IM 8.4.3 Lesson: Balanced Moves

Figures A, B, C, and D show the result of simplifying the hanger in Figure A by removing equal weights from each side.
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[/img][br][br]Here are some equations. Each equation represents one of the hanger diagrams.[br]Choose which figure matches each equation. [br][br][math]2(x+3y)=4x+2y[/math]
[math]2y=x[/math]
[math]2(x+3y)+2z=2z+4x+2y[/math]
[math]x+3y=2x+y[/math]
Each variable (x, y, and z) represents the weight of one shape.
Which shape goes with [math]x[/math]?
Which shape goes with [math]y[/math]?
Which shape goes with [math]z[/math]?
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.[color=#ff0000][br][/color]
[size=150]Noah and Lin both solved the equation [math]14a=2(a-3)[/math].[br][/size][br][table][tr][td]Noah's solution[/td][td][/td][td]Lin's solution:[/td][/tr][tr][td][math]\begin{align} 14a&=2(a-3) \\ 14a&=2a-6 \\ 12a&=\text-6 \\ a&=\text-\frac12 \\ \end{align}[/math][/td][td][/td][td][math]\begin{align} 14a&=2(a-3) \\ 7a&=a-3\\ 6a&=\text-3\\a&=\text-\frac12 \end{align}[/math][/td][/tr][/table][br]Do you agree with either of them? Why?
[size=100]Elena is asked to solve [math]15-10x=5(x+9)[/math]. What do you recommend she does to each side first?[/size]
Diego is asked to solve [math]3x-8=4(x+5)[/math]. 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.
[size=150]HANGER + HANGER + HANGER = ALGEBRA[/size]
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Information: IM 8.4.3 Lesson: Balanced Moves