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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