**Unit 1: Number Sense**

*The first unit of this course involves extending your prior knowledge
of fractions and decimals. You will use models to show how the division
equation works. This will help you make sense of finding quotients
involving fractions. During this unit, you will also work with negative
integers along a number line. This might involve negative temperatures
(cold!), having credit or debt with money, or changing elevation as you
hike up a mountain or scuba dive into the ocean. During this
number-sense unit, make your best effort to do just as the unit title
implies - make sense of numbers. Don’t try to memorize equations;
rather, understand the numbers and operations, so you can continue to
make sense of the math in future situations.*

**Unit 1 Time Advisory**

Completing this unit should take you approximately 13 hours.

☐ Subunit 1.1: 5 hours and 15 minutes

☐ Subunit 1.2: 30 minutes

☐ Subunit 1.3: 2 hours and 45 minutes

☐ Subunit 1.4: 1 hour and 45 minutes

☐ Subunit 1.5: 2 hours and 45 minutes

**Unit1 Learning Outcomes**

Upon successful completion of this unit, you will be able to:

Compute quotients of fractions.

Solve word problems involving quotients of fractions.

Use visual models and equations to represent division of fractions.

Fluently compute multi-digit division of numbers.

Fluently add, subtract, multiply, and divide multi-digit decimals.

Solve for the greatest common factor of two numbers.

Solve for the least common multiple of two numbers.

Use the distributive property to change expressions.

Define the opposite of a number.

Extend a number line to represent negative rational points.

Order rational numbers using lists and inequalities.

Define absolute value and interpret how it is used in real world situations.

Standards Addressed (Common Core):

**1.1 Fractions**

*Fractions are used in our daily lives in a variety of ways. The U.S.
customary measurement system uses fractions as a measuring tool
(example: 3/8 inch). Fractions are also used in cooking and baking
(example: 3/4 cup), and fractions can even be used to describe partial
situations (example: I completed 1/4 of the project). These are just a
few general examples of how fractions are used. In this subunit you will
review addition and subtraction of fractions, as well as work with
multiplication and division. These concepts might already be familiar to
you. However, adding models and fluency will be a key concept that you
should focus on while working.*

**1.1.1 Operations with Fractions**
**1.1.1.1 Adding and Subtracting Fractions**

*You and a friend have decided to bake cookies. You both want to make
chocolate chip cookies, but you each have a different recipe. The two of
you decide to have a “bake-off” in order to do a taste test and figure
out which recipe is the best. You plan to go grocery shopping together,
buy everything that you need, and come back to your house to bake the
cookies. Since both recipes call for the same ingredients, just
different amounts of each, you decide to add your amounts together.*

*Adding fractions, as well as subtracting them, is an important concept
to understand when dealing with recipes because most ingredients are
listed as parts of a whole cup.*

**Explanation: YouTube: Mathispower4u: James Sousa’s “Addition of Mixed Numbers”**Link: YouTube: Mathispower4u: James Sousa’s “Addition of Mixed Numbers” (YouTube)Instructions: Work through the problems with the instructor in the videos. Pay attention to strategies that help you find a common denominator.

Watching this video and taking notes should take you 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, and the original version can be found here.

**Explanation: YouTube: Khan Academy’s “Subtracting Mixed Numbers 2”**Link: YouTube: Khan Academy’s “Subtracting Mixed Numbers 2” (YouTube)

Instructions: Work through the problems with the instructor in the video. Pay attention to the two different strategies of subtracting fractions.

Watching this video and taking notes should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

**Did I Get This? Activity: Howard County Public School System’s “Cookie Calculations”**Link: Howard County Public School System’s “Cookie Calculations” (HTML)

Instructions: On the above webpage, scroll down until you see “5.NF.1 Cookie Calculations Recipe.docx” under the first section. Download the document to display the two recipes.In your notebook, draw three columns and title them “Ingredients,” “Calculations,” and “Amount to Buy.” Use the amounts of each of the nine ingredients from each recipe to fill in your columns. In the “Ingredients” column, you will list the ingredients and their amounts that you need to buy based on the recipes. You will show your work in the “Calculations” column and your final answer in the “Amount to Buy” column. Here is an example of what the first row of your table might look like. Notice that the ingredients match the needed amounts from each recipe, the “Calculations” column shows the process and number sentence, including finding a common denominator and simplifying. The total combined amount of butter is listed under the “Amount to Buy” column.

**Ingredients****Calculations****Amount to Buy****1**2/3 cups of butter

**1**2/4 cups of butter**1**2/3 =**1**8/12**1**2/4 =**1**6/12

**1**8/12 +**1**6/12 =**2**14/12 =**3**2/12**3**1/6 cups of butterWhen you have completed the above activity, check your answers here.

Completing this activity should take you approximately 30 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under aCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to Howard County Public Schools Office of Secondary Mathematics Curricular Projects, and the original version can be found here.

**1.1.1.2 Multiplying Fractions**

*In the previous subunit you combined ingredients before you went to the
store. What happens if you want to double or triple a recipe to make
lots of cookies? This would involve multiplying each ingredient by two
or three. In this subunit you will see that multiplying fractions can be
modeled using a fraction bar. As you work through this subunit, pay
attention to how the fraction models work so you are able to use models
when you multiply fractions.*

**Explanation: College of the Redwoods Mathematics:***Prealgebra Textbook*: “Chapter 4, Section 2: Multiplying Fractions”Link: College of the Redwoods Mathematics:

*Prealgebra Textbook*: “Chapter 4, Section 2: Multiplying Fractions” (PDF)Instructions: In the table of contents, click on “4.2: Multiplying Fractions.” Read through the explanation on page 249 about how to draw a visual model of multiplying fractions. Copy the sample model in your notebook. Do “Example 1” using a visual model. Make sure to recognize how the word of is used in math.

Read about the multiplication rule on pages 250 - 251 to understand the formula for multiplying fractions. Try “Example 2” using this method.

Reading this section, working the examples, and taking notes should take approximately 30 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to the Department of Mathematics, College of the Redwoods, and the original version can be found here.

**Explanation: YouTube: Khan Academy’s “Multiplying Fractions and Mixed Numbers”**Link: YouTube: Khan Academy’s “Multiplying Fractions and Mixed Numbers” (YouTube)

Instructions: While watching this video, pay attention to how the instructor changed a whole number into a fraction and how you can simplify the fraction after multiplying or before multiplying. Sometimes it’s easier to simplify before multiplying because then you don’t have to deal with digits that are very large.

The last 1:20 on the video shows how this problem can also be solved using a model. Make sure you recognize how to model multiplication of fractions.

Write a paragraph explaining how the model of a fraction multiplication problem works. Your audience is a younger student who has never multiplied fractions using a model. Make sure to use math vocabulary. Drawing an example model and using arrows/labels might be helpful.

Watching this video, taking notes, and writing a paragraph should take you approximately 30 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under aCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

**Explanation: YouTube: Khan Academy’s “Multiplying Mixed Numbers”**Link: YouTube: Khan Academy’s “Multiplying Mixed Numbers” (YouTube)

Instructions: While watching this video, pay attention to how to change a mixed number into an improper fraction.

Watching this video and taking notes should take you approximately 15 minutes.

Standards Addressed (

*Common Core*):Terms of Use: This resource is licensed under aCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

**Checkpoint: Wade Ellis, Jr. and Denny Burzynski’s “Introduction to Fractions and Multiplication and Division of Fractions: Multiplication of Fractions”**Link: Wade Ellis, Jr. and Denny Burzynski’s Fundamentals of Mathematics: “Introduction to Fractions and Multiplication and Division of Fractions: Multiplication of Fractions” (HTML)

Instructions: Scroll through the models and samples (feel free to refer to these as additional resources, if needed) until you get to “Practice Set A.” In your notebook, complete all problems in the practice set. Check the solutions as you go. Make sure to always simplify your fraction.

Complete the problems in “Practice Set B.” Use the “simplify before multiplying” strategy. Check the solutions as you go.

Complete the problem in “Practice Set C.” Remember when you have a mixed number you have to convert it to an improper fraction before you can use the multiplication formula. Check the solutions as you go.

Skip all parts of “Sample Set D” and “Practice Set D.”

Continue practicing the problems beginning with “Exercise 28” and working through “Exercise 89.” Do all the even problems. Use the odd numbered problems as extra practice, as needed. The types of questions vary as you work. Check the solutions as you go.

With all of the above problems, if you are not able to solve for the correct product, figure out your mistake. Read back through the sample items in each section or re-watch the videos provided.

Completing these practice sets should take you approximately 45 minutes.

Standards Addressed (

*Common Core*):Terms of Use: This resource is licensed under aCreative Commons Attribution 3.0 Unported License. It is attributed to Wade Ellis and Denny Burzynski, and the original version can be found here.

**1.1.1.3 Dividing Fractions**

*How do you feel about sharing? Sometimes we have to share, or split up,
parts of a whole. Other times, we have to share something that isn’t
whole - like 2/3 of a leftover pizza shared among four family members.
How much pizza will you get? In this unit you will work to model
division of fractions. It is important to know and use the formula that
works for always dividing fractions. However, make sure you are able to
follow the models given to you in this subunit. Modeling division of
fractions is an important skill to have in this course. *

**Explanation: CK-12: “Division of Fractions by Whole Numbers”**Link: CK-12: “Division of Fractions by Whole Numbers” (HTML)

Instructions: Read about Julia trying to figure out how many strips of paper she can cut from her poster board. Continue reading under the “Guidance” section about how you can model division of fractions. Do examples A - C. Write down the vocabulary words (Inverse Operation and Reciprocal) and their definitions in your notebook, as these concepts will be used often in this subunit.

Watch the first video, “Khan Academy Dividing Fraction Example.” Work the problems while the video instructor completes them. Pay attention to the model he shows you at the end.

Watch the third video, “James Sousa Example of Dividing Fractions.” Work through the problems while the video instructor completes them. Pay attention to the different strategies of how to simplify the fractions before solving.

Reading this explanation, watching the videos, working the problems, and taking notes should take you approximately 30 minutes.

Standards Addressed

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

**Explanation: YouTube: Khan Academy’s “Dividing Mixed Numbers”**Link: YouTube: Khan Academy’s “Dividing Mixed Numbers” (YouTube)

Instructions: Watch this video about dividing mixed numbers. Similar to multiplication of fractions, you will want to pay attention to how the instructor first makes the mixed numbers into improper fractions.

Watching this video and taking notes should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

**1.1.2 Solving Word Problems with Fractions**

*Understanding “how to” operate with fractions is important; however,
more importantly you need to know how to put your fraction skills into
real-life situations. When you encounter fractions - whether it’s in
baking, measurement, traveling distances, or just working with parts of
a whole - it is essential that you can define the necessary operation
and put your math skills into action. This subunit will help you break
down word problems and solve them successfully.*

**Explanation: YouTube: Khan Academy’s “Dividing Fractions Word Problem”**Link: YouTube: Khan Academy’s “Dividing Fractions Word Problem” (YouTube)

Instructions: Begin watching this video. However, click the pause button after you have a chance to read the problem provided. Try solving the problem before you watch the video. Check your process and your work once you have completed the problem on your own.

Watching this video and working the problem on your own should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

**Explanation: YouTube: Khan Academy’s “Dividing Fractions Word Problem (Ex 2)”**Link: YouTube: Khan Academy’s “Dividing Fractions Word Problem (Ex 2)” (YouTube)

Instructions: Begin watching the video. However, click the pause button after you have a chance to read the problem provided. Try solving the problem before you watch the video. Check your process and your work once you have completed the problem on your own.

Watching this video and working the problem on your own should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:**Explanation: YouTube: Khan Academy’s “Multiplying Fractions Word Problem”**Link: YouTube: Khan Academy’s “Multiplying Fractions Word Problem” (YouTube)

Instructions: Begin watching the video. However, click the pause button after you have a chance to read the problem provided. Try solving the problem before you watch the video. Check your process and your work once you have completed the problem on your own.

Watching this video and working the problem on your own should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under aCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

**Explanation: YouTube: Khan Academy’s “Multiplying Fractions Word Problem (Ex 1)”**Link: YouTube: Khan Academy’s “Multiplying Fractions Word Problem (Ex 1)” (YouTube)

Instructions: Begin watching the video. However, click the pause button after you have a chance to read the problem provided. Try solving the problem before you watch the video. Check your process and your work once you have completed the problem on your own.

Watching this video and working the problem on your own should you approximately 15 minutes.

Standards Addressed

*(Common Core)*:**Checkpoint: Khan Academy’s “Multiplying Fractions Word Problems”**Link: Khan Academy’s “Multiplying Fractions Word Problems” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice the word problem questions until you feel confident that you understand how to successful multiply fractions within word problems (recommended a minimum of 10 minutes of practice).

Completing these practice problems should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:**Checkpoint: Khan Academy’s “Dividing Fractions Word Problems”**Link: Khan Academy’s “Dividing Fractions Word Problems” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice the word problems questions until you feel confident that you understand how to successful divide fractions within word problems (recommended a minimum of 10 minutes of practice).

Completing these practice problems should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:

**1.2 Long Division**

*Fluently using division is valuable to your daily life. This subunit
will cover the formula for using long division as well as the different
options for what to do when you have a remainder.*

**Explanation: YouTube: Khan Academy’s “More Long Division and Remainder Examples”**Link: YouTube: Khan Academy’s “More Long Division and Remainder Examples” (YouTube)

Instructions: Depending on your current level of understanding with division - and specifically long division - watch the first problem as an example, but stop it when you are given the problem for the second example. Try to solve it yourself before watching the solution.

Watching this video and working the problem on your own should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:**Explanation: YouTube: James Olsen’s “Long Division with Remainders - Three Ways to Handle Them”**Link: YouTube: James Olsen’s “Long Division with Remainders - Three Ways to Handle Them” (YouTube)

Instructions: The purpose of this video is to make you aware of the different ways mathematicians deal with remainders. As you continue in your math career, you want to make sure you are confident with writing a remainder as a fraction and a decimal. Also, it is important in word problems to understand what the remainder might mean for that particular word problem.

Watching this video and taking notes should take you approximately 15 minutes.

Standards Addressed

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

**1.3 Decimals**

*Decimals are used all around us. Most commonly, we use decimals when we
deal with money. It is important to know how to find an exact answer
while using decimals, and to use estimation skills. In this subunit you
will work with addition, subtraction, multiplication, and division of
decimals. You should have some prior knowledge about decimal placement,
place value with decimals, and saying a decimal number using proper math
grammar (example: 2.35 = two and thirty-five hundredths). If you don’t
feel confident with place value of decimals, do a little research on
your own at this time. An Internet search for “decimal place value”
should give you a good place to start.*

**1.3.1 Adding and Subtracting Decimals**
- **Explanation: YouTube: Mathispower4u: James Sousa’s “Adding and
Subtracting Decimals”**

```
Link: YouTube: Mathispower4u: James Sousa’s [“Adding and Subtracting
Decimals”](http://www.youtube.com/watch?v=CEHku41nb60) (YouTube)
Instructions: While watching this video, pay close attention to the
decimal placement throughout the addition and subtraction problems.
Otherwise, you’ll notice that the addition and subtraction
strategies remain the same.
Watching this video and taking notes should take you approximately
15 minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.B.3](http://www.corestandards.org/Math/Content/6/NS/B/3)
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, and the original version can be found
[here](http://www.youtube.com/watch?v=CEHku41nb60).
```

**Did I Get This? Activity: Wade Ellis, Jr. and Denny Burzynski’s “Decimals: Addition and Subtraction of Decimals”**Link: Wade Ellis, Jr. and Denny Burzynski’s “Decimals: Addition and Subtraction of Decimals” (HTML)

Instructions: Click on the link above and scroll down to the “Exercises” section. Do exercises 12 - 36 and check your solutions as you go.

Completing these exercises should take you approximately 30 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 Wade Ellis and Denny Burzynski, and the original version can be found here.

**1.3.2 Multiplying Decimals**
- **Explanation: CK-12: “Decimal Multiplication”**

```
Link: CK-12: [“Decimal
Multiplication”](http://www.ck12.org/arithmetic/Decimal-Multiplication/lesson/Decimal-Multiplication/) (HTML)
Instructions: Read through the text about multiplying decimals.
Notice that decimal multiplication is not much different from
regular multiplication. Ignore the decimal until you have the final
product, and then place the decimal in the proper location. Both
strategies of “counting decimal places” and “estimation” work for
knowing where to place the decimal in the product.
Do the example problems and check your solutions as you read through
the text.
Of the four videos accompanying the text, watch the first video
“James Sousa Multiplying Decimals.” Pause the video at each example,
solve it on your own, and then check your solution and steps with
the instructor. (You are welcome to watch the other videos for
additional practice.)
Do the practice problems beneath the videos, and check your solution
on a calculator.
Reading this article, watching the video, and working through the
problems should take you approximately 45 minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.B.3](http://www.corestandards.org/Math/Content/6/NS/B/3)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial 3.0 Unported
License](http://creativecommons.org/licenses/by-nc/3.0/). It is
attributed to CK-12, and the original version can be found
[here](http://www.ck12.org/arithmetic/Decimal-Multiplication/lesson/Decimal-Multiplication/).
```

**1.3.3 Dividing Decimals**
- **Explanation: CK-12: “Decimal Division”**

```
Link: CK-12: [“Decimal
Division”](http://www.ck12.org/arithmetic/Decimal-Division/lesson/Decimal-Division/) (HTML)
Instructions: Read through the text about dividing decimals. Notice
that decimal division is not much different from regular long
division. Pay attention to how and why mathematicians (you!) move
the decimal place in both the divisor and dividend.
Do the example problems, and check your solutions as you read
through the text.
While watching the Khan Academy video, pause the video at each
example, solve it on your own, and then check your solution and
steps along with the instructor.
Do the practice problems beneath the video, and check your solution
on a calculator.
Reading this article, watching the video, and working through the
problems should take you approximately 45 minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.B.3](http://www.corestandards.org/Math/Content/6/NS/B/3)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial 3.0 Unported
License](http://creativecommons.org/licenses/by-nc/3.0/). It is
attributed to CK-12, and the original version can be found
[here](http://www.ck12.org/arithmetic/Decimal-Multiplication/lesson/Decimal-Multiplication/).
```

**Did I Get This? Activity: Howard County Public School System’s “School Store Task”**Link: Howard County Public School System’s “School Store Task” (PDF)

Instructions: On the webpage above, scroll down until you find the activity titled “School Store.” (You will have to search carefully to find this.) Download the “6.NS.3 School Store Task Resource Sheet.” Follow the instructions on the document to solve each of the problems about buying school supplies. Think of different strategies that could be used to solve the problems.

Use this answer key (PDF) to check your answers. This document has extension questions that you can use to challenge yourself. The solutions are at the bottom.

Completing these problems should take you approximately 30 minutes.

Standards Addressed

*(Common Core)*:Terms of Use: This resource is licensed under aCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to Howard County Public Schools Office of Secondary Mathematics Curricular Projects, and the original version can be found here.

**1.4 Factors and Multiples**

*Factors and multiples are used when you are finding patterns with
numbers. Developing fluency in factors and multiples will help you when
working with expanding and reducing fractions. As you will also see in
this unit, factors can be used to help with the distributive property.*

**1.4.1 Greatest Common Factors**
- **Explanation: YouTube: Mathispower4u: James Sousa’s “Factors”**

```
Link: YouTube: Mathispower4u: James Sousa’s
[“Factors”](http://www.youtube.com/watch?v=v9dsxTCjdhE) (YouTube)
Instructions: While watching the video, find the factors of each
number on your own as the instructor does it. Fluently knowing your
multiplication facts will benefit you greatly when finding factors.
Watching the video and taking notes should take you approximately 15
minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.B.4](http://www.corestandards.org/Math/Content/6/NS/B/4)
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, and the original version can be found
[here](http://www.youtube.com/watch?v=v9dsxTCjdhE).
```

**Explanation: YouTube: Mathispower4u: James Sousa’s “Example: Determining the Greatest Common Factor”**Link: YouTube: Mathispower4u: James Sousa’s “Example: Determining the Greatest Common Factor” (YouTube)

Instructions: Find the prime factorization of each number on your own as the instructor does it in the video. Pause the video if you need more time.

Watching this video and taking notes should take you 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, and the original version can be found here.

**1.4.2 Least Common Multiples**
- **Explanation: YouTube: Mathispower4u: James Sousa’s “Example:
Determining the Least Common Multiple Using Prime Factorization”**

```
Link: YouTube: Mathispower4u: James Sousa’s [“Example: Determining
the Least Common Multiple Using Prime
Factorization”](http://www.youtube.com/watch?v=hZvRDG-HgMY) (YouTube)
<span>Instructions: While watching the video, notice how the
instructor shows a different method for determining the LCM. Either
method works; however, this method using prime factorization will be
a lot less time consuming if you need to find an LCM of larger
numbers.</span>
<span>Watching this video and taking notes should take you
approximately 15 minutes.</span>
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.B.4](http://www.corestandards.org/Math/Content/6/NS/B/4)
<span>Terms of Use: </span><span>This resource is licensed under
a </span>[Creative Commons Attribution 3.0 Unported
License](http://creativecommons.org/licenses/by/3.0/)<span>. It is
attributed to James Sousa, and the original version can be found
</span>[here](http://www.youtube.com/watch?v=hZvRDG-HgMY)<span>.</span>
```

**Explanation: YouTube: Mathispower4u: James Sousa’s “Example: Determining the Least Common Multiple Using a List of Multiples”**Link: YouTube: Mathispower4u: James Sousa’s “Example: Determining the Least Common Multiple Using a List of Multiples” (YouTube)

Instructions: While watching the video, notice how the instructor makes a list of multiples for each number before looking for the least common multiple (LCM).

Watching this video and taking notes should take you 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, and the original version can be found here.

**1.4.3 Distributive Property**
- **Explanation: YouTube: Mathispower4u: James Sousa’s “Using the
Distributive Property to Multiply Quickly”**

```
Link: YouTube: Mathispower4u: James Sousa’s [“Using the Distributive
Property to Multiply
Quickly”](http://www.youtube.com/watch?v=VyDN3wUjYZs) (YouTube)
Instructions: While watching this video, think about how this
strategy could be beneficial to you when multiplying mentally. You
will continue to use the distributive property in many ways
throughout your math career.
Watching this video and taking notes should take you approximately
15 minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.B.4](http://www.corestandards.org/Math/Content/6/NS/B/4)
Terms of Use: This resource is licensed under
a[ ](http://creativecommons.org/licenses/by/3.0/)[Creative Commons
Attribution 3.0 Unported
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to James Sousa, and the original version can be
found [here](http://www.youtube.com/watch?v=hZvRDG-HgMY).
```

**Did I Get This? Activity: College of the Sequoias: Ross Rueger’s Math 360 - PreAlgebra: “Chapter 1, Section 5: Greatest Common Factor and Least Common Multiple”**Link: College of the Sequoias: Ross Rueger’s

*Math 360 - PreAlgebra*: “Chapter 1, Section 5: Greatest Common Factor and Least Common Multiple” (PDF)Instructions: Do “Exercise Set 1.5,” problems 1 - 27 (ODD) and 61 - 64 (ALL). Answers can be found on pages 61 - 62.

Completing these problems and checking your answers should take you approximately 30 minutes.

Standards Addressed

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

**1.5 Rational Numbers**

*Using negative numbers in life usually means that it’s very cold
outside (temperatures below zero), you lost points in a game you are
playing, or possibly you are in debt to someone and owe them money.
Knowing and understanding the number line as it extends into negative
numbers is important as you relate the entire rational number system to
your real life.*

**Explanation: Cheryl Wilcox’s***Free PreAlgebra*: “Chapter 4, Lesson 19: Negative Numbers”Link: Cheryl Wilcox’s

*Free PreAlgebra*: “Chapter 4, Lesson 19: Negative Numbers” (PDF)Instructions: This textbook introduces concepts covered in this entire subunit. This is a chance for you to begin to get an understanding of rational numbers. Separate your notebook paper into three sections. Label the sections “Definitions,” “Real-Life Situations,” and “Number Lines.” As you read pages 1 - 5, fill in the columns with information from text. These are the vocabulary words that you should look for to put in the definitions column: negative numbers, positive numbers, opposites, and absolute value. In the text, many real-life situations are mentioned, explained, and even illustrated with images. The more of these you can learn, the more beneficial this text will be to your understanding of rational numbers. Under the “Number Lines” column, you should use the type 2 models to draw a few number lines and plot points to help compare greater than and less than.

Do the entire worksheet on page 6 as practice. You could also do practice problems 8 and 9 on the two homework pages, page 8 and page 12.

Reading this chapter, taking notes, and working the practice problems should take you approximately 30 minutes.

Standards Addressed

*(Common Core)*:- CCSS.Math.Content.6.NS.C.5
- CCSS.Math.Content.6.NS.C.6a
- CCSS.Math.Content.6.NS.C.6c
- CCSS.Math.Content.6.NS.C.7a
- CCSS.Math.Content.6.NS.C.7b
- CCSS.Math.Content.6.NS.C.7c
- CCSS.Math.Content.6.NS.C.7d
- CCSS.ELA-Literacy.RST.6-8.4
- CCSS.ELA-Literacy.RST.6-8.7
- CCSS.ELA-Literacy.RST.6-8.9

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Cheryl Wilcox, and the original version can be found here.

**Explanation: YouTube: Mathispower4u: James Sousa’s “Integers”**Link: YouTube: Mathispower4u: James Sousa’s “Integers” (YouTube)

Instructions: While watching this video, add notes to your notebook paper that has three columns from the previous activity. You should add the word integers to the definitions column. Also, pay attention when the video gives examples of how negatives numbers are used in real-life situations.

Watching this video and taking notes should take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:- CCSS.Math.Content.6.NS.C.5
- CCSS.Math.Content.6.NS.C.6a
- CCSS.Math.Content.6.NS.C.6c
- CCSS.Math.Content.6.NS.C.7a
- CCSS.Math.Content.6.NS.C.7b
- CCSS.Math.Content.6.NS.C.7c
- CCSS.Math.Content.6.NS.C.7d

**1.5.1 Ordering Rational Numbers**
- **Did I Get This? Activity: Khan Academy’s “Number Line 2”**

```
<span style="font-size: 12px;">Link: Khan Academy’s </span>[“Number
Line
2”](http://www.khanacademy.org/math/arithmetic/absolute-value/add-sub-negatives/e/number_line_2) (HTML)
Instructions: This page provides a series of practice problems that
you can answer and check online. Each question has a solution worked
out step-by-step if you need hints along the way. Practice these
exercises to make sure you feel confident with number lines.
Practicing these problems will take you approximately 15 minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.C.6c](http://www.corestandards.org/Math/Content/6/NS/C/6/c)
- [CCSS.Math.Content.6.NS.C.7a](http://www.corestandards.org/Math/Content/6/NS/C/7/a)
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/). It is
attributed to the Khan Academy.
```

**Did I Get This? Activity: Khan Academy’s “Ordering Negative Numbers”**Link: Khan Academy’s “Ordering Negative Numbers” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice these exercises to make sure you feel confident with ordering negative numbers.

Practicing these problems will take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:**Did I Get This? Activity: Khan Academy’s “Number Line 3”**Link: Khan Academy’s “Number Line 3” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice these exercises to make sure you feel confident with number lines.

Practicing these problems will take you approximately 15 minutes.

Standards Addressed

*(Common Core)*:**Checkpoint: The Mathematics Common Core Toolbox: “Cake Weighing, Part A” and “Part B”**Link: The Mathematics Common Core Toolbox: “Cake Weighing, Part A” and “Part B” (HTML)

Instructions: Read about the Tasty Treats Cake Factory in the gray box in “Part A.” Answer the question and check your answer with the Submit Answer button. Do not move on until you have the correct answer.

For “Part B,” answer the question and check your answer with the Submit Answer button. Do not move on until you have the correct answer.

Completing these two questions and checking your work should take you approximately 15 minutes.

Standards Addressed

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

**1.5.2 Absolute Value**
- **Did I Get This? Activity: Khan Academy’s “Comparing Absolute
Value”**

```
Link: Khan Academy’s [“Comparing Absolute
Value”](http://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/e/comparing_absolute_values) (HTML)
Instructions: This page provides a series of practice problems that
you can answer and check online. Each question has a solution worked
out step-by-step if you need hints along the way. Practice the
absolute value questions until you feel confident that you
understand how to compare integers and absolute value (recommended a
minimum of 10 minutes of practice).
Practicing these problems will take you approximately 15 minutes.
Standards Addressed *(Common Core)*:
- [CCSS.Math.Content.6.NS.C.6c](http://www.corestandards.org/Math/Content/6/NS/C/6/c)
- [CCSS.Math.Content.6.NS.C.7c](http://www.corestandards.org/Math/Content/6/NS/C/7/c)
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/). It is
attributed to the Khan Academy.
```

**Checkpoint: The Mathematics Common Core Toolbox: “Cake Weighing, Part C” and “Part D”**Link: The Mathematics Common Core Toolbox: “Cake Weighing, Part C” and “Part D” (HTML)

Instructions: In “Part C,” read about the Tasty Treats Cake Factory in the gray box. Answer the question and check your answer with the Submit Answer button. Do not move on until you have the correct answer.

In “Part D,” answer the question and check your answer with the Submit Answer button. Do not move on until you have the correct answer.

Completing these two questions and checking your work should take you approximately 15 minutes.

Standards Addressed

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

**Checkpoint: College of the Redwoods Mathematics: Prealgebra Textbook: “Chapter 2, Section 1: An Introduction to the Integers”**Link: College of the Redwoods Mathematics:

*Prealgebra Textbook*: “Chapter 2, Section 1: An Introduction to the Integers” (PDF)Instructions: If needed for extra guidance, read through the sections under “2.1: An Introduction to the Integers.” As a checkpoint to see how well you know these concepts, click on “Exercises” under section 2.1 or scroll to page 106. Do all the ODD problems 1 - 69. Check your answers starting on page 110.

Completing this checkpoint should take you approximately 30 minutes.

Standards Addressed

*(Common Core)*:- CCSS.Math.Content.6.NS.C.5
- CCSS.Math.Content.6.NS.C.6a
- CCSS.Math.Content.6.NS.C.6c
- CCSS.Math.Content.6.NS.C.7a
- CCSS.Math.Content.6.NS.C.7b
- CCSS.Math.Content.6.NS.C.7c
- CCSS.Math.Content.6.NS.C.7d

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

**Checkpoint**
- **Checkpoint: The Saylor Foundation’s “K12MATH006 Unit 1
Checkpoint”**
Link: The Saylor Foundation’s “K12MATH006 Unit 1
Checkpoint” (HTML)

```
Instructions: Test your knowledge by completing this checkpoint.
Note: You must be logged into your Saylor Foundation School account
in order to access this checkpoint. If you do not yet have an
account, you will be able to create one, free of charge, after
clicking the link.
```