day 9 - review - answers.notebook · 4.8.2 Review Relay (Continued) 2. Calculate the following...

day 9 review answers.notebook

1

April 30, 2014

Apr 233:58 PM

Reviewpg 57 - 62

May 103:18 PM

4.8.2 Review Relay

1. Reduce the ratio to lowest terms:

15:35 =

18 = 6

144:72 =

pg 57


2

April 30, 2014

Jul 1312:34 PM

4.8.2 Review Relay (Continued)2. Calculate the following percents:

45% of 220 =

120% x 555=

1.5% x 1400 =

pg 57

Jul 1312:36 PM

4.8.2 Review Relay (Continued)3. The driving distance from Thunder Bay to Vancouver is approximately 2500 km. How long would it take you to drive from Thunder Bay to Vancouver at 90 km/hour without making any stops?

Individual Work / Group Work

Solution

pg 57


3

April 30, 2014

Jul 1312:37 PM

4.8.2 Review Relay (Continued)

4. If the ratio of the Canadian dollar to the US dollar is $1.04:$1.00, how much Canadian money is equivalent to US$250?

Individual Work / Group Work

Solution

pg 57

Jul 1312:38 PM


5. Measure the length indicated in centimetres. What is the actual length of the shark, in metres?Scale Diagram

1:70

pg 58


4

April 30, 2014

Jul 1312:47 PM


6. You want to purchase a new shirt that costs $22.50. a) How much tax will you have to pay including GST and PST?

b) What is the total cost of your shirt?

HST only

pg 58

Jul 1312:50 PM

4.8.2 Review Relay (Continued)7. You are shopping for DVDs at the video store with a $30.00 gift certificate that you received from a friend. You find a great DVD that was $34.50 on sale for 25% off. Do you have enough money to buy the DVD including GST and PST?

pg 58

HST only


5

April 30, 2014

Jul 1312:54 PM

4.8.2 Review Relay (Continued)8. You are working at Tecky Television Sales. Recall that the HDTV's width:height ratio is 16:9. A customer wants to know:

a) If he has an entertainment centre that has an opening that is 48 inches wide, how high will the cabinet opening have to be?

Apr 206:43 PM

b) If the cabinet opening is 48 inches by 32 inches, will a 50inch HDTV fit inside?

pg 58


6

April 30, 2014

Consolidate Debreif Page 1

4.8.3 Practice1. Express each of the following as a unit rate. Round answers to two decimal places, if necessary, and state the units for each answer.a) 40 mm of rain in 4 h ______________

b) $6.49 for 24 cans of pop ___________

c) $58.00 for 8 h of work _____________

2. A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg at birth, what is the baby likely to weigh on her first birthday?

pg 59

Jul 131:15 PM

4.8.3 Practice (Continued)

3. A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates that she will ride the bus 25 times this month. Boris estimates that he will ride the bus 16 times. Should they each buy a monthly pass? Explain.

pg 59


7

April 30, 2014

Jul 131:16 PM

4.8.3 Practice (Continued)4. The price for gold is usually given in US dollars per ounce. Find the cost in Canadian dollars for an ounce of gold selling at US$559.00 when the exchange rate is $1 USD = $1.17 CDN.

pg 59

Jul 131:24 PM


5. Determine the better buy for each of these school supplies. Show your calculations.a) A box of 12 pens for $2.59 or a box of 15 pens for $3.35.

b) 250 sheets of graph paper for $2.39 or 120 sheets for $1.15.

pg 60


8

April 30, 2014

Jul 131:34 PM


6. Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the greater average speed? Explain.

pg 60

Jul 131:42 PM

4.8.3 Practice (Continued)7. Carl bought a football jersey with a regular price of $129.49. The jersey was on sale for 30% off, and the taxes were 13%. Determine each amount.a) the discount b) the sale price

c) the taxes d) the total amount Carl paid

pg 60


9

April 30, 2014

Jul 131:44 PM


8. Determine the missing value for each of the following.

a) 64 = ______ % b) 15% of _____ = 6 72

c) 32% of 65 = ________ d) 0.08% of 25 000 000 = _______

e) 124 = _____ % f) 135% of ______ is 108. 96

pg 61

Jul 131:47 PM


9. A stop sign has an actual width of 60 cm. Determine the scale of the diagram below.

3.6 cm

pg 61


10

April 30, 2014

Jul 131:53 PM


10. A scale drawing of the Canadian Flag gives a ratio of 1:50. The width of the drawing is 13 cm. A real Canadian Flag has a width to height ratio of 2:1. What are the actual dimensions of a real Canadian flag?

Actual Height = _______

Actual Width = __________

pg 62

Jul 131:20 PM

Attachments

4.8.32 Practice ﴾Solutions﴿.notebook

4.8 MindsOnGameInstructions.notebook

4.8.1 TeacherNotes.notebook









BLM 4.8.14.8.3.doc

BLM 4.8.14.8.3.pdf

BLM 4.8.14.8.3 ﴾Solutions﴿.doc

BLM 4.8.14.8.3 ﴾Solutions﴿.pdf

4.8 Teacher Instructions.doc

4.8 Teacher Instructions.pdf

4.8.pdf

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Jul 13-2:23 PM 4.8.3 Practice (Solutions Continued) 3. A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates that she will ride the bus 25 times this month. Boris estimates that he will ride the bus 16 times. Should they each buy a monthly pass? Explain. Katelyn We know: · she will ride the bus 25 times Therefore: · $50.00/25 = $2.00/ride · This is cheaper than the single faire cost of $2.10. It is cheaper for Katelyn to buy a monthly bus pass. Boris We know: · he will ride the bus 16 times Therefore: · $50.00/16 = $3.13/ride · This is more expensive than the single fare rate of $2.10. It is cheaper for Boris to pay for a single bus fare for each ride.

SMART Notebook


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Jul 14-8:31 AM Teacher Notes Time: 10 minutes Preparation: Cut out 16 cards for each team of 4 students . Instructions: Distribute 16 cards randomly to each team so that each student receives 4 cards. Rules: Students may not talk to each other or give non-verbal signals to other members of the team. The dominoes in front of each player must remain visible to everyone on the team. Team members can only give dominoes; they cannot take dominoes from someone else. Each team member must have 2 dominoes in front of them at all times. The task is completed when everyone on the team has completed their domino doughnut. Materials: 16 cut-out cards for each team of 4 students , timer on Smartboard.

SMART Notebook


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Jul 13-11:23 AM Teacher Notes Time: 10 minutes Instructions: Create a transparency of BLM 4.8.1 and display on the overhead for students to observe. Students use grid paper and linking cubes to make another version of this shape that is twice as big. Allow students time to explore on their own and make mistakes, as this will help direct the discussion on what constitutes proportionality. Choose models to display that show proportionality and others that don’t. Discuss which shapes look proportionate, and ask students to explain what strategies they used to create the proportionate shapes, as well as the disproportionate ones. Students should understand that proportional shapes are created using multiplicative processes, not additive ones. Materials: 70 linking cubes & grid paper for each student pair , timer on Smartboard.

SMART Notebook


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Jul 13-2:06 PM 4.8.3 Practice (Solutions) 1. Express each of the following as a unit rate. Round answers to two decimal places, if necessary, and state the units for each answer. a) 40 mm of rain in 4 h ______________ b) $6.49 for 24 cans of pop ___________ c) $58.00 for 8 h of work _____________ 2. A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg at birth, what is the baby likely to weigh on her first birthday? = 10 mm/hour = $0.27/can = $7.25/hour We know: · "triples" means X 3 · after 1 year, the child will weigh 3 X the weight at birth Therefore: · 3.35 X 3 = 10.05 kg The child is likely to weigh 10.05 kg on her first birthday.

SMART Notebook


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Jul 13-2:32 PM 4.8.3 Practice (Solutions Continued) 4. The price for gold is usually given in US dollars per ounce. Find the cost in Canadian dollars for an ounce of gold selling at US$559.00 when the exchange rate is $1 USD = $1.17 CDN. Cross-multiply. The cost for an ounce of gold is $654.03 CDN.

SMART Notebook


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Jul 13-2:38 PM 4.8.3 Practice (Solutions Continued) 5. Determine the better buy for each of these school supplies. Show your calculations. a) A box of 12 pens for $2.59 or a box of 15 pens for $3.35. b) 250 sheets of graph paper for $2.39 or 120 sheets for $1.15. Box of 12 Pens for $2.59 $2.59/12=$0.216/pen Box of 15 Pens for $3.35 $3.35/15=$0.223/pen The box of 12 pens is the better buy. 250 sheets for $2.39 $2.39/250=$0.00956/sheet 120 sheets for $1.15 $2.39/250=$0.00958/sheet The package of 250 sheets is the better buy.

SMART Notebook


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Jul 13-2:53 PM 4.8.3 Practice (Solutions Continued) 6. Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the greater average speed? Explain. Kelly 8 laps in 18 minutes = 0.4 laps/min Jack 6 laps in 10 minutes = 0.6 laps/min Since Jack ran more laps per minute, Jack had the greater average speed.

SMART Notebook


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Jul 13-2:57 PM 4.8.3 Practice (Continued Solutions) 7. Carl bought a football jersey with a regular price of $129.49. The jersey was on sale for 30% off, and the taxes were 13%. Determine each amount. a) the discount b) the sale price c) the taxes d) the total amount Carl paid 30% = 0.3 Therefore: 0.3 X $129.49 = $38.85 The discount was $38.85. $129.49 - $38.85 = $90.64 The sale price was $90.64. Taxes are 13%. 13% = 0.13 Therefore: 0.13 X $90.64 = $11.78 The taxes were $11.78. Total = Sale Price + Taxes Total = $90.64 + $11.78 Total = $129.4 - $38.85 = $102.42 The total price was $102.42.

SMART Notebook


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Jul 13-3:09 PM 4.8.3 Practice (Solutions Continued) 8. Determine the missing value for each of the following. a) 64 b) 15% of x = 6 72 c) 32% of 65 d) 0.08% of 25 000 000 = e) 124 f) 135% of x is 108. 96 = 0.89 X 100 = 89% Cross-multiply. = 0.32 X 65 = 20.8 = 0.0008 X 25 000 000 = 20 000 = 1.29 X 100 = 129% Cross-multiply.

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Jul 13-3:26 PM 4.8.3 Practice (Continued) 9. A stop sign has an actual width of 60 cm. Determine the scale of the diagram below. 3.6 cm diagram : actual 3.6 cm : 60 cm 3.6 cm 3.6 cm 1 : 16.7 The scale of the diagram is 1:16.7 Recall, scale = diagram : actual

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Jul 13-3:31 PM 4.8.3 Practice (Solutions Continued) 10. A scale drawing of the Canadian Flag gives a ratio of 1:50. The width of the drawing is 13 cm. A real Canadian Flag has a width to height ratio of 2:1. What are the actual dimensions of a real Canadian flag? Actual Height? Actual Width? Recall, scale = diagram : actual Step 1: Find the actual width. Step 2: Find the actual height. The actual width is 650 cm and the actual height is 325 cm.

SMART Notebook

4.8.1: Double It!

4.8.2: Review Relay

1.Reduce the ratios to lowest terms:

15:35 =

18

6

=

144:72 =

2.Calculate the following percents:

45% of 220 =

120% ( 555 =

1.5% ( 1400 =

3.The driving distance from Thunder Bay to Vancouver is approximately 2500 km.

How long would it take you to drive from Thunder Bay to Vancouver at90 km/hour without making any stops?

4.If the ratio of the Canadian dollar to the US dollar is $1.04:$1.00, how much Canadian money is equivalent to US$250?

4.8.2: Review Relay (continued)

5.Measure the length indicated in centimetres. What is the actual length of the shark, in metres?

Scale Diagram

1:70

6.You want to purchase a new shirt that costs $22.50.

a)How much tax will you have to pay including HST?

b)What is the total cost of your shirt?

7.You are shopping for DVDs at the video store with a $30.00 gift certificate that you received from a friend. You find a great DVD that was $34.50 on sale for 25% off.

Do you have enough money to buy the DVD including HST?

8.You are working at Tecky Television Sales. Recall that the HDTV’s width:height ratio is 16:9. A customer wants to know:

a)If he has an entertainment centre that has an opening that is 48 inches wide, how high will the cabinet opening have to be?

b)If the cabinet opening is 48 inches by 32 inches, will a 50-inch HDTV fit inside?

4.8.3: Practice

1.

Express each of the following as a unit rate. Round answers to two decimal places, if necessary, and state the units for each answer.

(a)40 mm of rain in 4 h ______________________________

(b)$6.49 for 24 cans of pop ___________________________

(c)$58.00 for 8 h of work _____________________________

2.

A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg at birth, what is the baby likely to weigh on her first birthday?

3.

A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates that she will ride the bus 25 times this month. Boris estimates that he will ride the bus 16 times. Should they each buy a monthly pass? Explain.

4.

The price for gold is usually given in US dollars per ounce. Find the cost in Canadian dollars for an ounce of gold selling at US$559.00 when the exchange rate is $1 USD = $1.17 CDN.

4.8.3: Practice (continued)

5. Determine the better buy for each of these school supplies. Show your calculations.

(a)A box of 12 pens for $2.59 or a box of 15 pens for $3.35.

(b)250 sheets of graph paper for $2.39 or 120 sheets for $1.15.

6.Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the greater average speed? Explain.

7.

Carl bought a football jersey with a regular price of $129.49. The jersey was on sale for 30% off, and the taxes were 13%. Determine each amount.

(a)the discount

(b)the sale price

(c)the taxes

(d)the total amount Carl paid


8.

Determine the missing value for each of the following.

(a)64 = ______%

(b) 15% of _______ = 6

72

(c)32% of 65 = ______

(d)0.08% of 25 000 000 = ________

(e)124 = ______%

(f)135% of _____ is 108.

96

9.

A stop sign has an actual width of 60 cm. Determine the scale of the diagram below.


10.

A scale drawing of the Canadian Flag gives a ratio of 1:50. The width of the drawing is 13 cm. A real Canadian Flag has a width to height ratio of 2:1. What are the actual dimensions of a real Canadian flag?

Actual height: ____________ Actual width: ___________

3.6 cm

MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (July 2009)4-7

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SMART Notebook

MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (July 2009) 4-1

4.8.1: Double It!


4.8.2: Review Relay

1. Reduce the ratios to lowest terms: 15:35 =

18

6 =

144:72 =

2. Calculate the following percents: 45% of 220 = 120% × 555 = 1.5% × 1400 =

3. The driving distance from Thunder Bay to Vancouver is approximately 2500 km.

How long would it take you to drive from Thunder Bay to Vancouver at 90 km/hour without making any stops?




5. Measure the length indicated in centimetres. What is the actual length of the shark, in metres?

Scale Diagram

1:70

6. You want to purchase a new shirt that costs $22.50.

a) How much tax will you have to pay including HST?

b) What is the total cost of your shirt?

7. You are shopping for DVDs at the video store with a $30.00 gift certificate that you received from a friend. You find a great DVD that was $34.50 on sale for 25% off.


8. You are working at Tecky Television Sales. Recall that the HDTV’s width:height ratio is 16:9. A customer wants to know:


b) If the cabinet opening is 48 inches by

32 inches, will a 50-inch HDTV fit inside?


4.8.3: Practice 1. Express each of the following as a unit rate. Round answers to two decimal places, if necessary, and

state the units for each answer.

(a) 40 mm of rain in 4 h ______________________________ (b) $6.49 for 24 cans of pop ___________________________ (c) $58.00 for 8 h of work _____________________________

2. A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg at birth, what is the baby likely to weigh on her first birthday?

3. A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates that she will ride the bus 25 times this month. Boris estimates that he will ride the bus 16 times. Should they each buy a monthly pass? Explain.

4. The price for gold is usually given in US dollars per ounce. Find the cost in Canadian dollars for an ounce of gold selling at US$559.00 when the exchange rate is $1 USD = $1.17 CDN.


4.8.3: Practice (continued) 5. Determine the better buy for each of these school supplies. Show your calculations.

(a) A box of 12 pens for $2.59 or a box of 15 pens for $3.35.

(b) 250 sheets of graph paper for $2.39 or 120 sheets for $1.15. 6. Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the greater average

speed? Explain.

7. Carl bought a football jersey with a regular price of $129.49. The jersey was on sale for 30% off, and the taxes were 13%. Determine each amount. (a) the discount (b) the sale price

(c) the taxes (d) the total amount Carl paid



8.

Determine the missing value for each of the following. (a) 64 = ______% (b) 15% of _______ = 6 72 (c) 32% of 65 = ______ (d) 0.08% of 25 000 000 = ________ (e) 124 = ______% (f) 135% of _____ is 108. 96


3.6 cm




Actual height: ____________ Actual width: ___________

SMART Notebook

4.8.1 – 4.8.3 Solutions

4.8.1: Double It!

4.8.2: Review Relay

1.Reduce the ratios to lowest terms:

15:35 = 3: 7

18

6

= 3/1

144:72 = 2/1

2.Calculate the following percents:

45% of 220 = 99

120% ( 555 = 666

1.5% ( 1400 = 21

3.The driving distance from Thunder Bay to Vancouver is approximately 2500 km.

How long would it take you to drive from Thunder Bay to Vancouver at90 km/hour without making any stops?

2500/ 90 = 27.78 hours

Therefore it would take 27.78 hours to drive from Thunder Bay to Vancouver.

4.If the ratio of the Canadian dollar to the US dollar is $1.04:$1.00, how much Canadian money is equivalent to US$250?

1.04/1 = x/ 250

x = 260

Therefore Canadian equivalent to $250 US is $260.


5.Measure the length indicated in centimetres. What is the actual length of the shark, in metres?

Scale Diagram

1:70

1/70 = 5.5/x

x = 385 cm

6.You want to purchase a new shirt that costs $22.50.

a)How much tax will you have to pay (HST)?

22.5 x 0.13 = 2.93

Therefore you would have to pay $2.93.

b)What is the total cost of your shirt?

22.50 + 2.95 = $25.43

Therefore the total cost of the shirt is $25.43.

7.You are shopping for DVDs at the video store with a $30.00 gift certificate that you received from a friend. You find a great DVD that was $34.50 on sale for 25% off.


34.5 x 0.25 = 8.63

34.5 – 8.63 = 25.87

25.87 x 0.13 = 3.36

25.87 + 3.36 = 29.23

Therefore, yes if the total came to $29.23 and you had a $30.00 gift certificate then you would have enough money.

8.You are working at Tecky Television Sales. Recall that the HDTV’s width:height ratio is 16:9. A customer wants to know:

a)If he has an entertainment centre that has an opening that is 48 inches wide, how high will the cabinet opening have to be?

w: h

16 : 9 = 48 : h

h = 27

Therefore the height has to be 27 inches.

b)If the cabinet opening is 48 inches by 32 inches, will a 50-inch HDTV fit inside?

c2 = 482 + 322

c2 = 3328

c = 57.7

Therefore yes a 50 inch television will fit into a 57.7 opening. |

4.8.3: Practice

1.

Express each of the following as a unit rate. Round answers to two decimal places, if necessary, and state the units for each answer.

(a)40 mm of rain in 4 h 10 mm/h

(b)$6.49 for 24 cans of pop $0.27 / can

(c)$58.00 for 8 h of work $7.25 / h

2.

A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg at birth, what is the baby likely to weigh on her first birthday?

3.35 x 3 = 10.05 kg

The baby is likely to weigh 10.05 kg on her first birthday.

3.

A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates that she will ride the bus 25 times this month. Boris estimates that he will ride the bus 16 times. Should they each buy a monthly pass? Explain.

Katelyn 25 x 2.10 = 53.76

Boris 16 x 2.10 = 33.6

Therefore Katelyn should buy the monthly pass but Boris should not buy the monthly pass.

4.

The price for gold is usually given in US dollars per ounce. Find the cost in Canadian dollars for an ounce of gold selling at US$559.00 when the exchange rate is $1 USD = $1.17 CDN.

$559.00 x 1.17 = $ 654.03

The price for gold is $654.03 Canadian.


5. Determine the better buy for each of these school supplies. Show your calculations.

(a)A box of 12 pens for $2.59 or a box of 15 pens for $3.35.

2.59 / 12 = $0.22 per pen

3.35 / 15 = $0.22 per pen

The better deal is 12 pens for $2.59.

(b)250 sheets of graph paper for $2.39 or 120 sheets for $1.15.

2.39/ 250 = 0.00956

1.15/ 120 = 0.00958

The better deal is $2.39 for 250 sheets of graph paper.

6.Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the greater average speed? Explain.

8/18 = 0.44

6/10 = 0.6

Therefore Jack had the greater average speed.

7.

Carl bought a football jersey with a regular price of $129.49. The jersey was on sale for 30% off, and the taxes were 13%. Determine each amount.

(a)the discount

(b)the sale price

129.49 x 0.30 = $38.85 129.49 – 38.85 = $90.64

(c)the taxes

(d)the total amount Carl paid

90.64 x 0.13 = $11.78 90.64 + 11.78 = $102.42


8.

Determine the missing value for each of the following.

(a)64 = 89%

(b) 15% of 40 = 6

72

(c)32% of 65 = 20.8

(d)0.08% of 25 000 000 = 20 000

(e)124 = 129%

(f)135% of 80 is 108.

96

9.

A stop sign has an actual width of 60 cm. Determine the scale of the diagram below.

60 / 3.6 = 16.7

Therefore the scale for this diagram is 1: 16.7.


10.

A scale drawing of the Canadian Flag gives a ratio of 1:50. The width of the drawing is 13 cm. A real Canadian Flag has a width to height ratio of 2:1. What are the actual dimensions of a real Canadian flag?

Actual height: 325 cm Actual width:650 cm

1/50 = 13/x

x = 650

2/1 = 650/x

x = 325 cm

3.6 cm

MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (July 2009)4-1

_1192611891.unknown

SMART Notebook


4.8.1 – 4.8.3 Solutions 4.8.1: Double It!


4.8.2: Review Relay

1. Reduce the ratios to lowest terms: 15:35 = 3: 7

18

6 = 3/1

144:72 = 2/1

2. Calculate the following percents: 45% of 220 = 99 120% × 555 = 666 1.5% × 1400 = 21

3. The driving distance from Thunder Bay to Vancouver is approximately 2500 km.

How long would it take you to drive from Thunder Bay to Vancouver at 90 km/hour without making any stops?

2500/ 90 = 27.78 hours Therefore it would take 27.78 hours to

drive from Thunder Bay to Vancouver.


1.04/1 = x/ 250 x = 260 Therefore Canadian equivalent to $250

US is $260.



5. Measure the length indicated in centimetres. What is the actual length of the shark, in metres?

Scale Diagram

1:70

1/70 = 5.5/x x = 385 cm

6. You want to purchase a new shirt that costs $22.50.

a) How much tax will you have to pay (HST)?

22.5 x 0.13 = 2.93 Therefore you would have to pay

$2.93. b) What is the total cost of your shirt? 22.50 + 2.95 = $25.43 Therefore the total cost of the shirt

is $25.43.

7. You are shopping for DVDs at the video store with a $30.00 gift certificate that you received from a friend. You find a great DVD that was $34.50 on sale for 25% off.


34.5 x 0.25 = 8.63 34.5 – 8.63 = 25.87 25.87 x 0.13 = 3.36 25.87 + 3.36 = 29.23 Therefore, yes if the total came to

$29.23 and you had a $30.00 gift certificate then you would have enough money.

8. You are working at Tecky Television Sales. Recall that the HDTV’s width:height ratio is 16:9. A customer wants to know:


w: h 16 : 9 = 48 : h h = 27 Therefore the height has to be 27

inches. b) If the cabinet opening is 48 inches by

32 inches, will a 50-inch HDTV fit inside?

c2 = 482 + 322 c2 = 3328 c = 57.7 Therefore yes a 50 inch television

will fit into a 57.7 opening. |


4.8.3: Practice 1. Express each of the following as a unit rate. Round answers to two decimal

places, if necessary, and state the units for each answer.

(a) 40 mm of rain in 4 h 10 mm/h (b) $6.49 for 24 cans of pop $0.27 / can (c) $58.00 for 8 h of work $7.25 / h

2. A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg at birth, what is the baby likely to weigh on her first birthday? 3.35 x 3 = 10.05 kg The baby is likely to weigh 10.05 kg on her first birthday.

3. A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates that she will ride the bus 25 times this month. Boris estimates that he will ride the bus 16 times. Should they each buy a monthly pass? Explain. Katelyn 25 x 2.10 = 53.76 Boris 16 x 2.10 = 33.6 Therefore Katelyn should buy the monthly pass but Boris should not buy the monthly pass.

4. The price for gold is usually given in US dollars per ounce. Find the cost in Canadian dollars for an ounce of gold selling at US$559.00 when the exchange rate is $1 USD = $1.17 CDN. $559.00 x 1.17 = $ 654.03 The price for gold is $654.03 Canadian.


4.8.3: Practice (continued) 5. Determine the better buy for each of these school supplies. Show your calculations.

(a) A box of 12 pens for $2.59 or a box of 15 pens for $3.35.

2.59 / 12 = $0.22 per pen 3.35 / 15 = $0.22 per pen

The better deal is 12 pens for $2.59.

(b) 250 sheets of graph paper for $2.39 or 120 sheets for $1.15.

2.39/ 250 = 0.00956 1.15/ 120 = 0.00958

The better deal is $2.39 for 250 sheets of graph paper.

6. Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the greater average

speed? Explain.

8/18 = 0.44 6/10 = 0.6

Therefore Jack had the greater average speed.

7. Carl bought a football jersey with a regular price of $129.49. The jersey was on sale for 30% off, and the taxes were 13%. Determine each amount. (a) the discount (b) the sale price 129.49 x 0.30 = $38.85 129.49 – 38.85 = $90.64

(c) the taxes (d) the total amount Carl paid 90.64 x 0.13 = $11.78 90.64 + 11.78 = $102.42



8. Determine the missing value for each of the following. (a) 64 = 89% (b) 15% of 40 = 6 72 (c) 32% of 65 = 20.8 (d) 0.08% of 25 000 000 = 20 000

(e) 124 = 129% (f) 135% of 80 is 108. 96


60 / 3.6 = 16.7 Therefore the scale for this diagram is 1: 16.7.

3.6 cm




Actual height: 325 cm Actual width:650 cm

1/50 = 13/x

x = 650

2/1 = 650/x

x = 325 cm

SMART Notebook

Unit 4: Day 8: Proportion Potpourri

Grade 9 Applied

75 min

Math Learning Goals

· Investigate that proportionality is a multiplicative process and not an additive process.

· Consolidate concept understanding for ratio, proportion, and percents.

· Solve problems involving percents, fractions, and decimals in a variety of contexts.

Materials

· BLM 4.8.1 - 4.8.3 for each student

Pairs ( Peer Editing

Students compare solutions from the BLM 4.7.5 Journal Activity. They share the reference sheets on percents that they made and offer suggestions for improvement, if necessary.

Fours ( Game

In groups of 4, students will play the game “Doughnut Percents” to consolidate their understanding of ratios, proportions and percents. The teacher will have to cut out 16 cards found at http://nrich.maths.org/content/id/6945/Doughnut%20percents.doc for each team of 4 students in preparation for the activity. Alternatively, the teacher can find an article for the students to read that consolidates the connections between ratios, proportions, and percents and their relevance in everyday life.

Materials

· BLM 4.7.5 (Solutions)

· Game on Smart Board

· 16 cards (cut-out in advance) for each team of 4 students

· Internet connection to read rules of game.

Minds On ...

15 min.

Pairs ( Investigation

Display BLM 4.8.1 on overhead or Smart Board for students to observe. Students use grid paper and linking cubes to make another version of this shape that is twice as big.

Allow students time to explore on their own and make mistakes, as this will help direct the discussion on what constitutes proportionality. Choose models to display that show proportionality and others that don’t. Discuss which shapes look proportionate, and ask students to explain what strategies they used to create the proportionate shapes, as well as the disproportionate ones. Students should understand that proportional shapes are created using multiplicative processes, not additive ones.

Representing/Oral Questions/Mental Note: Assess how students explain why or why not their models represent proportional shapes.

Groups of 4 ( Review Relay

Make as many copies of BLM 4.8.2 as there are groups. Cut out the questions and create piles of each question number. Students are allowed to use their notes and reference sheets for this activity. Peer tutors can help the teacher to run the relay.

Form heterogeneous groups. Each group completes the first question (BLM 4.8.2). A group member verifies with the teacher that the answer is correct before receiving the next question; incorrect solutions must be corrected by the group.

Materials

· BLM 4.8.1-4.8.2 for each student

· BLM 4.7.5 (Solutions)

· Overhead projector OR Smart Board

· Coloured pencils

· Linking cubes (70 for each student group)

· BLM 4.8.1 (on transparency if using overhead projector)

· BLM 4.8.2 (Cut into 8 per group)

Action!

50 min.

Whole Class ( Discussion

Students share solutions to relay questions that posed problems.

Materials

· BLM 4.8.3 for each student

Consolidate Debrief

20 min.

Home Activity or Further Classroom Consolidation

Students prepare for the unit assessment by completing practice questions (BML 4.8.3), creating reference sheets, and organizing their notes. Students will need to bring in grocery flyers for the unit assessment activity.

Reference sheets could be an accommodation for identified exceptional students.

MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (July 2009)

SMART Notebook

MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (July 2009)

Unit 4: Day 8: Proportion Potpourri Grade 9 Applied

75 min

Math Learning Goals

• Investigate that proportionality is a multiplicative process and not an additive process.

• Consolidate concept understanding for ratio, proportion, and percents.

• Solve problems involving percents, fractions, and decimals in a variety of contexts.

Materials • BLM 4.8.1 -

4.8.3 for each student

Minds On ...

15 min.

Pairs �� Peer Editing Students compare solutions from the BLM 4.7.5 Journal Activity. They share the reference sheets on percents that they made and offer suggestions for improvement, if necessary.

Fours �� Game In groups of 4, students will play the game “Doughnut Percents” to consolidate their understanding of ratios, proportions and percents. The teacher will have to cut out 16 cards found at http://nrich.maths.org/content/id/6945/Doughnut%20percents.doc for each team of 4 students in preparation for the activity. Alternatively, the teacher can find an article for the students to read that consolidates the connections between ratios, proportions, and percents and their relevance in everyday life.

Materials • BLM 4.7.5

(Solutions)

• Game on Smart Board

• 16 cards (cut-out in advance) for each team of 4 students

• Internet connection to read rules of game.

Action!

50 min.

Pairs �� Investigation Display BLM 4.8.1 on overhead or Smart Board for students to observe. Students use grid paper and linking cubes to make another version of this shape that is twice as big.

Allow students time to explore on their own and make mistakes, as this will help direct the discussion on what constitutes proportionality. Choose models to display that show proportionality and others that don’t. Discuss which shapes look proportionate, and ask students to explain what strategies they used to create the proportionate shapes, as well as the disproportionate ones. Students should understand that proportional shapes are created using multiplicative processes, not additive ones.

Representing/Oral Questions/Mental Note: Assess how students explain why or why not their models represent proportional shapes.

Groups of 4 �� Review Relay Make as many copies of BLM 4.8.2 as there are groups. Cut out the questions and create piles of each question number. Students are allowed to use their notes and reference sheets for this activity. Peer tutors can help the teacher to run the relay.

Form heterogeneous groups. Each group completes the first question (BLM 4.8.2). A group member verifies with the teacher that the answer is correct before receiving the next question; incorrect solutions must be corrected by the group.

Materials • BLM 4.8.1-4.8.2

for each student

• BLM 4.7.5 (Solutions)

• Overhead projector OR Smart Board

• Coloured pencils

• Linking cubes (70 for each student group)

• BLM 4.8.1 (on transparency if using overhead projector)

• BLM 4.8.2 (Cut into 8 per group)

Consolidate Debrief

Whole Class �� Discussion Students share solutions to relay questions that posed problems.

Materials • BLM 4.8.3 for

each student

20 min.

Home Activity or Further Classroom Consolidation

Students prepare for the unit assessment by completing practice questions (BML 4.8.3), creating reference sheets, and organizing their notes. Students will need to bring in grocery flyers for the unit assessment activity.

Reference sheets could be an

accommodation for identified exceptional

students.

SMART Notebook

SMART Notebook

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