2. © Teacher Created Materials Today’s Lesson Adding and Subtracting Rational Numbers

3. © Teacher Created Materials Let’s warm up today by practicing adding and subtracting money. Warm-up Activity

4. © Teacher Created Materials Look at the following dollar amounts: $2.45 $5.82 $4.24 $3.00 $0.50 $6.89

5. © Teacher Created Materials If we add them together, what do we get? $2.45 $5.82 $4.24 $3.00 $0.50 $6.89 + $22.90

6. © Teacher Created Materials If we switch the order of the numbers and then add them, do we still get the same answer? $5.82 $0.50 $3.00 $6.89 $4.24 $2.45 + $22.90 YES!

7. © Teacher Created Materials The fact that you can arrive at the same answer, even after switching around the numbers, is called the commutative property of addition.

8. © Teacher Created Materials Write subtraction problems using the dollar amounts from the previous activity. Does the commutative property rule still apply? NO!

9. © Teacher Created Materials Today, you will be adding and subtracting decimals, fractions, and negative numbers. Whole-Class Skills Lesson

10. © Teacher Created Materials We can represent one-half by using the counters below. One-half of the counters is white.

11. © Teacher Created Materials We know this because there are two counters in the set (denominator). One of the counters is white (numerator). 1 2

12. © Teacher Created Materials How could we represent four-fifths with the counters? Four-fifths of the counters are red.

13. © Teacher Created Materials Like with one-half, there are five counters in the set (denominator). Four of the counters in the set are red (numerator).

14. © Teacher Created Materials Look at the counters below, what fraction of them are white? Two-fourths are white.

15. © Teacher Created Materials Look at the counters below, what fraction of them are white? Three-sixths are white.

16. © Teacher Created Materials Look at the counters below, what fraction of them are white? Four-eighths are white.

17. © Teacher Created Materials Notice, even though we added counters each time, each of these sets shows one-half of the counters white.

18. © Teacher Created Materials So, ===

19. © Teacher Created Materials Let’s add fractions now. Look at the counters below. + First, let’s convert these to fractions.

20. © Teacher Created Materials + are white We have the same denominator, so we can add. are white

21. © Teacher Created Materials 6868 5858 11 8 += Notice, the denominator stayed the same. We add the numerators. Same denominator, so we’re ready to add.

22. © Teacher Created Materials Another example … this can also be written as … 0.6 + 0.5 = 1.1 (one and one-tenth) + = =1

23. © Teacher Created Materials Try these problems. 0.9 + 0.1 = 1.6 + 0.8 = 6.2 + 5.2 = 7.9 – 4.6 = 3.5 – 2.5 = 1.0 2.4 11.4 5.3 1.0

24. © Teacher Created Materials To subtract from a negative, move further down the negative number line. – 9 – 5 = –9–10–11–12–13–14–15 Start at –9. Move five units in the negative direction (left). Your answer is –14.

25. © Teacher Created Materials Try these examples. 3.6 + 6.7 = 9.2 – 4.9 = –5.1 + 3.2 = 0.5 – 1.6 = –4.7 – 2.1 = 10.3 4.3 –1.9 –1.1 –6.8 = = + = 8 13 1 8 5 + – = 9 4 + = 6 4 3 2

26. © Teacher Created Materials Complete these rule statements: To add two positive numbers, _____________. To add two negative numbers, ____________. To add two numbers of different signs, _____. To subtract two numbers, ________________.