1. 6th grade Math Miss Quimby’s Class
Integers
6th grade Math
Miss Quimby’s Class

2. Table of Contents Lesson 1:What are integers?
Lesson 2: How do I add integers?
Lesson 3: How do I subtract integers?
Lesson 4: How do I multiply integers?
Lesson 5: How do I divide integers?
Lesson 6: How do I solve an expression that may contain integers using the order of operations?
Essential Question:
Students will write the essential question for each lesson on the next clean page of their notebooks. Any notes for the essential question will go directly below and continue until a new essential question.

3. EQ: What are Integers? Compare Compare a number line to a thermometer.
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Compare
Compare a number line to a thermometer.
How are they alike?
How are they different?
Activating Strategy:
Give students 2 minutes to brainstorm with a partner ways that a thermometer is like and unlike a number line. When time is up, call on students to share their ideas. Write their ideas on the board.
EQ: What are Integers?

4. EQ: What are Integers? Key Vocabulary
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Key Vocabulary
Integer: The set of whole numbers and their opposites.
Not a decimal or a fraction
Example:
…, -3, -2, -1, 0, 1, 2, 3…
… means to continue with no end
The opposite of 1 is -1
Construct Meaning:
Students will write the key vocabulary under the essential question. Discuss what an integer means.
EQ: What are Integers?

5. EQ: What are Integers? Positive vs. Negative Positive integers
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Positive vs. Negative
Positive integers
Integers greater than zero
Shown with a + or no sign
Example:
3, +3, (+3)
Negative Integers
Integers less than zero
Shown with a –
-3, (-3)
*Zero is neither positive or negative
Construct Meaning:
Students need to be able to recognize positive and negative integers when working with integers. A parentheses () will often help keep the problem organized so students don’t get confused as to what is a positive/negative sign vs. a plus/minus sign.
EQ: What are Integers?

6. EQ: What are Integers? Real-Life Words Positive Integer (+)
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Real-Life Words
Positive Integer
(+)
Negative Integer
(-) Up
Down
Forward
Backward
Gain
Lost
Organize:
Real life situations involve integers as well. Students should be familiar with the following terms and if they denote a positive or negative integer:
Up (+)
Down (-)
Forward (+)
Backward (-)
Gain (+)
Loose (-)
* Have students think of more words that they might see to show positive and negative integers.
EQ: What are Integers?

7. EQ: What are Integers? Examples
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Examples
Write an integer for the following situations.
1. The Dead Sea is 1,312 feet below sea level.
-1,312 feet
2. Cecilia lost 5 pounds.
-5 pounds
3. The quarterback gained 6 yards on the play.
+ 6 yards
4. A helicopter rises 75 feet in the air.
+ 75 feet
Construct Meaning:
Go through the examples. Prompt students in the beginning to get the answers you are looking for. Say things like: Would you write 1,312 as a positive or a negative integer?
Ask students to tell which word gave them a hint that they needed to use positive or negative.
As you work your way through examples, students will need less support.
EQ: What are Integers?

8. EQ: What are Integers? Comparing Integers Use a number line
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Comparing Integers
Use a number line
Numbers get smaller
Numbers get bigger
Construct Models:
Students need to understand that as you move right on the number line, integers get bigger, and as you move left on the number line numbers get smaller.
EQ: What are Integers?

9. EQ: What are Integers? Examples
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Examples
Graph the following integers on the number line.
1. + 9
2. -7
3. 3
Construct Models:
Show students how to graph integers on a number line.
EQ: What are Integers?

10. BUT EQ: What are Integers? Bigger or Smaller?
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Bigger or Smaller?
Integers can get tricky so watch out!
A bigger positive = bigger number
BUT
A bigger negative = smaller number
Think of the number line for help!
Store:
Students need to be careful when working with integers. Bigger negatives really mean smaller numbers. Have them think about a number line or a thermometer when working with negatives. I would rather is be -5 degrees then -20 degrees because -20 is way smaller temperatures.
EQ: What are Integers?

11. EQ: What are Integers? Its Way too Cold!!!! Think about it!
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Its Way too Cold!!!!
Think about it!
Would you rather it be -5 degrees or -20 degrees?
Which one is colder?
Which one is a smaller number?
Store:
Students need to be careful when working with integers. Bigger negatives really mean smaller numbers. Have them think about a number line or a thermometer when working with negatives. I would rather is be -5 degrees then -20 degrees because -20 is way smaller temperatures.
EQ: What are Integers?

12. EQ: What are Integers? Examples
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Examples
Use <, >, or = to compare the following integers.
1. + 3; -1
+3 > -1
2. -8; -4
-8 < -4
3. 0; -2
0 > - 2
EQ: What are Integers?

13. EQ: What are Integers? Explain
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Explain
Which is higher, 5 feet below seas level or 4 feet below seas level? Explain your answer using words, symbols or pictures.
EQ: What are Integers?

14. EQ: How do I add integers?
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Brain Pop
Adding and Subtracting Integers
EQ: How do I add integers?

15. EQ: How do I add integers?
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Try the Activity
Solve It
Complete the Brain Pop Activity page.
You will need two different colored pencils.
EQ: How do I add integers?

16. EQ: How do I add integers?
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Adding Integers
Same Signs Sum
Ignore the signs and add
Positive + Positive = Positive
Example:
5 + 3 = 8
Negative + Negative = Negative
Example
-5 + (-3) = - 8
EQ: How do I add integers?

17. EQ: How do I add integers?
Table of Contents
Adding Integers
Different Signs Difference
Ignore the signs and subtract: bigger – smaller
The answer gets the sign of the bigger number.
Example:
3 + (-5) = -2
= 2
EQ: How do I add integers?

18. EQ: How do I add integers?
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Examples
Different signs difference
6 - 4 = 2 2
(-7)
Same signs sum
2 + 7 = 9 -9
6 + 3 = 9 +9
= 2
(-5)
Different signs difference
5 – 3 = 2 -2
10 – 10 = 0
= -2
= -9
= 0
= 9
EQ: How do I add integers?

19. Class work Complete the Football Frenzy Adding Integers packet.
You may work with a partner or by yourself.
After you complete each page, raise your hand to get your work checked before you move on!
The last page in the packet will not be checked and collected for a quiz grade!

20. Mad Minute Integers
Do as many problems from 11-3 Practice Adding Integers as you can in 3 minutes.
Race yourself only.
How did you do?
Where are you going wrong?
Try to fix your mistakes on 5-4 Practice Adding Integers.
Do it again
Try to do better this time on 11-3 Practice Adding Integers.

21. How do you solve this using integer chips?
-5 – 4
First, you need 5 negative integer chips.
Next, subtraction tells you to take 4 positive integer chips away.
There are no positive integer chips to take away.
We must add 4 zero pairs
Now, take away 4 positive integer chips.
What is left is the answer.
-5 – 4 = -9 - - - - - - - - - + + + +

22. Subtracting Integers Keep-Change-Change
Keep the first integer the same
Change – to +
Change the second integer to its opposite
Now follow the rules for adding integers.
Same Signs Sum
Different Signs Difference

23. 4 + - (+5) (-5) Example 1. 4 – (-5) Now, you have 4 + (+5)
Same Signs Sum: = 9
Keep
Change
Change 4 + -
(+5)
(-5)

24. -3 + - (-2) 2 Example 2. -3 – 2 Now, you have -3 + (-2)
Same Signs Sum: -3 + (-2) = -5
Keep
Change
Change -3 + -
(-2) 2

25. Graphic Organizer Brainstorm
Think about what you have learned about adding and subtracting integers.
Then, complete the Brain Pop Graphic Organizer