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IM: 8.4.3: Balanced Moves (Lesson)

By Newsela Staff
Last updated 2 months ago
10 Questions
3.1: Matching Hangers
Figures A, B, C, and D show the result of simplifying the hanger in Figure A by removing equal weights from each side.

Here are some equations. Each equation represents one of the hanger diagrams.

  • 2(x + 3y) = 4x + 2y
  • 2y = x
  • 2(x + 3y) + 2z = 2z + 4x + 2y
  • x + 3y = 2x + y
1.

Write the equation that goes with figure A.

2.

Write the equation that goes with figure B.

3.

Write the equation that goes with figure C.

4.

Write the equation that goes with figure D.

5.

Each variable (x, y, and z) represents the weight of one shape. Which goes with which?

6.

Explain what was done to each equation to create the next equation. If you get stuck, think about how the hangers changed.

3.2: Matching Equation Moves
Your teacher will give you some cards. Each of the cards 1 through 6 show two equations. Each of the cards A through E describe a move that turns one equation into another.
  1. Match each number card with a letter card.
  2. One of the letter cards will not have a match. For this card, write two equations showing the described move
3.3: Keeping Equality
7.

Noah and Lin both solved the equation 14a = 2(a - 3).


Do you agree with either of them? Why?

8.

Elena is asked to solve 15 - 10x = 5(x + 9). What do you recommend she does to each side first?

9.

Diego is asked to solve 3x - 8 = 4(x + 5). What do you recommend he does to each side first?

Are you ready for more?
10.

In a cryptarithmetic puzzle, the digits 0–9 are represented with letters of the alphabet. Use your understanding of addition to find which digits go with the letters A, B, E, G, H, L, N, and R.


HANGER + HANGER + HANGER = ALGEBRA