**Unit 1: The Number System**
*Imagine that you are shopping. There are signs everywhere for different
sales. You only have a set amount to spend and need to calculate an
estimate for the discount and the tax. This is just one of the many
applications that you will be able complete at the end of Unit 1.*

*In this unit, you will continue to build on the decimal and fraction
skills you started in previous courses. These rational numbers will be
expanded upon by the addition of positive and negative numbers working
together within the four operations. A focus on the properties will help
you gain an understanding of how the rational numbers work. You will
then extend these skills to applications of percentages, including
discounts, taxes, commissions, and others.*

**Unit 1 Time Advisory**

Completing this unit should take approximately 20 hours and 25
minutes.

☐ Subunit 1.1: 10 hours and 5 minutes

☐ Subunit 1.2: 10 hours and 20 minutes

**Unit1 Learning Outcomes**

Upon successful completion of this unit, you will be able to:
- Solve problems involving integers.

- Extend the rules of integers to work with other rational numbers,
such as fractions and decimals.

- Apply the properties of operations in order to solve problems
involving all four operations.

- Write percentages as decimals and fractions.

- Use percentages to solve real-world problems.

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

- CCSS.Math.Content.7.NS.A.2

- CCSS.Math.Content.7.RP.A.3

- CCSS.ELA-Literacy.WHST.6-8.2

**1.1 Working with Rational Numbers**
*Rational numbers are used in everything we do. There are fractions in
cooking and baking, construction, and even using a ruler. Decimals are
also used when measuring items including amounts of money. This section
will build your skills with positive and negative numbers. Then you will
expand these skills to include positive and negative fractions and
positive and negative decimals. Becoming an expert in working with
rational numbers will help you to be more successful in the following
sections and units as the rational numbers are used throughout the
different applications.*

**Explanation: CK-12: Jack Hatert’s “Rational Numbers”**Link: CK-12: Jack Hatert’s “Rational Numbers” (PDF)

Instructions: Read “Rational Numbers” to learn about the properties used to complete operations with rational numbers. Then complete “Time to Practice” problems at the bottom of the webpage.

Completing this activity should take approximately 40 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Jack Hatert and CK-12 Foundation. The original version can be found here.

**1.1.1 Operations with Integers**
**1.1.1.1 Adding Integers**
- **Explanation: CK-12: “Adding Integers”**
Link: CK-12: “Adding
Integers”
(PDF)

Instructions: Read “Adding Integers” to learn about using the
number line to add positive and negative whole numbers. Watch the
first video, which is from Khan Academy. Then complete the “Time to
Practice” problems at the bottom of the webpage.

Completing this activity should take approximately 1 hour.

```
Standards Addressed (*Common Core*):
- [CCSS.Math.Content.7.NS.A.1](http://www.corestandards.org/Math/Content/7/NS/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/). The
text is attributed to CK-12 Foundation and the video is attributed
to Khan Academy. The original version can be
found [here](http://www.ck12.org/section/Adding-Integers/).
```

**Did I Get This? Activity: XP Math: “Integers Addition Blocks”**Link: XP Math: “Integers Addition Blocks” (Flash)

Instructions: After you hit the start button, you will be given a number on the right that will be your answer. You have to come up with the numbers that would make up the question. For example, if the answer is -10, your question could be -8 + -2. So you would click on the boxes -8 and -2. Play the game five times.

Completing this activity should take approximately 10 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: XP Math: “Integer Driving Test - Integer Addition & Subtraction”**Link: XP Math: “Integer Driving Test - Integer Addition & Subtraction” (Flash)

Instructions: Go to the left-hand side of the webpage and change the car, if you wish. Then click on “Take the Test,” and you will be given questions involving integers. You can either “Drive Forward” or “Drive Backward” to get your car to drive to the answer on the number line. Then press the license plate “Check” button to see if your answer is correct. Play this game twice. Note that this activity covers the material you need to know for Subunit 1.1.1.1 and Subunit 1.1.1.2.

Completing this activity should take approximately 10 minutes.

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

**1.1.1.2 Subtracting Integers**
*Note: This subunit is covered by the activity assigned beneath Subunit
1.1.1.1. Focus specifically on solving the subtraction questions and how
the steps are related to the method used for solving addition
questions.*

**Explanation: CK-12: “Subtracting Integers - Overview”**Link: CK-12: “Subtracting Integers - Overview” (YouTube)

Instructions: Watch the animation to learn how a number line can be used to solve subtraction questions with positive and negative whole numbers.

Completing this activity should take approximately 5 minutes.

Standards Addressed (*Common Core*):Terms of Use:This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to CK-12 Foundation. The original video can be found here.

**Explanation: CK-12: Shannon Newman’s “Subtracting Integers”**Link: CK-12: Shannon Newman’s “Subtracting Integers” (PDF)

Instructions: Read “Subtracting Integers” to learn how adding can be used to solve subtraction questions with positive and negative whole numbers. Watch the video from Khan Academy and then solve the 23 “Time to Practice” problems.

Completing this activity should take approximately 1 hour.

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. The text is attributed to CK-12 Foundation and Shannon Newman; the video is attributed to Khan Academy. The original version can be found here.

**1.1.1.3 Multiplying Integers**
- **Explanation: CK-12: “Multiplying Integers”**
Link: CK-12: “Multiplying
Integers”
(PDF)

Instructions: Read “Multiplying Integers” to learn how the signs
are used to determine the answer. Watch the first video and then
complete the “Time to Practice” questions.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.2](http://www.corestandards.org/Math/Content/7/NS/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/section/Multiplying-Integers/).
```

**Did I Get This? Activity: XP Math: “Integers Multiplication”**Link: XP Math: “Integers Multiplication” (Flash)

Instructions: Hit the start button. You will be given 60 seconds to answer as many integer multiplication questions as you can. The answers will range from -144 to 144. Play this game three times.

Completing this activity should take approximately 10 minutes.

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

**1.1.1.4 Dividing Integers**
- **Explanation: CK-12: “Dividing Integers”**
Link: CK-12: “Dividing
Integers”
(PDF)

Instructions: Read this webpage to learn how dividing integers is
similar to multiplying integers. Watch the first video and then
complete the “Time to Practice” questions.

Completing this activity should take approximately 45 minutes.

```
- [CCSS.Math.Content.7.NS.A.2](http://www.corestandards.org/Math/Content/7/NS/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/section/Dividing-Integers/).
```

**Did I Get This? Activity: XP Math: “Integers Division: -81 to 81”**Link: XP Math: “Integers Division: -81 to 81” (Flash)

Instructions: Hit the start button. You will be given 60 seconds to answer as many division questions as you can. Play the game as many times as you like.

Completing this activity should take approximately 10 minutes.

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

**1.1.2 Operations with Signed Decimals**
- **Explanation: CK-12: “Positive and Negative Fraction and Decimal
Comparison”**
Link: CK-12: “Positive and Negative Fraction and Decimal
Comparison”
(PDF)

Instructions: Read the article on comparing signed decimals and
fractions. This reading is meant to review concepts about positive
and negative rational numbers before you are asked to complete
operations with the numbers. Solve the 15 practice problems at the
bottom of the webpage.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
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/Positive-and-Negative-Fraction-and-Decimal-Comparison/lesson/Positive-and-Negative-Fraction-and-Decimal-Comparison/?__hstc=107423837.5c65aa60bd382096b5b470b3b31b53d6.1375210181314.1378388554828.1378395489229.64&__hssc=107423837.10.1378395489229).
```

**1.1.2.1 Adding Decimals**
- **Explanation: Vimeo: Jennifer Burke’s “Adding Decimals (Same as
Integers)”**
Link: Vimeo: Jennifer Burke’s “Adding Decimals (Same as
Integers)” (Flash)

Instructions: This video shows how the steps for adding positive
and negative decimals are very similar to the steps for adding
integers. Watch the video and write down at least one way that
integer questions are similar to decimal questions and one way they
are different from each other.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
- [CCSS.ELA-Literacy.WHST.6-8.2.f](http://www.corestandards.org/ELA-Literacy/WHST/6-8/2/f)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Checkpoint: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*, 2nd edition: “Chapter 5, Section 5.2: Adding and Subtracting Decimals”*Prealgebra Textbook*, 2nd edition: “Chapter 5, Section 5.2: Adding and Subtracting Decimals” (PDF)

Instructions: Review the examples on pages 363 - 364. Then go to page 366 and complete odd problems 25 - 43. You can find the answers to the problems on pages 368 - 369. Use them to check your work. Note that this checkpoint covers the material you need to know for Subunit 1.1.2.1 and Subunit 1.1.2.2.

Completing this activity 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. It is attributed to Department of Mathematics, College of the Redwoods. The original version can be found here.

**1.1.2.2 Subtracting Decimals**
*Note: This subunit is covered by the checkpoint assigned beneath
Subunit 1.1.2.1. Focus specifically on the questions that ask you to
subtract decimals.*

**Explanation: Vimeo: Jennifer Burke’s “Subtracting Decimals”**Link: Vimeo: Jennifer Burke’s “Subtracting Decimals” (Flash)

Instructions: Watch the video and write down how the steps are similar to the steps used to subtract integers.

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.

**1.1.2.3 Multiplying Decimals**
- **Checkpoint: Department of Mathematics, College of the Redwoods:
Prealgebra Textbook, 2nd edition: “Chapter 5, Section 5.3:
Multiplying Decimals”**
Link: Department of Mathematics, College of the Redwoods:

*Prealgebra Textbook*, 2nd edition: “Chapter 5, Section 5.3: Multiplying Decimals” (PDF)

Instructions: Scroll down to page 381 and complete odd problems 29 - 47. Remember to use the signs of each number to help you determine the sign of the answer. You can find the answers to the problems on pages 384 - 385. Use them to check your work.

Completing this activity should take approximately 40 minutes.

Standards Addressed (

*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
Terms of Use: This work 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 Department of Mathematics, College of the Redwoods.
The original version can be found
[here](http://mathrev.redwoods.edu/PreAlgText/Prealgebra.pdf).
```

**1.1.2.4 “Dividing Decimals”**
- **Checkpoint: Department of Mathematics, College of the Redwoods:
Prealgebra Textbook, 2nd edition: “Chapter 5, Section 5.4:
Dividing Decimals”**
Link: Department of Mathematics, College of the Redwoods:

*Prealgebra Textbook*, 2nd edition: “Chapter 5, Section 5.4: Dividing Decimals” (PDF)

Instructions: Review the examples on page 390. Then go to page 396 to complete odd problems 41 - 63. You can find the answers to the problems on page 399. Use them to check your work.

Completing this activity should take approximately 40 minutes.

Standards Addressed (

*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
Terms of Use: This work 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 Department of Mathematics, College of the Redwoods.
The original version can be
found [here](mathrev.redwoods.edu/PreAlgText/Prealgebra.pdf).
```

**1.1.3 Operations with Signed Fractions**
**1.1.3.1 Adding Fractions**
- **Checkpoint: Department of Mathematics, College of the Redwoods:
Prealgebra Textbook, 2nd edition: “Chapter 4, Section 4.4: Adding
and Subtracting Fractions”**
Link: Department of Mathematics, College of the Redwoods:

*Prealgebra Textbook*, 2nd edition: “Chapter 4, Section 4.4: Adding and Subtracting Fractions” (PDF)

Instructions: Review the examples of adding and subtracting positive and negative fractions on page 283. Then go to page 287 and complete odd problems 81 - 99. You can find the answers to the problems on page 290. Use them to check your work. Note that this checkpoint covers the material you need to know for Subunit 1.1.3.1 and Subunit 1.1.3.2.

Completing this activity should take approximately 20 minutes.

Standards Addressed (

*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.2](http://www.corestandards.org/Math/Content/7/NS/A/2)
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
Terms of Use: This work 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 Department of Mathematics, College of the Redwoods.
The original version can be
found [here](mathrev.redwoods.edu/PreAlgText/Prealgebra.pdf).
```

**1.1.3.2 Subtracting Fractions**
*Note: This subunit is covered by the checkpoint assigned beneath
Subunit 1.1.3.1. Focus specifically on the questions asking you to
subtract fractions.*

**1.1.3.3 Multiplying Fractions**
- **Checkpoint: Department of Mathematics, College of the Redwoods:
Prealgebra Textbook, 2nd edition: “Chapter 4, Section 4.5:
Multiplying and Dividing Mixed Fractions”**
Link: Department of Mathematics, College of the Redwoods:

*Prealgebra Textbook*, 2nd edition: “Chapter 4, Section 4.5: Multiplying and Dividing Mixed Fractions” (PDF)

Instructions: Review the examples of multiplying and dividing fractions on pages 295 - 296. Then go to page 298 and complete odd problems 29 - 61. The answers can be found on page 300. Use them to check your work. Note that this checkpoint covers the material you need to know for Subunit 1.1.3.3 and Subunit 1.1.3.4.

Completing this activity should take approximately 1 hour.

Standards Addressed (

*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
Terms of Use: This work 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 Department of Mathematics, College of the Redwoods.
The original version can be
found [here](mathrev.redwoods.edu/PreAlgText/Prealgebra.pdf).
```

**1.1.3.4 Dividing Fractions**
*Note: This subunit is covered by the checkpoint assigned beneath
Subunit 1.1.3.3. Focus specifically on odd problems 49 - 61 that ask you
to divide fractions.*

**1.1.3.5 Computing Complex Fractions**
- **Checkpoint: Department of Mathematics, College of the Redwoods:
Prealgebra Textbook, 2nd edition: “Chapter 4, Section 4.7: Order
of Operations with Fractions: Complex Fractions”**
Link: Department of Mathematics, College of the Redwoods:

*Prealgebra Textbook*, 2nd edition: “Chapter 4, Section 4.7: Order of Operations with Fractions: Complex Fractions” (PDF)

Instructions: Review pages 315 - 317, which explain the meaning of complex fractions and show the steps for several examples. Then go to page 323 and complete odd problems 57 - 67 to try your hand at working with complex fractions. The answers can be found on page 325. Use them to check your work.

Completing this activity should take approximately 30 minutes.

Standards Addressed (

*Common Core*):

```
- [CCSS.Math.Content.7.NS.A.3](http://www.corestandards.org/Math/Content/7/NS/A/3)
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 Department of Mathematics, College of the Redwoods.
The original version can be
found [here](mathrev.redwoods.edu/PreAlgText/Prealgebra.pdf).
```

**Did I Get This? Activity: Howard County Public School System: “Triple Triumph”**Link: Howard County Public School System: “Triple Triumph” (HTML)

Instructions: Scroll down to the task for 7.NS.3 entitled “Triple Triumph.” Then click to download the activity. You will use the skills you have been practicing with all types of rational numbers to complete the puzzle.

Completing this activity should take approximately 30 minutes.

Note for Educators: This link will bring you to several lessons and other activities specifically created for the classroom and directly aligned to the Common Core State Standards.

Standards Addressed (*Common Core*):

**1.2 Percentages**
*Rational numbers have many uses in real-life applications. One of the
most obvious examples would be money and percentages. Throughout the
second half of this unit, you will be looking at how decimals,
fractions, and percentages are related to each other. Then you will use
the different types of numbers to work on examples of these real-life
applications, which include calculating prices after discounts, after
adding a tip or gratuity, or even after you add on the sales tax, just
to name a few examples.*

**1.2.1 Writing Percentages as a Decimal**
**1.2.1.1 Percentages between 1 and 100**
- **Explanation: CK-12: “Percents as Decimals”**
Link: CK-12: “Percents as
Decimals”
(PDF)

Instructions: Read “Percents as Decimals” to learn how you can move
the decimal point back and forth to convert. Watch the Khan Academy
video and 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.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/).The text
is attributed to CK-12 Foundation and the video is attributed to
Khan Academy. The original version can be found
[here](http://www.ck12.org/arithmetic/Percents-as-Decimals/lesson/Percents-as-Decimals/).
```

**Checkpoint: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.1: Percent, Decimals, Fractions”*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.1: Percent, Decimals, Fractions” (PDF)

Instructions: Scroll down to page 508 and complete odd problems 19 - 43, which will help you practice changing a percentage to a decimal. The answers can be found on page 511. Use them to check your work.

Completing this activity should take approximately 20 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 Department of Mathematics, College of the Redwoods. The original version can be found here.

**1.2.1.2 Percentages Less than 1 and Greater than 100**
- **Explanation: CK-12: “Small and Large Percents as Decimals”**
Link: CK-12: “Small and Large Percents as
Decimals”
(PDF)

Instructions: Read “Small and Large Percents as Decimals” to learn
how numbers over 100% can be written as decimals. Then complete the
15 practice questions at the bottom of the page.

Completing this activity should take approximately 25 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/Small-and-Large-Percents-as-Decimals/lesson/Small-and-Large-Percents-as-Decimals/).
```

**1.2.2 Writing Percentages as Fractions**
- **Explanation: CK-12: “Percents as Fractions”**
Link: CK-12: “Percents as
Fractions”
(PDF)

Instructions: Read “Percents as Fractions” to learn how using
100ths can help convert percentages to fractions and fractions to
percentages. You do not need to view the review videos. Then solve
the 16 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.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/Percents-as-Fractions/lesson/Percents-as-Fractions/).
```

**Checkpoint: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.1: Percent, Decimals, Fractions”*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.1: Percent, Decimals, Fractions” (PDF)

Instructions: Scroll down to pages 508 - 509 and complete odd problems 1 - 17 and 51 - 67, where you can try your hand at changing a percentage to a fraction. The answers can be found on pages 510 -- Use them to check your work.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*): - CCSS.Math.Content.7.RP.A.3

Terms of Use: This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Department of Mathematics, College of the Redwoods. The original version can be found here.

- Use them to check your work.

**1.2.3 Relating Fractions, Decimals, and Percentages**
- **Explanation: CK-12: “Conversion of Decimals, Fractions, and
Percents”**
Link: CK-12: “Conversion of Decimals, Fractions, and
Percents”
(PDF)

Instructions: Watch the first two videos and then read through the
article to see how to put all of the conversions together. You will
learn how to change back and forth from all three types of numbers.
Finally, solve the 20 practice problems at the bottom of the page.

Completing this activity should take approximately 1 hour.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/concept/Conversion-of-Decimals-Fractions-and-Percent---Intermediate/?ref=%2Fconcept%2FConversion-of-Decimals-Fractions-and-Percent%2F).
```

**1.2.4 Percentage Word Problems**
- **Explanation: CK-12: “Solving Ratio and Percent Problems Using
Proportional Reasoning”**
Link: CK-12: “Solving Ratio and Percent Problems Using Proportional
Reasoning”
(PDF)

Instructions: Read through the different types of word problems
that percentages can be used to solve. For each example in the
reading, try the problem on your own paper before scrolling through
to see the answer. There are nine examples to try while reading
through the article.

Completing this activity should take approximately 1 hour.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/na/Solving-Ratio-and-Percent-Problems-Using-Proportional-Relationships---7.RP.3-1/lesson/user%3Ac2ZveDJAb3N3ZWdvLm9yZw../Solving-Ratio-and-Percent-Problems-Using-Proportional-Relationships---7.RP.3/).
```

**Explanation: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.3: General Applications of Percent”*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.3: General Applications of Percent” (PDF)

Instructions: Read page 521 to learn about solving world problems that involve percentages. Then complete odd problems 1 - 23 on pages 525 - 527. The answers can be found on page 528. Use them to check your work.

Completing this activity should take approximately 45 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 Department of Mathematics, College of the Redwoods. The original version can be found here.

**1.2.4.1 Sales Tax**
- **Explanation: CK-12: “Prices Involving Sales Tax”**
Link: CK-12: “Prices Involving Sales
Tax”
(PDF)

Instructions: Read “Prices Involving Sales Tax” to see how the
price of an item changes once the tax has been added to it. Then
solve the first 10 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.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/Prices-Involving-Sales-Tax/lesson/Prices-Involving-Sales-Tax/).
```

**Explanation: CK-12: “Prices Involving Discounts”**Link: CK-12: “Prices Involving Discounts” (PDF)

Instructions: Now that you have seen how a price increases with tax, check out how a price can become lower after a discount (sale or coupon) is applied. Then solve the 15 practice problems at the bottom of the page.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to CK-12 Foundation. The original version can be found here.

**1.2.4.2 Gratuities**
- **Explanation: CK-12: “Prices Involving Sales Tax”**
Link: CK-12: “Prices Involving Sales
Tax”
(PDF)

Instructions: Although the title mentions sales tax, the article is
really about calculating the tip that you should leave for services,
like when you go out for a meal at a restaurant. Check out how the
steps are similar to finding the new price after sales tax has been
added. Then solve the 15 practice problems at the bottom of the
page.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/concept/Prices-Involving-Sales-Tax-Grade-7/?ref=%2Fconcept%2FPrices-Involving-Sales-Tax%2F).
```

**1.2.4.3 Simple Interest**
- **Explanation: CK-12: “Simple Interest”**
Link: CK-12: “Simple
Interest”
(PDF)

Explanation: As you read through the article on simple interest,
try to come up with some examples of where you might be able to
apply this lesson in real life. Then solve the 15 practice problems
at the bottom of the page.

Completing this activity should take approximately 1 hour.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.RP.A.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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/concept/Simple-Interest-Grade-7/?ref=%2Fconcept%2FSimple-Interest%2F).
```

**1.2.4.4 Percentage Increase and Decrease**
- **Explanation: CK-12: “Percent of Increase”**
Link: CK-12: “Percent of
Increase”
(PDF)

Instructions: This article will show you how to calculate the
percentage when an amount increases. As you read through the
article, think about how you could use the steps to calculate the
percentage increase when measuring your height from one year to the
next. Then complete the 15 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.3](http://www.corestandards.org/Math/Content/7/RP/A/3)
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 accessed
[here](http://www.ck12.org/arithmetic/Percent-of-Increase/lesson/Percent-of-Increase/).
```

**Explanation: CK-12: “Percent of Decrease”**Link: CK-12: “Percent of Decrease” (PDF)

Instructions: As you read through the article on the percentage of decrease, write down at least one way that the steps are similar to finding the percentage of increase. Then complete the 15 practice questions at the bottom of the page.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to CK-12 Foundation. The original version can be found here.

**Assessment: Department of Mathematics, College of the Redwoods:**Link: Department of Mathematics, College of the Redwoods:*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.4: Percent Increase and Decrease”*Prealgebra Textbook*, 2nd edition: “Chapter 7, Section 7.4: Percent Increase and Decrease” (PDF)

Instructions: Use what you have learned in the two previous readings to complete odd problems 1 - 15 on page 538. There are examples on pages 529 - 534 if you would like to refer back to them. The answers can be found on page 541. Use them to check your work.

Completing this activity should take approximately 20 minutes.

Standards Addressed (*Common Core*):**Did I Get This? Activity: Howard County Public School System: “7th Grade Dance”**Link: Howard County Public School System: “7th Grade Dance” (HTML)

Instructions: Scroll down to the task for 7.RP.A.3 entitled “7th Grade Dance.” Then click to download the activity. You will use your knowledge from the second half of the unit to complete the task on costs for the seventh-grade dance.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):**Checkpoint: Illustrative Mathematics: “Chess Club”**Link: Illustrative Mathematics: “Chess Club” (PDF)

Instructions: Find the overall percentage change for the club. Then scroll to the second page to check your work.

Completing this checkpoint and checking your work 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. It is attributed to Illustrative Mathematics. The original version can be found here.