1. Warm up: Fill in Agenda. Complete the number sort on the board
Warm up: Fill in Agenda! Complete the number sort on the board. Tape in to your notebook over the notes we did on Friday! CW: Integers and Absolute Value HW: Pg. 195 #'s 1,2,6,8,11,16

2. Integers and Absolute Value
What is the important vocab. for this lesson?
Integer: any number from a set 
{…,-4, -3, -2, -1, 0, 1, 2, 3, 4,…}, where ...means continues without end.
Negative integer-less than zero (-)
Positive integer- greater than zero (+)
Absolute Value- numbers that are the same distance from zero.

3. How can I graph an integer?
Integers can be shown on number lines.
To graph, I would put a dot where the number is on the number line.

4. How would I write these integers?
An average temperature of 5 degrees below normal.
An average rainfall of 5 inches above normal
What are the key terms?
How would I graph them?

5. Graphing Integers
Take a moment and graph these integers on a number line in your notebook.
{-4, -2, 0, 4, 7}
Check with my answer.

6. Absolute Value
 IS ALWAYS POSITIVE!!!!!!!!

7. Hit the lights!!!!!!!!! Example Practice on the board!

8. Integers with Manipulatives

9. Arizona College and Career Ready Standards:
7.NS.A.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
a. Describe situations in which opposite quantities combine to make 0.
b. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
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 differences, and apply this principle in real-world contexts.
7.NS.A.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐world contexts.
b. Understand that integers can be divided, provided that the divisor in not zero, and every quotient of integers is a rational number. If p and q are integers, then –(p/q) = (-p)/q = p/(-q)

10. Operations with integers can be modeled using two-colored counters.
Positive +1
Negative -1

11. The following collections of counters have a value of +5.
Build a different collection that has a value of +5.

12. The collections shown here are “zero pairs”.
They have a value of zero.

13. When using two-colored counters to model addition, build each addend then find the value of the collection.
5 + (-3)
= 2
zero pairs

14. Build the following addition problems:=
2) =
4 + 5 =
-6 + (-3) =

15. When using two-colored counters to model subtraction, build a collection then take away the value to be subtracted.
For example: 9 – 3
= 6
take away

16. Here is another example: –8 – (–2) = –6
take away

17. Build the following:
–7 – (–3) =
6 – 1
–5 – (–4)
8 – 3 = = =

18. Can’t do it? Think back to building collections in different ways.
Now try to subtract +5.
Can’t do it? Think back to building collections in different ways.

19. Now build –6, then add 5 zero pairs. It should look like this:
This collection still has a value of –6. Now subtract – 5 = -11

20. Another example:
5 – (–2)
Build 5:
Add zero pairs:
Subtract –2:
5 – (–2) = 7

21. Try building the following:
1) 8 – (–3)
–4 – 3
–7 – 1
9 – (–3) = = = =

22. When using two-colored counters to model multiplication, 3 × 4 means 3 groups(or copies) of 4+
3 × 4 = 12

23. 3 × (–2) means 3 groups of –2 or 3 copies of -2:+
3 × (–2) = –6

24. Solve the following:
1) 5 × 6
2) –8 × 3
3) 7 × (–4)
4) 6 × (–2) = = = =

25. When using two-colored counters to model division, build the collection of tiles to separate into equal groups (or copies) ÷ +5 = -3
Divide -15 into 5 equal groups
5 equal groups of -3

26. Solve the following:
1 ) ÷ +6 =
2) ÷ + 2 =
3) ÷ + 5 =
4) 9 ÷ - 3 =