Unit 6, Lesson 8
Reasoning about Solving Equations (Part 2)
Grade 7
8.2
Activity
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Explain why either of these equations could represent this hanger:
or
- Find the weight of one circle. Be prepared to explain your reasoning.
8.3
Activity
Here are some balanced hanger diagrams. Each piece is labeled with its weight.
First diagram, left side, two groups, each group has circle x, square 5, right side, rectangle, 16.
Second diagram, left side, two groups, each group has triangle y, square 200, right side, rectangle, 3000.
Third diagram, left side, rectangle 20 point 8, right side 4 groups, each group has pentagon z, square 1 point 1.
Fourth diagram, left side, rectangle, 20 over 3, left side, two groups, each group has crown w and square 2 over 3.
For each diagram:
- Explain how to figure out the weight of a piece labeled with a variable by reasoning about the diagram.
-
Identify which of the following equations matches the diagram. Then explain how to figure out the weight of a piece labeled with a variable by reasoning about the equation.
Student Lesson Summary
The balanced hanger diagram shows the amounts on the left equal the amounts on the right. The left side has 3 pieces that each have unknown weight and 3 pieces that each weigh 2 units. So, the left side shows 3 ’s plus 6 units. The right side shows 18 units. We could represent this diagram with an equation and solve the equation the same way we did before.
Since there are 3 groups of on the left, we could represent this hanger with a different equation: .
The two sides of the hanger balance with these weights: 3 groups of on one side, and 18, or 3 groups of 6, on the other side.
Balanced hanger, left side, circle labeled x, square labeled 2, circle labeled x, square labeled 2, circle labeled x, square labeled 2, right side, rectangle not labeled. A dotted line is drawn around three groups, each group contains one circle and one square from the left side and a third of the rectangle on the right side. To the side, an equation says 1/3 * 3 ( x + 2 ) = 1/3 * 18.
The two sides of the hanger will balance with of the weight on each side:
We can remove 2 units of weight from each side, and the hanger will stay balanced. This is the same as subtracting 2 from each side of the equation.
Balanced hanger. Left side, circle labeled x and square labeled 2, the square appears to be loose from the hanger. Right side, rectangle labeled 4 and square labeled 2, the square appears to be loose from the hanger. To the side, an equation says x + 2 - 2= 6 - 2.
An equation for the new balanced hanger is . This gives the solution to the original equation.
Here is a concise way to write the steps above:
None