Transcript Module 1Lesson 9 and 10

Math Module 1
Ratios and Unit Rates
Topic B: Collections of Equivalent Ratios
Lesson 9: Tables of Equivalent Ratios
6.RP.3a
PowerPoint designed by Beth Wagenaar
Material on which this PowerPoint is based is the Intellectual Property of Engage NY and can be
found free of charge at www.engageny.org
Lesson
Target
• I will understand that a ratio is often used
to describe the relationship between the
amount of one quantity and the amount of
I’ve asgot
another quantity
in thethis!
cases of mixtures
or constant rates.
• I will understand that a ratio table is a table
of equivalent ratios and use them to solve
problems.
Classwork
Example 1: 10 minutes
Lesson 9
Example 1
To make Paper Mache,
the art teacher mixes
water and flour. For
every two cups of
water, she needs to mix
in three cups of flour to
make the paste.
Classwork
Example 1: 10 minutes
What does this
ratio mean?
For every 2
cups of water,
there are 3 cups
of flour.
Every time we have a set of two cups of water, we
need to have a set of three cups of flour.
Lesson 9
Classwork
Example 1: 10 minutes
Lesson 9
Why is it worded,
“For every 2 cups of water,
there are 3 cups of flour”?
This suggests that we might
be doing that action
repeatedly, adding 2 cups
of water and 3 cups of
flour. Why would I do it
more than once?
Because you want to make a REALLY big paper
mache piñata for my birthday party?
Can we list all of the possible recipes for this mixture in order
Classwork
in a table? Let’s startExample
with1:the
ratio that uses the smallest
10 minutes
whole numbers. Is there an equivalent ratio that uses smaller
whole numbers than the ratio 2 to 3?
No!
Lesson 9
Classwork
Example 1: 10 minutes
2
3
Lesson 9
Then let’s
What
would
make
cups
the2next
ofpossibility
water andbe?
3
ofwant
flour to
Icups
don’t
be
first
skipour
over
any
entry.
numbers.
Classwork
Example 1: 10 minutes
Is that what we
What is the
expected? Should the
value of each
value of all of these
ratio in the
ratios be equal to each
table?
other?
2
4
6
8
10
3
6
9
12
15
2:3
2:3
2:3
2:3
2:3
Lesson 9
Classwork
What we have created Example
here is
a minutes
ratio table, a table in which all
1: 10
of the values of the ratios are equivalent to one another.
2
4
6
8
10
3
6
9
12
15
Lesson 9
Classwork
Example 1: 10 minutes
Lesson 9
What kinds of
questions could we
answer with the
data in our table?
Can anyone think of
a question we might
have had at the start
of this problem that
this table could help
us answer?
Classwork
Example 1: 10 minutes
Woo hoo! I got
a REALLY BIG
piñata for my
birthday!
Lesson 9
Classwork
Example 2: 5 minutes
Javier has a new job
designing websites. He is
paid at a rate of $700 for
every 3 pages of web content
that he builds. Create a ratio
table to show the total
amount of money Javier has
earned in ratio to the
number of pages he has
built.
Lesson 9
Classwork
Example 2: 5 minutes
WeIswill
start
there
anour
table withratio
the
equivalent
pages
toentry
700:33that
still
built
$700
usesand
smaller
earned.
whole
numbers?
Javier has a new job designing websites.
He is paid at a rate of $700 for every 3
pages of web content that he builds.
Create a ratio table to show the total
amount of money Javier has earned in
ratio to the number of pages he has built.
Lesson 9
Noo…
Classwork
Go ahead and fill in the table without
Example 2: 5 minutes
skipping over any possible ratios.
Lesson 9
Classwork
Exercise 1: 10 minutes
Lesson 9
Classwork
Exercise 1: 10 minutes
Lesson 9
Classwork
Exercise 1: 10 minutes
Lesson 9
Classwork
Exercise 2: 10 minutes
Lesson 9
Classwork
Exercise 2: 10 minutes
Lesson 9
Classwork
Exercise 2: 10 minutes
Lesson 9
Lesson 9
Lesson Summary
A ratio table is a table of
pairs of numbers that form
equivalent ratios
Lesson
Closing
I will understand
that a ratio table
is a table of
equivalent ratios
and use them to
solve problems.
I’m thinking
about ratios…
not about my
lack of clothing.
• When creating a ratio table,
what does each pair of values
represent?
• Can anyone think of a
situation where you have seen
a ratio table other than here in
class?
• Can you think of an example
of a table of numbers you’ve
seen that was not a ratio
table?
Lesson 8
Exit Ticket
Lesson 1
Problem Set
Problem Set
Problem Set
Problem Set
Bell Ringer!
Math Module 1
Ratios and Unit Rates
Topic B: Collections of Equivalent Ratios
Lesson 10: The Structure of Ratio Tables – Additive and Multiplicative
6.RP.3a
PowerPoint designed by Beth Wagenaar
Material on which this PowerPoint is based is the Intellectual Property of Engage NY and can be
found free of charge at www.engageny.org
Lesson 10
Target
• I can identify both the additive and
multiplicative structure of a ratio table and
use the Foodfight!!!
structure to make additional
I’ve entries
in the table.
got great aim…
• I can use ratio tables to solve problems.
Classwork
Lesson 10
Exploratory Challenge Exercise 1: 33 minutes
Imagine you are making a fruit
salad. For every quart of
blueberries you add, you
would like to put in 3 quarts of
strawberries.
Classwork
Exploratory Challenge Exercise 1: 33 minutes
Lesson 10
Classwork
Lesson 10
Exploratory Challenge Exercise 1: 33 minutes
Create 3 ratio tables that show
the amounts of blueberries
and strawberries you would
use if you needed to make fruit
salad for greater numbers of
people.
We want fruit
salad!!!
Classwork
Lesson 10
Exploratory Challenge Exercise 1: 33 minutes
Table 1 should contain
amounts where you have
fewer than 10 quarts of
blueberries to the salad.
Table 3 should contain
amounts of blueberries
greater than 100 quarts.
Table 2 should
contain amounts of
blueberries
between 10 and 50
quarts.
Lesson 10
Classwork
Exploratory Challenge Exercise 1: 33 minutes
The value in the
second column is
always three times as
much as the
corresponding value in
the first column.
Lesson 10
Classwork
Lesson 10
Exploratory Challenge Exercise 1: 33 minutes
In the first table, the
entries in the first
column increase by 1,
and the entries in the
second column
increase by 3.
Classwork
Exploratory Challenge Exercise 1: 33 minutes
In the second table,
the entries in the first
column increase by
10, and the entries in
the second column
increase by 30.
Lesson 10
Classwork
Lesson 10
Exploratory Challenge Exercise 1: 33 minutes
In the third table, the
entries in the first
column increase by
100, and the entries in
the second column
increase by 300.
Classwork
Exploratory Challenge Exercise 1: 33 minutes
The amount of
strawberries is always
three times the amount of
blueberries. The ratio of
the number of quarts of
blueberries to the number
of quarts of strawberries is
always equivalent to 𝟏: 𝟑.
Lesson 10
Classwork
Exploratory Challenge Exercise 1: 33 minutes
Lesson 10
Classwork
Exploratory Challenge Exercise 1: 33 minutes
Lesson 10
Classwork
Lesson 10
Exploratory Challenge Exercise 1: 33 minutes
We could extend
our table until
we get to 𝟕 in
the blueberry
column.
Classwork
Exploratory Challenge Exercise 1: 33 minutes
We could start with the ratio 𝟏:
𝟑 that was given in the
description and then multiply by
ten to get 𝟏𝟎 and 𝟑𝟎. These
would be the first values in my
table. Then, I would count up by
tens in the blueberries column
and count up by 𝟑𝟎s in the
strawberries column.
Lesson 10
One person from each group will fill in
these charts based on the group’s data
using a dry erase marker.
The number of quarts of
strawberries is always three
times the number of quarts
of blueberries or the
number of quarts of
blueberries is one-third the
number of quarts of
strawberries.
Lesson 10
Lesson 10
Lesson 10
Lesson 10
Closing
I can identify both
the additive and
multiplicative
structure of a ratio
table and use the
structure to make
additional entries in
the table.
I’m thinking
about ratios…
not about my
lack of clothing.
• In a vertically oriented ratio table,
how are the values across the
rows related?
• The values across the rows form a
ratio of 𝑎: 𝑏. So, the value of the
second column will be
determined by multiplying the
𝑏
value in the first column by ,
𝑎
and the value of the first column
will be determined by multiplying
the value in the second column
𝑎
by .
𝑏
Lesson 10
Closing
I can identify both
the additive and
multiplicative
structure of a ratio
table and use the
structure to make
additional entries in
the table. Wait,
there’s
more?
• In a vertically oriented ratio table, how
are the values related as we move
down a column?
• The values in the column depend on
how the table was created, but they
could be increasing by the same sum
or by the same multiple. For example,
the values in the first column could be
increasing by 5 each time. So, the
values could go from 6, 11, 16, 21, 26,
etc. or the numbers could be formed
by multiplying. In other words, the
values could go from 6, 12, 24, 48, etc.
if the values were multiplied by 2 each
time.
Lesson 10
Closing
I can identify both
the additive and
multiplicative
structure of a ratio
Being the
table and use the
thinkerstructure to make
isn’t easy.
additional entries in
the table.
• Is there a way to use addition to
figure out the next row in a ratio
table?
• I can use the ratio to help me use
addition to get the next row. For
example, if the ratio of 𝑥: 𝑦 is 2: 5, I
can add 2 to the value in the first
column and add 5 to the value in
the second column to get the next
row in the table. I cannot just add
the same thing to both the values
in the first and second columns.
Lesson 10
Closing
I can identify both
the additive and
multiplicative
structure of a ratio
table and use the
structure to make
I’m not
additional entries in
having any
the table.
trouble...
• Is there a way to use multiplication to
figure out the next row in a ratio
table?
• If I use multiplication to get the next
row in the table, I need to multiply
both the values in the first column and
the values in the second column by
the same number. So, if the original
row is (4, 5) and I want to multiply by
3 to get the next row, I would multiply
4 × 3 and 5 × 3 to get a row that is (12,
15). Unlike the addition method, I
would do the same thing to both the
values in the first column and the
values in the second column.
Lesson 10
Exit Ticket
Lesson 1
Problem Set
Problem Set
Problem Set
Problem Set