MPM 1D - PBworksmdhsmath.pbworks.com/w/file/fetch/83963056/MPM1Dunit1... · 2020-06-22 · MPM 1D...
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MPM 1D Principals of Mathematics
Gr. 9 Academic
E-mail / iMessage : [email protected] 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
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MPM
1DLessonGuide
201
9-20
20Sem
ester2
Februa
ry
March
April
May
June
Sat
1
Sun
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Wed
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U3L6
Fri
1PD
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U5Re
view
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Tu
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2U5Te
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Mon
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Tues
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U2L6
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U3L7
Sun
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Wed
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EQAOReview
Tues
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U1L1
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Sat
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U4L3
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EQAOReview
Wed
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U1L2
Thurs
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EQAOReview
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U1L3
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Mon
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U2Review
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EQAODAY1
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EQAODAY2
Thurs13
U1L8
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EasterM
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U1L9
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MB
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FamilyDay
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U1Review
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RE
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VictoriaDay
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CA
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U5L1
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Exam
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U2L1
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HK
Mon
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U5L4
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Exam
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U3L1
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Exam
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U2L3
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Exam
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Exam
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U2L4
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U3L3
Sun
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Tues
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U5L6
Fri
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PDDay
Thurs27
Fri
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U3L4
Mon
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U4L1-1
Wed
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U5L7
Sat
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Fri
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U2L5
Sat
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Tues
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U4L1-2
Thurs
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U5L8
Sun
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U4L1-3
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U3L5
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***PleaseNote–thisscheduledoesNOTtakeintoaccountthefollowing:Snowdays,ThinkingTasks,Drills,Assembliesoranyotherclassdisruption.
Youwillhavetoadjustyourownstudyscheduleaccordingly***
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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
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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,
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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...
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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
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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)
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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
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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
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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%
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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
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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%
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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
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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
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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
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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
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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.
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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.
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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
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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
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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"
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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=
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Examples: Simplify use exponent laws to simplify BUT do not EVALUATE
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