BASE TEN SYSTEM

1 0 0 0 0 0 0, .x10x10x10x10x10x10

i Move to the left, the number is 10 times as large.b Move to the right and the number is 10 times less

or 1

10of the pervious number.

1,000,000 = 10 x 10 x 10 x 10 x 10 x 10

106The base is the number you are

multiplying repeatedly.

g

The exponent is the number of times you are multiplying the

base.

Value Exponent Form

1 , 0 00 , 000 1 0 6

1 0 0 , 000 1 0 5

1 0 , 0 00 1 0 4

1 , 0 00 1 0 3

1 0 0 1 0 2

1 0 1 0 1

1 1 0 2

Standard Form

5 4 7 , 2 6 4

Expanded Form

( 5 x 1 0 5 ) + ( 4 x 1 0 4 ) +( 7 x 1 0 3 ) + ( 2 x 1 0 2 ) +( 6 x 1 0 1 ) + ( 4 x 1 0 0 )

8 9 5 4 2 6 0 0 0•,Standard Form

8,954.26

Word Form

Eight thousand, nine hundred, fifty-four and twenty-six hundredths

Expanded Form

(8x1,000) + (9x100) + (5x10) + (4x1) + (2x0.1) + (6x0.01) = 8,954.26

Comparing decimals

1.254 2.254 0.602 0.452< >

0.235 1.235 3.258 3.258< =

exponentsbExponents show repeated multiplication.

bExponents represent how many times a number (the base) is multiplied by itself.

64 = 6x6x6x6exponent

base

1 time 3 times2 times 4 times

Exponential Form

25

Word Form

Two to the fifth power

Expanded Form

2 2 2 2 2

Standard Form

32

bAny number raised to the first power is itself. Example: 31 = 3 bAny number raised to the zero power is

always one. Example: 30 = 1

• • • •

exponentsbExponents show repeated multiplication.

bExponents represent how many times a number (the base) is multiplied by itself.

64 = 6x6x6x6exponent

base

1 time 3 times2 times 4 times

Exponential Form Word Form

Expanded Form Standard Form

bAny number raised to the first power is itself. Example: 31 = 3 bAny number raised to the zero power is

always one. Example: 30 = 1

MULTIPLICATIONmulti - digit

1

1 3

3 2 5

x 2 6

1 9 5 0

+ 6 5 0 0

8 4 5 0

1. Multiply 5x62. Multiply 6 x 2, add 33. Multiply 6 x 3, add 14. Put a zero as a place

holder5. Multiply 2 x 56. Multiply 2 x 2, add 17. Multiply 2 x 38. Add your answers

steps

Box and Cluster

300 20 5

20 6000 400 100

6 1800 120 30

MULTIPLICATIONmulti - digit

1

1 3

3 2 5

x 2 6

1 9 5 0

+ 6 5 0 0

8 4 5 0

1. Multiply 5x62. Multiply 6 x 2, add 33. Multiply 6 x 3, add 14. Put a zero as a place

holder5. Multiply 2 x 56. Multiply 2 x 2, add 17. Multiply 2 x 38. Add your answers

steps

Box and Cluster

300 20 5

20 6000 400 100

6 1800 120 30

division

)373515-30

249

73Q

-60135

QQ

-135000

DOES MCDONALDS SERVE BURGERS?

Step 2

Step 1

ADDING & SUBTRACTINGdecimals

5 6

- 2 4 3

6 7

+ 3 7 9

Step 1Line the

5.6 – 2.43 6.7 + 3.79

Step 2Put the decimal below

5 6

- 2 4 3

6 7

+ 3 7 9

decimals up.

in the answer row.

Step 4

Step 3

ADDING & SUBTRACTINGdecimals

5.6 – 2.43 6.7 + 3.79

5 6 0

- 2 4 3

6 7 0

+ 3 7 9

Step 3Fill in zeros as place holders.

Step 4 Add or subtract normally.

5 6 0

- 2 4 3

3 1 7

6 7 0

+ 3 7 9

1 0 4 9

5 110

thousandsHundred

thousandsTen

thousandsThousands

5 6 7

ones

Hundreds Tens Ones

4 9 3

decimals

Tenths Hundredths Thousandths

7 1 2

Decimalsvisual model

rounding

comparing

HUNDREDTHS

THOUSANDTTHS

0.482

6.35 =

6.40

Find the place value you are rounding to, look at the digit to the right. If the digit is 1, 2, 3, 4 then leave the place value number the same. If the digit is 5, 6, 7, 8, or 9, push the place value digit up to the next number.

Start with the digit all the way to the left and see which number is higher. If the digits are the same, move to the next place value to the right. Check the place of the decimal.

5.62 < 56.2

Visual models

ADDING & SUBTRACTINGdecimals1.26 + 0.32 = 1.58 c

Color in each decimal, then count all the

blocks colored.

0.52 – 0.23 = 0.29 c Color in the blocks for the first decimal, cross out the

second decimal and the

remaining color blocks are your

answer.

XXXXX

XXXXXXXXXX

XXXXX

XXX

visual model0.8 x 0.6 = 0.48

56.3 x 4.5 = ? 1 Multiply like you would

normally. 2 Count how many digits follow each decimal in the

problem.3 Move the decimal in the

answer the amount of

digits in the problem.

The answer is where the

colors overlap.

L The decimals DO NOT need to be lined up.

56.3x 4.5

281522520253.35

1312

+

1

standard algorithm

))

visual model0.4 ÷ 0.8 =

3.65 ÷ 0.5 = ?

1 Color in the amount in the first number (dividend).

2 The amount in each group is the second number (divisor).

3 The quotient (answer) is the amount of groups as a whole

number.

standard algorithm

5 groups

36.5-35

7.35

3.650.5 1 5- 1 5

0 0

Q

Move the decimal to make the dividend a

whole number.

Fraction=Equivalent Fractions

Fractions that represent the same amount.

H f=

vocabulary

h h kdenominator

numeratorMix

numberImproper fraction

E H

_ )

fractionsADDING

step 1: Find the least common denominator and change the

fractions to equivalent fractions.

E H+

Rewrite the problem with the new like denominators.

x4

x4

x3

x3

step 2:

+

step 3: Add the numerators.

8 + 6 = 14

step 4: C1412

=Convert to a mix number or the

simplest form of the fraction.

convertingImproper fractions to mix numbers

5 goes into 14 TWO times.

d=2Figure out how many times the denominator

can go into the numerator.

NThe remaining amount becomes the new numerator over the same denominator. 4

remains so it becomes 4/5

convertingMix numbers to improper fractions

1

2

3

Multiply the whole number by the denominator then add the numerator, and that is

your new denominator. The denominator in the mix

number stays the same.

fmultiply

2 x 8 + 7 = 23

add 8

=23

fractionssimplifyingSynonyms: simplifying, reducing

* Writing the fraction using the smallest numbers as the numerator and

denominator.

Find the LARGEST

number both the

numerator and

denominator are divisible by.

mdR

÷ 3

÷ 3

÷ 2

÷ 2

÷ 3

÷ 3

b

b

b

D

BD

8 dmix numbers

Add/subtract

Step 1: Change the denominators to a common

denominators.

+

IN bb

X5

X5

X4

X4

2015

2016

Step 2: Add the fractions and with the like denominators. 20

152016

+ =2031

Step 3: Convert the fraction into a mix number. 20

31 11201b

Step 4: Add the whole numbers.4+2+1

Step 5: Write the whole number and fraction and

reduce if needed. 7 1120

f H

D S

multiplyingfractions

USING A VISUALrows

X =

2

18columns

s i m p l i f y

4

18184c

Using the algorithm

GMultiply straight across for the numerator

and denominator.

c

cX

4x28x4

c 832c

g

multiplyingfractions

FRACTIONS AND a whole number

Put the whole number over one and multiply straight across.

X1 J10

Step 1. Convert the mix number to an improper

fraction

2 gX =2c8cdcE

FRACTIONS AND a mix number

k fX134 fX Step 2: Multiply straight

across.

Step 3: Convert back to a mix number. Simplify if

needed.

c

c

5232

=

20321 cK

c

c

G T

keep change

FRACTIONS AND a whole number

Keep the first

fraction the same.

Step 1. Put the whole number over one.

Step 2: Change the division to multiplication.

Fraction by a fraction

3 f

1X

Step 3: Flip the second fraction and multiply

straight across.

c

flip

÷

Flip the second fraction.

Change the

symbol to X

G DX =

620c 3

10

÷

3 84

244c6

D i v i d i n g F r a c t i on s

Converting measurements

CAPACITY1 cup = 8 fluid ounces

1 pint = 2 cups1 quart = 2 pints

1 gallon = 4 quarts1 liter = 1,000 milliliters

weight1 pound = 16 ounces1 ton = 2,000 pounds

1 kilogram = 1,000 grams

linear1 foot = 12 inches

1 yard = 3 feetI centimeter = 10 millimeters

1 meter = 100 centimeters1 kilometer = 1,000 meters