Licensing information
• Users should treat this material as a working draft. This
material can be used in its current form, customized,
and/or printed or displayed by the user.
• The author(s) request feedback on all materials so that
they can be continually improved and updated.
• This material is licensed under the Creative Commons
Attribution-Share Alike license:
(http://creativecommons.org/licenses/by-sa/3.0/).
• Author: Kevin Hall
Wording for the legal statement above is adapted from the legal statement for
Trigonometry, published in 2009 by The CK-12 Foundation: http://about.ck12.org/
• Today, some slides are just for discussion.
• On other slides, you should practice on your own (by
writing on the handout).
− How can you tell which slides involve
writing on the handout?
− You will see a little number fly in, like this:
1).
That’s the question
number on the handout.
We’ll Play “Attack & Defend” with Integer Subtraction
• “Integers” are whole numbers or negative whole numbers.
1).
Integers:
Not Integers:
-3
-3.5
same as 5
List all the integers?
72
3
7
-0.3249
-3,249
5.0
5.1
{…-3, -2, -1, 0, 1, 2, 3, …}
2). Quick Review of Addition:
8+
-5
= 3
10
What’s left
is 3.
5
0
-5
New Topic:
• Now that we know how to ADD
integers, we’re going to learn …
how to SUBTRACT integers.
• Examples:
8–5
5–8
8 – -5
-8
– -5
-8
–5
-5 – -8
-5 – 8
5 – -8
• How do you tell them all apart?
-10
Discussion 1
Please show how to subtract with your fingers
a). 4 – 2 = ?
Who can demonstrate?
b). 2 – 4 = ?
What’s
wrong?
Please show how to subtract with your fingers
c). 3 – 9 = ?
d). 9 – 3 = ?
9–4=5
Start:
9 Pos.
Take away
4 Pos.
-9
– -4 = -5
Start: Take away
9 Neg.
4 Neg.
10
10
What’s left
is 5.
5
5
0
0
-5
-5
What’s left
is -5.
-10
-10
3).
Please draw pictures for these, on your own:
-6
– -2 = -4
Start: Take away
6 Neg. 2 Neg.
10
0
-10
– 2=
10
5
0
What’s left is -4.
can’t do yet
Start: Take away
6 Neg. 2 Pos.
Uh-oh. What’s
the problem?
5
-5
-6
-5
-10
4). Please do each problem, showing a picture:
2 – 7=
can’t do
Start: Take away:
2 Pos. 7 Pos.
7–2= 5
Start: Take away:
7 Pos. 2 Pos.
10
10
5
5
Oops, not
enough to
take away.
7 – -2 =
Start: Take away:
7 Pos. 2 Neg.
10
What’s
left is 5.
5
0
0
0
-5
-5
-5
-10
-10
can’t do
-10
Oops. We
have no
negatives to
take.
Discussion 2
Discussion about “taking away”
What’s the problem we sometimes have
with “taking away?
11 – 3 = 8
11 – 3 = 8
Start with
11 Pos.
To take away
3 positives…
10
What’s left
is 8.
How can you
get rid of 3 Pos
without “taking
away”?
5
0
10
What’s left
is 8.
5
Take away
3 Pos.
0
Your ideas?
-5
-10
-5
-10
we’ll add 3
negatives
5). To “take away” something, we’ll cancel it out
a). 4 – 12 How do you take
c). 3 + -2
b). 3 – -2 How do you take
away 12 Pos?
away 2 Neg?
You add 12 Neg.
You add 2 Pos.
You are NOT supposed to take away 2 Neg
here. What are you supposed to do? Why?
You’re supposed to ADD 2 Neg,
because it has a “+” sign.
6). Please try on your own. To “take away” something, cancel it out.
8–6= 2
Start Take away
8 Pos. 6 Pos.
10
-4
– -3 =
Start:
4 Neg.
-1
Take away
3 Neg.
10
What’s left
is 2.
5
5
0
0
-5
-5
-10
What’s left is -1.
-10
7). Let’s practice just drawing the picture for each problem:
3 – -8 =
3–8 =
Start: Take away:
3 Pos. 8 Pos. by adding
8 Neg.
10
Start: Take away:
3 Pos. 8 Neg. by adding
8 Pos.
3 + -8 =
Start:
3 Pos.
10
10
5
5
5
0
0
0
-5
-5
-5
-10
-10
-10
Add:
8 Neg.
The biggest mistake people make is…
8).
• Forgetting the difference between ADDING
and SUBTRACTING.
• Let’s practice that skill.
9). Please explain the steps in this example.
a). What’s the difference between the two questions below?
Let’s try to solve the questions using pictures.
-5
b). Can you
explain this?
–2 =
-5
Start:
5 Neg.
Start:
5 Neg.
5
5
+2=
d). Why do we
do this?
0
-5
0
-7
c). Why do
this?
-5
-3
10). Please do these questions on your own.
a).
-1
+
-4
=
b).
-1
– -4 =
Start: Take away:
5 Neg. 4 Neg.
Start: Add:
1 Neg. 4 Neg.
5
5
3
0
-5
0
-5
-5
Example: Study this to help with #11.
11). Practice: Try this on your own.
What question goes with this picture?
What question goes with this picture?
_______=
-6
_______=
10
10
5
5
0
Take 0
away
4 Neg
– -4
b).
Add
4 Pos.
+4
-5
-5
- 10
-5
Start with -10
Start with -9
- 10
Right:
Example: Is this picture shown
correctly?
8 + -5 =
8 + -5 =
Add: 5 Neg.
10
10
5
5
0
What do
you think?
0
-5
-5
- 10
- 10
12). Practice: Is this picture correct?
a).
-2
– 10 =
Example: Is this picture correct?
a).
-2
Take away: 10 Pos.
Add: 10 Pos.
10
10
5
5
What do
you think?
0
-5
0
-5
- 10
+ 10 =
- 10
Drill Practice
13). Practice: Draw each picture and find each answer.
-1
– -9 =
Start: Take away:
1 Neg. 9 Neg.
10
5
8
3 + -6 =
Start: Add:
3 Pos. 6 Neg.
3 – -6 =
Start:
3 Pos.
10
10
5
5
Take away:
6 Neg.
9
0
0
-5
-5
-10
-10
0
-3
-5
-10
14). Practice: Draw each picture and find each answer.
5–7 =
Start: Take away:
5 Pos. 7 Pos.
10
7–5 =
Start: Take away:
7 Pos. 5 Pos.
10
5
5
0
0
-5
-10
-2
-4
Start:
4 Neg.
+ -6 =
Add:
6 Neg.
10
2
5
0
-5
-5
-10
-10
-10
The game of Attack & Defend
with subtraction
How to play Attack & Defend with subtraction
• Cards look like this:
t+
-2
Shows how this card will add or take away
chips.
t = your total points right now.
How to Track Your Chips:
Chips you
already have
5
0
-5
New chips
from
this card
Practice:
Chips you
already have
5
15).
• You have 5 chips right now.
• You get this card:
t +
-2
0
Add -2
-5
New chips
from
this card
Example:
This person started the round with ____ chips.
The card said
t +1
5
0
-3
-5
Add 1 Pos.
16).
BEFORE this card, you
-2 chip(s).
had ___
The card you get is:
AFTER this card, you
1 chip(s).
have ___
t – -3
10
Take away
3 Neg.
5
0
-5
-10
By adding
3 Pos.
17).
Before this card, you
1 chip(s).
had ___
The card you get is:
t –4
10
Cancel out
4 Pos.
5
0
-5
-10
By adding
-3 4 Neg.
After this card, you
have _____ chip(s).
18).
Before this card, you
-3
had _____
chip(s).
The card you get is:
t + -4
10
Add
4 Neg.
5
0
= -7
-5
-10
After this card, you
have _____ chip(s).