1. UNIT 2
Integers

2. Integers Integers (comparing and ordering) (Page 74-81)
Place value after the decimal (Page 88-91)
Estimating/rounding Products and Quotients (Page 92-94)
Multiplying Decimals (Page )
Dividing Decimals (Page )

3. Integers (comparing and ordering) (Page 74-81)
Integers are numbers, both positive or negative. They cannot be decimals or fractions.
The best example of integers is temperature.
1, 5, -8, 450,  all examples of integers
Opposite integers are the positive and negative of the same number. Example 5 and -5 or +134 and - 134

4. Integers (comparing and ordering) (Page 74-81)
Words associated with integers
Positive
Negative
Above
Over
Gain
Forward
Earning money
Win
Deposit Up
Plus
Below
Down
Lost
Owe
Backwards
Spend
Under
Withdraw
Minus

5. Integers (comparing and ordering) (Page 74-81)
+ or no sign means a positive integer
- means a negative integer
We usually use yellow tiles to represent positive integers
We usually use red tiles to represent negative integers

6. Integers (comparing and ordering) (Page 74-81)
Ordering integers is easiest when you use a number line.
Let’s use this number line to order the following integers: -3, 7, -7, 9, 5, -10
Which integer is the LOWEST? Which is the HIGHEST/BIGGEST?

7. Integers (comparing and ordering) (Page 74-81)
What spot is 5 units to the right from -7?
This means you need to find -7 on the number line and move 5 ticks or notches to the right. What did you land on?
Let’s try another: What spot is 4 units to the left from 6 and three units to the right of -1? *Remember the step above*

8. Practice What’s the opposite integer of -45?
How many integers does the following tiles represent?
If Suzie owes Sally ten dollars, what integer would reflect that?
Order the following integers from least to greatest: -4, 10, -6, 6, 5, 3, -8, -1

9. Integers Example PAT Question

10. Assignment Textbook Page 76-77, questions 1-6

11. Place value after the decimal (Page 88-91)

12. Place value after the decimal (Page 88-91)
It’s important when you get a decimal number to put it on your place value chart. This helps you recognize the the value of each number and helps you read the number.

13. Place value after the decimal (Page 88-91)

14. Place value after the decimal (Page 88-91)
Copy this chart down in your notes.

15. Place value after the decimal (Page 88-91)
If you place the following number on the chart above what would each numbers value be?
4= 4 tens or 40, 5= 5 ones or 5, 8 = 8 tenths or .8,
9= 9 hundredths or . 09, 7 = 7 thousandths or …. Can you do the rest?

16. Place value after the decimal (Page 88-91)
When reading decimals start at the left and read the whole number, say the word AND when you get to the decimal, then read the number as you see it after the decimal, finishing with the place value spot it ends on.
Example from above: Three thousand six hundred eighty four and twenty six hundredths. Let’s do some more on the board.

17. Place value after the decimal (Page 88-91)
Remember you can write numbers in three different ways:
Standard form:
Expanded form:
**Every spot you move away from the decimal you need to have a zero(s) in those spaces.**
Number-Word form: twenty three thousand, four hundred fifty six and ninety eight hundredths OR 23 thousand 456 and 98 hundredths.

18. Practice Write the following in Number-Word form and Expanded form:
What is the value of the 5 in the number ?
Write a decimal between 1.1 and 1.2

19. Place value after the decimal Example Pat Question

20. Assignment
Textbook page 90-91, questions 1-8

21. Estimating/rounding Products and Quotients (Page 92-94)
You can round to the nearest whole number, tenth, hundredth, thousandth, millionth, and so on. Make sure you read your question(s) carefully to see what it’s asking for.

22. Estimating/rounding Products and Quotients (Page 92-94)
When rounding make sure you look at the number after the number place you are rounding to.
Example: If I asked you to round to the nearest tenths spot and your number was 2.34 you need to look at the number after the tenths spot to decide if you are round up or down (keeping it the same.)
3 is the number in the tenths spot and 4 is unit after in the hundredths spot.

23. Estimating/rounding Products and Quotients (Page 92-94)
When the number after the target digit (the place value you are rounding to) is 0, 1, 2, 3, 4 then you keep your target digit.
When the number after the target digit (the place value you are rounding to) is 5, 6, 7, 8, 9 then you round your target digit up one number.
Example: If I was asked to round to the nearest tenth
34.57= (Because the number after the 5 is a 7, I need to round up)
54.63= (Because the number after the 6 is a 3, I need to round down (keep it the same)
Do you think I need to keep the zeros after the tenth spot?

24. Practice Round the following numbers to the nearest tenth place:
Round the following numbers to the nearest hundredth place:
Round to the nearest ten thousandths place:
Round to the nearest whole number:

25. Estimating/rounding Products and Quotients (Page 92-94)
When estimating or rounding decimals used in a multiplication or division equation always round to the nearest whole number.
Example: X 5= become 3
3 X 5 = 15
You would do this to give you a target number. You can estimate your answer. You know that 2.53 X 5 is going to be close to 15.

26. Practice
Try these equations, first estimate your answer then check the actually answer on the calculator. How close were you?
1.45 X 6=
20.2 ÷ 2 =
5.6 X 5 =
23.86 ÷ 6 =

27. Estimating/rounding Products and Quotients (Page 92-94) Example PAT Question
Sally and four of her friends are sharing the cost of a hotel room. The desk clerk informs Sally that the total cost will be to rent the room for one night. If the cost is divided evenly amoung them, what is the estimated amount that each person will need to pay?
A. $20 B. $30
C. $40 D. $50

28. Assignment
Textbook page 94, questions 1-7

29. Multiplying Decimals (Page 95- 102)
You can’t use a calculator for the next two learning outcomes.
When multiplying a whole number with a decimal we can try two ways:
The estimate
The swap

30. Multiplying Decimals (Page 95- 102)
The Estimate
Step 1: Estimate or round the decimal to a whole number and answer the equation.
3.2 X 5 = X 5 = 15
Step 2: Act like the decimal disappeared
3.2 X 5 = X 5= 160
Step 3: To put the decimal back in your need to compare your answers from step 1 and step 2.
Is 15 closer to .160, 1.60, 16.0, 160.0?
Step 4: Pick the closest answer and re-write the equation:
3.2 X 5= 16

31. The Estimate

32. Practice
**Remember the steps
on the last slide. **

33. Assignment
Textbook page 97, questions 1-10

34. Multiplying Decimals (Page 95- 102)
The Swap
Step 1: Move the decimal out, remember to keep count.
3.2 x 5 = X 5
Step 2: Multiply the “new” whole number.
32 X 5 = 160
Step 3: Move the decimal back in
32 x 5 = X 5 = 16.0
1 spot to remove the decimal
1 spot to add the decimal back

35. Practice

36. Assignment
Textbook page 101, questions 1-8

37. Dividing Decimals (Page 103-114)
You can’t use a calculator for the next two learning outcomes.
When multiplying a whole number with a decimal we can try two ways:
The Estimate
The Swap

38. First you need to remember how to do long division.

39. Dividing Decimals (Page 103-114)
The Estimate
Step 1: Estimate or round the decimal to a whole number and answer the equation.
16.44 ÷ 4 = 16 ÷ 4 = 4
Step 2: Act like the decimal disappeared (use long division to solve the problem)
16.44 ÷ 4 = ÷ 4 = 411
Step 3: To put the decimal back in your need to compare your answers from step 1 and step 2.
Is 4 closer to .411, 4.11, 41.1, 411.0?
Step 4: Pick the closest answer and re-write the equation:
16.44 ÷ 4 = 4.11

40. Practice

41. Dividing Decimals (Page 103-114)
The Swap
Step 1: Move the decimal out, remember to keep count.
44.8 ÷ 8 = ÷ 8 =
Step 2: Divide the “new” whole number.
44.8 ÷ 8 =
Moved out one spot
056
448 -0
4 4
-40 48
- 48
Step 3: Move the decimal back in
448 ÷ 8 = 56
44.8 ÷ 8 = 5.6
Moved in one spot

42. Practice

43. Dividing Decimals (Page 103-114)
What happens when you do the swap out but there is a remainder? Let’s go through a few examples on the board ÷ 4 or 3.05 ÷ 2 or 0.024÷6

44. Assignment Textbook pages 106-107, questions 1-5
Textbook page 111, question 1-3

45. Games for Practice