Download Adding and subtracting integers

Teacher Version
Adding and subtracting integers
Student Activity Sheet 2; use with Exploring “Modeling with algebra tiles”
Note to teachers: The sheet refers to algebra tiles, but you may use any 2 color counters;
just make sure you are clear about which color is negative.
[EX1, pages 2–4]
Two numbers are additive inverses if their sum is zero. Opposites are also called zero pairs
because they “pair up” to form a sum of 0. We can use algebra tiles to model integer
equations. Look for zero pairs:
6 + -4 =
4 zero pairs
6 + -4 = 2
Use the space below to record the problems that you do and/or your work with algebra tiles.
Think about the question below as you work.
Note to teachers: Students can record the problems they do, and draw one or two
problems. Students should do 5 + -9, and -3 + -4, from pages 4 and 5; in addition to other
problems that are displayed in the Explorings.
When adding integers, when will your result be negative? Positive? Zero? [EX1, page 6]
The result will be negative if both integers are negative, or if there are more negative
tiles than positive tiles (the absolute value of the negative integer is greater than the
absolute value of the positive integer.)
The result will be positive if both integers are positive, or if there are more positive tiles
than negative tiles (the absolute value of the positive integer is greater than the
absolute value of the negative integer.)
The result will be zero if the integers are opposites, additive inverses, or form a zero
pair
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 1 of 4
Teacher Version
Adding and subtracting integers
Student Activity Sheet 2; use with Exploring “Modeling with algebra tiles”
Note to teachers: Although we did not show an example in the topic, you can use algebra
tiles or 2 color counters to model subtraction as well as addition. This Student Activity
Sheet gives you an opportunity to do so with your students. The sheet refers to algebra
tiles, but you may use any 2 color counters; just make sure you are clear about which color
is negative.
REINFORCE Using algebra tiles to subtract integers
To model subtraction, begin by representing the first integer. But for the second integer
don’t move counters onto the workspace. Instead “take away” counters. If there are no
counters, or not enough, already on the workspace to take away, add zero pairs until you
have the number needed to subtract.
Example: Model 3 – 5.
First, model the first integer, 3.
Next, you want to take away, or subtract, 5. But you only have 3. So you need to add in 2
zero pairs. Remember adding zero pairs does not change the sum, because it is the same as
adding zero.
Now, you have enough to subtract 5. You are left with the answer, -2.
Now it’s your turn.
1. Model -3 – (-2). Answer -1
Model -3 by drawing in the tiles.
Model subtracting -2 by marking through the tiles you are removing. If you need to add in
zero pairs first, draw them in and then mark through.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 2 of 4
Teacher Version
Adding and subtracting integers
Student Activity Sheet 2; use with Exploring “Modeling with algebra tiles”
2. Model 5 – (-1). Answer 6
Model 5 by drawing in the tiles.
Model subtracting -1 by marking through the tiles you are removing. If you need to add in
zero pairs first, draw them in and then mark through.
3. Model -5 – (-8). Answer 3
Model -5 by drawing in the tiles.
Model subtracting -8 by marking through the tiles you are removing. If you need to add in
zero pairs first, draw them in and then mark through.
4. Model 10 – 12. Answer -2
Model 10 by drawing in the tiles.
Model subtracting 12 by marking through the tiles you are removing. If you need to add in
zero pairs first, draw them in and then mark through.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 3 of 4
Teacher Version
Adding and subtracting integers
Student Activity Sheet 2; use with Exploring “Modeling with algebra tiles”
5. Model -4 – 8. Answer -12
Model -4.
Model subtracting 8 by marking through the tiles you are removing. If you need to add in
zero pairs first, draw them in and then mark through.
Model and record additional problems. Think about how subtraction of integers might be
related to addition of integers. This will be discussed further in the other Explorings.
Note to teachers: Students can record any additional problems without drawing, but still
using number tiles. Students may begin to see the connection between subtracting a
number, and adding its opposite. This does not need to be explained or written at this
point, but students can begin to think about the relationship.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 4 of 4