Model Equivalent Expressions

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Key Ideas Easy Medium Hard

What to Remember

Zero pairs

A +x tile and a −x tile make a zero pair. A +1 tile and a −1 tile make a zero pair.

Remove every zero pair. Those tiles add nothing.

What remains

The tiles that are left form the simplified expression.

Count the remaining x tiles, then count the remaining 1 tiles.

Two colors

A teal x tile is +x. A rose x tile is −x.

An emerald 1 tile is +1. A rose 1 tile is −1.

Level 1

Easy

Count the tiles. There are no zero pairs to remove.

Example

Write the simplified expression for these tiles.

xxx+1+1+1+1

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

3x + 4

Answer: 3x + 4

Write the simplified expression for these tiles.

xxx+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

3x + 2

Answer: 3x + 2

Write the simplified expression for these tiles.

xxxx+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

4x + 1

Answer: 4x + 1

Write the simplified expression for these tiles.

xx+1+1+1+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

2x + 5

Answer: 2x + 5

Write the simplified expression for these tiles.

xxxxxxx+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

7x + 1

Answer: 7x + 1

Write the simplified expression for these tiles.

x+1+1+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

x + 4

Answer: x + 4

Write the simplified expression for these tiles.

−x−x−x+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

−3x + 2

Answer: −3x + 2

Write the simplified expression for these tiles.

xxxx−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

4x − 2

Answer: 4x − 2

Write the simplified expression for these tiles.

−x−x+1+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

−2x + 3

Answer: −2x + 3

Write the simplified expression for these tiles.

xxxxxx+1+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

6x + 3

Answer: 6x + 3

Write the simplified expression for these tiles.

xx−1−1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

There are no zero pairs.

2x − 4

Answer: 2x − 4

Level 2

Medium

Remove zero pairs of one kind, then write what is left.

Example

Write the simplified expression for these tiles.

xxxxx−x−x+1

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of x tiles.

3x + 1

Answer: 3x + 1

Write the simplified expression for these tiles.

xxx−x+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 1 pair of x tiles.

2x + 2

Answer: 2x + 2

Write the simplified expression for these tiles.

xxxx−x−x+1+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of x tiles.

2x + 3

Answer: 2x + 3

Write the simplified expression for these tiles.

xxxxx−x+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 1 pair of x tiles.

4x + 1

Answer: 4x + 1

Write the simplified expression for these tiles.

xx−x−x+1+1+1+1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of x tiles.

Answer: 4

Write the simplified expression for these tiles.

xxx−x

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 1 pair of x tiles.

Answer: 2x

Write the simplified expression for these tiles.

xx+1+1+1+1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 1 pair of 1 tiles.

2x + 3

Answer: 2x + 3

Write the simplified expression for these tiles.

xxx+1+1+1+1+1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of 1 tiles.

3x + 3

Answer: 3x + 3

Write the simplified expression for these tiles.

x+1+1+1−1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 3 pairs of 1 tiles.

Answer: x

Write the simplified expression for these tiles.

−x−x+1+1+1+1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 1 pair of 1 tiles.

−2x + 3

Answer: −2x + 3

Write the simplified expression for these tiles.

xxxx+1+1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of 1 tiles.

Answer: 4x

Level 3

Hard

Remove zero pairs of x tiles and of 1 tiles.

Example

Write the simplified expression for these tiles.

xxxxx−x+1+1+1+1+1+1−1−1

A positive tile and its matching negative tile make a zero pair.

Remove 1 pair of x tiles and 2 pairs of 1 tiles.

4x + 4

Answer: 4x + 4

Write the simplified expression for these tiles.

xxxxxx−x−x+1+1+1+1+1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of x tiles and 1 pair of 1 tiles.

4x + 4

Answer: 4x + 4

Write the simplified expression for these tiles.

xxxxxxx−x−x−x+1+1+1+1+1+1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 3 pairs of x tiles and 2 pairs of 1 tiles.

4x + 4

Answer: 4x + 4

Write the simplified expression for these tiles.

xxxxx−x−x+1+1+1+1+1+1+1−1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of x tiles and 3 pairs of 1 tiles.

3x + 4

Answer: 3x + 4

Write the simplified expression for these tiles.

xxxxxxxx−x−x−x+1+1+1+1+1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 3 pairs of x tiles and 2 pairs of 1 tiles.

5x + 3

Answer: 5x + 3

Write the simplified expression for these tiles.

xxxxxx−x−x−x−x+1+1+1+1+1+1+1+1−1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 4 pairs of x tiles and 3 pairs of 1 tiles.

2x + 5

Answer: 2x + 5

Write the simplified expression for these tiles.

xxxx−x−x−x+1+1+1+1+1+1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 3 pairs of x tiles and 2 pairs of 1 tiles.

x + 4

Answer: x + 4

Write the simplified expression for these tiles.

xxxxxxx−x−x+1+1+1+1+1−1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 2 pairs of x tiles and 3 pairs of 1 tiles.

5x + 2

Answer: 5x + 2

Write the simplified expression for these tiles.

xxxxx−x−x−x−x+1+1+1+1+1+1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 4 pairs of x tiles and 1 pair of 1 tiles.

x + 5

Answer: x + 5

Write the simplified expression for these tiles.

xxxxxxxx−x−x−x−x−x+1+1+1+1+1+1+1−1−1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 5 pairs of x tiles and 4 pairs of 1 tiles.

3x + 3

Answer: 3x + 3

Write the simplified expression for these tiles.

xxxxxx−x−x−x+1+1+1+1+1+1+1+1+1−1−1

Show Answer

A positive tile and its matching negative tile make a zero pair.

Remove 3 pairs of x tiles and 2 pairs of 1 tiles.

3x + 7

Answer: 3x + 7

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