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.
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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.
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