**Unit 2: Expressions and Equations**
*Suppose your parents recently told you they would help you purchase
your first cell phone. Your job is to figure out which company to use.
Call for Less Phone Company offers a low cost up front, but they charge
you per text message. Text for Less Phone Company is costly to enroll,
but they offer free text messaging. Which company is better for you? You
might compare two different cell phone companies using a system of
equations. In this unit, you will learn about proportional
relationships. You can express proportional relationships in tables,
graphs, and equations. Throughout the unit, you will focus on finding
slope, finding y-intercept, finding patterns, and comparing graphs to
equations. *

**Unit 2 Time Advisory**

Completing this unit should take approximately 11 hours.

☐ Subunit 2.1: 3 hours and 15 minutes

☐ Subunit 2.2: 1 hour

☐ Subunit 2.3: 3 hours

☐ Subunit 2.4: 3 hours and 45 minutes

**Unit2 Learning Outcomes**

Upon successful completion of this unit, you will be able to:
- Graph proportional relationships.
- Interpret the slope of a graph.
- Compare different proportional relationships that are represented in
different forms.
- Explain how graphs and equations use slope and y-intercept to
compare proportional relationships.
- Use similar triangles to explain slope on a coordinate plane.
- Solve linear equations involving expanding expressions using the
distributive property.
- Solve linear equations involving combining like terms.
- Solve linear equations with rational number coefficients.
- Interpret the solution of two linear equations using a coordinate
graph.
- Solve simultaneous linear equations algebraically.
- Estimate simultaneous linear equation solutions.
- Recognize and solve real-world examples of two linear equations in
two variables.

Standards Addressed (*Common Core*):
- CCSS.Math.Content.8.EE.B.5
- CCSS.Math.Content.8.EE.B.6
- CCSS.Math.Content.8.EE.C.7
- CCSS.Math.Content.8.EE.C.8
- CCSS.ELA-Literacy.WHST.6-8.2

**2.1 Proportional Relationships**
*A proportional relationship is when two quantities vary directly with
each other. This means that when one quantity is doubled, the other
quantity is doubled. Proportional relationships can be written as
equations, tables, or graphs. In this subunit you will use proportional
relationships to compare different situations, and you will graph
proportional relationships and interpret the unit rates.*

**2.1.1 Slope**
- **Explanation: Monterey Institute for Technology and Education:
HippoCampus: “Graphing Linear Equations”**
Link: Monterey Institute for Technology and Education: HippoCampus:
“Graphing Linear
Equations” (Flash)

Instructions: On the left side of the screen, select *Developmental
Math – Beginning Algebra*, which you will find under the
“Presentations” heading. On the pop out menu, scroll down to the
“Graphing” heading, select *Graphing Linear Equations*, and play the
video. While you watch, copy the example, including the information,
table, and graph. Understand what *linear relationship *and *linear
equation *mean. You should understand how to find information by
using the table, graph, and equation.

Watching the video and taking notes should take approximately 15
minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.8.EE.B.5](http://www.corestandards.org/Math/Content/8/EE/B/5)
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/).
```

**Explanation: Monterey Institute for Technology and Education: HippoCampus: “Finding the Slope of a Line”**Link: Monterey Institute for Technology and Education: HippoCampus: “Finding the Slope of a Line” (Flash)

Instructions: On the left side of the screen, select*Developmental Math – Beginning Algebra*under the “Presentations” heading. On the pop out menu, scroll down to the “Graphing” heading and select*Finding the Slope of a Line*. While you watch the video, make sure you are taking notes and writing down examples. Focus on the following questions while you watch the video:- What is slope?
- How do I find slope?
- How does the slope change as the steepness of the line changes?
- What is the formula for slope?
- What is the slope for horizontal and vertical lines?
- What is the difference between a positive slope and a negative slope?

Stop the video while you watch if you need extra time to take notes.

Watching the video and taking notes should take approximately 15 minutes.

Standards Addressed (*Common Core*): - CCSS.Math.Content.8.EE.B.5

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**Did I Get This? Activity: Illustrative Mathematics: “Peaches and Plums”**Link: Illustrative Mathematics: “Peaches and Plums” (PDF)

Instructions: Solve questions a-b on page 1. Read the commentary and check your solution on page 2.

Completing this activity and checking your solution 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: Illustrative Mathematics: “Coffee by the Pound”**Link: Illustrative Mathematics: “Coffee by the Pound” (PDF)

Instructions: Solve questions a–d on page 1. Read the commentary and check your solution on page 2. Understand the two different ways you could have graphed the situation as explained in the solution for parts c and d.

Completing this activity and checking your solution 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.

**2.1.2 Comparing Graphs and Equations**
- **Explanation: Monterey Institute for Technology and Education:
HippoCampus: “Writing the Equation of a Line”**
Link: Monterey Institute for Technology and Education: HippoCampus:
“Writing the Equation of a
Line” (Flash)

Instructions: On the left side of the screen, under the
“Presentations” heading, select *Developmental Math – Beginning
Algebra*. On the pop out menu, scroll down to the “Graphing” heading
and select *Writing the Equation of a Line*. While you watch the
video, make sure you are taking notes and writing down examples. The
video will show and explain the formula *y = mx + b*. You will use
the information from the previous subunit to help you find *m*. Make
sure you understand how to find the y-intercept and slope, and how
to write a linear equation. Stop the video while you watch if you
need extra time to take notes.

Watching the video and taking notes should take approximately 15
minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.8.EE.B.5](http://www.corestandards.org/Math/Content/8/EE/B/5)
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/).
```

**Explanation: CK-12: “Writing Equations Given a Slope and a Point”**Link: CK-12: “Writing Equations Given a Slope and a Point” (HTML and YouTube)

Instructions: This lesson will build on the concepts from the previous video regarding how to write an equation. Read the introduction and take notes. Complete examples A, B, and C and understand the solutions. Complete the “Guided Practice” and understand the solution. Watch the video in the “Practice” section. In the video the instructor shows a problem before solving it. You should pause the video each time you see a new problem, answer the problem on your own, and then watch the video to check your solution.

Reading this lesson, taking notes, completing practice problems, and checking solutions should take approximately 45 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.**Did I Get This? Activity: Howard County Public School System’s**Link: Howard County Public School System’s*Grade 8 Common Core Mathematics*: “Drops in a Bucket Math Task”*Grade 8 Common Core Mathematics*: “Drops in a Bucket Math Task” (PDF)

Instructions: Read the situation about the rain in the bucket. Solve the problem using at least two strategies. Your strategies may include graphing, making a table, finding the slope, using an equation, writing a proportion, and working backwards. Check your answer here. Answers are on pages 2-5.

Completing this task and checking your solutions should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

**2.1.3 Comparing Different Proportional Relationships**
- **Did I Get This? Activity: Illustrative Mathematics: “Proportional
Relationships, Lines, and Linear Equations”**
Link: Illustrative Mathematics: “Proportional Relationships, Lines,
and Linear
Equations” (PDF)

Instructions: Use the graph to solve the question on page 1. Make
sure to explain your response. Read the commentary and check your
answer on page 2.

Completing this task and checking your solution should take
approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.8.EE.B.5](http://www.corestandards.org/Math/Content/8/EE/B/5)
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/).
```

**Did I Get This? Activity: Illustrative Mathematics: “Who Has the Best Job?”**Link: Illustrative Mathematics: “Who Has the Best Job?” (PDF)

Instructions: The table explains Kell’s situation, and the statement explains Mariko’s job situation. Using each of these, answer questions a-d on page 1. Read the commentary and check your answers on page 2.

Completing this activity and checking your solutions 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: Illustrative Mathematics: “Comparing Speeds in Graphs and Equations”**Link: Illustrative Mathematics: “Comparing Speeds in Graphs and Equations” (PDF)

Instructions: Use the graph to solve the question on page 1. Make sure to explain your response. Read the commentary and check your answer on page 2.

Completing this task and checking your solutions 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.

**2.2 Using Triangles on the Coordinate Plane**
*You learned in the previous subunit how to find slope using any two
points on a line. In this subunit you will use similar right triangles
to explain why slope is the same between any two points on a
non-vertical line in the coordinate plane.* Similar triangles *have the
same shape, but can be different sizes. Triangles can be similar even if
one is rotated or one is a mirror image of the other. Similar triangles
will have the same angles, and their side lengths will be proportional.*
Congruent *means the same shape and same size, so congruent triangles
will have the same angles and same side lengths. You may encounter these
vocabulary words throughout this subunit.*

**Activity: Howard County Public School System’s**Link: Howard County Public School System’s*Grade 8 Common Core Mathematics*: “Similar Triangles and Slope”*Grade 8 Common Core Mathematics*: “Similar Triangles and Slope” (PDF)

Instructions: Start on page 3 looking at the downhill skier. Answer the three questions beneath the picture to help develop ideas for what slope really means and how you can think of it in your own life. Answer questions 1-8 on page 4. You might need to zoom in on the graph to see the grid lines. Skip page 5, for now. On page 6, complete questions 1-7. On page 7, complete questions 1-3.

Challenge (optional) – complete the slide and ski slope activity on page 5. The activity gives you a lot of numbers. Sketch a picture and label the information. Answer the questions on page 5 as well. Finally, write one equation each for the slide and the ski slope. Completing the challenge should take approximately 15 minutes.

Check all answers on pages 8-10.

Completing this activity and checking your solutions should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.**Did I Get This? Activity: Illustrative Mathematics: “Slopes Between Points on a Line”**Link: Illustrative Mathematics: “Slopes Between Points on a Line” (PDF)

Instructions: This resource gives you the opportunity to use similar triangles to explain the relationship of the triangles to the slope on a line. Read through the information on page 1 and answer questions a-b. Read the commentary and check your solutions on pages 2-4.

Completing this task and checking your solutions should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**2.3 Solving Linear Equations**
*In sixth and seventh grade, you worked with solving expressions and
inequalities. This subunit will review some of the same skills you
worked on in the past. The subunit will continue to use rational numbers
and integers while you learn about the distributive property and
collecting like terms.*

**Explanation: Monterey Institute for Technology and Education: HippoCampus: “Solving One-Step Equations Using Properties of Equality”**Link: Monterey Institute for Technology and Education: HippoCampus: “Solving One-Step Equations Using Properties of Equality” (Flash)

Instructions: On the left side of the screen, select*Developmental Math – Beginning Algebra*from beneath the “Presentations” heading. On the pop out menu, scroll down to the “Solving Equations and Inequalities” heading and select*Solving One-Step Equations Using Properties of Equality*. While you watch the video, take notes and write down examples. Focus on the vocabulary words at the beginning of the video. Although the words might be review, copy the definitions in your notebook for reference. Stop the video while you watch if you need extra time to take notes. Make sure to copy the notes about how to solve equations found in the last 0:35 of the video.

Watching the video and taking notes 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: HS Tutorials: “One Step Equation Practice”**Link: HS Tutorials: “One Step Equation Practice” (HTML)

Instructions: This interactive activity will help you practice the steps to solve simple linear equations. There is a hint button to use if necessary. Practice for at least 10 minutes.

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.

**2.3.1 Distributive Property and Collecting Like Terms**
- **Explanation: James Sousa’s Mathispower4u: “Combining Like
Terms”**
Link: James Sousa’s

*Mathispower4u*: “Combining Like Terms” (YouTube)

Instructions: Watch the video and take notes. Make sure you understand what terms can be combined. Pause the video at the 1:25 mark to take notes on the slide about similar terms. The next slide introduces the

*distributive law*, which is also called the distributive property. Take notes on how you can change the way expressions are written by rearranging the values in specific ways. Listen closely at the 2:35 mark. The instructor mentions the

*commutative property*as a reason for why

*a*can be placed either before or after the set of parenthesis. This is another good vocabulary word to know. Watch and practice the examples with the instructor.

Watching the video and working through the examples should take approximately 15 minutes.

Standards Addressed (

*Common Core*):

```
- [CCSS.Math.Content.8.EE.C.7](http://www.corestandards.org/Math/Content/8/EE/C/7)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0 Unported
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to James Sousa.
```

**Explanation: James Sousa’s**Link: James Sousa’s*Mathispower4u*: “Simplifying Algebraic Expressions”*Mathispower4u*: “Simplifying Algebraic Expressions” (YouTube)

Instructions: The video starts with another review of the distributive property. Add to your notes as necessary. Pause the video at the 0:53 mark and try to solve the problem. Watch the video and listen to the instructor as you check your work. Pause the video again at the 2:41 mark and try to solve the problem. Watch the video and listen to the instructor as you check your work. Pause the video once more at the 4:04 mark and try to solve the problem. Watch the video and listen to the instructor as you check your work. Don’t try to skip steps to speed up the process. Write down each step, as it helps you remember what you are doing and also allows other mathematicians to follow your thinking.

Watching the video and working through the examples should take approximately 15 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to James Sousa.**Did I Get This? Activity: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*: “Chapter 3, Section 3: Simplifying Algebraic Expressions”*Prealgebra Textbook*: “Chapter 3, Section 3: Simplifying Algebraic Expressions” (PDF)

Instructions: Start at page 187. Read about and take notes on the gray box that explains the commutative and associative properties. Look at Examples 1, 2 and 3 on pages 187-188. Be sure you understand the solutions. Go to page 195 and complete problems 1-35 ODD. Check your answers on page 196. Make sure you understand the solutions before you move on.

Completing the practice problems and checking your solutions should take approximately 30 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: Illustrative Mathematics: “Coupon versus Discount”**Link: Illustrative Mathematics: “Coupon versus Discount” (PDF)

Instructions: Answer the question on page 1. Make sure you use a strategy that includes combining like terms. Do not just guess and check. Read the commentary and check your solution on page 2.

Completing the problem and checking your solution 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.

**2.3.2 Solving Multi-Step Equations**
- **Explanation: Monterey Institute for Technology and Education:
HippoCampus: “Solving Multi-Step Equations”**
Link: Monterey Institute for Technology and Education: HippoCampus:
“Solving Multi-Step
Equations” (Flash)

```
Instructions: On the left side of the screen, select *Developmental
Math – Beginning Algebra* from beneath the “Presentations” heading.
On the pop out menu, scroll down to the “Solving Equations and
Inequalities” heading and select “Solving Multi-Step Equations.” At
the beginning of the video, the instructor explains the five steps
for solving multi-step equations. Make sure you take notes and
understand these steps. Stop the video while you watch if you need
extra time to take notes.
Watching the video and taking notes should take approximately 15
minutes.
Standards Addressed (*Common Core*):
- [CCSS.Math.Content.8.EE.C.7](http://www.corestandards.org/Math/Content/8/EE/C/7)
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/).
```

**Explanation: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*: “Chapter 3, Section 5: Solving Equations Involving Integers II”*Prealgebra Textbook*: “Chapter 3, Section 5: Solving Equations Involving Integers II” (PDF)

Instructions: On pages 208-212, you will work through examples and take notes on solving equations. For each example, solve the equation for the given variable. In seventh grade, you learned about operations with integers. You will be using those skills as you solve each equation throughout this section. You should also solve the problems in the “You Try It!”sections. The “You Try It!”answers are along the edges of the page.

Taking notes and working through examples should take approximately 30 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: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*: “Chapter 3, Section 5: Solving Equations Involving Integers II”*Prealgebra Textbook*: “Chapter 3, Section 5: Solving Equations Involving Integers II” (PDF)

Instructions: Go to pages 213-214 in Chapter 3, Section 5. Complete exercises 1-9 ODD, 17-25 ODD, 35-39 ODD, and 53-57 ODD. Check your answers on pages 214-215. If you get an answer wrong, go back through the five steps for solving multi-step equations and figure out how to solve it correctly.

Completing the practice problems and checking solutions should take approximately 30 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 Simultaneous Linear Equations**
*Often when working with linear equations, you are comparing two or more
situations. Perhaps, for example, you are trying to figure out which
cell phone plan is the cheapest for you based on the data plan you want.
In this subunit, you will learn how to solve simultaneous linear
equations using the coordinate plane and substitution with the
equations. You will also have the opportunity to work with real-life
situations. It is important that you know how to solve simultaneous
linear equations a few different ways because some situations lend
themselves to graphing, and some situations are more efficient when you
use the substitution method.*

**2.4.1 Solving Using the Coordinate Plane**
- **Explanation: Monterey Institute for Technology and Education:
HippoCampus: “Graphing Systems of Linear Equations”**
Link: Monterey Institute for Technology and Education: HippoCampus:
“Graphing Systems of Linear
Equations” (Flash)

Instructions: On the left side of the screen, select *Developmental
Math – Beginning Algebra* from beneath the “Presentations” heading.
On the pop out menu, scroll down to the “Systems of Equations and
Inequalities” heading and select “Graphing Systems of Linear
Equations.” While you watch the video, take notes and write down
examples. Pay attention to what it means when lines intersect.
Understand the difference between linear equations that have one
solution, infinite solutions, and no solutions. The instructor
explains what a *system of equations* is when the timer reads 1:00.
Make sure to take notes on this concept. Stop the video while you
watch if you need extra time to take notes.

Watching the video and taking notes should take approximately 15
minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.8.EE.C.8](http://www.corestandards.org/Math/Content/8/EE/C/8)
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/).
```

**Did I Get This? Activity: Illustrative Mathematics: “The Intersection of Two Lines”**Link: Illustrative Mathematics: “The Intersection of Two Lines” (PDF)

Instructions: Answer questions a-d on page 1. Read the commentary and check your solutions on pages 2-4.

Completing this task and checking your solutions should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**2.4.2 Solving Algebraically and through Estimation**
- **Explanation: Monterey Institute for Technology and Education:
HippoCampus: “The Substitution Method”**
Link: Monterey Institute for Technology and Education: HippoCampus:
“The Substitution
Method” (Flash)

Instructions: Instructions: On the left side of the screen, select
*Developmental Math – Beginning Algebra* under the “Presentations”
heading. On the pop out menu, scroll down to the “Systems of
Equations and Inequalities” heading and select “The Substitution
Method.” While you watch the video, take notes and write down
examples. The instructor explains why graphing is not always the
most efficient way to solve a system of equations. Understand the
difference between linear equations that have one solution, infinite
solutions, and no solutions. When there is 0:35 left in the video,
take notes and be sure you understand the steps for using the
substitution method to solve a system of equations. Stop the video
while you watch if you need extra time to take notes.

Watching the video and taking notes should take approximately 15
minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.8.EE.C.8](http://www.corestandards.org/Math/Content/8/EE/C/8)
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/).
```

**Did I Get This? Activity: Illustrative Mathematics: “Fixing the Furnace”**Link: Illustrative Mathematics: “Fixing the Furnace” (PDF)

Instructions: Read and solve the problem on page 1. Consider using strategies from the graphing subunit and/or the substitution subunit. Read the commentary and check your solution on pages 2-3.

Completing this task and checking your solution should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**2.4.3 Real-World Examples of Systems of Equations**
*So far in this unit, you have completed a variety of problems that
involve solving systems of equations. Your task in this subunit is to
relate these skills to real-world applications. As you work, think about
what the problem is asking, and solve each problem step-by-step. There
are often multi-step solutions that need to be solved. Don’t guess and
check – solve the problems algebraically. *

**Did I Get This? Activity: Illustrative Mathematics: “Cell Phone Plans”**Link: Illustrative Mathematics: “Cell Phone Plans” (PDF)

Instructions: Write an equation and graph the cell phone plans as described in part a of the question. Answer question b. Read the commentary and check your solutions on pages 2-3.

Completing this task and checking your solution should take approximately 30 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: Illustrative Mathematics: “Summer Swimming”**Link: Illustrative Mathematics: “Summer Swimming” (PDF)

Instructions: Solve questions a-e on the first page. Read the commentary and check your solutions on pages 2-3.

Completing this task and checking your solution should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.**Checkpoint: Illustrative Mathematics: “How Many Solutions?”**Link: Illustrative Mathematics: “How Many Solutions?” (PDF)

Instructions: This resource requires you to use skills from all of Unit 2. Answer the question on page 1. Try to solve the bonus question for the applicable cases. Read the commentary and check your solutions on pages 2-3.

Completing this task and checking your solution should take approximately 30 minutes.

Standards Addressed (*Common Core*):

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.**Checkpoint: Southern Nevada Regional Professional Development Program: “Pre-Algebra 8, Unit 15 Practice Test: Graphs and Functions II”**Link: Southern Nevada Regional Professional Development Program: “Pre-Algebra 8, Unit 15 Practice Test: Graphs and Functions II” (PDF)

Instructions: Solve questions 1-9 (skip 10-11; you will cover this material in the next unit). Check your answers here. Make sure you understand all the solutions.

Completing this checkpoint and checking your solutions should take approximately 45 minutes.

Standards Addressed (*Common Core*):- CCSS.Math.Content.8.EE.B.5
- CCSS.Math.Content.8.EE.B.6
- CCSS.Math.Content.8.EE.C.7
- CCSS.Math.Content.8.EE.C.8

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.