Students complete nine comparison problems using >, <, or = to compare expression pairs without calculating, including multiplier comparisons and divisor comparisons. The matching activity pairs four expression comparisons with their correct relational descriptions.
Comparing expressions without calculating — by identifying shared quantities and the multiplying or dividing factor applied — is the core algebraic reasoning skill that prepares fifth graders for symbolic thinking in middle school.
Style:
Numerical Expressions
Part A: Fill in the Blank
Write the missing word or number on each line.
1. Without calculating, 6 × (15 + 4) > 5 × (15 + 4). Use >, <, or =.
2. Without calculating, (30 − 7) ÷ 2 < (30 − 7) × 2. Use >, <, or =.
3. Without calculating, 4 × (9 + 3) < 4 × (9 + 5). Use >, <, or =.
4. Without calculating, (8 + 12) × 3 = 3 × (12 + 8). Use >, <, or =.
5. Without calculating, (40 ÷ 5) + 10 > (40 ÷ 5) + 7. Use >, <, or =.
6. Without calculating, 2 × (16 + 9) > (16 + 9). Use >, <, or =.
7. Without calculating, (50 − 20) ÷ 6 < (50 − 20) ÷ 3. Use >, <, or =.
8. Without calculating, 7 × (11 − 4) = 7 × (11 − 4). Use >, <, or =.
9. Without calculating, 10 × (5 + 3) > 9 × (5 + 3). Use >, <, or =.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
3 × (20 + 5) compared to (20 + 5)
→ first is 3 times as large
equal — same expression
(48 ÷ 6) compared to (48 ÷ 2)
→ second is larger — dividing by smaller gives more
second is larger — dividing by smaller gives more
(14 + 6) × 4 compared to (14 + 6) × 4
→ equal — same expression
first is 3 times as large
2 × (9 + 1) compared to 8 × (9 + 1)
→ second is larger — 8 times vs. 2 times
second is larger — 8 times vs. 2 times
Numerical Expressions
★ Part A: Fill in the Blank
Write the missing word or number on each line.
1) Without calculating, 6 × (15 + 4) > 5 × (15 + 4). Use >, <, or =.
2) Without calculating, (30 − 7) ÷ 2 < (30 − 7) × 2. Use >, <, or =.
3) Without calculating, 4 × (9 + 3) < 4 × (9 + 5). Use >, <, or =.
4) Without calculating, (8 + 12) × 3 = 3 × (12 + 8). Use >, <, or =.
5) Without calculating, (40 ÷ 5) + 10 > (40 ÷ 5) + 7. Use >, <, or =.
6) Without calculating, 2 × (16 + 9) > (16 + 9). Use >, <, or =.
7) Without calculating, (50 − 20) ÷ 6 < (50 − 20) ÷ 3. Use >, <, or =.
8) Without calculating, 7 × (11 − 4) = 7 × (11 − 4). Use >, <, or =.
9) Without calculating, 10 × (5 + 3) > 9 × (5 + 3). Use >, <, or =.
★ Part B: Matching
Match each item on the left to the correct answer on the right.
1) Match each item to its correct answer.
3 × (20 + 5) compared to (20 + 5)
→ first is 3 times as large
equal — same expression
(48 ÷ 6) compared to (48 ÷ 2)
→ second is larger — dividing by smaller gives more
second is larger — dividing by smaller gives more
(14 + 6) × 4 compared to (14 + 6) × 4
→ equal — same expression
first is 3 times as large
2 × (9 + 1) compared to 8 × (9 + 1)
→ second is larger — 8 times vs. 2 times
second is larger — 8 times vs. 2 times
Ready to Practice?
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10 Questions
10-15 minutes
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