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Lesson 3.2.1 – Teacher Notes Standard: 7.NS.1c Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. c) Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. • Full mastery by end of chapter Lesson Focus: Focus is to model with integer tiles and on a number line how to subtract integers. *Remember, “-“ can be read as “the opposite of”, this may come in handy with some of the problems. (3-26 and 3-27) • I can apply commutative, associative, and identity properties to add and subtract rational numbers. Calculator: No Literacy/Teaching Strategy: Think-Pair-Share (3-24); Pairs Check (3-26) Bell Work In Chapter 2, you worked with adding and multiplying integers (positive and negative whole numbers and zero). In this lesson, you will use + and – tiles to learn about subtraction of integers. Keep the following questions in mind as you work with your team today. At the end of the lesson, you will discuss your conclusions about them. How can we remove negative tiles when the collection has only positive tiles? How can we think about subtraction when there are not enough to “take away”? When does subtracting make the result larger? 3-24. Examine the assortment of positive and negative tiles. What integer does this assortment represent? a. What happens if three + tiles are removed? How can you use numbers and symbols to represent this action and the resulting value? b. What happens if three – tiles are removed from the original set of tiles? Again, how can you represent this action and the result using numbers and symbols? 3-25. It is often useful to represent operations and expressions in multiple ways. These ways include: • • • • A diagram (for example, using + and – tiles or with a number line) A numerical expression A situation described in words The total value In each part labeled (a) through (c) below, one representation is given. Work with your team to create each of the other representations. a. b. −8 −(−3) c. It is cold! The first time I looked at the thermometer today, it said it was 0 degrees Fahrenheit. Then it dropped 5 degrees! How cold is it now? 3-26. For each of the expressions below: • • • • Build an assortment of tiles that represents the first integer. Explain how to subtract using words. Find a way to draw the process on your paper. Record the expression and result as a number sentence. a. 7 − 5 b. 0 − 4 c. −6 − 2 d. 3 − (−4) e. −8 − (−5) f. −1 − (−9) 3-27. Subtraction can also be represented on the number line model. a. Sketch the number line above on your paper. b. How can you represent 2 − 7 using the number line? Discuss your ideas with your team and use the number line to represent your answer. c. How can you represent 1 − (−2) using the number line? Again, discuss your ideas with your team and use the number line to represent your answer. Practice 1.7 − 13 5. 318 − −864 2. −832 − 1129 6. 108719 − −8329 3. 63 − 94 7. −85 − −106 + 18 4. −231 − −231 8. 121 + −632 − −11