Algebra Tiles 2 | PDF - Free Printable

Let’s solve each row of the table step by step. We’ll fill in the missing parts: Equation, Tile Model (if not given), Written Description, and Mathematical Procedure.

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Row 1: Given Equation = 2x + 1 = 5

We need to describe how to solve this using algebra tiles.

→ Tile Model:
Imagine you have two long rectangles (each representing “x”) and one small square (representing +1) on the left side. On the right side, five small squares (representing +5).

→ Written Description of Procedure:
1. Start with two x-tiles and one unit tile on the left, and five unit tiles on the right.
2. Remove one unit tile from both sides to keep things balanced. Now you have two x-tiles on the left and four unit tiles on the right.
3. Split the four unit tiles into two equal groups — that means each x-tile equals two unit tiles.
4. So, one x equals two.

→ Mathematical Procedure (Algorithm):
2x + 1 = 5
–1 –1
2x = 4
÷2 ÷2
x = 2

✔ Final answer for Row 1: x = 2

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Row 2: Given Tile Model

The tile model shows:
- Left side: three vertical rectangles (each is an “x” tile) → so that’s 3x
- Right side: a group of four small squares (units) and one shaded gray square (which usually means negative) → so that’s 4 + (–1) = 3? Wait — let’s look again.

Actually, looking at the image description:
Left: three tall rectangles → 3x
Right: a 2x2 grid (so 4 units) plus one shaded square → if shaded means negative, then it’s 4 – 1 = 3? But that doesn’t match typical setups.

Wait — actually, in many algebra tile systems, when you see a separate shaded tile next to positive tiles, it often represents subtracting that amount. But here, the way it’s drawn: three x’s on left, and on right: four white squares and one gray square — likely meaning 4 positive and 1 negative → total value = 3.

But that would make equation: 3x = 3 → x=1. That seems too simple.

Alternatively — maybe the gray square is meant to be on the same side as the x’s? No, the divider line suggests left vs right.

Wait — perhaps the tile model is showing:
Left: 3x
Right: 4 units minus 1 unit → but that’s still 3.

But let’s think differently. Maybe the gray square is meant to represent a negative unit being added to the right side? Then right side = 4 + (–1) = 3.

So equation: 3x = 3 → x = 1.

But let’s check the written procedure in Row 3 — it talks about negative xs. So maybe this row is different.

Actually, re-examining: the tile model has three x-tiles on the left, and on the right: four small squares arranged in a 2x2 block, and then one separate shaded square. In some curricula, the shaded square might mean “remove one”, so effectively right side is 4 – 1 = 3.

But that gives 3x = 3 → x=1.

Alternatively — could the shaded square be part of a zero pair? Unlikely without more context.

I think safest interpretation:
Equation: 3x = 3
Because 3 x-tiles equal 3 unit tiles.

Then:

→ Equation: 3x = 3
→ Written Description:
1. You have three x-tiles on the left and three unit tiles on the right.
2. Divide both sides into three equal groups.
3. Each x-tile matches one unit tile.
4. So, x = 1.

→ Mathematical Procedure:
3x = 3
÷3 ÷3
x = 1

✔ Final answer for Row 2: x = 1

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Row 3: Given Written Description

Description says:
1. Three negative xs and two units are the same as 5.
→ So equation: -3x + 2 = 5

2. Subtract two units from each side → -3x = 3
3. Divide both sides into two equal groups? Wait — that doesn’t make sense. If we have -3x = 3, dividing into two groups isn’t helpful. Probably typo or misstatement.

Wait — step 3 says: “Divide both sides of the equation into two equal groups” — but -3x divided by 2? That would give fractional coefficients. Doesn’t match step 4.

Step 4: “Flip both sides to make them opposites” — ah! That suggests they’re going to multiply both sides by -1.

Step 5: “One x is equal to one negative unit” → so x = -1

Let’s verify:

Start: -3x + 2 = 5
Subtract 2: -3x = 3
Now, instead of dividing by -3, they say “flip both sides to make opposites” → multiply both sides by -1:
3x = -3
Then divide by 3: x = -1

Yes! So the “divide into two equal groups” must be a mistake — probably should be “divide into three equal groups”.

But since the description says “two”, maybe it’s wrong — but we go with what leads to correct answer.

Actually, step 3 says “divide both sides into two equal groups” — but -3x divided by 2 is not integer. So likely error in problem.

But step 5 says x = -1, which works if we do:

-3x + 2 = 5
-3x = 3
x = -1 (by dividing both sides by -3)

So perhaps step 3 is miswritten — should be “three equal groups”.

Anyway, based on steps 4 and 5, we can reconstruct:

→ Equation: -3x + 2 = 5
→ Tile Model:
Left: three shaded (negative) x-tiles and two positive unit tiles
Right: five positive unit tiles

→ Mathematical Procedure:
-3x + 2 = 5
–2 –2
-3x = 3
÷(-3) ÷(-3)
x = -1

Or as per their method: after -3x = 3, flip signs: 3x = -3, then x = -1.

✔ Final answer for Row 3: x = -1

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Row 4: Given Mathematical Procedure

Procedure shown:
2x – 3 = x + 2
–x –x
x – 3 = 2
+3 +3
x = 5

So equation is: 2x – 3 = x + 2

→ Equation: 2x – 3 = x + 2
→ Tile Model:
Left: two x-tiles and three negative unit tiles (shaded)
Right: one x-tile and two positive unit tiles

→ Written Description:
1. Start with two x-tiles and three negative units on the left; one x-tile and two positive units on the right.
2. Remove one x-tile from both sides. Now left has one x-tile and three negative units; right has two positive units.
3. Add three positive units to both sides to cancel the negatives on the left. Now left has one x-tile; right has five positive units.
4. So, x = 5.

✔ Final answer for Row 4: x = 5

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Now, compiling all answers:

Row 1: x = 2
Row 2: x = 1
Row 3: x = -1
Row 4: x = 5

Final Answer:
Row 1: x = 2
Row 2: x = 1
Row 3: x = -1
Row 4: x = 5