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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)


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)


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)


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 ___________________

_______________________


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


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)


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)


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!

collection

Number Sense (Intro to Negative Numbers & Comparing Negative Numbers)

What is a number line?


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?


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°

add or subtract positive and

negative numbers using a number line.

Number Sense (Number Opposites)

What is a number opposite?


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?


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)


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)


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)


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.

GCF

Multiples

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