4 + 6 –5 + 8 –4 + (–2) –6 + (–3) 7 + (–6) 4 + (–8) Extension Questions: Suppose a + b = c and c < 0, give an example when this might happen. What do you know about a and b relative to each other for c < 0? Spiral Review 1. Order the following rational numbers from least to greatest. 2. What is the opposite of 15? 3. What is 40% of 220? Use a bar model. 4. Without using a calculator, determine which fraction is bigger in each pair. Justify your answer with a picture and words.
You ride your bike 12 miles and then get a flat tire! You turn around and walk the bike 4 miles before you mom is able to pick you up. How far are you from the house when your mom picks you up? Review: Place each of the following integers on the number line below. Label each point: 5. A = 4 B = –4 C = –15 D = 7 E = 18 F = –19 6. A = –20 B = –17 C = 7 D = 13 E = –6 F = 19 7. How did you locate 7 on the number line? 8. How did you locate –15 on the number line? 9. In general, how do you locate a positive or negative number on a number line?
Circle the operation you are going to perform. Find the sum using a number line for the following addition exercises. 6 + (–3) –3 + (–9) 15. –4 + (–4) 6 + (–6) –9 + 8 20 + (–8)
5 + 8 –4 + (–3) 7 + (–9) Circle the operation you are going to perform. Use the chip/tile or number line model to find the sum for each. 4 + (–4) Circle the operation you are going to perform. Find the sum for each. Justify your answer. 2 + (–7)
Circle the operation. Model 8 – 7 on the number line. Circle the operation. Model 8 – (–7) on the number line. Explain why the answers for the two problems above are so different. 11. What is 8 – 7? Explain. Circle the operation. Locate each value in the difference expression on the number line and compute the difference. –3 – (–10) –3 – 10 3 – 10 14 – 20
41. –2 – (–5) 42. –4 – 5 43. –1 + –4 44. 7 – 3 45. 5 + –3 46. 6 – 9 2.1e Homework: More Subtraction and Integers Write an equivalent addition expression for each subtraction expression and then simplify the expression. Subtraction Expression Addition Expression Simplify –7 – 3 6 – 11 12 – (–3) –6 – (–8) 14 – 10 –2 – 7 –8 – (–10) 5 – (–9)
0.8 3. Solve each of the following problems with or without a model. a) Wanda has 90 bracelets. She sells of the bracelets. How many bracelets did she sell? b) Chad invested $840. If he earned 20% on his investment, how much interest did he earn? How much does he have now? 4. Write a context for the following numeric expression: 2.1f Integer Addition and Subtraction Practice Solve. –4 + 9 = 11. 14 + 18 = 21. 9 – (–11) = 8 + (–8) = 12. –4 – 4 = 22. 8 – (–2) = 3 − 4 = 13. –3 + (0 – 9) = 23. –7 – 8 = –7 + 8 = 14. 5 – (–6) = 24. –8 + 10 = 4 − 2 = 15. 4 + (–10) = 25. –5 – 21 = –5 − 13 = 16. 6 – 9 = 26. 8 + (–10) =
Solve contextual problems involving adding or subtracting integers. [5] I struggle to solve contextual problems involving integers. I can usually write an expression to solve a contextual problem involving integers, but I struggle using that expression to get an answer. I can solve contextual problems involving integers. I can solve contextual problems involving integers. I can explain the solution in context. Sample Problems for Section 2.1 Draw a model (chips/tiles or number line) to solve each of the following addition problems. c. 1 + (–7) d. –3 + 7 Draw a model (chips/tiles or number line) to solve each of the following subtraction problems. c. 9 – (–2) d. –4 – 7 Find each sum without a model. c. 98 + (–1) d. –6 + 7 Find each difference without a model. c. 5 – (–3) d. –90 – 87 Solve each of the following contextual problems involving integers. Juan’s football team gains 3 yards on one play. On the next play, the quarterback is sacked for a loss of 10 yards. What was the net change in their position? Kathryn, Loralie, and Madison are playing golf. Kathryn ends with a score of 8. Loralie’s score is 4. Madison scores +5. What is the difference between the scores of Madison and Kathryn?
4. 2 × (–3) Means: –2 × 3 Means: 6. –2 × (–3) Means: Model each multiplication problem using a number line. Write the product in the space provided. 6 × (–3) =
–5 × (–3) = Means: Model: –7 × (–2) = Means: Model: –3 × 4 = Means: Model: –1 × (–1) = Means: Model: –5 × 0 = Means: Model:
12 ÷ 6 = h. 12 ÷ 1/3 = 12 ÷ 4 = i. 12 ÷ 1/4 = 12 ÷ 3 = j. 12 ÷ 1/6 = 12 ÷ 2 = k. 12 ÷ 1/12 = 12 ÷ 1 = What do you notice? Divide each: 1/2 ÷ 12 = q. 1/2 ÷ 1/2 = 1/2 ÷ 6 = r. 1/2 ÷ 1/3 = 1/2 ÷ 4 = s. 1/2 ÷ 1/4 = 1/2 ÷ 2 = t. 1/2 ÷ 1/6 = 1/2 ÷ 1 = u. 1/2 ÷ 1/12 = What do you notice? What is your conjecture about 12 ÷ 0 or 1/2 ÷ 0? Justify your conjecture. What do you think would happen if we took any (nonzero) number, b, and divided by 0? 2.3c Homework: Multiply and Divide Rational Numbers Multiplying and dividing rational numbers. For #5 - 13 estimate first, then compute.