Measurement and Data: practice solutions, Grade 4 – download the PDF

1 Customary conversions ★★★

1. 1 ft = 12 in, so \( 3 \times 12 = 36 \). Answer: 36 in.
2. 1 yd = 3 ft, so \( 5 \times 3 = 15 \). Answer: 15 ft.
3. 1 mi = 5,280 ft, so \( 2 \times 5{,}280 = 10{,}560 \). Answer: 10,560 ft.

2 Metric length conversions ★★★

1. \( 4 \times 100 = 400 \) cm.
2. \( 7 \times 10 = 70 \) mm.
3. \( 6 \times 1{,}000 = 6{,}000 \) m.

3 Weight and capacity ★★★

1. \( 3 \times 16 = 48 \) oz.
2. \( 5 \times 1{,}000 = 5{,}000 \) g.
3. \( 4 \times 4 = 16 \) qt.
4. \( 6 \times 1{,}000 = 6{,}000 \) mL.

4 Choose the best unit ★★★

1. Inches: a pencil is about 7 inches long, far too short for miles.
2. Kilograms: a bicycle is about 12 kg; in grams the number would be huge.
3. Gallons: a pool holds thousands of gallons, so cups would be silly.
4. Kilometers: cities are far apart, so kilometers keep the number small.

5 A movie at the theater ★★★

From 4:10 to 5:00 is 50 minutes. From 5:00 to 6:00 is 1 hour. Total: \( 50 \text{ min} + 1 \text{ h} = 1 \text{ h } 50 \text{ min} \).

The movie lasts 1 hour 50 minutes.

6 Perimeter and area of a card ★★★

Perimeter: \( 2 \times (12 + 7) = 2 \times 19 = 38 \) cm.

Area: \( 12 \times 7 = 84 \) square centimeters.

7 Change at the store ★★★

Total cost: \( 2.75 + 1.40 = 4.15 \) dollars. Change: \( 5.00 - 4.15 = 0.85 \) dollars.

Maya gets $0.85 back.

8 True or false? ★★★

1. False. \( 2 \times 1{,}000 = 2{,}000 \) mL.
2. True. \( 3 \times 3 = 9 \) ft.
3. False. 1 m = 100 cm.
4. True. 16 oz is 1 lb, and \( 24 - 16 = 8 \) oz are left.

9 Mixed units ★★★

1. \( 2 \times 12 = 24 \), then \( 24 + 5 = 29 \) in.
2. \( 3 \times 100 = 300 \), then \( 300 + 40 = 340 \) cm.
3. \( 4 \times 16 = 64 \), then \( 64 + 6 = 70 \) oz.

10 Swim practice ★★★

1. From 5:35 to 6:00 is 25 min. From 6:00 to 7:00 is 1 h. From 7:00 to 7:10 is 10 min. Total: \( 25 + 10 = 35 \) min and 1 h, so 1 h 35 min.
2. Go back 45 minutes from 3:20: back 20 min gives 3:00, back 25 more min gives 2:35. The lesson started at 2:35 pm.

11 The missing side ★★★

Length: \( 72 \div 8 = 9 \) ft, since \( 8 \times 9 = 72 \).

Perimeter: \( 2 \times (9 + 8) = 2 \times 17 = 34 \) ft.

12 Reading a line plot ★★★

1. Add the marks: \( 2 + 3 + 4 + 1 + 2 = 12 \) plants.
2. There are 4 marks above \( 2\dfrac{1}{2} \): 4 plants.
3. Taller means to the right of \( 2\dfrac{1}{2} \): \( 1 + 2 = 3 \) plants.
4. \( 3 - 2 = 1 \) inch.

13 Cutting a rope ★★★

Convert first: \( 3 \text{ m} = 300 \) cm. Then divide: \( 300 \div 25 = 12 \).

There are 12 pieces.

14 At the movie snack bar ★★★

Tickets: \( 4 \times 6.50 = 26.00 \) dollars. With popcorn: \( 26.00 + 3.75 = 29.75 \) dollars.

Change: \( 30.00 - 29.75 = 0.25 \). They get $0.25 back.

15 Fencing a garden ★★★

Perimeter: \( 2 \times (14 + 9) = 46 \) ft.

Panels: \( 46 \div 3 = 15 \) remainder 1, so 15 panels leave 1 ft uncovered. Sam needs 16 panels.

Cost: \( 16 \times 12 = 192 \) dollars. The panels cost $192.

16 An L-shaped room ★★★

1. Big rectangle: \( 10 \times 6 = 60 \) sq m. Removed corner: \( 4 \times 3 = 12 \) sq m. Area: \( 60 - 12 = 48 \) sq m.
2. Add all the sides: \( 6 + 3 + 4 + 3 + 10 + 6 = 32 \) m. It is the same as the big rectangle: \( 2 \times (10 + 6) = 32 \) m.
3. \( 48 \times 9 = 432 \) dollars. The carpet costs $432.

17 Same perimeter, different areas ★★★

Length plus width must be \( 24 \div 2 = 12 \) cm.

The greatest area is 36 square centimeters, for the 6 cm by 6 cm square.

18 Same area, different perimeters ★★★

Look for pairs of factors of 24, then use \( P = 2 \times (\ell + w) \).

• \( 24 \times 1 \): \( P = 2 \times 25 = 50 \)
• \( 12 \times 2 \): \( P = 2 \times 14 = 28 \)
• \( 8 \times 3 \): \( P = 2 \times 11 = 22 \)
• \( 6 \times 4 \): \( P = 2 \times 10 = 20 \)

The 6 by 4 rectangle has the least perimeter, 20 units.

19 Punch for a party ★★★

(a) \( 3 \text{ gal} = 3 \times 4 = 12 \) qt \( = 12 \times 2 = 24 \) pt \( = 24 \times 2 = 48 \) c. Jordan can pour 48 servings.

(b) \( 48 - 35 = 13 \) cups left. Since 1 qt = 4 c, \( 13 = 3 \times 4 + 1 \), so 3 quarts and 1 cup remain.

20 Ribbon line plot ★★★

(a) Add the marks above \( \dfrac{1}{4} \), \( \dfrac{1}{2} \) and \( \dfrac{3}{4} \): \( 3 + 2 + 5 = 10 \) ribbons.

(b) \( 3 \times \dfrac{1}{4} = \dfrac{3}{4} \); \( 2 \times \dfrac{1}{2} = 1 \); \( 5 \times \dfrac{3}{4} = \dfrac{15}{4} \); \( 4 \times 1 = 4 \). Sum in fourths: \( \dfrac{3}{4} + \dfrac{4}{4} + \dfrac{15}{4} + \dfrac{16}{4} = \dfrac{38}{4} = 9\dfrac{2}{4} \). The total is \( 9\dfrac{1}{2} \) yards.

21 Train trip ★★★

(a) 9:48 to 10:00 is 12 min. 10:00 am to 1:00 pm is 3 h. 1:00 to 1:15 is 15 min. Total: 3 h and \( 12 + 15 = 27 \) min, so 3 h 27 min.

(b) Half of 18.50 is 9.25. Adults: \( 2 \times 18.50 = 37.00 \). Total: \( 37.00 + 9.25 = 46.25 \). They pay $46.25.