**Unit 2: Ratio and Proportional Reasoning**
*Imagine you are building a new tree house. The blueprint has the
design, but on a much smaller scale. You will be able to use
proportional reasoning to help solve problems like this one and change
the small design to life-size dimensions.*

*In this unit, proportional reasoning is the focus. You will begin by
taking a look at ratios and rates and how they help us to build
proportions. You will analyze proportional relationships including scale
drawing and similar figures. Once you have built the foundational
skills, you will model life situations using proportions and graphs.
This will help you build a definition of slope and begin to distinguish
proportional relationships from other relationships. *

**Unit 2 Time Advisory**

Completing this unit should take approximately 12 hours and 30
minutes.

☐ Subunit 2.1: 3 hours and 15 minutes

☐ Subunit 2.2: 5 hours and 30 minutes

☐ Subunit 2.3: 45 minutes

☐ Subunit 2.4: 3 hours

**Unit2 Learning Outcomes**

Upon successful completion of this course, you will be able to:
- Solve problems involving ratios and rates.

- Calculate the missing side of a proportion and determine whether two
ratios create a proportion.

- Use proportional reasoning to model and solve real-world problems.

- Analyze shapes to determine if they are similar and calculate the
missing side.

- Extend the use of proportions to analyze scale drawings.

Standards Addressed (*Common Core*):
- CCSS.Math.Content.7.RP.A.1
- CCSS.Math.Content.7.RP.A.2
- CCSS.Math.Content.7.G.A.1

**2.1 Ratios and Rates**
*We make comparisons every day. You might hear someone mention the
number of boys to girls, apples to oranges, or even missed basketball
shots to total shots taken. Sometimes we make more complex comparisons
with two different units like miles per hour or pages per minute. Theses
comparisons are ratios and rates and will be the focus of the first
section of Unit 2.*

**2.1.1 Ratios**
**2.1.1.1 What Is a Ratio?**
- **Explanation: CK-12: “Ratios”**
Link:
CK-12: “Ratios”
(PDF)

Instructions: Watch the first video for an introduction to the idea
of ratios. Then complete the reading and practice questions. You do
not need to watch the second video.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.1](http://www.corestandards.org/Math/Content/7/RP/A/1)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Ratios/lesson/Ratios/).
```

**2.1.1.2 Three Ways to Write a Ratio**
- **Explanation: CK-12: “Equivalent Ratios”**
Link: CK-12: “Equivalent
Ratios”
(PDF)

Instructions: Read through the passage on Casey’s errand. Take note
of the three different ways ratios can be written. Then try the
practice problems at the end. Be sure to write your answers three
times using each of the different forms. You do not need to watch
the videos.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.1](http://www.corestandards.org/Math/Content/7/RP/A/1)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Equivalent-Ratios/lesson/Equivalent-Ratios/).
```

**2.1.1.3 Reducing a Ratio**
- **Explanation: CK-12: “Ratios in Simplest Form”**
Link: CK-12: “Ratios in Simplest
Form”
(PDF)

Instructions: Read through the passage to see why simplifying
ratios is important. Then watch the review video to see the steps
for reviewing more difficult examples. Finally, solve the 17
practice questions at the bottom of the page.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.1](http://www.corestandards.org/Math/Content/7/RP/A/1)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Ratios-in-Simplest-Form/lesson/Ratios-in-Simplest-Form/).
```

**2.1.2 Rates**
**2.1.2.1 What Is a Rate?**
- **Explanation: CK-12: “Identification and Writing of Equivalent
Rates”**
Link: CK-12: “Identification and Writing of Equivalent
Rates”
(PDF)

Instructions: Read through the passage to see how rates are
different than ratios. Then watch the review videos to see solved
examples. After you watch the videos, try the 15 practice questions
that follow.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.1](http://www.corestandards.org/Math/Content/7/RP/A/1)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Identification-and-Writing-of-Equivalent-Rates/lesson/Identification-and-Writing-of-Equivalent-Rates/).
```

**2.1.2.2 Unit Rates**
- **Explanation: Khan Academy’s “Finding Unit Rates”**
Link: Khan Academy’s “Finding Unit
Rates”
(YouTube)

Instructions: Watch the video for examples of unit rate questions.
Take note of the key words that let you know the question is asking
for a unit rate. Then try rate problems 0.5, 1, and 2, which can be
found in the left-hand menu.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.1](http://www.corestandards.org/Math/Content/7/RP/A/1)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Khan Academy.
```

**2.1.2.3 Better Buy**
- **Explanation: CK-12: “Comparison of Unit Rates”**
Link: CK-12: “Comparison of Unit
Rates”
(PDF)

```
Instructions: Read through the passage on comparing unit rates to
see how they can tell us which product is a better purchase. Then
solve the 15 practice problems at the bottom of the page.
Completing this activity should take approximately 30 minutes.
Standards Addressed (*Common Core*):
- [CCSS.Math.Content.7.RP.A.1](http://www.corestandards.org/Math/Content/7/RP/A/1)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Comparison-of-Unit-Rates/lesson/Comparison-of-Unit-Rates-Grade-7/).
```

**2.2 Proportions**
*When two ratios or rates are equal to each other we have a proportion.
Proportions become very useful when trying to make predictions or
conversions. You might be designing a model for a new product or a
blueprint for the next building in the city. Both of these require
creating a smaller image of a real-life product. Then a proportion can
be used to make conversions from the models to the real-life object.*

**2.2.1 How to Write a Proportion**
- **Explanation: CK-12: “Proportions”**
Link:
CK-12: “Proportions”
(PDF)

Instructions: Read through the passage, which discusses how
proportions are formed and how to tell if two ratios form a
proportion. Then complete the 15 practice questions. You do not need
to watch the video. Note that this resource covers the material you
need to know for Subunit 2.2.1 and Subunit 2.2.2.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Proportions/lesson/Proportions-Grade-7/).
```

**2.2.2 Is it a Proportion?**
*Note: This subunit is covered by the resource assigned beneath Subunit
2.2.1. Focus specifically on how to determine if two ratios will form a
proportion. Practice questions 1 through 8 in Subunit 2.2.1 will give
you a chance to work on this skill.*

**2.2.2.1 Cross Multiplication**
- **Explanation: YouTube: Shaunteaches: “Cross Multiplication”**
Link: YouTube: Shaunteaches: “Cross
Multiplication” (YouTube)

Instructions: Watch the video. Take note of the introduction to why
cross multiplication works and how to use it to solve for missing
variables in proportional relationships. When you reach the
four-minute mark, there are problems that include variables. Please
stop to video and solve each proportion before watching the
solution.

Completing this activity should take approximately 15 minutes.

Standards Addressed (Common Core):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0 United States
License](http://creativecommons.org/licenses/by/3.0/us/). This video
is attributed to YouTube and Shaunteaches. The original version can
be found [here](http://www.youtube.com/watch?v=sYL5mKQmIDI).
```

**Did I Get This? Activity: Vimeo: Will Kimbley’s “Using Cross Multiplication”**Link: Vimeo: Will Kimbley’s “Using Cross Multiplication” (YouTube)

Instructions: You will be able to see five practice questions on the screen before hitting the play button. Solve questions 2, 4, and 7 in your notebook using cross multiplication. Then press the play button to view the solutions. (Note that you may solve questions 3 and 6 as well, but the solutions are not shown in the video.)

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Will Kimberly. The original version can be found here.

**2.2.2.2 Scale Factors**
- **Explanation: CK-12: “Proportions to find Scale Ratios”**
Link: CK-12: “Proportions to Find Scale
Ratios”
(PDF)

Instructions: Begin by scrolling down and watching the “Video
Review” to be introduced to the idea of a scale factor and how to
find the scale factor. Be sure to know how scale factors between 0
and 1 will change the size of a similar shape. Then solve the
practice questions below the video.

Completing this activity should take approximately 30
minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Proportions-to-Find-Scale-Ratios/lesson/Proportions-to-Find-Scale-Ratios/).
```

**Explanation: Khan Academy’s “Understanding Proportions”**Link: Khan Academy’s “Understanding Proportions” (YouTube)

Instructions: Watch the video for a discussion of how reducing can help you check whether two ratios will form a proportion.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use:This video is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to the Khan Academy.

**2.2.3 Solving Proportions for Missing Value**
- **Did I Get This? Activity: XP Math: “Solving Proportions”**
Link: XP Math: “Solving
Proportions” (Flash)

Instructions: This timed game will help you learn to solve
proportions. You will be given 1 minute to solve as many proportions
as possible. Play the game five times, each time try to increase the
number that you are able to answer correctly on the first try. If
you are getting the questions correct on the first try, you can
change to a higher level for the next round of the game.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-NoDerivs 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-nd/3.0/).
```

**2.2.3.1 Solving Using Cross-Multiplication**
- **Explanation: CK-12: “Proportions Using Cross Products”**
Link: CK-12: “Proportions Using Cross
Products”
(PDF)

Instructions: Read the “Guidance” and “Guided Practice” sections
that explain how you can multiply the number diagonally to solve for
missing values in a proportion. Next watch the “Video Review” to see
the steps in action. Finally, solve the 16 practice questions that
are below the video.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Proportions-Using-Cross-Products/lesson/Proportions-Using-Cross-Products-Grade-7/).
```

**2.2.3.2 Solving Using Scale Factors**
- **Explanation: YouTube: Wikispaces: EOC Pre-Algebra: “Using Scale
Factor to Solve Ratio Problems”**
Link: YouTube: Wikispaces: EOC Pre-Algebra: “Using Scale Factor to
Solve Ration Problems” (YouTube)

Instructions: Watch the video to see what a scale factor is and how
it is used with proportions.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-sa/3.0/). This video
is attributed to Wikispaces: EOC Pre-Algebra. The original version
can be found
[here](http://eocprealgebra.wikispaces.com/Using+Scale+Factor+to+Solve+Ratio+Problems+%282%29).
```

**2.2.4 Writing Proportions from Word Problems**
- **Explanation: Khan Academy’s “Writing Proportions”**
Link: Khan Academy’s “Writing
Proportions”
(YouTube)

Instructions: Watch the first two examples in the video. While
watching, take note of how the labels can be used to help write a
proportion. When the time reaches 4:15, pause the video and write
two different proportions to represent example number 3. Then
complete the video to see if your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use:This video is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 United States
License](http://creativecommons.org/licenses/by-nc-sa/3.0/us/deed.en_CA).
It is attributed to the Khan Academy.
```

**Activity: Beginning and Intermediate Algebra: Tyler Wallace’s “Rational Expressions - Proportions”**Link: Beginning and Intermediate Algebra: Tyler Wallace’s “Rational Expressions - Proportions” (PDF)

Instructions: Solve word problems #31 - 40 on page 5 and page 6 using proportions. The answers can be found on page 7.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):Terms of Use: This work is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace. The original version can be found here.

**2.2.5 Representing Proportional Relationships**
- **Explanation: CK-12: “Problem Solving Plan, Proportions”**
Link: CK-12: “Problem Solving Plan,
Proportions”
(PDF)

Instructions: Read the entire passage to see how you can find clues
in the word problem to set up your proportion for solving. Then view
the “Video Review.” Finally, try the 15 practice problems that
follow the video, using proportions.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.2](http://www.corestandards.org/Math/Content/7/RP/A/2)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Problem-Solving-Plan-Proportions/lesson/Problem-Solving-Plan-Proportions-Grade-7/).
```

**Activity: Gwinnett County Public Schools: “Ratios and Proportions”**Link: Gwinnett County Public Schools: “Ratios and Proportions” (HTML)

Instructions: Read the “Engage” section to learn about graphing proportional relationships. Then, before scrolling down to the “Explain” section, make a table that would represent the time in hours and the amount of money earned if you were told someone makes $9 an hour. Next, return to the “Explain” section and compare your table with the table provided. Finally, create a graph of the values to form a straight line.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.3 Similar Figures**
- **Explanation: CK-12: “Scale Factor of Similar Polygons”**
Link: CK-12: “Scale Factor of Similar
Polygons”
(PDF)

Instructions: Read through the “Guidance” and “Guided Practice”
sections to see how ratios and proportions can be used with
geometric shapes. As you are reading, take note of how the angles in
the similar figures are related and how the sides of similar figures
are related. Finally, solve practice problems 1 - 4 only at the
bottom of the page.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.G.A.1](http://www.corestandards.org/Math/Content/7/G/A/1)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/geometry/Scale-Factor-of-Similar-Polygons/lesson/Scale-Factor-of-Similar-Polygons/).
```

**Activity: GeoGebra: “Similar Polygons”**Link: GeoGebra: “Similar Polygons” (HTML)

Instructions: Read through the interactive worksheet. Then use your mouse with the points of the shapes to see how the similar figures change. Pay special attention to how the angles change and how the lengths change.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use:This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**Activity: orgLib: “Preview Questions for Test: 7.G.1 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.G.1 - Worksheet” (HTML)

Instructions: Scroll down to the six questions and click on “Consume” beneath them. You should be brought to a screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all six questions done, click on “Submit Test.” At this point, you will be brought to a screen that will show you whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**2.4 Scale Drawings**
- **Explanation: CK-12: “Proportions to Find Dimensions”**
Link: CK-12: “Proportions to Find
Dimensions”
(PDF)

Instructions: Read the information in the “Guidance” and “Guided
Practice” sections, and take note of how proportions can relate
scale drawings to actual objects. You do not need to watch the
video. Then complete the 15 practice problems at the bottom of the
webpage.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.G.A.1](http://www.corestandards.org/Math/Content/7/G/A/1)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/arithmetic/Proportions-to-Find-Dimensions/lesson/Proportions-to-Find-Dimensions/).
```

**Did I Get This? Activity: Gwinnett County Public Schools “Geometry: Introduction to Scale Drawings”**Link: Gwinnett County Public Schools “Geometry: Introduction to Scale Drawings” (HTML)

Instructions: Scroll down under the images of the flags to where it says “Scale Drawings and Geometric Figures.” Located here are four practice problems. Solve each of the practice problems provided. If the “Check My Answer” feature is not working and you are unable to input any numbers, please write your answers on paper.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.4.1 Maps**
- **Checkpoint: Wikispaces: romanpercentage: “Land Expansion with
Proportions”**
Link: Wikispaces: romanpercentage: “Land Expansion with
Proportions”
(PDF)

Instructions: Use proportions to solve the four problems posed on
Romans using a map to help them travel. You can ignore the
directions above the questions.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.G.A.1](http://www.corestandards.org/Math/Content/7/G/A/1)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-sa/3.0/). It is
attributed to Wikispaces: romanpercentage. The original version can
be found
[here](http://romanpercentage.wikispaces.com/2+Land+Expansion+with+Proportion).
```

**2.4.2 Blueprints**
- **Activity: Commonwealth of Australia: “Building Scales”**
Link: Commonwealth of Australia: “Building
Scales”
(HTML)

Instructions: Read from the “Introduction” section to the “Working
with a Scale” section to see how ratios are used to relate
blueprints to the actual building. Then solve the three “Determining
Length” questions. Hit the submit button for each problem to see if
your answers are correct.

```
Note to Educators: The lesson entitled [“Developing a Sense of
Scale”](http://map.mathshell.org/materials/download.php?fileid=1306) includes
challenging tasks to use in your classroom that are already aligned
to the Common Core State Standards for mathematics. In addition,
examples of student work are included, for example [“Proportion and
Non-Proportion
Situations”](http://www.svmimac.org/images/SVMIPD.091312.ProportionNonPropotion.pdf).
Note to Students and
Educators: [orgLib](http://www.orglib.com/7.RP-Ratios-Proportional-Relationships-displayFolderContents_0d1520c2bb_A1CD0C5C74C44858A6FF25CD48CD9945.html) offers
some wonderful practice questions related to
CCSS.Math.Content.7.RP.1 and 7.RP.2.
Completing this activity should take approximately 15 minutes.
Standards Addressed (*Common Core*):
- [CCSS.Math.Content.7.G.A.1](http://www.corestandards.org/Math/Content/7/G/A/1)
Terms of Use: This work is licensed under a [Creative Commons
Attribution-ShareAlike 3.0 Australia
License](http://creativecommons.org/licenses/by-sa/3.0/au/deed.en_GB).
```

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.RP.1 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.RP.1 - Worksheet” (HTML)

Instructions: Scroll down to the six questions and click on “Consume” beneath them. You should be brought to a screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all six questions done, you will click on “Submit Test.” At this point you will be brought to a screen that will show you whether your answers are correct.

Completing this activity should take approximately 15 minutes

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.RP.2 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.RP.2 - Worksheet” (HTML)

Instructions: Scroll down to the six questions and click on “Consume” beneath them. You should be brought to a screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all six questions done, you will click on “Submit Test.” At this point you will be brought to a screen that will show you whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**Checkpoint: EngageNY: “Ratios and Proportional Relationships”**Link: EngageNY: “Ratios and Proportional Relationships” (PDF)

Instructions: Complete the Mid-Module Assessment on page 93 and the End-of-Module Assessment on page 207. Each assessment is followed by a rubric and an answer key. Be sure to check your work using the answer keys with sample students’ solutions.

Completing this checkpoint and checking your work should take approximately 1 hour, 30 minutes.

Standards Addressed (*Common Core*):Terms of Use: This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to EngageNY. The original file can be found here.