IM 8.4.3 Lesson: Balanced Moves

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GeoGebra Classroom Activities, IM 6 – 8 Math

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. Choose which figure matches each equation.

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Each variable (x, y, and z) represents the weight of one shape.

Which shape goes with ?

Which shape goes with ?

Which shape goes with ?

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

What was done to go from A to B?

What was done to go from B to C?

What was done to go from C to D?

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. Match each number card with a letter card.

One of the letter cards will not have a match. For this card, write two equations showing the described move.

Noah and Lin both solved the equation .

Noah's solutionLin's solution:

Do you agree with either of them? Why?

Elena is asked to solve . What do you recommend she does to each side first?

Diego is asked to solve . What do you recommend he does to each side first?

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

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