Page 185 - NUMINO TG_6A
P. 185
12Unit Increasing at the Same Rate
jOb ective Find and use ratios and rates of increase.
1. Textbook Instructions 12 Increasing at the Same Rate
In this unit, students will learn how to use There are 4 pencils and 8 erasers. What is the ratio of pencils to erasers in
both ratios and proportions to solve problems each group?
and to learn how objects relate to one
another.
Solve the problems with students. The ratio of pencils to erasers
Why do we put the pencils on top of the number of pencils = 4
number of erasers 8
ratio? Because the smaller number goes on
top. 4
8
The first ratio is . What does the ratio
style remind you of? A fraction. The ratio of pencils to erasers
Notice we’re using the same total number number of pencils in each group = 2
number of erasers in each group 4
of pencils and erasers each time. Why? To
show how ratios function even if totals do not
change.
What do you notice about the three ratios The ratio of pencils to erasers
we’ve found?They’re all equal. number of pencils in each group 1
number of erasers in each group 2
Note to students that all three of these ratios =
are the same as 1 , and discuss that this
2
type of similarity is referred to as a 2 and 1 are equivalent to 4 . An equation that shows
4 2 8 two equivalent ratios is
proportion, which will be discussed in called a .proportion
greater detail later in the unit. 4 2 1
8 4 2
= =
Introduce a proportion by relating it to ratios.
100
2. Build Understanding
Writing Ratios
Ratios are structured the same way as fractions, but express different things about the numbers they
contain. Ratios express how two values relate to one another, while fractions express a part of a whole.
Emphasize to students that writing ratios involves answering a few simple questions. Use the problems on
the page as an example.
What are the two values to be expressed? Pencils and erasers.
Which of these has the smallest value? Pencils.
How should the ratio be structured? Least value on top, greatest value on bottom.
168 NUMINO Teacher s Guide
jOb ective Find and use ratios and rates of increase.
1. Textbook Instructions 12 Increasing at the Same Rate
In this unit, students will learn how to use There are 4 pencils and 8 erasers. What is the ratio of pencils to erasers in
both ratios and proportions to solve problems each group?
and to learn how objects relate to one
another.
Solve the problems with students. The ratio of pencils to erasers
Why do we put the pencils on top of the number of pencils = 4
number of erasers 8
ratio? Because the smaller number goes on
top. 4
8
The first ratio is . What does the ratio
style remind you of? A fraction. The ratio of pencils to erasers
Notice we’re using the same total number number of pencils in each group = 2
number of erasers in each group 4
of pencils and erasers each time. Why? To
show how ratios function even if totals do not
change.
What do you notice about the three ratios The ratio of pencils to erasers
we’ve found?They’re all equal. number of pencils in each group 1
number of erasers in each group 2
Note to students that all three of these ratios =
are the same as 1 , and discuss that this
2
type of similarity is referred to as a 2 and 1 are equivalent to 4 . An equation that shows
4 2 8 two equivalent ratios is
proportion, which will be discussed in called a .proportion
greater detail later in the unit. 4 2 1
8 4 2
= =
Introduce a proportion by relating it to ratios.
100
2. Build Understanding
Writing Ratios
Ratios are structured the same way as fractions, but express different things about the numbers they
contain. Ratios express how two values relate to one another, while fractions express a part of a whole.
Emphasize to students that writing ratios involves answering a few simple questions. Use the problems on
the page as an example.
What are the two values to be expressed? Pencils and erasers.
Which of these has the smallest value? Pencils.
How should the ratio be structured? Least value on top, greatest value on bottom.
168 NUMINO Teacher s Guide
