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Number Sense (Adding Decimals)
©2017 Math in Demand
Step 1:
Step 2:
Step 3:
I can ___________________
_______________________
Examples:
add two or more
decimals to determine the sum.
Line up your decimals. Fill
in any blank spots to the
right of a decimal with “0”.
Add from right to left,
column by column. If sum
is 10 or greater, then you
need to “carry a 1”.
Place the decimal point
in line with the other
decimals.
137.92 + 9.86 23 + 4.09 + 1.1
45.879 + 5.480
45.879 + 5.480
51 . 359
45.879 + 5.48
137.92 + 9.86 147.78
147.78
23.00 4.09
+ 1.10 28.19
28.19
How do I add decimals?
45.879 + 5.480
5 1 3 5 9
1 1
1 1 1
Number Sense (Subtracting Decimals)
©2017 Math in Demand
Step 1:
Step 2:
Step 3:
I can ___________________
_______________________
Examples:
subtract two decimals.
Line up your decimals. Fill
in any blank spots to the
right of a decimal with “0”.
Subtract from right to left, column by column. You will need to “borrow” if the top number is greater
than the bottom.
Place the decimal point
in line with the other
decimals.
215.7 – 24.98 3.755 – 0.18
15.96 - 8.20
15.96 - 8.20
7.76
15.96 - 8.2
215.70 - 24.98 190.72
190.72 3.575
How do I subtract decimals?
15.96 - 8.20
7 7 6
1 1 4 6 1
0 1
0 1
3.755 - 0.180
3.575
1 6 1
Number Sense (Multiplying Decimals)
©2017 Math in Demand
Step 1:
Step 2:
Step 3:
I can ___________________
_______________________
Examples:
multiply two
decimals together.
Multiply the numbers
together and ignore the
decimals.
Count the total number of digits past the decimals.
Place a decimal point
with the same number of
digits behind the point.
0.006 x 1.2 1,456 x 12.5
14.6 x 0.8
0.0072 18,200
How do I multiply decimals?
14.6 x 0.8 1 1 6 8
+ 0000 1168
14.6 and 0.8 has 2 digits
11.68
0.006 x 1.2 0012
+ 00060 0.0072
1456 x 12.5
7280 2 9 1 20 + 145600 18200.0
4 37.08 - 36 10 - 8 28 - 28 0
Number Sense (Dividing Decimals)
©2017 Math in Demand
Step 1:
Step 2:
Step 3:
I can ___________________
_______________________
Examples:
divide two decimals.
The divisor needs to be a whole number. If it is not, then you will need to move
the decimal point to the right until it becomes a whole
number. Move the dividend the same number of places.
Place a decimal point
directly above the decimal
point in the dividend.
118.72 ÷ 21.2 37.08 ÷ 4
10.35 ÷ 4.5
5.6 9.27
How do I divide decimals?
Divide as you
normally do.
10.354.5
= 103.5
45
45 103.5 - 90 135 - 135 0
2 3
45 103.5
2.3
212 1187.2 - 1060 1272 - 1272 0
5.6 9.27
Number Sense (Dividing Fractions with
Fraction Bars)
2.) How many 18 cup servings are in
12 of a cup of yogurt?
4
I can ___________________
_______________________
©2017 Math in Demand
How can we divide fractions by using fraction bars?
divide fractions visually
by using fraction bars.
1.) 14 ÷
34 =
13
Examples:
We can split fraction bars into equal amounts to create the same divisors (denominators). We are determining how many times one amount fits into
the other amount.
1
3
4
1
Number Sense (Dividing Fractions)
Example: Example: 12 ÷
912 =
12 ⋅ 12
9
= 1218
= 23
510 ÷
2530 =
510 ⋅ 30
25
= 150250
= 1525
= 35
©2017 Math in Demand
a b
c d
÷
a⋅d b⋅c
=
a b
d c
⋅ =
I can ___________________
_______________________
divide fractions including
mixed numbers and whole numbers.
35 2
3
When we divide fractions, we will take the “reciprocal” of the second fraction then change the division sign to multiplication.
If possible, make sure to
reduce!
How do we change mixed numbers into improper fractions?
3 510 = 3 5
10 = 3510 =
72 x
+
Take the reciprocal of the second fraction. Multiply the two
fractions together. Reduce!
© 2017 Math in Demand
Recap:
How do we divide fractions?
1
2
Hilary is baking cakes for a party. The recipe uses 1¼ cups of oil for each cake. How many cakes can Hilary bake if the bottle of oil has 7 cups?
Hilary has enough oil to bake 535 cakes. This means,
that she can actually only bake 5 cakes. A big dog can eat roughly 2¾ pounds of dog food a day. How many days would it take for a big dog to
consume a 30½ pound bag of dog food?
Number Sense (Word Problems involving
Dividing Fractions)
71 ÷ 1 1
4 = 71 ⋅ 4
5 = 285 = 5
35
30 12 ÷ 2 3
4 = 612 ⋅ 11
4 = 671
8 = 83 78
It would take 83 78 days to run out of dog food.
I can ___________________
_______________________
analyze and solve word
problems that involve dividing
14 ÷
56
= 14
⋅ 65 =
620
= 3
10
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝐷𝑖𝑣𝑖𝑠𝑜𝑟
We can divide fractions in word problems. Don’t confuse the difference
between the divisor and dividend!
fractions.
Number Sense (Exponents)
©2017 Math in Demand
I can ___________________
_______________________
simplify exponents & evaluate
expressions containing exponents.
An exponent (also called a power) is a short way to write a number being multiplied by
itself a certain number of times.
What is an exponent?
ab a ⋅ a ⋅ a ⋅ a
b times
ab exponent (power)
base
Examples:
43 4 ⋅ 4 ⋅ 4 = 64
Rules
Word Problem
Example
a-b 1
𝑎𝑏
a0
1
5-2 1
52 = 1
25
70
1
Four to the power of
three
The negative square of
five
Seven raised to the zero
power
ab + cd ab - cd
Expressions containing exponents
Number Sense (Order of Operations)
What does order of operations mean?
I can ___________________
_______________________
Please Excuse My Dear Aunt Sally!
Glue “P” Here Glue “E” Here Glue “MD” Here Glue “AS” Here
Example: 92 + (21 – 9) x (11 + 2)2
Step 1: Parentheses Æ 92 + (12) x (13)2
Step 2: Exponents Æ 81 + 12 x 169
Step 3: Multiplication Æ 81 + 2,028
(Left to Right)
Step 4: Addition Æ 2,109
(Left to Right)
©2017 Math in Demand
2,109
use the order of operations
to simplify and solve expressions.
Order of operations is a collect of rules that say which calculation comes first in an expression.
Parentheses Do everything
inside parentheses
first! ( )
Exponents
Exponents come second!
x2
Multiplication and Division Multiply and
divide from left to right!
Addition and Subtraction
Add and subtract from left to right!
Number Sense (Intro to Negative Numbers & Comparing Negative Numbers)
What is a number line?
©2017 Math in Demand
I can ___________________
_______________________
Numbers to the
_______ of ____
Numbers to the
_______ of ____ left zero right zero
How do I know which
negative numbers are
greater?
0 -6 6 -1 -2 -3 -4 -5 5 4 3 2 1
determine the least
value between two numbers.
A number line is a line that has marks on certain intervals. The number line consists of all real numbers.
The further to the _____, the ______ the negative numbers.
This means that if you are comparing two numbers, the
number _______ to the left is the _____ number of the two!
ARE ARE
NEG. POS.
What number is the least value:
-1 or -6? -6 because it is
further to the left on the number line
left greater
furthest least
● ●
Number Sense (Positive and Negative Numbers)
Andy loves to go scuba diving. He jumps from his boat to the water. If Andy’s boat is 8 feet above sea level and he goes 57 feet below sea level, then what was the total distance traveled by Andy?
©2017 Math in Demand
I can ___________________
_______________________
divide fractions including
mixed numbers and whole numbers.
We just learned that __________ numbers are to
the left of zero on the number line and that _________
numbers are to the right of zero on the number line.
We can use this information to think about positive and negative values in the real world:
Examples of Real World +/-:
Temperature, elevation, credit/debit
1 2
negative
positive
Given below is the temperature at 5 PM and 8 PM. Did it get warmer or cooler? How many
degrees did the temperature change?
5 PM 8 PM
82° 58°
65 ft 24°
57 ft + 8 ft = 65 ft
82° - 58° = 24°
Number Sense (Number Opposites)
What is a number opposite?
©2017 Math in Demand
I can ___________________
_______________________
0 -6 6
Example: -6 + 6 = ____
If we look at a number line:
What is the opposite of -10?
10
Number opposite is also known as “additive inverse”.
What is the opposite of 21?
-21
Examples:
When added together, number opposites equal zero. This means that they have equal distance from zero on the
number line but in opposite directions.
determine the opposite
of a number.
We will notice that -6 is the same distance from 0 on the number line as 6. Also, -6 is to the left of 0 and 6 is the
right of 0. This makes them number opposites.
0
Number Sense (Absolute Value)
What is absolute value?
©2017 Math in Demand
I can ___________________
_______________________
0 -6 6
Distance is always __________________.
|−6| = ___ |3| = ___
2.) |−12| = 12
Since the negative is inside the absolute value bars,
the answer will be positive.
Negatives outside of the absolute value
bars will remain negative!
1.) −|4| = -4
Since the negative is outside the absolute value bars, the answer will be
negative.
Examples:
Absolute value is the distance from zero on the number line.
determine the absolute
value of a number.
POSITIVE
6 3
The distance from -6 and 0 on the number line is 6.
The distance from 0 and 3 on the number line is 3.
(x,-y)
(x,y)
(-x,-y)
(-x,y)
Number Sense (Coordinate Plane)
©2017 Math in Demand
Plot the point: (4,-2)
Plot the point: (-1,3)
What is the coordinate plane?
The coordinate plane is a two-dimensional number line. The horizontal line is the x-axis and the vertical line is the y-axis.
I can ___________________
_______________________
plot points on the
coordinate plane.
Quadrant II
Quadrant III
Quadrant I
Quadrant IV
y
x
What quadrant does the point
fall in? Quadrant IV
What quadrant does the point
fall in? Quadrant II
●
●
Number Sense (Distance between Points with a
Same Coordinate)
©2017 Math in Demand
Determine distance:
(5,-2) and (5,4)
Determine distance:
(4,2) and (-5,2)
What is the difference between horizontal and vertical?
Horizontal is left to right (side to side) and vertical is up and down.
I can ___________________
_______________________
determine the distance between
two points that have a same x or y
coordinate.
The same x-coordinates The same y-coordinates
y
x
●
●
y
x
● ●
Plot: (-4,3) and (-4,-2)
Plot: (-3,-3) and (5,-3)
Points are: ___________ Distance = ______
Points are: ___________ Distance = ______
Vertical Horizontal 5 8
5
8
●
● ● ●
6 9
I can ___________________
_______________________ Number Sense
(Least Common Multiple & Greatest Common Factor)
©2017 Math in Demand
LCM of 6 and 8
GCF of 2 and 8
What is the difference between LCM and GCF?
find the least common multiple
and greatest common factor given
two numbers.
Multiplies of 6 and 8 are:
6 = 6, 12, 18, 24, …
8 = 8, 16, 24, 32, …
They both have in common 24,
which is the least common
multiple. Hence, LCM is 24.
Factors of 2 and 8 are:
2 = 1, 2
8 = 1, 2, 4, 8
They both have in common 1
and 2, with 2 being the largest.
Hence, GCF is 2.
GFC is looking at common factors while LCM is looking at the common multiples.
The smallest common multiple that is divisible by
both of the numbers.
The greatest common factor
that is divisible by both of the numbers.