BLM 1–2 Chapter 1 Prerequisite Skillspjk.scripts.mit.edu/lab/2p/Chapter_1_ALL.pdf · ... McGraw-Hill Ryerson Limited, ... BLM 1–3 Copyright © 2009, McGraw-Hill Ryerson Limited,

Name: ___________________________________________ Date: _____________________________

BLM 1–2

Copyright © 2009, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved. This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Chapter 1 Prerequisite Skills 1. Fill in the blanks.

a) There are ______ centimetres in 1 m. b) There are ______ millimetres in 1 m. c) There are ______ millimetres in 3.5 m. d) There are ______ centimetres in 1 km.

2. Estimate the total length of the line segment(s) connecting S and T. Then, measure to determine how close your estimates are to the actual measurements. Give your answers in centimetres. a) b)

c)

3. The diagram shows an SI ruler.

a) What is the length measured at A? b) What is the distance from A to B? c) What is the smallest unit you can read on

this ruler?

4. Mark the position of each letter on the ruler.

a) L = 1.7 cm b) M = 2.5 cm c) N = 32.5 mm d) P = 55 mm

5. Suppose each diagram is drawn on centimetre grid paper. What is the shortest distance from A to B? a)

b)

c)

6. a) Describe the meaning of scale factor. Use an example.

b) Suppose the scale factor for a diagram of a digital camera is less than 1. Describe what you know about the diagram.

c) The diameter of a Canadian toonie is 28.03 mm. What scale was used to create the image shown? Express your answer in lowest terms, to the nearest hundredth.

Name: ___________________________________________ Date: _____________________________

BLM 1–2 (continued)


7. What is the lowest common denominator for each set of fractions?

a) 12

, 38

b) 516

, 14

, 32

c) 58

, 34

d) 14

, 532

, 78

8. Simplify. Express your answer as a fraction and as a decimal. 12

– 34

+ 78

9. Solve each proportion for x. Explain how you determined your answer in part b).

a) 8x = 5

4

b) 3x

= 25

c) 2.56

= 3x

d) 49

= 10x

10. What is the perimeter of each figure? Give each distance to the nearest hundredth of a unit, if necessary. a)

b)

c)

11. For each figure described, draw a labelled diagram to help you calculate the unknown distance. Express your answer to the nearest tenth of a metre. a) Rectangle: perimeter = 16 cm length of one side = 5 cm length of other side = b) Isosceles triangle: perimeter = 18.4 mm length of equal sides = 5.6 mm length of third side = c) Circle: circumference = 18 m diameter =

BLM 1–3


Chapter 1 Warm-Up Section 1.1 Warm-Up

1. Name three instruments that are used to measure length.

2. Estimate in either centimetres or millimetres. a) the thickness of your student resource b) the thickness of Chapter 1 in the student

resource

3. Use mental mathematics to complete the following operations.

a) 5.2 ÷ 102 b) 371 × 103 c) 1.85 × 104

d) 2.78 ÷ 105

4. What is the value of x in each ratio?

a) 1000

x = 0.0191

b) 3 : x = 9 : 15

c) 15x

= 1001

d) 2 : 8 = x : 24

5. Estimate the circumference of each circle. Then, calculate the circumference to the nearest tenth of a centimetre. a)

b)

Section 1.2 Warm-Up

1. What is your height, in feet and inches?

2. A line has been divided into equal parts. Match each of the letters to one or more of the following fractions. 12

, 14

, 24

, 34

, 18

, 28

, 38

, 48

, 58

, 68

3. Convert each mixed number to an improper fraction.

a) 2 38

b) 1 716

c) 3 34

4. Determine each product without using a

calculator.

a) ( )7 153

⎛ ⎞⎜ ⎟⎝ ⎠

b) ( )52 612

⎛ ⎞⎜ ⎟⎝ ⎠

c) ( )17 82

⎛ ⎞⎜ ⎟⎝ ⎠

5. What is the length of each unknown side?

a)

b)



Section 1.3 Warm-Up

1. Fill in the blanks. a) 48 inches = ______ feet b) ______ yards = 15 feet c) 1 mile = ______ yards

2. Fill in the blanks. a) 1500 cm = ______ m b) ______ m = 380 cm c) 50 cm = ______ mm

3. Estimate each of the following measurements. a) your height in centimetres b) the length of your thumb in inches c) the length of your foot in centimetres

4. Show how you would multiply 518

and 2.1

without a calculator.

5. A walkway has a length of 3.5 m and a width of 1.2 m. A decorative planted edge that is 10 cm wide is placed along the longer sides of the walkway. a) What is the total width of the walkway and

the decorative edge? b) What is the length of the walkway?

Name: ___________________________________________ Date: _____________________________

BLM 1–4


Chapter 1 Unit 1 Project Section 1.1

1. The music industry involves the production, distribution, and sale of music in a variety of forms. Since the 1960s, music distribution has evolved from vinyl records to cassette tapes, to CDs, and to MP3s. Each change emphasized that smaller is better.

a) For the actual-size cassette shown, use a suitable referent to estimate the dimensions of the cassette case. Explain why you used that referent.

b) Measure and calculate the perimeter of each different face of the cassette case, in millimetres. How many perimeters do you need to calculate?

c) Vinyl records are available in three sizes — 45 rpm (revolutions per minute), 78 rpm, and 1333

rpm

or LP size. A 45 record has an actual diameter of 17.5 cm. Estimate the diameter of the LP in the photograph using a referent. Then, by measuring and determining a scale, calculate the actual diameter of the LP, in millimetres.

Name: ___________________________________________ Date: _____________________________



Section 1.2

2. Today’s music storage devices tend to be smaller than those of the past, but they can store many more songs. Find a cassette tape case, a CD, and an MP3 player. Use an imperial unit to measure each of the following dimensions. Justify your choice of unit.

a) the diameter of the CD

b) the dimensions of the cassette case

c) the perimeter of the largest face of the MP3 player

Section 1.3

3. One type of 80 GB MP3 player has dimensions of 4.14 cm (width) by 9.15 cm (height) by 0.85 cm (thickness). The storage capacity is about 20 000 songs. Each LP vinyl record holds an average of

12 songs and is approximately 19

in. thick.

a) Calculate the number of LPs you would need to store as many songs as the MP3 player. Use mental mathematics to show that your answer is reasonable.

b) Suppose you stack the LPs. Calculate the height of the stack. Compare it with the height of the MP3 player. Give your answer as a ratio in lowest terms.

Name: ___________________________________________ Date: _____________________________

BLM 1–5


Section 1.1 Extra Practice

1. What referent would you use to estimate each of the following measurements in SI units? a) the height of the classroom door b) the thickness of your calculator c) the distance from home to school

2. What reading is shown on the ruler at points A, B, C, and D? Give each reading in both centimetres and millimetres.

3. What reading is shown on the caliper? Give the reading in both millimetres and centimetres.

4. A cylindrical gasoline tank has a radius of 28 cm. It is hung to a truck using a metal strap. What is the length of the strap if an extra 5 cm is used at each end for bolts A and B? Express your answer to the nearest centimetre.

5. The province of Alberta is approximately 1300 km long from the northern border to the southern border. a) What is the scale for each map of Alberta

in the diagram? b) Determine the width of the province at its

northern border and at its southern border, to the nearest 10 km.

6. Convert each of the following measurements. a) 7 cm = ______ mm b) 32 m = ______ cm c) 58 km = ______ m d) 75 km = ______ cm e) 65 000 cm = ______ km f) 56 m = ______ km

7. State whether you think each measurement is reported in the most appropriate unit. If not, explain why and convert it to a more appropriate SI unit. a) The length of a housefly is 0.005 m. b) The depth of the Pacific Ocean is

4 188 000 mm. c) The length of a table-tennis table is

0.002 74 km. d) The height of the CN Tower in Toronto,

Ontario, is 55 300 cm.

Name: ___________________________________________ Date: _____________________________

BLM 1–6


Section 1.2 Extra Practice 1. What reading is shown on the imperial ruler

below at points A, B, C, and D?

2. What reading is shown on this imperial caliper?

3. Convert each measurement to the unit indicated. a) 72 inches = ____________ feet b) 3 miles = __________ feet c) 5' 10" = ___________ inches d) 4400 yards = _________ miles e) 500 inches = ______________ feet and

_________ inches 4. Convert each measurement to the unit

indicated. a) Mount Everest is 29 028 ft high.

(nearest quarter of a mile)

b) The width of a calculator is 932

ft.

(nearest eighth of an inch)

5. According to Guinness World Records, the longest total length of the fingernails for a

female is 9 1124

yd.

a) Convert the measurement to the nearest half of an inch.

b) Calculate the average length of each fingernail, to the nearest inch.

6. In the diagram, the window on top is semicircular. The rectangular window in the middle measures 28 in. by 55 in. The two side windows measure 16 in. by 55 in. Calculate the perimeter of the windows. Express your answer in feet and inches.

7. On a recent trip to Butchart Gardens in Victoria, BC, Mary took a photograph of a flower that measures 4 in. by 6 in. She wants to enlarge a copy of the photo for the frame below.

a) What is the length of the unknown side of

Mary’s frame? Hint: You will need to use a ruler.

b) By what scale factor will Mary need to enlarge the photo?

c) Calculate the dimensions of the enlarged photo.

Name: ___________________________________________ Date: _____________________________

BLM 1–7


Section 1.3 Extra Practice 1. Convert each measurement to the unit

specified. a) The mean radius of Earth is 6400 km.

(nearest hundred miles) b) The size of a dust particle is 0.004 in.

(nearest tenth of a millimetre) c) In baseball, the distance from home plate

to the pitcher’s mound is 60 ft 6 in. (nearest hundredth of a metre)

d) The distance from Edmonton to Calgary is 184 mi. (nearest kilometre)

2. A rectangular flower bed has a border of

grass that is 128

ft wide. The outside

dimensions of the grass are 1124

ft by 7168

ft.

Calculate the dimensions of the flower bed in inches and in centimetres.

3. Consider the myth that long-tailed, South American monkeys cling to each other forming a bridge between trees. Suppose a monkey chain contains 17 monkeys, each one extending 3 ft. a) Estimate the length of the chain in feet.

Predict whether the actual length is greater than your estimate. Explain your reasoning.

b) What SI unit would be most appropriate for measuring the length of the monkey chain?

c) Calculate the length of the monkey chain in the unit you selected in part b). Express your answer to the nearest tenth of a unit.

4. A toy car is being measured.

a) Identify the unit represented on the ruler. b) Measure the length of the toy car, to the

nearest tenth of a centimetre and then to the nearest quarter of an inch.

c) Calculate the height to length ratio of the car, to the nearest hundredth of a unit.

5. The Longs travelled, from Lethbridge, AB, to Great Falls, Montana, to visit friends. The distance from Lethbridge to the Canada-U.S. border is 130 km. The distance, from the border to Great Falls, is 114 miles. Calculate the total distance for the round trip, in both miles and kilometres.

6. Clara is renovating her bedroom. She measures her bedroom to be 3.8 m by 4.1 m. She wants to buy new baseboards and carpet. When she gets to the store, she discovers that baseboards and carpeting are sold in imperial units. a) Calculate the dimensions of Clara’s room

to the nearest quarter of a foot. b) What is the minimum length of baseboards

she requires? c) Suppose baseboards are sold in 12-ft

lengths. How many lengths should Clara purchase (allow 10% extra for cuts and waste)?

Name: ___________________________________________ Date: _____________________________

BLM 1–8


Chapter 1 Test Multiple Choice For #1 to #5, select the best answer.

1. Which of the following referents is not appropriate to estimate the specified measurement unit? A one rotation of a mountain bike wheel, foot B height at waist level, metre C width of paper clip, millimetre D width of pinky finger, half an inch

2. A 42″ TV is recommended if the viewing distance is 10′, a 46″ TV for 12', and a 50″ TV for 14′. Cale and Jess each measured the distance from their couch to their TV in a different manner.

• Cale counted 12 foot lengths and determined they should buy the 46″ TV.

• Jess counted 3 long paces and agreed they should buy the 46″ TV.

Which statement regarding the choice of televisions is true? A Cale’s personal strategy is more accurate

than Jess’s. B Jess’s personal strategy is more accurate

than Cale’s. C Both Cale and Jess have an accurate

strategy. D Neither Cale nor Jess has an accurate

strategy.

3. Suppose the width of your palm is 6.5 cm. How many palm widths do you need to measure an object that is one foot long? A 3 B 4 C 5 D 6

4. What is the reading on the caliper, in centimetres?

A 3.35 cm B 3.37 cm C 3.44 cm D 3.47 cm

5. Which of the following is not a reasonable conversion between SI and imperial units? A 1 km ≈ 0.6 mi B 10 yd ≈ 9 m C 1 m ≈ 5 ft D 4 in. ≈ 10 cm

Short Answer

6. The perimeter of a rectangular room measuring 8′6″ by 9′ is _____ feet.

7. Vlad estimates that his index finger is 3 in. long. He calculates the circumference of one drum of his bongo set to be 24 in. Suppose Vlad uses this referent to measure the circumference. How many finger lengths along the circumference of the drum would he have counted?

Name: ___________________________________________ Date: _____________________________



8. The length of a loveseat is 1.5 m and the length of a couch is 2.1 m. Suppose the length of the box on a moving truck is 14 ft. How many linear feet are remaining after the loveseat and couch are placed in the box end to end?

9. Convert each measurement to a more appropriate unit in the SI system.

a) 51 430 cm b) 2650 mm c) 0.54 m

10. Convert each measurement to the indicated unit. a) 63 inches = ____ feet b) 7 yards = ____ inches

11. Write the conversion factor(s) required to convert the following: a) 6 mi to kilometres b) 19.2 m to centimetres

c) 142

ft to inches

d) 500 cm to yards

12. Calculate each conversion in #11, to the nearest half of a unit.

Extended Response

13. Alicia and her friends want to estimate the diameter of a Douglas fir tree. They know that a person’s arm span is approximately equal to his or her height. So, they decided to join hands and determine how many people were needed to reach around the circumference of the tree. It takes five people⎯Alicia, 5′ 2″, Tal 5′ 8″, Julia 5′ 6″, Paul 6′ 1″, and Colin 6′ 3″⎯to reach around the tree. What is the radius of the tree, to the nearest inch?

14. Yvon draws a diagram of his backyard. The scale of his diagram is 1 : 400.

a) What distance on the ground is

represented by 2 cm on the drawing? b) What are the dimensions of the actual

yard? c) Estimate the length of the diagonal in

Yvon's drawing of his backyard. d) Show two ways to calculate the diagonal

distance of Yvon’s backyard.

15. Tom made a sketch of some flowers that were sitting on his mother’s dresser.

a) Estimate the height of the vase in the

drawing in imperial units. b) Use a referent to estimate the height of

the vase in SI units. c) Measure the height of the vase in

centimetres. Then, convert the measurement to inches. How does the converted imperial measurement compare to your estimate?

d) The height of the real vase Tom sketched is 27 cm. If the flowers touch the bottom inside the vase, how tall are the flowers?

BLM 1–9


Chapter 1 BLM Answers BLM 1–2 Chapter 1 Prerequisite Skills 1. a) 100 b) 1000 c) 3500 d) 100 000 2. a) 5.2 cm b) 4.2 cm c) 3.2 cm 3. a) 0.8 cm or 8 mm b) 5.7 cm or 57 mm c) 1 mm 4.

5. a) 3 cm b) 7 cm c) 5 cm 6. a) Scale factor refers to the constant factor by which all dimensions of an object are enlarged or reduced in a scale drawing. For example, if the dimensions of a drawing of a square are enlarged by a factor of 2, then each side of the square is 2 times as long as the original. b) If the scale factor is less than 1, the diagram is a reduction. c) 1:1.45 7. a) 8 b) 16 c) 8 d) 32

8. 58

= 0.625

9. a) x = 10 b) x = 7.5. Example: If you look at the numerators, you can see that you can get from 2 to 3 by multiplying by 1.5. Then, you do the same with the denominators. c) x = 1.25 d) x = 22.5 10. a) 25.8 cm b) 8x mm c) 50.27 cm 11. a) 3 cm

b) 7.2 mm

c) 5.7 m

BLM 1–3 Chapter 1 Warm-Up Section 1.1 1. Example: ruler, odometer, measuring tape 2. a) Example: 2.7 cm or 27 mm b) Example: 0.4 cm or 4 mm 3. Examples: a) 0.052 b) 37 100 c) 185 d) 0. 0278 4. a) 19 b) 5 c) 0.15 d) 6 5. a) Estimate: Example: 30 cm; calculate: 31.4 cm b) Estimate: Example: 18 cm; calculate: 18.8 cm Section 1.2

2. A: 18

; B: 14

, 28

; C: 12

, 24

, 48

; D: 58

, E: 34

, 68

3. a) 198

b) 2316

c) 154

4. a) 35 b) 292

or 12

14 c) 60

5. a) 10 cm b) 13 cm Section 1.3 1. a) 4 b) 5 c) 1760 2. a) 15 b) 3.8 c) 500

4. Example: Change 58

1 to 138

, and 2.1 to 110

2 ,

which becomes 2110

. Then, multiply.

5. a) 1.4 m or 140 cm b) 3.5 m

BLM 1–5 Section 1.1 Extra Practice 1. Examples: a) waist height ≈ almost 1 m b) width of fingernail ≈ 1 cm c) ten city blocks ≈ 1 km 2. A: 1.1 cm = 11 mm, B: 3.2 cm = 32 mm, C: 4.9 cm = 49 mm, D: 6.8 cm = 68 mm 3. 6.2 mm = 0.62 cm 4. 154 cm 5. a) large map: 1:27 083 333, small map: 1:216 666 666 b) northern border approx. 600 km, southern border approx. 300 km 6. a) 70 mm b) 3200 cm c) 58 000 m d) 7 500 000 cm e) 0.65 km f) 0.056 m 7. a) 5 mm b) 4188 m or 4.188 km c) 2.74 m d) 553 m

BLM 1–6 Section 1.2 Extra Practice

1. 34

A in.= 1316

B 1 in.= 1316

C 2 in.= 58

D 4 in.=

2. 1.312 in. 3. a) 6 feet b) 15 840 feet c) 70 inches

d) 2 12

miles e) 41 feet 8 inches



4. a) 5 12

miles b) 38

3 inches

5. a) 12

340 inches b) 34 inches

6. perimeter = 20 12

feet

7. a) 12

7 in. b) 1.875 = 78

1 c) 1 1 in. by in.2 4

7 11

BLM 1–7 Section 1.3 Extra Practice 1. a) 4000 mi b) 0.1 mm c) 18.44 m d) 296 km

2. 96 inches by 12

151 inches ; 244 cm by 385 cm

3. a) Estimate: 45 ft = 15 × 3. Actual answer is greater because 17 > 15. b) Example: metre c) 15.5 m

4. a) centimetres b) 3.0 cm = 14

1 inch

c) 1:3.33 cm 5. 627 km = 390 mi

6. a) 12 12

ft by 13 12

ft b) 52 feet

c) 5 lengths

BLM 1–8 Chapter 1 Test 1. C 2. A 3. C 4. D 5. C 6. 35 7. 8 8. 2 ft 9. a) 514.3 m b) 2.65 m c) 54 cm

10. a) 1 ft4

5 b) 252 in.

11. a) 1 mi ≈ 1.609 km b) 1 m = 100 cm c) 12 in. = 1 ft d) 100 cm = 1 m and 1 yd = 0.9144 m

12. a) 9.5 km b) 1920 cm c) 54 in. d) 152

yd

13. 55 in. 14. a) 800 cm or 8 m b) 12 m by 18 m c) estimate: 5.5 cm d) Method 1: Measure the length of the diagonal in the diagram or use the Pythagorean theorem to calculate the length of the hypotenuse in the drawing. Then, use the scale to calculate the actual distance. 5.4 cm

x= 1

400

Method 2: Use the measurements calculated in part b) and apply the Pythagorean theorem.

2 2 2

2

2

2160 cm or 21.6 m

12 18

144 324

468 21.6 m

x

x

x

xx

=

= +

= +

=≈

15. a) estimate: 14

1 in.

b) referent: width of 1 fingernail ≈ 1 cm estimate: 3 cm

c) 3 cm = 115

in. Estimate is slightly greater than

measurement. d) 40.5 cm

Documents

BLM 1–2 Chapter 1 Prerequisite Skillspjk.scripts.mit.edu/lab/2p/Chapter_1_ALL.pdf · ... McGraw-Hill Ryerson Limited, ... BLM 1–3 Copyright © 2009, McGraw-Hill Ryerson Limited,