Standard:NS 1.2
Interpret and use ratios in different contexts (e.g.,
batting averages, miles per hour) to show the relative
sizes of two quantities, using appropriate notations (
a/b, a to b, a:b ).
Objective - -Students will interpret, write and
compare ratios within different contexts and use
rates to compare two or more quantities with
different units by using steps, identifying key
information, and scoring 80% on an exit slip.
Observe,
Question,
Comment
1/11/10
Lesson 5-1:
Pg. 194, # 12-16 & # 23-25
1/11/10
Lesson 5-1: Ratios [Pg. 192-195]
Hook:
36L
36R
Discuss with your partner:
How do the number of white keys compare to
the number of black keys?
Observe,
Question,
Comment
1/11/10
Lesson 5-1:
Pg. 194, # 12-16 & # 23-25
1/11/10
Lesson 5-1: Ratios [Pg. 192-195]
Hook:
Standards/ Objective:
35L
35R
Standards:
Number Sense 1.2***: Interpret and use
ratios in different contexts (e.g., batting
averages, miles per hour) to show the
relative sizes of two quantities, using
appropriate notations (a/b, a to b, a:b).
Learning Targets:
5A: Describe a ratio in your own
words.
5B: Give a variety of examples of
ratios written in different ways
(a/b, a to b, a:b).
5C: Represent a real life situation
using a ratio and explain the
connection between the situation
and the mathematical model.
Can you explain
what the
learning targets
mean?
What will you
be able to do by
the end of this
lesson?
Ratio:
Ratios are used to compare two
quantities using division.
Observe,
Question,
Comment
1/11/10
Lesson 5-1:
Pg. 194, # 12-16 & # 23-25
1/11/10
Lesson 5-1: Ratios [Pg. 192-195]
Hook:
Standards/ Objective:
Notes/ Examples:
35L
35R
Ratios can be used to:
Compare a part to a whole.
1 rectangle to 7 shapes
Compare a whole to a part.
7 shapes to 6 triangles
Compare a part to a part.
1 rectangle to 6 triangles
Compare a whole to another whole.
7 shapes to 4 shapes
There are 12 boys and 10 girls in a class. The
classroom has 24 desks.
Use ratios to compare:
A part to a whole:
Boys to all students
A whole to a part:
All students to girls
A part to a part:
Girls to boys
A whole to another whole:
Students to classroom desks
Example 1.
The photo on the left
shows one block of a
music keyboard’s key
pattern. The keys have a
repeating pattern of five
black keys and seven
white keys. Use ratio to
describe the pattern.
Number of black keys: 5
Number of white keys: 7
The ratio of black keys to white keys is 5 to 7. This means that for every
5 black keys, there are 7 white keys.
There are 3 ways to write this ratio.
5 to 7
5/7
5:7
The photo on the left
shows a piece of a quilt
called a block. Compare
the number of blue
squares to the number
of purple squares.
Number of blue squares: 12
Number of purple squares: 9
The ratio of blue to purple squares is 12 to 9. This means that for every
12 blue squares, there are 9 purple squares.
There are 3 ways to write this ratio.
12 to 9
12/9
12:9
Example 2.
1.
2.
3.
Write each ratio in three ways. Use the
pattern shown.
Green squares to blue squares
Red squares to blue squares
Green squares to all squares
Example 3.
Two ratios that name the same number are
equivalent ratios. You can find equivalent
ratios by writing a ratio as a fraction and
finding an equivalent fraction.
The Identity Property of Multiplication states that you can
multiply a number by 1 and not change its value. Is this
true?
For this reason, when 1 is written in a different form, such
as a fraction like 3/3 or 5/5, and then multiplied with
another fraction, the value of the fraction remains the
same.
2/ = 2/ x 4/ = 8/
3
3
4
12
You can also divide to find equivalent fractions.
12/ = 12/ ÷ 3/ = 4/
15
15
3
5
http://www.mathsisfun.com/equivalent_fr
actions.html
Find a ratio equivalent to 4/5.
4 = 4 x 2 = 8 Multiply the numerator and
5 5 x 2 10 denominator by 2.
Write 2/20 as a ratio in simplest form.
2 = 2 ÷ 2 = 1 Divide the numerator and
20 20 ÷ 2 10 denominator by the GCF, 2.
Find a ratio equivalent to 7/9.
Write 10/2 as a ratio in simplest form.
Example 4.
Write two ratios equivalent to 14/4. Use
multiplication to write one and division to
write the second.
Example 5.
Are the ratios equivalent?
Write = or ≠ in the O.
5:8
3/12
4/6
9 to 8
O
O
O
O
15:24
9/36
16/20
45 to 40
Example 6.
Are these equivalent ratios?
19
10
505
255
If they are equivalent (showing the same
number just in different form), then dividing
them should result in the same decimal.
For example:
5
8
0.625
=
15
24
0.625
So…
19
10
1.9
505
255
≠
1.98
Since 1.98 is not equal to 1.9, these are not
equivalent ratios.
Tell whether the ratios are equivalent or not
equivalent.
7:3 and 128:54
180/240 and 25/34
Example 7.
The ratio of girls to boys enrolled at King
Middle School is 15:16. There are 195 girls
and 208 boys in Grade 8. Is the ratio of girls
to boys in Grade 8 the same as the ratio of
girls to boys in the entire school?
Example 8.
Tell whether the ratios are equivalent or not
equivalent.
12/24 and 50/100
1 to 3 and 2 to 9
2:3 and 24:36
Example 9.
Observe,
Question,
Comment
1/11/10
Lesson 5-1:
Pg. 194, # 12-16 & # 23-25
1/11/10
Lesson 5-1: Ratios [Pg. 192-195]
Hook:
Standards/ Objective:
Notes/ Examples:
Vocabulary:
35L
35R
Own Definition:
What is a ratio?
What are the three ways a ratio can be written?
Give an example.
Class Definition: A comparison of two
quantities. Notation [how you can write a
ratio]:
(1) 16 to 10
(2) 16:10
(3) 16/10
Own Definition:
What are equivalent ratios?
How are they created?
Class Definition: Ratios that represent the
same value, even if they do not look the same.
They are created by multiplying or dividing
both terms of the ratio by the same number.
Observe,
Question,
Comment
1/11/10
Lesson 5-1:
Pg. 194, # 12-16 & # 23-25
1/11/10
Lesson 5-1: Ratios [Pg. 192-195]
Hook:
Standards/ Objective:
Notes/ Examples:
Vocabulary:
Moral of the Story:
35L
35R
•In one sentence, what was the
most important thing you learned
from this lesson?
• Math Link: How will you use
ratios in the real world?
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