Vertical Expression Stacks Worksheet
Vertical Expression Stacks
Adding & Subtracting Linear Expressions by Vertical Alignment
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Instructions: Rewrite each problem vertically by stacking like terms in columns. For subtraction, distribute the negative sign to every term in the subtrahend or add the opposite.
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LEVEL 1: Binomial Stacks 2-Term Basics
1 Find the sum: \((5a + 7) + (2a + 4)\)
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2 Find the sum: \((8x - 3) + (4x + 9)\)
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3 Find the difference: \((7m + 6) - (3m + 2)\)
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4 Find the difference: \((9y - 4) - (5y - 8)\)
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5 Find the sum: \((6p - 11q) + (-2p + 5q)\)
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LEVEL 2: Trinomials & Variables Matching Columns
6 Find the sum: \((4x + 7y - 5) + (3x - 2y + 8)\)
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7 Find the diff: \((8a + 5b - 6) - (3a + 2b - 9)\)
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8 Anchor
Sum: \((5a + 3b - 6c) + (2a - 4b + 13c)\)
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9 Find the diff: \((6r - 7s + 12) - (9r - 4s - 5)\)
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10 Diff: \((10u - 8v + 3w) - (4u - 11v - 7w)\)
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Vertical Expression Stacks • Grade 7/8 Pre-Algebra Turn over for Level 3 (Placeholders) & Level 4 (Advanced) →
Vertical Expression Stacks
Levels 3 & 4
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Strategy Reminder: When terms do not match up directly, leave an empty space or insert a \(0\) placeholder (e.g., \(0y\)) to keep your like-term columns aligned!
LEVEL 3: Missing Terms & Gaps Use Placeholders
11 Anchor
Diff: \((2x + 3y - 4) - (5x + 2)\)
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12 Find the sum: \((7m + 4n - 9) + (3m - 8)\)
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13 Find the diff: \((6a - 5b + 8c) - (2a + 3c)\)
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14 Find the diff: \((9x + 4) - (3x - 7y + 1)\)
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15 Sum: \((8p - 5r + 14) + (-3q + 4r - 6)\)
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LEVEL 4: Advanced Stacks Decimals, Fractions, 3 Stacks
16 Diff: \((-4x + 9y - 15) - (-7x - 3y + 8)\)
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17 Sum: \((1.5a - 3.2b + 6) + (2.8a + 1.7b - 4.5)\)
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18 Diff: \((\frac{3}{4}x - 2y + 5) - (\frac{1}{4}x + 3y - 7)\)
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19 Diff: \((12k - 4m - 9n + 3) - (5k + 2m - 14)\)
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20 3 Stacks
Sum: \((3x - 4y + 2) + (5x + 6y - 7) + (-2x + y + 9)\)
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Vertical Expression Stacks • Grade 7/8 Pre-Algebra Check your solutions with the Answer Key • Great job!
Vertical Expression Stacks Answer Key
Answer Key • Page 1
Vertical Expression Stacks • Levels 1 & 2 Complete Solutions
Teacher Reference Key
Problems 1 – 10
QUICK SCAN: 1: 7a+11 • 2: 12x+6 • 3: 4m+4 • 4: 4y+4 • 5: 4p-6q • 6: 7x+5y+3 • 7: 5a+3b+3 • 8: 7a-b+7c
LEVEL 1: Binomial Solutions Add & Subtract Basics
Problem 1 \((5a + 7) + (2a + 4)\)
5a + 7
+ 2a + 4
7a + 11
Final Answer 7a + 11
Problem 2 \((8x - 3) + (4x + 9)\)
8x − 3
+ 4x + 9
12x + 6
Final Answer 12x + 6
Problem 3 \((7m + 6) - (3m + 2)\)
7m + 6
+ -3m − 2 (Add opp.)
4m + 4
Final Answer 4m + 4
Problem 4 \((9y - 4) - (5y - 8)\)
9y − 4
+ -5y + 8 (- • - = +)
4y + 4
Final Answer 4y + 4
Problem 5 \((6p - 11q) + (-2p + 5q)\)
6p − 11q
+ -2p + 5q
4p − 6q
Final Answer 4p − 6q
LEVEL 2: Trinomial Solutions Multi-Variable Matching
Problem 6 \((4x + 7y - 5) + (3x - 2y + 8)\)
4x + 7y − 5
+ 3x − 2y + 8
7x + 5y + 3
Final Answer 7x + 5y + 3
Problem 7 \((8a + 5b - 6) - (3a + 2b - 9)\)
8a + 5b − 6
+ -3a − 2b + 9
5a + 3b + 3
Final Answer 5a + 3b + 3
Problem 8 • Anchor a \((5a + 3b - 6c) + (2a - 4b + 13c)\)
5a + 3b − 6c
+ 2a − 4b + 13c
7a − b + 7c
Final Answer 7a − b + 7c
Problem 9 \((6r - 7s + 12) - (9r - 4s - 5)\)
6r − 7s + 12
+ -9r + 4s + 5
-3r − 3s + 17
Final Answer -3r − 3s + 17
Problem 10 \((10u - 8v + 3w) - (4u - 11v - 7w)\)
10u − 8v + 3w
+ -4u + 11v + 7w
6u + 3v + 10w
Final Answer 6u + 3v + 10w
Vertical Expression Stacks • Teacher Solutions Reference Turn over for Page 2 (Problems 11 – 20) →
Answer Key • Page 2
Vertical Expression Stacks • Levels 3 & 4 Complete Solutions
Teacher Reference Key
Problems 11 – 20
