Name Core Date Accentuate the Negative

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1 Name Core Date Accentuate the Negative Investigation 2 Additional Practice Problem 1 Extending Addition to Rational Numbers FOCUS QUESTION: How can you predict whether the results of addition of two numbers will be positive, negative, or zero? Find the sum without using a calculator. 1) ) ) ) ) ) ) ) ) ) + 1/ /3 11) - 2/ /12 12) - 6/ /5 13) Find each sum. a) b) c) d) ) Write an addition number sentence that matches each diagram. a) b) c) d)

2 Complete the chip board below so that it has 14 black chips and 8 red chips. 15) What is the value on the board? 16) Write a number sentence to represent each situation. Then, find the new value of the chip board. a) Remove 5 black chips from the original board. b) Then add 4 red chips. c) Then add 16 red chips and 16 red chips. 17) Use the commutative property of addition to find each value. a) b) - 7/ c) / What confused you on your first attempt? What do you GET now? Describe the strategy you are using find the total value of a combination of positive and negative integers?

3 Name Core Date Accentuate the Negative Investigation 2 Additional Practice Problem 2 Extending Subtraction to Rational Numbers. FOCUS QUESTION: How is a chip model or number line useful in determining an algorithm for subtraction? Find the difference without using a calculator. 1) ) ) ) ) ) ) ) ) ) + 3/ /2 11) - 3/ /5 12) - 3/ /10

4 13) ) ) ) ) ) ) ) ) ) ) ) What confused you on your first attempt? What do you GET now? Describe the strategy you are using find the total value of a combination of positive and negative integers?

5 Name Core Date Accentuate the Negative Investigation 2 Additional Practice Problem 3 The + / - Connection. FOCUS QUESTION: How are the algorithms for addition and subtraction of integers related? Graph What confused you on your first attempt? What do you GET now? Name Core Date Accentuate the Negative Investigation 2 Additional Practice Problem 4 Fact Families. FOCUS QUESTION: What related sentence is equivalent to 4 + n = 43 and makes it easier to find the value of n? Follow Name Core Date

6 Accentuate the Negative Investigation 2 Test Review Problems 1-4. FOCUS QUESTIONS: How can you predict whether the results of addition of two numbers will be positive, negative, or zero? How is a chip model or number line useful in determining an algorithm for subtraction? How are the algorithms for addition and subtraction of integers related? What related sentence is equivalent to 4 + n = 43 and makes it easier to find the value of n? Write the algorithm for adding numbers with the same sign. Write the algorithm for adding numbers with different signs. Write the algorithm for subtracting numbers. What does it mean to say that an operation in commutative? Describe when you would need to use a zero pair.

7 1. Write 1 equivalent statement to Write 1 equivalent statement to Write 1 equivalent statement to Insert <, >, or = to make the following statements true. Explain your reasoning. a) -1/2-0.3 b) c) d) -4/ Use the number line below to show this problem and find its value. -2/ /5

8 6. Rewrite these numbers in order from least to greatest. a. -5/4, 1 2/3, -1/2, 14/6 b , -4, 1.23, Heather wrote the equation x - 13 = 5. Find the value of x and explain how you found it. 8. Find the distance between the following numbers on a number line. Explain your reasoning. a. 10 and -7 b. 14 and 29 c. -5 and -20 d. -5 and 10

9 9. Find each value. a b c d e f g h Decide whether the statements below are true or false. If it is false, give a number sentence for proof. a. The sum of a positive number plus a positive number is always positive. b. The sum of two negative numbers is always negative. c. The sum of a negative number and a positive number is always positive. d. The difference of two positive numbers is always positive. e. The sum of a number and its opposite is always zero. Negative 0 Positive

10 Accentuate the Negative Investigation 2 ReTest Practice Problems 1-4. FOCUS QUESTIONS: How can you predict whether the results of addition of two numbers will be positive, negative, or zero? How is a chip model or number line useful in determining an algorithm for subtraction? How are the algorithms for addition and subtraction of integers related? What related sentence is equivalent to 4 + n = 43 and makes it easier to find the value of n? Write the algorithm for adding numbers with the same sign. Write the algorithm for adding numbers with different signs. Write the algorithm for subtracting numbers. What does it mean to say that an operation in commutative? Describe when you would need to use a zero pair.

11 1. Write 1 equivalent statement to Write 1 equivalent statement to Write 1 equivalent statement to Insert <, >, or = to make the following statements true. Explain your reasoning. a) -1/4-0.3 b) c) d) -2/ Use the number line below to show this problem and find its value. -3/ /10

12 6. Rewrite these numbers in order from least to greatest. a. -3/4, 2 1/3, -1/3, -11/6 b , -3, 2.3, -1/3 7. Heather wrote the equation x - 6 = 13. Find the value of x and explain how you found it. 8. Find the distance between the following numbers on a number line. Explain your reasoning. a. 12 and -4 b. 8 and 23 c. -12 and -18 d. -9 and 11

13 9. Find each value. a b c d e f g h Decide whether the statements below are true or false. If it is false, give a number sentence for proof. a. The sum of a number and its opposite is always zero. b. The difference of two positive numbers is always positive. c. The sum of a positive number plus a positive number is always positive. d. The sum of a negative number and a positive number is always positive. e. The sum of two negative numbers is always negative. Negative 0 Positive

14 Using a Number Line for Adding and Subtracting Rational Numbers ADDING: When adding on a number line follow this pattern Start + Change = Finish 1. First label your problem 2. Next, place your Start number on the number line 3. Now, draw an arrow for the change number (to the right for positive, to the left for negative) 4. Find where your arrow ends, that is your Finish number (the answer) Try it!! a b c d e f g h

15 Using a Number Line for Adding and Subtracting Rational Numbers SUBTRACTING: When subtraction on a number line follow this pattern Finish - Start = Change 1. First label your problem 2. Next, place your Start number on the number line and label it with an S 3. Next, place your Finish number on the number line and label it with an F 4. Now draw your arrow from the Start number to the Finish number 5. Your arrow is your Change (the answer), find how long it is and what direction it is pointing (to the right is positive, to the left is negative) Try it!! a b c d e f g h