Vocabulary Teacher Resourcesswunvideos.s3.amazonaws.com/ccss_lessons/G6 U6 L1 TE.pdf · 2019-06-11 · numbers or quantities whose units of measure are related 1. Part-to-Part Ratio:

Copyright © Swun Math Grade 6 Unit 6 Lesson 1 C TE

MPs Applied MP

* Embedded MP

Conceptual Lesson Grade 6 · Unit 6 · Lesson 1 MC: 6.RP.1

Today I will compare quantities using ratios and express the relationship in a sentence.

Vocabulary Teacher Resources

Ratio: a comparison of two non–zero numbers or quantities whose units of measure are related

1. Part-to-Part Ratio: For every 3 hearts there are 4 stars

a to b a:b a/b

3 to 4 3:4 3/4

2. Part-to-Whole Ratio: 3 out of 10 shapes are stars

a out of b a:b a/b

3 out of 10 3:10 3/10

Three Types of ratios:

• Part-to-Part • Part-to-Whole (sometimes

expressed as Whole-to-Part) • Part-to-One (Unit Rate)

Considerations: This is the first time the students are exposed to ratios. The language used to describe ratios must be precise and accurate.

1. Part-to-part ratios use the language, “for every.” For example:

• “For every___ there are ___.” • “There are ___ for every ___.”

2. Part-to-whole ratios use the language, “out of” or “of the.” For example:

• “___ out of ___ are ___.” • “___ of the ___ are ___.”

3. Sometimes part-to-whole ratios are stated with the whole first. In this case, the wording would be reversed. For example:

• “Out of every ___, ___ are ___.” • “Of the ___, ___ are ___”

Also, the order of the words is important. For example, when describing the relationship between the number of hearts and arrows, the number of hearts must come first because it is listed first.

Steps: 1. Read the problem. 2. Identify the compared quantities. 3. Determine whether the ratio is part-to-part or part-to-

whole. 4. Write the ratio.

Application of MPs: MP1: How can you determine if your answer is correct? I know my answer is correct because

________________ . MP2: What is the difference between a part-to-part

ratio and a part-to-whole ratio? A part-to-part ratio compares ___________ and a part

-to-whole ratios compares a __________ .

1 2 3 4 5 6 7 8

*

*

Student Journal Pages

1-4


Answer Key:

I/M SGP FCU HW

1. 5 to 7, 5:7, 5/7

Five of the seven shapes are cubes.

Five out of seven shapes are cubes.

1. 2 triangles to 6 polygons, 2:6 (or 1:3), and 2/6 (or 1/3); part-to-whole

1. 3 to 5; 3/5 part-to-part

1. 31.92

2. 3 to 6, 3:6, 3/6

For every 1 sun, there are 2 stars.

There is 1 sun for every 2 stars. See I/M #2

2. 3 trapezoids to 12 squares, 3:12 (or 1:4), and 3/12 (or 1/4); part-to-part

2. 2 to 8 (or 1:4); 2/8 or 1/4

part-to-whole

2. 77.289

3. 55.18

4. 13.93

5. Three of the eight fruits are bananas. Three out of eight fruits are bananas. 3 to 8, 3:8, 3/8

part-to-whole

6. For every 3 drinks, there is 1 bucket of popcorn.

There are 3 drinks for every 1 bucket of popcorn.

3 to 1, 3:1, 3/1 part-to-part

Sample Response to MP questions:

MP1: How can you determine if your answer is correct? I know my answer is correct because when I read my ratio out loud, it matches the ratio

given in the problem . MP2: What is the difference between a part-to-part ratio and a part-to-whole ratio? A part-to-part ratio compares the number of individual items with another number of

individual items and a part-to-whole ratios compare a the number of parts with a whole.


1. Compare the number of cubes to the total number of shapes.

• Using the fraction notation may cause some confusion since a ratio is not always a part-to-whole relationship. A ratio can show a part-to-part or a part-to-whole relationship, while a fraction shows only a part-to-whole relationship.

• Provide these illustrations on the board. • In previous grades, we used <, > or =, ≠ to compare numbers or quantities. Today I

will compare two quantities in a new way called a ratio. As stated in the vocabulary, there are three kinds of ratios 1) Part-to-Part Ratio 2) Part-to-Whole Ratio 3) Part-to-One (This will be discussed in lesson 3 because rate is a special type of ratio)

• The problem asks me to compare the number of cubes to the total number of shapes. So, this is a part-to-whole ratio.

• First, I need to count how many cubes and circles there are in this group. I see I have five cubes and two circles. I am going to use a ratio to compare or describe the relationship of the number of cubes to the number of shapes.

• Since the question tells me to compare “the number cubes of to the total number of shapes,” I have to write the number that represents cubes first, and then the total number of shapes. 5 to 7

• The comparison or ratio of 5 cubes to the total number of shapes can be expressed in three ways:

5 to 7 5:7 or 5/7

(continued on the next page)

*MP1: Make sense of the problem and persevere in solving it!

*MP8: Find a strategy to help solve the problem.

Directions: Identify the compared quantities. Find the ratio. Identify whether the ratio is part-to-part or part-to-whole.



1. (continued)

• The last notation should remind you of a fraction. However, it is different in that a fraction can only express a part-to-whole relationship while a ratio expresses three different kinds of relationships.

• I can express this ratio by stating:

“Five of the seven shapes are cubes.” “Five out of seven shapes are cubes.”

• Ensure that students express part-to-whole ratios using sentence frames:

“ of the are .” “ out of are .”

Whole-to-Part

• This ratio can also be expressed whole-to-part.

“Out of every seven shapes, five are cubes.” “Of the seven shapes, five are cubes.”

• Allow students the opportunity to express whole-to-part relationships using

sentence frames:

“Out of every , are .” “Of the , are ”


Directions: Identify the compared quantities. Find the ratio. Identify whether the ratio is part-to-part or part-to-whole

2. Identify the ratio of suns to stars.

• Provide these illustrations on the board.

• The problem asks me to find the ratio of suns to stars. This is a part-to-part ratio. • First I need to count how many suns and stars there are in this group. I see there

are three suns and six stars. • Since the ratio states “suns to stars,” I have to write the number that represents

suns first. 3 to 6 • The ratio can be written in three ways:

3 to 6 3:6 3/6 • As a fraction, 3/6 is not in its simplest form. I know 3/6 = 1/2. • Since a ratio is a comparison of two quantities by division, I wonder if I can

regroup the given shapes into equal groups. • Model how the shapes can be regrouped.



2. (continued)

• The shapes were rearranged into groups with one sun and two stars which allowed me to find the equivalent ratio 1/2 to the original ratio of 3:6.

• I can express this ratio by stating: For every one sun, there are two stars. • Ensure that students express part-to-part ratios using sentence frames:

“For every , there are .” “There are for every .”

• This problem demonstrates that a ratio describes a pattern. For every 1 sun, there are 2 stars. There is 1 sun for every 2 stars.

• I can repeat the pattern, “For every 2 suns, there are 4 stars”. • If I repeat the pattern three times, “For every 3 suns, there are 6 stars.”

• The ratio describes how the pattern is repeating.


/


1. Compare the number of triangles to the total number of polygons in the

group.

of the are .

out of are .

Identify the three ways to write the ratio:

: /

2. Stephanie drew 3 trapezoids for every 12 squares.

For every , there are . There are for every .


: /



1. Mark uses 3 circles for every 5 squares.

Recap today’s lesson with one or more of the following questions: MP1: How can you determine if your answer is correct?

MP2: What is the difference between a part-to-part and a part-to-whole ratio?

2. Identify the ratio of pentagons to polygons.

:

/

:

/


Name: ____________________________ Date: ______________________________

Directions: Solve.

1. 21.3 + 4.6 + 6.02 =

2. 27.2 + 6.07 + 44.019 =

3. 68.1 — 9.3 — 3.62 =

4. 27.04 — 5.7 — 7.41 =



5. Compare the number of bananas to the total number of fruits in the

group.

of the are .

out of are .


: / Is the ratio part-to-part or part-to-whole?

6. The movie goers ordered 3 drinks for every bucket of popcorn.

For every , there are . There are for every .


: / Is the ratio part-to-part or part-to-whole?

Documents

Vocabulary Teacher Resourcesswunvideos.s3.amazonaws.com/ccss_lessons/G6 U6 L1 TE.pdf · 2019-06-11 · numbers or quantities whose units of measure are related 1. Part-to-Part Ratio: