Download Unit 2 Integers

UNIT 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 95- 102)
 Dividing Decimals (Page 103-114)
Integers (comparing and ordering)
(Page 74-81)
 https://www.youtube.com/watch?v=x0E4vxLydNY
 Integers are numbers, both positive or negative. They
cannot be decimals or fractions.
 The best example of integers is temperature.
 1, 5, -8, 450, -7 954  all examples of integers
 Opposite integers are the positive and negative of the
same number. Example 5 and -5 or +134 and - 134
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
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
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?
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*
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
Integers
Example PAT Question
Assignment
 Textbook Page 76-77, questions 1-6
 Textbook Page 80- 81, questions 1-7
Place value after the decimal (Page
88-91)
Place value after the decimal (Page
88-91)
 https://www.youtube.com/watch?v=qQ4YaNkA7_4
 https://www.youtube.com/watch?v=0JB3bNfLqEM
 https://www.youtube.com/watch?v=68TBZRfaKnA
 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.
Place value after the decimal (Page
88-91)
Place value after the decimal (Page
88-91)
Copy this chart down in your notes.
Place value after the decimal (Page
88-91)
If you place the following number on the chart above what would
each numbers value be?
45.89732
4= 4 tens or 40, 5= 5 ones or 5, 8 = 8 tenths or .8,
9= 9 hundredths or . 09, 7 = 7 thousandths or .007 …. Can you do the
rest?
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.
Place value after the decimal (Page
88-91)
 Remember you can write numbers in three different
ways:
 Standard form: 23 456. 98
 Expanded form: 20 000 + 3000 + 400 + 50 + 6 + .9 +.08
 **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.
Practice
Write the following in Number-Word form and
Expanded form:
- 23.67
- 5.819
-1.09
-345.345
- 0.349702
 What is the value of the 5 in the number 46.357?
Write a decimal between 1.1 and 1.2
Place value after the decimal
Example Pat Question
Assignment
 Textbook page 90-91, questions 1-8
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.
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.
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= 34.60 (Because the number after the 5 is a 7, I need
to round up)
 54.63= 54.60 (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?
Practice
 Round the following numbers to the nearest tenth place:
- 1.45679
-23.14095
-45.67933
-0.90135
 Round the following numbers to the nearest hundredth place:
-1.45679
-23.14095
-45.67933
-0.90135
 Round to the nearest ten thousandths place:
-1.45679
-23.14095
-45.67933
-0.90135
 Round to the nearest whole number:
-1.45679
-23.14095
-45.67933
-0.90135
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: 2.53 X 5=
2.53 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.
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 =
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 192.52 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
C. $40
B. $30
D. $50
Assignment
 Textbook page 94, questions 1-7
Multiplying Decimals (Page 95- 102)
https://www.youtube.com/watch?v=unsDhvtuhqQ
https://www.youtube.com/watch?v=Gl-3BrwpawA
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:
1. The estimate
2. The swap
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 =
3X 5 = 15
 Step 2: Act like the decimal disappeared
3.2 X 5 =
32 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
The Estimate
Practice
**Remember
the steps
on the last
slide. **
Assignment
 Textbook page 97, questions 1-10
Multiplying Decimals (Page 95- 102)
The Swap
Step 1: Move the decimal out, remember to keep count.
1 spot to remove the decimal
3.2 x 5 =
32 X 5
Step 2: Multiply the “new” whole number.
32 X 5 = 160
Step 3: Move the decimal back in
1 spot to add the decimal back
32 x 5 = 160
32 X 5 = 16.0
Practice
Assignment
 Textbook page 101, questions 1-8
Dividing Decimals (Page 103-114)
https://www.youtube.com/watch?v=ZPoXnNi7WIQ
https://www.youtube.com/watch?v=cfr-yZxTH8Y
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:
1. The Estimate
2. The Swap
First you
need to
remember
how to do
long
division.
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 =
1644 ÷ 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
Practice
Dividing Decimals (Page 103-114)
The Swap
 Step 1: Move the decimal out, remember to keep count.
Moved out one spot
44.8 ÷ 8 =
448 ÷ 8 =
 Step 2: Divide the “new” whole number.
056
44.8 ÷ 8 =
8 448
-0
44
-40
48
- 48
0
Step 3: Move the decimal back in
448 ÷ 8 = 56
Moved in one spot
44.8 ÷ 8 = 5.6
Practice
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.
9.45 ÷ 4
or
3.05 ÷ 2
or 0.024÷6
Assignment
 Textbook pages 106-107, questions 1-5
 Textbook page 111, question 1-3
Games for Practice
 http://www.sheppardsoftware.com/mathgames/place
value/scooterQuest.htm
 http://www.math-play.com/baseball-math-roundingdecimals/rounding-decimals-game.html
 http://www.math-play.com/multiplying-decimalsgame.html