MPM 1D Principals of Mathematics

Gr. 9 Academic

E-mail / iMessage : Kelly.caldwell@ed.amdsb.ca Website : mdhsmath.pbworks.com

Unit 1 Numeracy Review

Lesson Lesson Title Questions to Ask About

1 Number Systems

2 Operations with Rationals

3 Converting Percent, decimal, Fractions

4 Application of Percent

5 Applications for Fractions, Percents & Decimals

6 Unit Rate

7 Proportion Word Questions

8 Applying Ratio, Rate & Proportion

9 Exponent Laws

MPM

1DLessonGuide

201

9-20

20Sem

ester2

Februa

ry

March

April

May

June

Sat

1

Sun

1

Wed

1

U3L6

Fri

1PD

Day

Mon

1

U5Re

view

Sun

2

Mon

2

Thurs

2

Sat

2

Tu

es

2U5Te

st

Mon

3

Tues

3

U2L6

Fri

3

U3L7

Sun

3

Wed

3

EQAOReview

Tues

4

U1L1

Wed

4

Sat

4

Mon

4

U4L3

Thurs

4

EQAOReview

Wed

5

U1L2

Thurs

5U2L7

Sun

5

Tues

5

Fri

5

EQAOReview

Thurs

6

U1L3

Fri

6

Mon

6U3L8

Wed

6

U4L4

Sat

6

Fri

7

U1L4

Sat

7

Tues

7

Thurs

7

Sun

7

Sat

8

Sun

8

Wed

8

U3L9

Fri

8

U4L5

Mon

8

PDDay

Sun

9

Mon

9

U2L8

Thurs

9

Sat

9

Tues

9

EQAOReview

Mon

10

U1L5

Tues

10

Fri

10

Goo

dFriday

Sun

10

Wed

10

EQAOReview

Tues

11

U1L6

Wed

11

U2Review

Sat

11

Mon

11

Thurs11

EQAODAY1

Wed

12

U1L7

Thurs

12

U2Te

st

Sun

12

Tues

12

U4L6

Fri

12

EQAODAY2

Thurs13

U1L8

Fri

13

Mon

13

EasterM

onda

yWed

13

Sat

13

Fri

14

U1L9

Sat

14

Tues

14

U3L10

Thurs

14

U4Re

view

Sun

14

Sat

15

Sun

15

Wed

15

Fri

15

U4Te

st

Mon

15

Sun

16

Mon

16

MB

Thurs

16

U3L11

Sat

16

Tues

16

Mon

17

FamilyDay

Tues

17

AR

Fri

17

U3L12

Sun

17

Wed

17

Tues

18

U1Review

Wed

18

RE

Sat

18

Mon

18

VictoriaDay

Thurs18

Wed

19

U1Te

st

Thurs

19

CA

Sun

19

Tues

19

U5L1

Fri

19

Exam

sThurs20

U2L1

Fri

20

HK

Mon

20

Wed

20

U5L2

Sat

20

Fri

21

U2L2

Sat

21

Tues

21

U3L13

Thurs

21

U5L3

Sun

21

Sat

22

Sun

22

Wed

22

Fri

22

U5L4

Mon

22

Exam

sSun

23

Mon

23

U3L1

Thurs

23

U3Re

view

Sat

23

Tu

es

23

Exam

sMon

24

U2L3

Tues

24

U3L2

Fri

24

U3Te

st

Sun

24

Wed

24

Exam

sTues

25

Wed

25

Sat

25

Mon

25

U5L5

Thurs

25

Exam

sWed

26

U2L4

Thurs

26

U3L3

Sun

26

Tues

26

U5L6

Fri

26

PDDay

Thurs27

Fri

27

U3L4

Mon

27

U4L1-1

Wed

27

U5L7

Sat

27

Fri

28

U2L5

Sat

28

Tues

28

U4L1-2

Thurs

28

U5L8

Sun

28

Sat

29

Sun

29

Wed

29

U4L1-3

Fri

29

Mon

29

Mon

30

U3L5

Thurs

30

U4L2

Sat

30

Tues

30

Tues

31

Sun

31

***PleaseNote–thisscheduledoesNOTtakeintoaccountthefollowing:Snowdays,ThinkingTasks,Drills,Assembliesoranyotherclassdisruption.

Youwillhavetoadjustyourownstudyscheduleaccordingly***

1

Overall Goals

1. Working knowledge of the number system

2. Operations with integers, rationals, and radicals

3. Applying exponent laws

4. Ratio/rate/percent conversions and calculations.

Unit One: Numeracy

2

Lesson Goal: I can sort numbers into their appropriate number systems.

There are 5 different number systems you are responsible for:.

1. Natural/Counting (N)­ numbers we use to count with OR numbers above zero that do not have decimals or fractions.

Number Systems

2. Whole numbers (W)

­ all the natural numbers PLUS zero

3. Integers (I)­ positive and negative numbers that never have decimals or fractions

4. Rational Numbers (Q)

­ numbers that can be written in the form and would include decimals that repeat or terminate.

eg. 0.3, 0.125, 0.5

5. Irrational Numbers (Q)

­ numbers that cannot be written in the form and include non­terminating and non­repeating decimals

eg. π, √3, √8, ...

radicals (square roots) except perfect squares:

√4, √9, √16, ...

1.1

eg 1,2,3,4,5,.....

ab

b≠0,

ab

b≠0,

3

Examples:

1. For the following numbers, check off all of the systems that they belong to.

N W I Q Q

3

­102

2.684 61...

1.3535...

0

2. Provide 3 examples of each of the following:

Natural numbers

Whole numbers

Integers

Rational numbers

Irrational numbers

Practice work ­ handout

1, 2, 30, 1, 2

­1, ­2, ­32, √9, 0.2929...√11, π, 0.6312...

1

Goal: I can Multiply/Divide and Add/subtract rational numbers.

Operations with Rational Numbers1.2

Adding/Subtracting Integers

1. (+2) + (+3)

= 2 + 3

= 5

Replace double signs with one sign.

If signs are the same

If signs are the different

2. (­3) + (+5)

= ­3 + 5

= 2

3. (+4) ­ (+6)

= 4 ­ 6

= ­2

4. (­6) + (­5)

= ­6 + 5

= ­1

Adding/Subtracting FractionsMUST have common denominators. In other words the "bottom number" must be the same

1. x35xx35x

2.x12x15x20

3.

Keep answer as a reduced IMPROPER fraction

Review VideoCalculator and fractions

1 1

2

Negatives and Fractions

­ negative signs can be placed where you want/need it.

Multiplying and Dividing

1. 2.

3. 4.

­multiply numerators

­multiply denominators

­reduce

­reciprocate and multiply

Handout ­ odd numbers (front and back)

1

I can convert between fractions, decimals, and percents.

Goal:

1.3 Converting Fractions, Decimals, and Percents

Fractions to Decimals Decimals to Percent

Divide the numerator by the denominator

Multiply the decimal by 100.

Percent to Decimal Decimal to Fraction

Divide the percent by 100

The numbers after the decimal will be the same number of zeros used in the denominator.

= 0.5 0.25 = 25%

0.5 % = 0. 005

0.2 = 2 10

= 15

0.35 = 35

720

=100

= 40610 000

0.0406

=2035 000

2

Example : Determine the missing values

Fraction Decimal Percent23

75

0.35

0.245

12.5%

0.005%

35%

24.5%

0.6

1.4

66.7%

140%

0.125

0.000 05

35100

720

2451000

49200

1251000

5100 000 =

=

=

= 18

120 000

Worksheet

1

Goal: I can solve missing information related to percent questions.

1.4 Working with Percent

There are 3 types of questions you must be able to solve.

1. Find the percentage

2. Finding the numerator value

3. Finding the denominator value

Examples: Determine the following.

1. What percent is 45 of 70?

Percent is always OUT OF 100

2. What percent is 64 of 120?

100 ÷ 70 = 1.43

x1.43

64%

64120

=100? 64 ÷ 120 x 100

53.3%

2

2. Determine the following

a) What is 35% of 90?

b) What is 115% of 60?

3. Determine the following

a) 70% of what number is 35?

b) 48% of what number is 120?

Textbook ­ page 82 #1­22

35100 90

=

0.9 x 35 = 31.5

Cross ­ multiply35100 90=

100x = 35(90)÷100

÷100

x = 31.5

115100 =

x60

0.9

0.6

0.6 x 115 = 69

69

31.5

70100

= 35x

35 ÷ 70 = 0.50.5

x = 100 x 0.5

= 50

48100

120x

=120 ÷ 48 = 2.5

x = 2.5 x 100

= 250

2.5

1

1.5 Applications for Fractions, Percents and Decimals

Goal: I can use decimals and percents to solve word problems.

1. A magazine sells for $12.00 this year. Last year it sold for

$9.00. Determine: a) The percent increase over last years' price.

Examples:

b) The percent of the old price compared to the new price.

old pricenew price

=912

= 0.75

= 75%

the percent of old price to new price is 75%

$ increase = 12­9

= 3increase

original price39

=

.3=

= 33.3%

the percent increase was 33.3%

2

taxes, determine how many months she subscribed.(only one magazine is produced PER MONTH)

12% tax was included. If each magazine was $5.99 before Katelyn purchased a magazine subscription for $322.08 after 2.

322.08 = cost + tax

1 magazine = 5.99 + tax

= 5.99 + 12% of 5.99

= 5.99 + 0.12x5.99

= 5.99 + 0.72

= 6.71 total $ ÷ one

# mag = 322.08 ÷ 6.71

= 48

she subscribed the magazine for 48 months

1 magazine = 5.99 + tax

3

David is selling his collector hockey cards. He has decided to sell them at a markup of 35%. If each card is of equal value, determine the value prior to mark­up if they are priced at $215 each.

4.

215 = original price + mark­up

Working with %: original price + mark­up

= 100% + 35%

= 135% ­­­­­­­­­­­ ($215)

Need to compare $ with % between the original and mark­up price

originalmarkup

x215

100135

=

215 ÷ 135 = 1.592

x = 100 x 1.592

= 159.2592...

= $159.26 the price before mark­up is $159.26

Page 83 # 45­48, 52­55, 57 & Worksheet

1

Goal: I can calculate unit rate and find missing information within proportions.

Unit Rate ­

Ratio, Rate and Proportion1.6

­is a comparison of a quantity of one item to ONE UNIT

to another.

examples of unit rate:

100km / 1hr #calories / cup 30 rotations /1 minute

PER ÷

General equation: item of interest item being compared

Example: Determine the unit rate for the following.

1. It costs $1.50 for 20 pencils

2. A plane travels 1200km in 3 hours

3. Kylie makes $390 per 40 hours

How much for 1 pencil?

How many km for 1 hour?

$ for 1 hour?

item of interest item being compared

1 pencil$1.5020

= $0.075/pencil

km1 hr

12003 = 400km/hr

$hr

39040

= $9.75/hr

2

A ratio is a comparison between 2 or more quantities where the units DO NOT HAVE to be the same.

It can be written as:

A proportion is 2 ratios that are equal.

eg. 1:2 = 2:4

Example: Determine the unknown values.

13 ; 1:3 ; one to three

1. 3 : 5 = ___ : 25

2. ___ : 4 = 38 : 60

3. 4 : ___: 9 = ____ : 22 : 70

x5

x515

÷15

÷152.5

70 ÷ 9 = 7.7x7.7

÷7.7

2.8 31.2

1

Goal ­I can use proportions to solve mixture quantities.

Ratio & Proportion Word Questions1.7

1. A bronze statue is made from a mixture of tin and copper in the ratio 5:2. If you require 200kg of bronze for a project, how much tin and copper are required?

When working with word questions, it is IMPORTANT to make sure that you have the various items in the ratios matched up with the proportions on each side.

tin : copper tin + copper = bronze

5 : 2 : 7 = ___ : ___ : 200 200÷7=28.57

x28.57x28.57

tin = 5 x 28.57

= 142.85copper = 2 x 28.57

= 57.14

you need 142.85kg of tin and 57.14kg of copper.

2

2. Concrete is made from a mixture of sand, gravel, and cement in a volume ratio of 10:30:12.a) Determine how much of each product is needed if 40 shovels of sand are used.

b) Determine how much of each product is needed if 50 m3 of concrete is required for a job

s : g : c

10 : 30 : 12 : ____ = ____ : ____ : ____ : 50

x4

120 48

you need 120units of gravel and 48 units of cement.

s : g : c : concrete

10 : 30 : 12 = 40 : ____ : _____

concrete = 10+30+12

50÷52=0.9615x0.9615

sand = 0.9615 x 10

=9.615m3

gravel = 0.9615 x 30= 28.845m3

cement = 0.9615 x 12= 11.538m3

you would need 9.615m3 of sand, 28.845m3 of gravel, and 11.538m3 of cement.

1

Goal ­ determine missing measures in scale and other proportions

I can

Applying Ratio, Rate & Proportion

Scale ­ is the relationship between a measurement on a drawing and a measurement of the actual object.

When you read a scale: 1 : 100

100 : 1

Examples:1. Determine the distance between Mitchell and Seaforth if they are 0.33cm apart on a map that has a scale of 1:75 (cm:km)

1.8

measurement of drawing

measurement in real life

The units of measurement between the drawing and real life can be different.

ie. 1: 100

1cm 100km

1 : 75 = 0.33 : ______

x0.33 0.33x75=24.75

the distance is 24.75km away

2

$2.25/Zorg. If David just completed his intergalactic space tour and has 45 000 Zorgs left, determine how much Canadian he has.

3. The exchange rate for Canadian to alien Zorg's is

2. (SHADOW) A 200m tall building casts ashadow of 45m long. If you are approximately 1.75 m tall, determine the length of your shadow.

Building : Shadow

200 : 1.75 = 1.75 : _____

1.75÷200 =0.00875

x

0.39

the shadow would be 0.39m

Canadian $ : Zorg

$2.25 : 1 = ______ : 45 000

x45 000

$

$ = 45 000 x 2.25

=101 250

he would have $101 250

1

Goal: I can apply exponent laws to expressions that have numerical and algebraic bases.

Exponent Laws

Repeated multiplication:

34 =

Five Laws

1. Law of Multiplication

am x an

2. Law of Division

am ÷ an =

am an =

341.9 Part One

Base

Exponent

"3 to the exponent of 4"

3 x 3 x 3 x 3

2 x 2 x 2 x 2 x 2 = 25

http://www.online­calculator.com/scientific­calculator/

Most common power buttons: ^ yx xy

35 = 243

Bases must be the same

= am + n 34 x 35

=3x3x3x3x3x3x3x3x3=39 3 4 + 5

am ­ nam ­ n

3432

3x3x3x33x3=

32=3 4 ­ 2

"3 to the power of 4"

2

4. Zero Exponent Law

5. Negative Exponent Law

­ reciprocate the base (flip) AND change the exponent to a positive number

3. Law of Power of Powers

(am)n = a mn( 32 )3 = 32 x 32 x 32

=363 2x3 = 36

a 0 = 1

BUT a ≠ 0 , 0 0 is undefined

43 ÷ 43 =43­3

=40

but 43 ÷ 43 =64÷64=1

40 = 1

(1) a ­m = 1am

1a­m = a m(2)

12 = 0.5

2 ­1 =0.5

12 2 ­1=

3

Examples: Simplify use exponent laws to simplify BUT do not EVALUATE

1.

2. 3.

4.