 Unit 1: Number Sense   Have you heard of the golden ratio, Euler’s number, or pi? All of these are examples of irrational numbers. This unit will guide you through the difference between rational and irrational numbers. While you learn about how irrational numbers exist more often outside of a math book, you will work to find a decimal approximation for these numbers. Whether your interests are in music, math, art, finance, or history, you will recognize that irrational numbers have an interesting place in your mathematical understanding.

The unit will continue with radicals, integer exponents, and scientific notation. Have you ever tried to express the population of the whole world? What about a really small number like how many meters the tectonic plates move in a year? In this unit, you will learn about how to express these numbers without having to write out lots of place values.

Completing this unit should take approximately 15 hours and 45 minutes.

☐    Subunit 1.1: 4 hours and 30 minutes

☐    Subunit 1.2: 7 hours and 45 minutes

☐    Subunit 1.3: 3 hours and 30 minutes

Unit1 Learning Outcomes
Upon successful completion of this unit, you will be able to: - Explain the difference between a rational and irrational number. - Define an irrational number by an approximate rational number. - Compare the size of irrational numbers by locating them approximately on a number line. - Evaluate powers that have integer exponents. - Represent solutions to equations using square root and cube root symbols. - Evaluate square roots of small perfect squares and cube roots of small perfect cubes. - Express any number, including negative exponents, using scientific notation. - Perform operations with numbers expressed in scientific notation and decimal values. - Interpret scientific notation that has been generated by technology.

1.1 Rational and Irrational Numbers   Throughout your entire school career, you have worked with numbers. Your earliest interaction with numbers was probably holding up a few fingers to represent your current age. You continued to progress as you learned to count, decipher odd and even numbers, and use the counting numbers (whole numbers) to do math operations. When you reached about sixth grade, you learned about integers (negative numbers) and fractions/decimals (rational numbers). When you learned how to find the area of a circle, you first encountered the number π, and how it relates to the ratio of a circle’s circumference to its diameter. Pi is an irrational number. In this subunit you will continue your learning about what defines an irrational number, how these numbers are used, and how they can be approximated.

• Explanation: James Sousa’s Mathispower4u: “Real Numbers” Link: James Sousa’s Mathispower4u: “Real Numbers” (YouTube)

Instructions: While you watch the video, take notes on the words or phrases written in bold. The tree diagram that is displayed and explained between the 1:00 and 3:00 marks is very important. Listen and watch as the instructor explains the diagram. Pause the video at the 3:00 mark and copy the diagram into your notebook. Take special interest of the term irrational number, as this is probably the most unfamiliar term to you.

Watch the video until the 3:40 mark. Pause the video when you see four problems displayed to compare. Use both an inequality symbol as shown in the previous slide and a number line to compare these values. Once you have solved them in your notebook, continue watching as the instructor solves and explains.

Watch the video until the 6:33 mark. Pause the video when you see the three true/false problems. Solve them in your notebook, and then continue watching as the instructor solves and explains.

The final topic, absolute value, is not relevant to this subunit. You can stop watching the video at the 7:30 mark.

Watching the video, taking notes, and working examples should take approximately 30 minutes.

• Explanation: CK-12: “Properties of Rational Numbers versus Irrational Numbers” Link: CK-12: “Properties of Rational Numbers versus Irrational Numbers” (HTML and YouTube)

Instructions: Read in the “Guidance” section about square roots that result in non-whole numbers, these are irrational numbers. Add to your notes any additional definitions or ideas about irrational and rational numbers that you find useful. Complete the problems in examples A, B, and C and be sure you understand the solutions.

Write the words and definitions from the “Vocabulary” section into your notebook. You can ignore the term tabular interpolation, as it does not directly apply to eighth-grade math.

Watch the video. Sketch the Venn diagram in the first slide. How does this compare to the tree diagram you already have in your notebook? They are essentially displaying the same information, though one might be easier for you to understand. Complete the problems with the instructor as you watch the video.

Complete the practice problems and check your solutions here.

Taking notes, working examples, and watching the video should take approximately 30 minutes.

Instructions: When the video first begins, pause it to read the question and the various choices. Decide which numbers are irrational numbers. Watch the video to hear the explanation and to check your answer.

Watching this video should take approximately 15 minutes.

• Did I Get This? Activity: Khan Academy’s “Recognizing Rational and Irrational Numbers” Link: Khan Academy’s “Recognizing Rational and Irrational Numbers” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question provides you with numbers that need to be classified as rational or irrational. There are also step-by-step hints along the way if you need additional guidance. Practice classifying rational and irrational numbers until you feel confident that you understand how to find and recognize each (a minimum of 10 minutes of practice is recommended).

Completing this activity should take approximately 15 minutes.

• Web Media: Colin Dodds’s “Number Types (Math Song)” Link: Colin Dodds’s “Number Types (Math Song)” (YouTube)

Instructions: Watch this video about natural numbers. This video does not include irrational numbers. Write a short paragraph that could be an added verse to the song that explains an irrational number. Focus more on the math understanding of irrational numbers than worrying about making it “catchy” for a song.

Completing this activity should take approximately 15 minutes.

• Did I Get This? Activity: Illustrative Mathematics: “Identifying Rational Numbers” Link: Illustrative Mathematics: “Identifying Rational Numbers” (PDF)

Instructions: Answer questions a-h. Make sure you explain if necessary. Read the commentary and check your solutions on page 2.

Completing the problems and checking your solutions should take approximately 15 minutes.

1.1.1 Approximating Irrational Numbers   - Explanation: CK-12: “Irrational Square Roots” Link: CK-12: “Irrational Square Roots” (HTML)

Instructions: Read the “Guidance” section. Take special note of the information just below the notebook. This explains what to do when approximating a number. Solve examples A, B, and C and understand the solutions. Complete the “Guided Practice,” and watch the video. While watching the video, solve the problems with the instructor. Pausing the video while you solve each problem might be useful. Remember to use the appropriately equal to symbol, when approximating a value. Solve the “Practice” questions and check your solutions here. Approximate all values to the nearest hundredth.

Taking notes, working examples, and watching the video should take approximately 30 minutes.

``````-   [CCSS.Math.Content.8.NS.A.1](http://www.corestandards.org/Math/Content/8/NS/A/1)
-   [CCSS.Math.Content.8.NS.A.2](http://www.corestandards.org/Math/Content/8/NS/A/2)

attributed to CK-12, and the original version can be found
[here](http://www.ck12.org/algebra/Irrational-Square-Roots/lesson/Approximate-Solutions-to-Equations-Involving-Irrational-Numbers/).
``````
• Did I Get This? Activity: Illustrative Mathematics: “Comparing Rational and Irrational Numbers” Link: Illustrative Mathematics: “Comparing Rational and Irrational Numbers” (PDF)

Instructions: Answer questions a-d. Make sure you do NOT use a calculator, and be sure to explain your reasoning for each answer. Check the solutions on page 2.

Completing the problems and checking your solutions should take approximately 15 minutes.

• Did I Get This? Activity: Illustrative Mathematics: “Estimating Square Roots” Link: Illustrative Mathematics: “Estimating Square Roots” (PDF)

Instructions: Solve the question provided. Read the commentary and the solution on page 2. The solution page provides a couple of different strategies as to how to solve this. Obviously the square root of 800 is not a perfect square, but you can use perfect squares to guide your estimation.

Completing the problem and checking your solution should take approximately 15 minutes.

1.1.2 Comparing and Ordering Irrational Numbers   - Activity: CK-12: “Rational and Irrational Numbers” Link: CK-12: “Rational and Irrational Numbers” (HTML)

Instructions: Read about Candice as she figures out how to get more dirt for her class garden. Read the “Teaching Time” section and take notes on anything that you find useful.

In the second section, “Compare and Order Rational Numbers on a Number Line,” follow the example and draw the number line in your notebook. Write down the steps you would take to decide where to place numbers based on the decimal approximation.

In the third section, “Approximate Solutions to Equations Involving Irrational Numbers,” read through the information and solve the examples in your notebook. Continue using the hundredth place and the approximately equal to symbol while you work.

Solve the real world examples. Try to think of situations in your life where you might need to use irrational numbers to solve everyday problems. Complete the “Time to Practice” problems. Additionally, using the values in questions 1-10, plot the numbers on a number line that ranges from -10 to 10 (you will ignore the values for questions 3, 6, and 7 to complete this exercise). Check your solutions here.

Taking notes, working examples, and completing the practice problems should take approximately 45 minutes.

``````-   [CCSS.Math.Content.8.NS.A.1](http://www.corestandards.org/Math/Content/8/NS/A/1)
-   [CCSS.Math.Content.8.NS.A.2](http://www.corestandards.org/Math/Content/8/NS/A/2)

attributed to CK-12, and the original version can be found
[here](http://www.ck12.org/section/Rational-and-Irrational-Numbers-%3A%3Aof%3A%3A-Using-Real-Numbers-and-Right-Triangles/).
``````
• Did I Get This? Activity: Illustrative Mathematics: “Irrational Numbers on a Number Line” Link: Illustrative Mathematics: “Irrational Numbers on a Number Line” (PDF)

Instructions: Draw a number line and label the approximate locations for values a-d. Read the commentary and check your solutions on page 2.

Completing the problem and checking your solution should take approximately 15 minutes.

• Checkpoint: Southern Nevada’s Regional Professional Development Program: “Rational and Irrational Numbers” Link: Southern Nevada’s Regional Professional Development Program: “Rational and Irrational Numbers” (PDF)

Instructions: Complete all the problems on the page. While answering questions 2 and 3, also use a number line to represent the approximate location of each rational and irrational number. Check your solutions here.

Completing the problems and checking solutions should take approximately 30 minutes.

1.2 Exponents and Radicals   Exponents and radicals are used in math to represent both rational and irrational numbers. The financial industry uses rational exponents to compute interest rates. Radicals are often used in the real world where geometry is involved, such as a carpenter trying to figure out square footage. In this subunit, you will build on your prior knowledge of exponents and integers to learn about integer exponents. You will also focus on radicals, which is the mathematical term for square roots.

1.2.1 Integer Exponents   - Explanation: Khan Academy’s “Exponent Rules Part 1” and “Part 2” Link: Khan Academy’s “Exponent Rules Part 1” and “Part 2” (YouTube)

Instructions: Part 1 of this video shows you what to do when you multiply or divide numbers with exponents. Part 2 explains two more rules for exponents. Take notes as you watch the videos. When the instructor writes a new example, pause the video and solve the example before continuing to watch the solution. You will have the opportunity to practice these problems later in this course. Understanding the examples and listening to the explanations is the goal of this resource.

Watching the videos and taking notes should take approximately 30 minutes.

``````-   [CCSS.Math.Content.8.EE.A.1](http://www.corestandards.org/Math/Content/8/EE/A/1)

``````
• Did I Get This? Activity: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 1: Exponential Notation” Link: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 1: Exponential Notation” (PDF)

Instructions: The box at the top of the first page offers a quick review of exponents, even when there is a fractional base. As you work through the activities in this resource, you will check your understanding of working with exponents and establish an idea of what to do with a negative base. On pages 1-3, Lesson 1, complete exercises 1-14. Check your answers on page 10 of this document. Within the answers for each exercise are some additional explanations and “teacher talk.” Read this if you are struggling with any of the concepts you just practiced. Specifically, make sure you have an understanding of what happens when a negative number is raised to an odd power versus an even power.

Completing the practice problems and checking your work should take approximately 45 minutes.

• Did I Get This? Activity: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 2: Multiplication of Numbers in Exponential Form” Link: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 2: Multiplication of Numbers in Exponential Form” (PDF)

Instructions: In Lesson 2, the box at the top does a quick review of multiplication of numbers in exponential form. Complete exercises 1-31, ODD. Note: You are not actually solving the expressions (don’t just punch numbers into your calculator). The goal is to simplify the expressions. Check your answers here, on page 17. Within the answers for each exercise are some additional explanations and “teacher talk.” Read this if you are struggling with any of the concepts you just practiced.

Completing the practice problems and checking your work should take approximately 45 minutes.

• Did I Get This? Activity: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 3: Numbers in Exponential Form Raised to a Power” Link: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 3: Numbers in Exponential Form Raised to a Power” (PDF)

Instructions: In Lesson 3, the box at the top does a quick review of numbers in exponential form raised to a power. You learned about this in the Khan Academy video earlier in subunit 1.2.1.

Complete exercises 1-12. Note: You are not actually solving the expressions (don’t just punch numbers into your calculator). The goal is to simplify the expressions. Check your answers here on pages 28-30. Within the answers for each exercise are some additional explanations and “teacher talk.” Read this if you are struggling with any of the concepts you just practiced.

Completing the practice problems and checking your work should take approximately 30 minutes.

Instructions: This video begins with a quick exponent review. Pause the video - as the instructor recommends - at the 0:35 mark, and consider the question he poses. Continue watching and copying the examples in your notebook. You will have the opportunity to practice problems like these later in the course. Understanding the examples and listening to the explanation is the goal of this resource.

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

Instructions: This video might answer some of your questions about why exponents work the way they do. As you watch the video, take notes. If you are confused because the instructor always uses letters, pause the video and try your own example with numbers. Understanding the examples and listening to the explanation is the goal of this resource.

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

• Did I Get This? Activity: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 5: Negative Exponents and the Laws of Exponents” Link: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 5: Negative Exponents and the Laws of Exponents” (PDF)

Instructions: Scroll down to Lesson 5, which starts on page 17. The box at the top of the page does a quick review of negative exponents. Complete exercises 1-10. Note: You are not actually solving the expressions (don’t just punch numbers into your calculator). The goal is to simplify the expressions. Check your answers here, on pages 47-48 . Within the answers for each exercise are some additional explanations and “teacher talk.” Read this if you are struggling with any of the concepts you just practiced.

Completing the practice problems and checking your work should take approximately 30 minutes.

• Explanation: CK-12: “Negative Exponents” Link: CK-12: “Negative Exponents” (HTML and Vimeo)

Instructions: This resource is a review of what you’ve learned about negative exponents so far. Add any additional notes to your notebook as you go. Start by watching the video, and then read the “Guidance” section, where you will review the rules for exponents. Complete examples A, B, and C. Check your solutions as you go. Watch the second video and complete the problems in the “Guided Practice” section.

Completing the practice problems and checking your work should take approximately 30 minutes.

• Checkpoint: Illustrative Mathematics: “Extending the Definitions of Exponents, Variation 1” Link: Illustrative Mathematics: “Extending the Definitions of Exponents, Variation 1” (PDF)

Instructions: This is an in-depth problem covering the concepts from the entire unit up until this point. Answer questions a-h. Take your time and make sure you answer the questions completely. Some questions have multiple questions within the question. When you finish answering the questions, scroll down and read through the commentary and solutions on pages 2 and 3.

Completing the problems and checking your solutions should take approximately 1 hour.

Instructions: Complete the assessment questions found on pages 65-68. Use the rubric on pages 69-71 to make sure your answers are complete before you check the solutions. Check your answers on pages 72-75. If you answered a problem incorrectly, go back through the solution and make corrections.

Completing the problems and checking your work should take approximately 1 hour.

1.2.2 Square Roots   - Explanation: Department of Mathematics, College of the Redwoods: Prealgebra Textbook: “Chapter 5, Section 7: Introduction to Square Roots” Link: Department of Mathematics, College of the Redwoods: Prealgebra Textbook: “Chapter 5, Section 7: Introduction to Square Roots” (PDF)

Instructions: Read and take notes about square roots on pages 425-428. Specifically, focus on the example problems, the information in the gray boxes, and the list of perfect squares on the edge of the page. You are expected to know square roots of small perfect squares. In the next resource, you will have the chance to practice learning the first 25 perfect squares. As you work through the example problems, also do the problems in the “You Try It!” sections. Scroll down the page slowly, taking care to see only the problem; don’t look at the answer until after you have solved or simplified the problem.

Skip to page 433, and complete problems 1-31 ODD. On page 434, complete problems 71-76 ODD. The problems on page 434 are a review from the previous subunit of approximating irrational numbers and locating them on a number line. Check your answers on pages 435-436.

Reading, taking notes, and completing the practice problems should take approximately 45 minutes.

``````-   [CCSS.Math.Content.8.EE.A.1](http://www.corestandards.org/Math/Content/8/EE/A/1)
-   [CCSS.Math.Content.8.EE.A.2](http://www.corestandards.org/Math/Content/8/EE/A/2)

attributed to the Department of Mathematics, College of the
Redwoods, and the original version can be found
[here](http://mathrev.redwoods.edu/PreAlgText/chapter5.pdf).
``````
• Did I Get This? Activity: Khan Academy’s “Square Roots of Perfect Squares” Link: Khan Academy’s “Square Roots of Perfect Squares” (HTML)

Instructions: This page provides a series of practice problems about square roots that you can answer and check online. There are also step-by-step hints along the way if you need additional guidance. Practice solving perfect squares until you feel confident that you understand how to recognize a perfect square (a minimum of 10 minutes of practice is recommended).

Completing this activity should take approximately 15 minutes.

Instructions: As you watch the video, write down the instructor’s example for finding a cube root. You should write down the entire process in your notebook to use for future reference.

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

``````-   [CCSS.Math.Content.8.EE.A.2](http://www.corestandards.org/Math/Content/8/EE/A/2)

``````

Instructions: As you watch the video, write down the instructor’s example for finding a cubed root of a non-perfect cube. You should write down the entire process in your notebook to use for future reference. As an eighth-grade student, you will be responsible for understanding perfect cubes. However, understanding how to find a cube root of a non-perfect cube is good practice.

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

Instructions: This page provides a series of practice problems about cube roots that you can answer and check online. There are also step-by-step hints along the way if you need additional guidance. Practice solving perfect cubes until you feel confident that you understand how to recognize a perfect cube (a minimum of 10 minutes of practice is recommended).

Completing this activity should take approximately 15 minutes.

1.3 Scientific Notation   In life, we often encounter numbers that are very large (world population) or very small (movement of plate tectonics in meters per week). In this subunit you will learn how to use scientific notation to express numbers.

• Explanation: James Sousa’s Mathispower4u: “Scientific Notation” Link: James Sousa’s Mathispower4u: “Scientific Notation” (YouTube)

Instructions: Watch as the instructor introduces two examples of scientific notation. Pause the video at the 0:40 mark. Write down the definition and two examples in your notebook. As you write down the examples, think about how each number converts into scientific notation. On the next slide, you will notice that strategies learned with integer exponents will also be used in scientific notation.

Pause the video at the 2:10 mark. Write down the information at the top of the slide, and solve the two examples at the bottom of the slide. Continue watching to check your solution.

Pause the video at the 4:20 mark. Write down the information at the top of the slide, and solve the two examples at the bottom of the slide. Continue watching to check your solution.

Pause the video at the 6:02 mark. Think about how subunit 1.2.1, “Integer Exponents,” will relate to multiplying and dividing numbers in scientific notation. Complete the examples on the next slide. It’s OK to check your work on the calculator, as shown in the video; however, using the rules of scientific notation does not usually require a calculator.

Pause the video at the 8:10 mark and complete the example problems. Watch the remainder of the video and check your solutions.

Watching the video, completing the practice problems, and taking notes should take approximately 15 minutes.

Instructions: This video provides you with a handful of problems to practice. Pause the video at 1:30 and solve the six problems listed. Watch the video to check your solutions. Continue watching as the instructor solves a multiplication problem and a division problem involving scientific notation. Follow along while taking notes in your notebook. At the end of the last two problems, the instructor shows that you have to make sure that the first number is greater than 1 and less than 10. It is important that you understand this and are able to write your answers in proper scientific notation.

Watching the video, completing the practice problems, and taking notes should take approximately 15 minutes.

1.3.1 Expressing Large and Small Quantities   - Explanation: CK-12: “Scientific Notation” Link: CK-12: “Scientific Notation” (HTML and YouTube)

Instructions: Read about scientific notation in the “Guidance” section. Make sure you feel comfortable expressing the powers of 10. Continue to read, and complete examples A, B, and C. Understand the solutions. Skip the two videos under “Video Review” and move into the “Guided Practice.” Watch the Khan Academy video. While watching, solve the problems with the instructor.

Reading this lesson, completing the examples, and watching the video should take approximately 30 minutes.

``````-   [CCSS.Math.Content.8.EE.A.3](http://www.corestandards.org/Math/Content/8/EE/A/3)
-   [CCSS.Math.Content.8.EE.A.4](http://www.corestandards.org/Math/Content/8/EE/A/4)

attributed to CK-12, and the original version can be found
[here](http://www.ck12.org/algebra/Scientific-Notation/lesson/Scientific-Notation/).
``````
• Did I Get This? Activity: Khan Academy’s “Scientific Notation Intuition” Link: Khan Academy’s “Scientific Notation Intuition” (HTML)

Instructions: This page provides a series of practice problems about scientific notation that you can answer and check online. There are also step-by-step hints along the way if you need additional guidance. Practice expressing scientific notation until you feel confident that you understand how to convert between scientific notation and decimal notation (a minimum of 10 minutes of practice is recommended).

Completing this activity should take approximately 15 minutes.

1.3.2 Operations with Scientific Notation   - Explanation: CK-12: “Operations with Numbers in Scientific Notation” Link: CK-12: “Operations with Numbers in Scientific Notation” (HTML and YouTube)

Instructions: This resource will help you understand how to complete operations while using scientific notation. One thing to recognize is that you don’t want to rely on needing to change a number into decimal notation to complete an operation. Use this resource to help you understand how numbers within scientific notation can be added, subtracted, multiplied, and divided.

Read the introduction and “Guidance” section. Take notes of the bold phrases and write down the example as you read. Read through the information about how to add and subtract. Notice the relationship between integer exponents and scientific notation when multiplying and dividing. Complete examples A, B, and C and understand their solutions.

Add the vocabulary words to your notes. Complete the “Guided Practice” and understand the solution. Watch the three videos. While you watch, solve the problems with the instructor.

Complete the “Practice” problems and check your solutions here.

Taking notes, solving practice problems, and watching the videos should take approximately 1 hour.

``````-   [CCSS.Math.Content.8.EE.A.3](http://www.corestandards.org/Math/Content/8/EE/A/3)
-   [CCSS.Math.Content.8.EE.A.4](http://www.corestandards.org/Math/Content/8/EE/A/4)
-   [CCSS.ELA-Literacy.RST.6-8.4](http://www.corestandards.org/ELA-Literacy/RST/6-8/4/)

attributed to CK-12, and the original version can be found
[here](http://www.ck12.org/algebra/Operations-with-Numbers-in-Scientific-Notation/lesson/Operations-with-Numbers-in-Scientific-Notation/).
``````
• Did I Get This? Activity: Illustrative Mathematics: “Giantburgers” Link: Illustrative Mathematics: “Giantburgers” (PDF)

Instructions: Solve the question using the information on page 1, trying to keep your values in scientific notation. In other words, don’t convert out of scientific notation just to have to deal with big values. Check your solution on page 2.

Completing the problem and checking your solution should take approximately 15 minutes.

• Did I Get This? Activity: Illustrative Mathematics: “Ant and Elephant” Link: Illustrative Mathematics: “Ant and Elephant” (PDF)

Instructions: Complete problems a and b. You do not need to research two cities that match the distance found for question b. Scroll down and read the commentary and the solutions on page 2.

Completing the problems and checking your solutions should take approximately 15 minutes.

• Checkpoint: Engage NY’s Grade 8 Mathematics: “Module 1, Lesson 9: Scientific Notation” and “Lesson 10: Operations with Numbers in Scientific Notation” Link: Engage NY’s: Grade 8 Mathematics: “Module 1, Lesson 9: Scientific Notation” and “Lesson 10: Operations with Numbers in Scientific Notation” (PDF)

Instructions: For Lesson 9, which begins on page 32, complete the “Classwork” problems, EVEN, and both problems under “Problem Set.” When you are done, check your “Classwork” here on pages 99-102 and the “Problem Set” here on pages 105-106.

For Lesson 10, which begins on page 37, complete the three “Problem Set” questions on the last page. When you are done, check your answers here on pages 112-113.

If you get a question wrong, learn from your mistake by re-solving the question. The solution pages have lots of extra information and teaching points. Use those pages to your advantage if you are struggling with a specific concept.

Completing the problems and checking your solutions should take approximately 45 minutes.