Hanger Diagrams: Solving Equations

This worksheet helps sixth-grade students understand and solve algebraic equations using hanger diagrams, aligning with CCSS standards for expressions and equations.

Grade 6 Math AlgebraHanger Diagrams

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CustomFill in the BlanksMultiple ChoiceShort Answer

Standards

CCSS.MATH.CONTENT.6.EE.B.5CCSS.MATH.CONTENT.6.EE.B.6CCSS.MATH.CONTENT.6.EE.B.7

Topics

mathalgebrahanger diagramsequationsgrade 6

6 sections · Free to use · Printable

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Hanger Diagrams: Solving Equations

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Carefully read each question and use the hanger diagrams to help you solve the equations. Remember that a hanger diagram represents a balanced equation.

1. Look at the hanger diagram below. If each circle weighs 1 unit, what is the weight of the square?

The square weighs: units

2. Write an equation that represents the hanger diagram above.

3. If the hanger below is balanced, and each triangle weighs 3 units, what is the weight of one star?

Equation:

The star weighs: units

4. Draw a hanger diagram to represent the equation: 2x + 1 = 7. Then solve for x.

x =

5. Which equation is represented by the hanger diagram where one side has 'x' and two circles (each 2 units), and the other side has one circle (2 units) and a square (4 units)?

x + 2 = 4 + 2

x + 4 = 6

x + 2 + 2 = 2 + 4

x + 2 = 6

6. If a hanger diagram shows 3 'y' blocks on one side and 9 unit blocks on the other, what is the value of 'y'?

y = 3

y = 6

y = 9

y = 27

7. A hanger diagram has one 'x' block and 5 unit blocks on the left side. The right side has 12 unit blocks. What is the value of 'x'?

8. Explain how a hanger diagram helps you visualize and solve an equation like x + 3 = 10.