Bridge to Grade 6 Mathematics

Fluency Drill Book

Use these short drills for warm-ups, stations, tutoring, homework, or re-teach cycles. Recommended timing: 6 minutes for attempts, 4 minutes for correction and strategy talk.

Part 1: Decimals and Estimation

Drill 1A: Compare and Round

  1. 4.06 ___ 4.6
  2. 0.305 ___ 0.350
  3. Round 18.947 to tenths.
  4. Round 18.947 to hundredths.
  5. Write 7.082 expanded.
  6. Order: 2.2, 2.02, 2.202.
  7. 10 x 0.48
  8. 100 x 0.48
  9. 0.48 / 10
  10. 0.48 / 100

Drill 1B: Decimal Operations

  1. 6.4 + 2.87
  2. 12 - 3.58
  3. 0.7 x 0.6
  4. 4.5 x 0.2
  5. 15.6 / 3
  6. 8.4 / 0.7
  7. Estimate 39.8 x 5.1
  8. Estimate 81.2 / 9.8
  9. 2.35 + 0.8
  10. 5.01 - 0.9

Part 2: Fractions

Drill 2A: Equivalence

  1. 3/5 = ?/10
  2. 4/6 simplest form
  3. 6/8 simplest form
  4. 2/3 ___ 3/4
  5. 5/12 ___ 1/2
  6. Write a fraction equal to 9/12.
  7. Find a common denominator for 1/4 and 1/6.
  8. Find a common denominator for 2/5 and 1/3.
  9. Place 7/10 near 0, 1/2, or 1.
  10. Place 11/12 near 0, 1/2, or 1.

Drill 2B: Operations

  1. 1/4 + 1/8
  2. 2/3 + 1/6
  3. 5/6 - 1/3
  4. 3/5 - 1/10
  5. 2/3 x 9
  6. 3/4 x 2/5
  7. 5 / 1/5
  8. 3/4 / 3
  9. 1 1/2 + 2 1/4
  10. 4 1/3 - 2 2/3

Part 3: Ratios, Rates, Percent

Drill 3A: Ratios and Rates

  1. Simplify 6:9.
  2. Simplify 12:16.
  3. 3 for $12 = $___ each.
  4. 150 miles in 3 hours = ___ mph.
  5. 2 cups to 5 cups scaled by 4 = ___ to ___.
  6. Are 4:6 and 10:15 equivalent?
  7. 8 pencils for $2.40 = $___ each.
  8. 45 pages in 5 min = ___ pages/min.
  9. Complete: 7:4 = 21:___.
  10. Complete: 5:8 = ___:40.

Drill 3B: Percent Benchmarks

  1. 10% of 90
  2. 50% of 76
  3. 25% of 48
  4. 1% of 600
  5. 20% of 35
  6. 15% of 80
  7. 75% of 40
  8. $30 with 10% off
  9. $24 with 25% off
  10. Estimate 49% of 102.

Part 4: Algebra and Coordinates

Drill 4A: Expressions

  1. Evaluate 3x + 2 when x=5.
  2. Evaluate 20 - 4n when n=3.
  3. Write: 6 less than y.
  4. Write: twice the sum of a and 4.
  5. 8 + 2 x 6
  6. (8 + 2) x 6
  7. 4 squared + 3
  8. 18 / 3 + 7
  9. 5(2 + 6)
  10. 30 - 12 / 4

Drill 4B: Equations and Points

  1. x + 9 = 20
  2. m - 7 = 18
  3. 6p = 54
  4. q / 8 = 5
  5. Check x=11 in x+9=20.
  6. Plot (3, 6): x or y first?
  7. Same y-coordinate means horizontal or vertical?
  8. Distance from (2,1) to (2,7).
  9. Write three points with x=4.
  10. Write an equation: a number times 3 is 27.

Part 5: Geometry and Data

Drill 5A: Measurement

  1. Area: 9 by 7
  2. Perimeter: 9 by 7 rectangle
  3. Triangle area: b=12, h=5
  4. Volume: 4 x 3 x 8
  5. Surface area of cube side 3
  6. Missing side: area 56, side 8
  7. Convert 3 ft to inches.
  8. Convert 2 yd to feet.
  9. Which unit: pencil length?
  10. Which unit: classroom floor area?

Drill 5B: Data

  1. Mean: 2,4,6,8
  2. Median: 9,3,7,5,5
  3. Mode: 1,2,2,3,4
  4. Range: 11,15,20,22
  5. Outlier in 4,5,6,7,50
  6. Best graph for categories?
  7. Best graph for change over time?
  8. Add one value to make mean of 4,6,8,? equal 7.
  9. Find total if mean is 9 for 5 values.
  10. Explain median in one sentence.

Part 6: Mixed Readiness

Drill 6A: Multi-Step

  1. 6 packs of 8 minus 13
  2. $7.50 x 4 + $6
  3. 15 x 8 + 3 x 4
  4. 3/4 of 20
  5. 25% of 72
  6. 2.4 x 5 + 1.6
  7. x + 14 = 39
  8. 5 pens cost $6. What is 1 pen?
  9. Area of triangle b=9, h=4
  10. Estimate 198 x 49

Drill 6B: Explain and Audit

  1. Find the mistake: 1/2 + 1/3 = 2/5.
  2. Find the mistake: 0.4 x 0.5 = 2.0.
  3. Which strategy solves 4n=36?
  4. Which strategy solves a recipe ratio?
  5. Write an estimate for 51 x 19.
  6. What unit for volume?
  7. What does the denominator tell?
  8. What does "per" mean?
  9. Why check with substitution?
  10. Write one question before solving a word problem.

Answer Key

DrillAnswers
1A<; <; 18.9; 18.95; 7 + 0.08 + 0.002; 2.02, 2.2, 2.202; 4.8; 48; 0.048; 0.0048.
1B9.27; 8.42; 0.42; 0.9; 5.2; 12; about 200; about 8; 3.15; 4.11.
2A6; 2/3; 3/4; <; <; 3/4 or equivalent; 12; 15; near 1/2 or 1; near 1.
2B3/8; 5/6; 1/2; 1/2; 6; 3/10; 25; 1/4; 3 3/4; 1 2/3.
3A-6BUse teacher guide for selected keys; accept equivalent ratios, equivalent fractions, and correct explanations.