### Rates_ Unit Rates_ Similar Figures_

```Standard
NS 1.2
NS 2.2
Score
First Name and Last Name
Period
Date
Mr. Menjivar/Pre-Algebra
Unit 1 Test Part 2
Number Sense 2.2
Number Sense 1.2
9
1)
16
5
4) −
24
+
1
2) 1
2
1
3)
4
3
4
−
−
1
3
4
2
5
5
5)
6
⋅
15
6)
19
÷
7
12
3
−1
10
÷
15
19
By: Mr. Menjivar
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Standard:
9L
9R



Measurement and Geometry 1.1: Compare
units within and between measurement
systems
Measurement and Geometry 1.2: Construct
Measurement and Geometry 1.3: Use
measures expressed as rates to solve
problems.
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Standard:
Objectives:
9L
9R



To find rates and unit rates
To use measures expressed as rates and
products to solve problems
To solve problems that involve similar
figures and scale drawings
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Standard:
Objectives:
Vocabulary:
9L
9R

A comparison of two quantities by
division

A ratio that compares quantities in different
units
◦ Note: a unit rate is a rate that has a
denominator of 1

Have the same shape, but not necessarily
the same size
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Standard:
Objectives:
Vocabulary:
Notes/Examples:
9L
9R
Ratios


A ratio is a comparison between two numbers
by division.
It can be written in three different ways:
5 to 2
5:2
5
2
Equal Ratios

When two ratios name the same number,
they are equal. It’s like writing an equivalent
fraction.
20 : 30
Equal Ratios:
10 : 15 2 : 3 80 : 120
Ratios in Simplest Form


Ratios can be written in simplest form.
Divide both terms in the ratio by their
GCF.
Example: 12 to 8
3 to 2
Examples
Rate:
150 heartbeats
2 minutes
Find The Unit Rate
Find the Unit Rate
Amy can read 90 pages in 4 hours. What is the
unit rate? (How many pages can she read per
hour?)
Using Unit Rates
• You can find the missing terms of
equal ratios.
• Use the unit rate, and set it equal to
another ratio.
• Solve for what is missing by dividing
or multiplying.
Example
Joe’s car goes 25 miles per gallon of
gasoline. How far can it go on 8 gallons of
gasoline?
Comparing Unit Prices
• Use division to find the unit prices of
the two products in question.
• The unit rate that is smaller (costs
less) is the better value.
Example
Juice is sold in two different sizes. A 48-fluid
ounce bottle costs \$2.07. A 32-fluid ounce
bottle costs \$1.64. Which is the better buy?
\$2.07
48 fl.oz.
\$1.64
32 fl.oz.
0.043125
0.05125
The 48 fl.oz. bottle is the better value.
\$0.04 per fl.oz.
\$0.05 per fl.oz.
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
Classwork #1:
09/09/11
Rates, Similar Figures, and Scale
Drawings
Standard:
Objectives:
Vocabulary:
Notes/Examples:
9L
9R
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Classwork #1:
Standard:
Homework:
Objectives:
Vocabulary:
Notes/Examples:
9L
9R


Pg. 335 [1-9 all and 19]
Pg. 337 [10-19 all]
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Classwork #1:
Standard:
Homework:
Objectives:
Warm-Up:
Vocabulary:
Notes/Examples:
9L
9R
2
1)

3
2)
6
=
1
8
3
3)
4
=
7

4
4)
11
=
21

=

22
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Classwork #1:
Standard:
Homework:
Objectives:
Warm-Up:
Vocabulary:
Notes/Examples:
Back to the Notes
9L
9R
Proportions
What are proportions?
- If two ratios are equal, they form a proportion.
Proportions can be used in geometry when working with
similar figures.
1
4
2
=
8
1:3 = 3:9
What do we mean by similar?
- Similar describes things which have the same shape
but are not the same size.
Examples
These two stick figures are
similar. As you can see both
are the same shape. However,
the bigger stick figure’s
dimensions are exactly twice
the smaller.
8 feet
4 feet
So the ratio of the smaller
figure to the larger figure is 1:2
(said “one to two”). This can
also be written as a fraction of
½.
2 feet
relating the height and the
width of the smaller figure to
the larger figure:
4 ft
2 ft
=
8 ft
4 ft
4 feet
Try One Yourself
8 feet
Knowing these two stick
figures are similar to
each other, what is the
ratio between the
smaller figure to the
larger figure?
12 feet
4 feet
x feet
Set up a proportion.
What is the width of the
larger stick figure?
Similar Shapes
In geometry similar shapes are very important.
This is because if we know the dimensions of one
shape and one of the dimensions of another shape
similar to it, we can figure out the unknown
dimensions.
Proportions and Triangles
What are the unknown values on these triangles?
20 m
16 m
xm
ym
4m
3m
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Classwork #1:
Standard:
Homework:
Objectives:
Warm-Up:
Vocabulary:
Interactive Practice:
Notes/Examples:
9L
9R
Current Measurements
Parts of the
body
Measurements
in Inches
Parts of the
body
Measurements
in Inches
Height
Height
120 inches
Right arm
Right arm
Left arm
Left arm
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Classwork #1:
Standard:
Homework:
Objectives:
Warm-Up:
Vocabulary:
Interactive Practice:
Notes/Examples:
Classwork #2:
9L
9R
Observe,
Question,
Comment
09/09/11
Rates, Similar Figures, and
Scale Drawings Reflection
09/09/11
Rates, Similar Figures, and Scale
Drawings
Classwork #1:
Standard:
Homework:
Objectives:
Warm-Up:
Vocabulary:
Interactive Practice:
Notes/Examples:
Classwork #2:
Homework:
9L
9R


Pg. 338 [1-9 all]
Pg. 339 [7-14 all]
```