400

Which expressions are solutions to the equation 3/4x = 15? Select all that apply

L5, P2

A, C, E

400

120% of x is equal to 78

  1. Write an equation that shows the relationship of 120%, x , and 78.
  2. Use your equation to find x . Show your reasoning.

1.   1.2x=78

2.   x = 65 (78/1.2=65)

500

Create a hanger diagram for the equation:

4x=14

Solve for x


Create a different hanger diagram for the equation:
2.13 + y = 5

Solve for y

3.5

2.87

500

Use the distributive property to write two expressions that equal 360. (There are many correct ways to do this.) 

Answers vary: possible expressions: 36(7+3) ,  10 (20+16)

500

For both equations write and solve a story problem:

3/4 + X = 2

1.5x = 6

1 1/4

4

500

A trash bin has a capacity of 50 gallons. What percentage of its capacity is each amount? Show your reasoning.

  1. 5 gallons
  2. 30 gallons
  3. 45 gallons
  4. 100 gallons
  1. 5 gallons is 10% of 50 gallons.
  2. 30 gallons is 60% of 50 gallons.
  3. 45 gallons is 90% of 50 gallons.
  4. 100 gallons is 200% of 50 gallons.