CC Course 1 Beta Version Homelogout

CC Course 1 Beta Version Homelogout

CC Course 1 — Beta Version
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  • Introduction
  • Chapter 1
  • Chapter 2
  • Chapter 3
  • 3 Opening
  • 3.1.1
  • 3.1.2
  • 3.1.3
  • 3.1.4
  • 3.1.5
  • 3.1.6
  • 3.2.1
  • 3.2.2
  • 3.2.3
  • 3.2.4
  • 3 Closure
  • Chapter 4
  • Chapter 5
  • Chapter 6
  • Chapter 7
  • Chapter 8
  • Chapter 9
  • Reference
  • Teacher
  • Lesson
  • Answers
  • Teacher Notes
  • Sharing

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  • Doyou remember the famous frog-jumping contest from Chapter 1? Today you will work with more jumping frogs as you begin Section 3.2. In this section, you will work to solve problems that involve distances and directions using diagrams and numbers. This work will begin your investigation of integers(positive and negative whole numbers and zero).

In the frog-jumping contest described in Chapter 1, the final measurement represents the distance the frog moves away from a starting pad after three separate hops. The three hops of each frog in the contest can be different lengths and go in different directions. However, for today’s lesson, assume that frogs always hop along a straightline.

Now… hop to it!

  • 3-89. GETTING THERE
  • Elliott has been watching Dr. Frog take practice jumps all day. The frog keeps landing 15 feet from the starting pad after making three hops. Answer the questions below to consider ways that Dr. Frog can travel 15 feet in threehops.
  • How many combinations of hops can you find to move Dr. Frog 15 feet from where he started? Show your work with pictures, words, numbers, or symbols.
  • Can the frog move 15 feet in three equal hops?
  • If two of the frog’s hops are each 10 feet long, how could you describe the third hop so that he still lands 15 feet away from the starting pad? Is there more than one possibility?
  • 3-90. Elliott is so interested in the frogs that he is developing a video game about them. In his game, a frog starts on a number line like the one below. The frog can hop to the left and to the right.
  • For each part below, the game starts with the frog sitting at the number 3 on the number line. Use your Lesson 3.2.1 Resource Pageor3-90 Student eTool(CPM)to answer Elliott’s challenges below.
  • If the frog starts at 3, hops to the right 4 units, to the left 7 units, and then to the right 6units, where will the frog end up?
  • If the frog makes three hops to the right and lands on 10, list the lengths of two possible combinations of hops that will get it from 3 to 10.
  • Could the frog land on a positive number if it makes three hops to the left? Use an example to show your thinking.
  • Additional Challenge: The frog made two hops of the same length to the right and then hopped 6 units to the left. If the frog ended up at 11 on the number line, how long were the first two hops?
  • 3-91. OPPOSITES
  • Find the Math Notes box titled “Opposites,” which follows problem 3-93. After reading about opposites in the Math Notes box, answer the questions below.
  • Elliottplayed the frog video game twice. In each game, the frog made one hop. After the second game, the frog ended up the same distance from zero as after the first game, but on the opposite side of zero.

Describe the two games: How could the frog start at 3, hop once, and then in the second game again start at 3 and end up the same distance from zero, but in opposite direction as the first game? Give a possible set of hop directions, lengths, and ending points.

  1. How would the frog hop to meet the following requirements?
  2. From 3, make one hop and land on 6.
  3. From 6, make one hop and land on the opposite of 6.
  4. From the opposite of 6, make one hop to land on the opposite of the opposite of 6.
  5. How could you write “the opposite of the opposite of 6” using math symbols? Where would this be on the number line?
  • 3-92. While designing his video game, Elliott decided to replace some of his long sentences describing hops with symbols. For example, to represent where the frog traveled and landed in part(a) of problem 3-90, hewrote:

3 + 4 − 7 + 6

  1. How does Elliott’s expression represent the words in part (a) of problem 390? Where did the 3 come from? Why is one numbersubtracted?
  2. If another set of hops was represented by 5 − 10 + 2 + 1, describe the frog’s movements. Where did the frog start and where did it end up?
  3. One game used the expression −5 + 10. Where does the frog start? Where does it end up? What is special about the ending point?
  4. Another game had a frog start at the opposite of –3, hop 5 units to the left, 9units to the right, and then hop to its opposite position. Write an expression to represent the frog’s motion on the number line. Where did the frog end up?
  5. Where does the frog start in the expression −(−2) + 6? Where does it land?
  • 3-93. Another frog starts at −3 and hops four times. Its hops are listed at right.

Hop Lengths
Right 2 units
Left 7 units
Right 10 units
Left 3 units
  • If you have not done so already, write an expression (adding and subtracting) for the frog’s movements. Where does the frog end up?
  • Is it possible for the frog to finish at 2 on the number line if it makes the same hops in a different order?
  • Does the frog land in the same place no matter which hop the frog takes first, second, etc.?
  • Kamille says that for the frog to end up at –1, she can ignore the last three hops on the list. She says she only needs to move the frog to the right 2units. Is she correct? Why?
  • Give another set of four hops that would have the frog end up where it started at –3. Make the hops different lengths from one another. What needs to be true about the frog’s four hops? Are they somehow related to each other?
  • Opposites
  • The opposite of a number is the same number but with the opposite sign (+ or –). A number and its opposite are both the same distance from 0 on the number line.
  • For example, the opposite of 4 (or + 4) is −4, and the opposite of−9 is −(−9)=9 (or + 9). The opposite of 0.5 (or +0.5) is −0.5.
  • The opposite of an opposite is the original number.
  • Examples:
  • The opposite of the opposite of 5 is −(−(5)), or 5.
  • The opposite of the opposite of −3 is −(−(−3)), or−3.
  • The opposite of zero is zero.
  • 3-94. Lucas’ frog is sitting at −2on the number line. 3-94 HW eTool (CPM).Homework Help ✎
  • His frog hops 4 units to the right, 6 units to the left, and then 8 more units to the right. Write an expression (sum) to represent his frog’s movement.
  • Where does the frog land?
  • What number is the opposite of where Lucas’ frog landed?
  • 3-95. Draw and label a set of axes on your graph paper. Plot and label the following points: (1,3), (4,2), (0,5), and (5,1). Homework Help ✎
  • 3-96.Rewrite each product below using the Distributive Property. Homework Help ✎
    Then simplify to find the answer.
  • 18(26)
  • 6(3405)
  • 21(35)
  • 3-97. Compute each sum or difference. Homework Help ✎
  • 3-98. A seed mixture contains ryegrass and bluegrass. If 40% of the mixture is ryegrass, what is the ratio of ryegrass to bluegrass? Homework Help ✎

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