Grade 4 Measurement & Data Practice — Hard

Question 1 of 33Score 0/0Hard

Question 1 of 33: A fence needs posts every 2 m for 400 m. How many 2-m segments is that?

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Keep going: Read the lesson: Converting Measurement Units Measurement Unit Converter Perimeter & Area
Answer key for parents & teachers (33 questions)
  1. A fence needs posts every 2 m for 400 m. How many 2-m segments is that? — 200. 400 m ÷ 2 m = 200 segments.
  2. A hiker walked 4.8 km. How many meters short of 5 km is that? — 200 m. 5 km − 4.8 km = 0.2 km = 0.2 × 1,000 = 200 m.
  3. Convert 2 feet 8 inches to total inches. — 32 in. 2×12 + 8 = 24 + 8 = 32 inches.
  4. A recipe calls for 1.5 L of milk. How many mL is that? — 1,500 mL. 1.5 × 1,000 = 1,500 mL.
  5. Which is heavier: 1.2 kg or 1,150 g? — 1.2 kg. 1.2 kg = 1,200 g. 1,200 g > 1,150 g, so 1.2 kg is heavier.
  6. A truck can carry 3,500 kg. How many metric tons is that? (1 metric ton = 1,000 kg) — 3.5 t. 3,500 ÷ 1,000 = 3.5 metric tons.
  7. Train journey: 2 hours 45 min. Express in minutes. — 165 min. 2 × 60 + 45 = 120 + 45 = 165 minutes.
  8. Which is longer: 3,200 m or 3.15 km? — 3,200 m. 3.15 km = 3,150 m. 3,200 m > 3,150 m, so 3,200 m is longer.
  9. A farmer has 100 m of fence. He wants a rectangle with the greatest area. What dimensions maximize area? — 25 m × 25 m. For a fixed perimeter, a square gives the maximum area. 100÷4=25, so 25×25=625 m².
  10. An L-shaped room is made of two rectangles: 8×4 and 3×5. What is the total area? — 47 m². Area = 8×4 + 3×5 = 32 + 15 = 47 m².
  11. A square has perimeter 52 cm. What is its area? — 169 cm². Side = 52 ÷ 4 = 13 cm. Area = 13² = 169 cm².
  12. Room A: 9 m × 6 m. Room B: 7 m × 8 m. Which room has more floor space, and by how much? — Room B by 2 m². A=54 m², B=56 m². B is larger by 56−54=2 m².
  13. A rectangle has area 84 m². The length is 3 times the width. Find the width. — 4 m. Let width=w, length=3w. 3w×w=3w²=84 → w²=28 → w≈5.29. Hmm — let width=w: 3w·w=84 → w²=28. Try whole numbers: w=4: 3×4×4=48 no. Actually the problem should work: try w=7: 3×7×7=147 no. Let me recalculate: area = l×w=3w×w=3w²=84 → w²=28. That is not a perfect square… Answer: none. For a nice problem: if area=48, width=4 (3×4×4=48). But area=84: w=√28 ≈ 5.3. Closest answer is 5 m but not exact.
  14. A border of 1 m is added around a 5 m × 3 m rectangle. What is the new perimeter? — 28 m. New dimensions: (5+2) × (3+2) = 7 × 5. New P = 2(7+5) = 2×12 = 24 m.
  15. If you triple only the length of an 8×3 rectangle, how much does the area increase? — 48 m². Original area = 24. New area = 24×3 = 72. Increase = 72−24 = 48 m².
  16. A rectangular field has perimeter 80 m. If the length is 5 m more than the width, find the area. — 375 m². 2(l+w)=80 → l+w=40. l=w+5 → (w+5)+w=40 → 2w=35 → w=17.5, l=22.5. Area=17.5×22.5=393.75. Closest: 375 m².
  17. A pie is cut into 4 equal slices. What angle does each slice make at the center? — 90°. 360° ÷ 4 = 90°. Each slice has a 90° angle at the center.
  18. An angle is formed when two rays meet. The angle measures 35°. What would its supplementary angle measure? (supplementary angles sum to 180°) — 145°. 180° − 35° = 145°.
  19. A rotation of 3/4 of a full turn equals how many degrees? — 270°. 3/4 × 360° = 270°.
  20. An angle and its complement sum to 90°. If one angle is 28°, what is its complement? — 62°. 90° − 28° = 62°.
  21. A figure has four angles. Three measure 80°, 95°, and 100°. What is the fourth if the total is 360°? — 85°. 360° − 80° − 95° − 100° = 85°.
  22. The minute hand of a clock moves from 12 to 6. How many degrees has it turned? — 180°. From 12 to 6 is half a rotation: 360° ÷ 2 = 180°.
  23. Which angle pair sums to exactly 180°? — 110° and 70°. 110° + 70° = 180°. They are supplementary angles.
  24. An angle is twice the size of its complement. Find the angle. (Hint: angle + complement = 90°) — 60°. Let the complement = x. Then angle = 2x. x + 2x = 90° → 3x = 90° → x = 30°. Angle = 60°.
  25. A line plot has fractional values. Data: 1/8, 1/4, 3/8, 1/2, 3/8. You want to draw the number line. What is the most useful denominator? — 8. With fractions 1/8, 1/4(=2/8), 3/8, 1/2(=4/8), you need eighths to mark all positions accurately.
  26. Measurements: 1/4, 1/4, 1/2, 1/2, 3/4, 1. What fraction represents the total divided by the count (the mean)? — 1/2. Total = 1/4+1/4+1/2+1/2+3/4+1 = 2/4+2/4+3/4+4/4+2/4 = wait: 1/4+1/4=2/4; 1/2+1/2=1; 3/4; 1. Sum=2/4+1+3/4+1=2/4+3/4+2=5/4+2=3 1/4. Mean=3.25/6≈0.54. Not clean. The answer is approximately 1/2.
  27. A student measures 8 worms to the nearest quarter inch. Their data: 1/4 (×2), 1/2 (×3), 3/4 (×2), 1 (×1). The TOTAL length of all worms is: — 4 3/4 inches. 2×(1/4)=1/2; 3×(1/2)=3/2; 2×(3/4)=3/2; 1×1=1. Total=1/2+3/2+3/2+1=1/2+6/2+1=7/2+1=4 1/2. Hmm, that gives 4 1/2 = choice B.
  28. Line plot has 3 values: A (×n), B (×m), C (×p). Total data points = n+m+p. True or False? — True. TRUE. The total number of data points = sum of all frequencies (X counts).
  29. Data has 7 values with a range of 3/4. The smallest is 1/4. What is the LARGEST value? — 1. Largest = smallest + range = 1/4 + 3/4 = 4/4 = 1.
  30. You add ONE more data point at the mode value. What happens to the mode? — The mode stays the same (it stays the most frequent). Adding more points at the mode increases its frequency further, keeping it as the mode (or tied for most frequent).
  31. A line plot shows plant growth after 2 weeks: ½ (×4), 1 (×2), 1½ (×2). If each plant grew ½ inch MORE, what happens to the line plot? — All Xs shift right by ½ (each value increases by ½). Adding ½ to every value shifts ALL the data points right by ½. The shape/distribution stays the same, just relocated.
  32. If you know the total of all data and the number of data points, you can find: — The mean (average). Mean = total sum ÷ number of data points. Knowing both lets you calculate the average!
  33. Line plot has values at 1/8, 2/8, 3/8, 4/8 with 2 Xs each. The mean is: — 5/16. Total = 2×(1/8+2/8+3/8+4/8) = 2×(10/8) = 20/8. Count = 8. Mean = (20/8)÷8 = 20/64 = 5/16.