4th Grade Math Anchor Charts - Color - FULL PAGE

Place Value

These are the digits that make up numbers in our number
system.

0,1,2,3,4,5,6,7,8,9

When these digits create a number, each digit sits in a
different place. Each place has a different value.

5, 5 5 5 ,5 5 5, 5 5 5

We would read this number as five billion, five hundred
fifty five million, five hundred fifty five thousand, five
hundred fifty five.

Even though the number is made using only the digit 5,
each digit has a different value.

The five with the circle around it is in the millions place,
and it has a value of 5 million.

The five with the line under it is in the hundreds place,
and it has a value of 5 hundred.

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billions
hundred millions

ten millions
millions

hundred thousands

ten thousands
thousands
hundreds
tens
ones

Interpreting

Place Value

The place and value of a number can change when you multiply or
divide by powers of 10. When you multiply, the value of the place
gets larger. When you divide, the value of the place gets smaller.

Multiply Divide

23 x 10 = 230 230 ÷ 10 = 23

The digits move 1 space to the The digits move 1 space to the
left. right.

23 x 100 = 2,300 2,300 ÷ 100 = 23

The digits move 2 spaces to the The digits move 2 spaces to the
left. right.

23 x 1,000 = 23,000 23,000 ÷ 1,000 = 23

The digits move 3 spaces to the The digits move 3 spaces to the
left. right.

Do you notice a pattern?

When you multiply a number by When you divide a number by
10, you add 1 zero to the 10, you remove 1 zero from the

number you are multiplying. number you are dividing.
When you multiply a number by When you divide a number by
100, you remove 2 zeros from the
100, you add 2 zeros to the
number you are multiplying. number you are dividing.
When you multiply a number by When you divide a number by
1,000, you add 3 zeros to the 1,000, you remove 3 zeros from
number you are multiplying. the number you are dividing.
What would happen if you What would happen if you divide
multiply a number by 10,000? a number by 10,000? 100,000?

100,000? 1,000,000? 1,000,000?

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Representing Numbers

You can represent whole numbers in a variety of ways.
Representing a number simply means you are showing

the place and value of that number.

Standard Form

writing the number using only digits

632

Base 10 Models Expanded Form

using a model to show writing the number by
the value of the adding the value of
number
the digits

600 +

30 + 2

Expanded Notation Word Form
writing the number to writing the number

show the value of using only words
each digit
six hundred
6x100 + 3x10 thirty two
+ 2x1

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Representing Decimals

Just like whole numbers, you can represent decimals in
different ways. You can represent whole numbers in a
variety of ways. Representing a number simply means
you are showing the place and value of that number.

Standard Form
writing the number using only digits

2.35

Base 10 Models Expanded Form

using a model to show writing the number by
the value of the adding the value of the
number
digits

2 + .3 + .05

Expanded Notation Word Form
writing the number to writing the number

show the value of using only words
each digit
two and thirty
2x1 + 3x.1 + five
5x.01
hundredths

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Comparing &

Ordering Numbers

All numbers have value. You can compare the value of
two whole numbers by using the following symbols:

>Greater Than <Less Than =Equal To

Follow these steps to compare two numbers.

Step 1: Line up the numbers according to place value.

13,453

13,623

Step 2: Compare the numbers in each place starting with

Start here the largest.
1=1
3=3 13,453
4 is less than 6 13,623
So……

13,453 is less than 13,623

Step 3: Use the symbols to show the relationship between
the two numbers

13,453 < 13,623

13,453 is less than 13,623

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Rounding

Rounding a number is when you find the nearest group of
ten, hundred, thousand, ten thousand, etc. You can
round numbers to help estimate answers.

Round the following number to the nearest thousand.

17,932

To round a number follow these steps.
1. Identify the place of the number you are rounding to.

Underline that digit.

17,932

2. Look at the digit to the right of the place you are rounding to.

17, 932

3. Use the rule to determine if you will round up or round down.

0-4 the digit you are rounding stays the same
5-9 the digit you are rounding goes up one digit

17, 932 The digit to the right of the
place we are rounding is 9 so
we will round up.

4. Change all of the digits to the right of the number you are
rounding to zeros.

17,932 rounds to18,000

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Decimals

Whole numbers can be broken down in to smaller parts. When you
break a whole number into groups of tens or hundreds it becomes a

decimal. You can represent decimals using visuals and money.

One Whole One Tenth One

1 0.1 Hundredth
$1.00 $0.10
1 dollar 1 dime 0.01
there are 10 tenths $0.01
in one whole 1 penny
there are 100
hundredths in one
whole

When an entire shape There are 10 columns The square is split into
is shaded in it and 1 entire column is 100 little square. One

represents 1 whole. shaded in. This of the squares is
represents 1 tenth. shaded. This represents

1 hundredth.

This is one dollar. It is There are 10 dimes in There are 100 pennies
made up of 10 dimes. one dollar. One dime is in one dollar. One
You can also make a one tenth of a dollar. penny is one
dollar with 100 pennies. hundredth of a dollar.

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Comparing & Ordering

Decimals

All numbers have value. You can compare the value of two
numbers by using the following symbols:

Greater Than Less Than Equal To

>< =

Follow these steps to compare two numbers.
Step 1: Line up the numbers according to place value.

12.40

12.39

Step 2: Compare the numbers in each place starting with the

Start here largest.

1=1 12.40
2=2 12.39
4 is more than 3
So……
12.4 is greater than 12.39

Step 3: Use the symbols to show the relationship between the two
numbers

12.4 > 12.39

12.4 is greater than 12.39

To order a group of numbers, you complete steps 1-3 with more

Start here than 2 numbers.

3=3

3.454 is more than 3 (3.45 is the greatest)
9 is greater than nothing (3.39 is next
3.39
largest)

So……

3.45 is greater than 3.39 which is 3.30 Created by Mrs. M’s Style © 2017
greater than 3.3

Relating Decimals to
Fractions

Decimals and fractions both name a part
of a whole.

Decimals can be written as fractions.

.3 = and .45 =



Fractions can be written as decimals.

= .6 and = .18



Decimals Fractions

.2 2
.25 10
25
.6 100
.68 6
10
68
100

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Represent a Fraction

A fraction is a part of a whole. Just like whole numbers, and
decimals, you can represent fractions in a variety of ways.

FF FF FF
FF FF FF

This model shows squares divided into one-fourth sections.

Parts of a Fraction Fractions as a Sum

There are specific terms to name You can represent fractions as
each part of a fraction. sum of smaller fractions. The
model can be represented as
• The top number is called the different sums of fractions.
numerator
4 + 4 + 1 or 3 + 3 + 3
• The bottom number is called 444 444
the denominator

• The bar in the middle is called
the fraction bar

Improper Fractions Mixed Numbers

An improper fraction is a fraction A mixed number is a combination of
where the numerator is larger than a whole number and a fraction.

the denominator. 241

9 The model above can be written as
a mixed number. Even though each
4 square is divided into fourths, there
are two whole squares shaded and
The model above shows an improper
fraction. Each square is divided into one fourth of another square.

fourths (denominator) and nine
(numerator) of them are shaded in.

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Decomposing
Fractions

When you decompose a fraction you break it down into
smaller parts. You can decompose fractions in a variety of
ways. When you decompose a fraction, the denominator

stays the same, you just break apart the numerator.

=+

= +



You can also decompose a fraction as a series of unit
fractions. A unit fraction will always have 1 in the
numerator.

=++

= + +


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Equivalent Fractions

Equivalent fractions are fractions that have the same
value. When looking at models of equivalent fractions,

they have to be the same shape and size.

= =


These models all show equivalent fractions. The same
amount is shaded on each rectangle.

Drawing a model can help you identify equivalent fractions,
but you can also find equivalent fractions by multiplying or

dividing.

Find Equivalent Fractions Find Equivalent Fractions
by Multiplying by Dividing

x = ÷ =


You can find an equivalent You can find an equivalent
fraction by multiplying the fraction by dividing the
numerator and denominator
numerator and denominator
by the same number. by the same number.

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Comparing Fractions

All fractions have value. You can compare two or more
fractions using the following symbols.

>Greater Than Less Than =Equal To

<

Remember these rules when comparing fractions!

Same Numerator Same Denominator

> <



The smaller denominator is the The larger numerator is the
greater fraction. greater fraction.

Different Numerators and Denominators

If you are comparing two fractions with You can also use the butterfly method.
different numerators and denominators, Cross multiply and then compare the
find equivalent fractions with the same products. The larger product is the side

denominator. of the greater fraction.

1202=44 x > x 55=1200 5x2 = 10 > 3x4 = 12



3/5 is greater than 2/4 because when you 12 is greater than 10 so 3/5 is greater
multiply to get the common denominator than 2/4.

of 20, 12 is greater than 10.

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Adding and

Subtracting Fractions

You can easily add and subtract fractions with the
same denominator. When you add or subtract

fractions you need to make sure that you are adding
parts of the same whole.

Both the circle and square are
spilt into fourths, but the fourths
aren’t the same size or shape
so you are not able to add or

subtract them together.

How To Add Fractions How To Subtract Fractions

FF FF O O O

FF FF O O O

4 + 3 = 7 = 143 5 - 3 = 2
4 4 4 6 6 6

1. Add the numerators. 1. Subtract the numerators.

2. Keep the denominators the 2. Keep the denominators the

same. same.

3. Draw a model to check your 3. Draw a model to check

work. your work.

4. If needed, convert the

fraction to a mixed number.

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Estimating Fractions

When you estimate fractions you are making a thoughtful
guess. You can use your knowledge of benchmark

fractions to help you estimate. Estimating fractions can be
helpful for you to determine if an answer is reasonable.

0 ¼½ ¾ 1

Benchmark fractions are ¼, ½, and ¾. These are some of
the easiest fractions for you to visualize and work with.

The 4th grade class took a survey. 4/8 of the class said they
liked chocolate chip cookies. 1/8 of the class said they liked sugar
cookies. 3/8 of the class said they didn’t like cookies. The teacher

wanted to know which fraction of the class liked cookies.

Jack added the fractions and Carrie added the fractions

said the sum was 3/8. and said the sum was 5/8.

Whose answer is more reasonable?

THINK:
• 4/8 is the same as ½. We can use ½ as a benchmark fraction.
• 1/8 is a little larger than 0, but to help estimate we will use the

benchmark fraction 0.
• If you add 0 and ½ the answer is ½, but we know that our

answer should be slightly larger than ½ to account for the 1/8

we are adding.

• Carrie gave an answer that is slightly larger than ½.
Carrie’s answer is more reasonable than Jack’s.

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Fractions on a Number Line

You can show fractions by using a number line. You can
break up the space between two whole numbers into

different fractions.

1 1 1 1 1 1 11
8 8 8 8 8 8 88

1 181 182 183 184 185 186 178 2

The number line above shows the space between the whole numbers 1 and
2. It is divided into eighths. There are eight sections between 1 and 2.

11 11
44 44

1 114 142 143 2

The number line above shows the same space between the whole numbers

1 and 2, but It is divided into fourths. There are four sections

between 1 and 2.

Notice there are two eighths in every one fourth section.

11
22

1 11 2
2

The number line above shows the same space between the whole numbers
1 and 2, but it is divided into halves. There are two sections
between 1 and 2.
Do you notice any small sections in the halves?

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Add and Subtract Whole
Numbers and Decimals

When you add whole numbers and decimals, the most important thing
to remember is to line up the numbers according to place value.

Adding Subtracting

Step 1: Line up 16.9 If you miss 16.9 You might be
numbers + 4.62 this step, your - 4.62 tempted to line

according to answer will up the 9 and
place value be incorrect. the 2, make
sure you line up
the decimals

instead.

Step 2: Fill in a 16.90 Adding a zero 16.90 Adding the zero
zero as a place + 04.62 as a place - 04.62 reminds you to
subtract the 2
-holder if holder doesn’t rather than just
needed change the bring it down.
value!

1 1 8 10 Since you can’t

Step 3: Solve. 16.90 Don’t forget 16.90 subtract 2 from
Start with the to carry the zero, you have
lowest place
value (right) + 04.62 one! - 04.62 to borrow from
the 9.
21 52
12 38

Step 4: Bring 16.9 Make sure 16.90 Make sure
down decimal + 04.62 you check - 04.62 you check
your work! your work!
and check 21.52 12.38

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Multiplying by Multiples of 10

When you are multiplying, you can use your knowledge of
place value to help you do mental math quickly.

When you multiply a number by 10, you add a
zero to the end of the factor you are
multiplying.

8 x 10 = 80

When you multiply a number by a multiple of
10, you multiply the factor by the digit in the

tens place and add a zero to the end.

8 x 20 = 160

Think: 8x2 = 16. Add a 0 = 160

When you multiply a number by 100, you add
two zeros to the end of the factor you are
multiplying.

8 x 100 = 800

When you multiply a number by a multiple of
100, you multiply the factor by the digit in the
hundreds place and add two zeros to the end.

8 x 400 = 3,200

Think: 8x4 = 32. Add two 0s = 3,200

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Finding Products

Using Arrays

You can use arrays to help you multiply. An array has
equal rows with equal numbers in each row. It is a way

to help you visualize the multiplication problem.

This is a row. ⃝⃝⃝⃝⃝ This is a
Each row has the ⃝⃝⃝⃝⃝ column.
same number of ⃝⃝⃝⃝⃝ Each
circles. ⃝⃝⃝⃝⃝ column has
the same
number of
circles.

You can find the total of the array different ways.

You can count the You can add up the
circles. circles in each row.

20 5 + 5 + 5 + 5 = 20

You can add up the You can multiply the rows

circles in each column. by the columns.

4 + 4 + 4 + 4 + 4 = 20 5 x 4 = 20

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Properties of

Multiplication

There are four properties of multiplication. Understanding
these properties are rules will make solving multiplication

problems easier.

Commutative Property Associative Property

You can switch the order of You can change the
the factors, and it won’t placement of the parenthesis
change the answer.
but it won’t change the
3 x 6 = 18 answer.
6 x 3 = 18
(3 x 2) x 4 = 24
6 x 4 = 24

3 x (2 x 4) = 24
3 x 8 = 24

Distributive Property Identity Property

A multiplication fact can The product of any number
broken into (distributed) a sum and 1 is always that number.

of two other multiplication 4x1=4
facts. 32 x 1 = 32

24 x 3 = ? The product of any number
(20 + 4) x 3 = ? and 0 is 0.
(20 x 3) + (4 x 3) = ?
(80) + (12) = 92 4x0=0
32 x 0 = 0

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Standard Algorithm

An algorithm is a set of steps or rules that you can follow to solve a
basic mathematical problem. These are the steps for the standard

algorithm for multiplication.

Step 1: Multiply the top number by the digit in the ones place.

154
x 28
1, 232

Step 2: Put a zero as a place holder.

154
x 28
1, 232

0

Step 3: Multiply the top number by the digit in the tens place.

154
x 28
1, 232
3,080

Step 4: Add the numbers together.

154
x 28
1,232
+ 3,080
4,312

The standard algorithm isn’t the only way to multiply, but can be an
efficient way to solve multiplication problems.

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Partial Products &

Box Method

There are many strategies you can use to solve multiplication
problems. The Box Method and Partial Products are two

strategies. The most important thing is that you feel confident
with whatever strategy you choose.

Box Method Partial Products

23 x 42 23 x 42

20 + 3 42 think (40 +2)
X 23 think (20 + 3)
20 x 40 3 x 40 =
40 = 800 120 6 (3 x 2)
+ 120 (3 x 40)
2 20 x 2 = 3x2=
6 40 (20 x 2)
40 + 800 (20 x 40)

800 + 120 + 40 + 6 = 966 966

Step 1: Expand each of the Step 1: Multiply by the ones.
factors you are multiplying. Step 2: Multiply by the tens.
Step 2: Set up the numbers Step 3: List all the partial
above the boxes. products.
Step 3: Multiply the numbers Step 4: Add all of the partial
in the rows and columns. products together to get
Step 4: Add all of the the total.
products found in each of
the boxes to get the total.

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Finding the Quotient

When you are dividing you are trying to find the quotient,
which is the same thing as the answer. There are several

strategies you can use to help you find the quotient.

Finding The Quotient Using Arrays

You can draw an array to help you find a
quotient and remainder.

19÷4
Start with 19 tiles.
Put them in rows of 4.
The number leftover is your remainder.
The answer is 19÷4 = 4 remainder 3

Finding The Quotient Using Area Models

You can draw an area model on grid 10 3
paper to help you find the quotient.

39÷3 3
Break 39 into two parts 30 + 9.
You can draw a rectangle to represent
each part.
The answer is 39÷3 = 13

Finding The Quotient Using Equations

You can break apart division problems into smaller equations to help you
find the quotient.

84 ÷ 6 = ______
You can break 84 into two numbers that can easily divide by 6.

• 84 ÷ 6 = (60 ÷ 6) + (24 ÷ 6) Think: 60 + 24 = 84
• 84 ÷ 6 = 10 + 4 Think: 60 ÷ 6 = 10 and 24 ÷ 6 = 4
• 84 ÷ 6 = 14 Think: 10 + 4 = 14

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Standard Algorithm

for Long Division

An algorithm is a set of steps or rules that you can follow

to solve a basic mathematical problem. These are the

steps for the standard algorithm for long division.

Standard set up for Set up for long division
division
7 8,281
8,281 ÷ 7

Dad 1, 183 Step 1: Divide 8 by 7.
divide 8÷7 = 1
7 8,281
Mom Step 2: Multiply 7 by 1.
multiply 7 7x1=7
12
Sister Step 3: Subtract 7 from 8.
subtract 7 8–7=1
58
Brother 56 Step 4: Bring down the
bring 021 next digit in the dividend
down in this case it is the 2
21
Rover 0 Step 5: Repeat Steps 1-5
repeat with the remaining digits

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Compatible Numbers

You can use compatible numbers or rounding to help you
estimate solutions.

Compatible Numbers Rounding

Compatible numbers are Rounding helps you estimate
sometimes called friendly numbers to the nearest group of
numbers. These are numbers that
are easy to put together. 10. There are specific rules to
rounding.
Numbers that Numbers that
Rules to Rounding:
end in 0 end in 5
4 or less, let it rest
10, 100, 1000 5, 15, 105 (stay the same)

Doubles Facts Numbers that 5 or more, add 1 more
Make 10 (add 1 to the place you
8+8 = 16
1 + 9 = 10 are rounding)
20 + 20 = 40

Estimating to Find Solutions

When you estimate to find a solution you always want to
estimate first. The goal is not to estimate the actual answer,
but to estimate to help you find a number close to the answer.
You can use Compatible Numbers or Rounding to help you

find the solution.

Compatible Actual Rounding
Numbers Numbers

75 76 80
+ 65 + 66 + 70

140 142 150

For this set of numbers, which estimation strategy worked the best?
Why?

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Interpret the Remainder

When you solve multi-step problems involving division you
sometimes get a remainder. Depending on the situation in the

problem, you can do different things with the remainder.

Ignore it: Use only the quotient as your answer

Marco is making treat bags for his birthday party. He has 163 pieces of
candy and has to make 8 treat bags. How many pieces of candy will he be
able to put in each bag?

163 ÷ 8 = 20 remainder 3.
In this case, the remaining 3 pieces won’t get used in treat bags. Marco only
needs to use the quotient 20 to help figure out how many pieces of candy

to put in each bag.

Use it: Use only the remainder as your answer

Craig is organizing his baseball cards in a book. He has 187 cards and can
put 9 cards on each page. He only wants to put full pages of cards in the
book. After he makes all his full pages, how many cards will he have left?

189 ÷ 6 = 31 remainder 3.
Craig can fill up 31 pages completely. If he only wants to put full pages in his

book, he will have 3 leftover cards.

Share it: Write the remainder as a fraction

Jenn is wrapping gifts for her dad’s birthday. She has four gifts to wrap and
has 145 inches of ribbon to use on the 4 gifs. How much ribbon can she use
on each gift?

145 ÷ 4 = 36 remainder 1.
Jenn can take the remaining 1 inch and divide it into fractions so each of

the four gifts gets an extra ¼ inch.
145 ÷ 4 = 36 ¼ inches

Round it: Add one to the quotient

Kelly is baking cookies. She rolled 80 cookie dough balls and can bake 9
cookies at a time. How many rounds of cookies will she need to bake?

80 ÷ 9 = 8 remainder 8.
Kelly can bake 8 full pans of cookies. She needs to bake the 8 remaining
cookies on another pan which means you need to add one to the quotient.

Kelly will bake a total of 9 pans of cookies.

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Strip Diagrams

A strip diagram is a useful tool you can use to help solve problems. You
can draw a strip diagram for any problem using the four operations.
You can use multiple strip diagrams to solve multi-step problems.

Problem Step 1: Multiplication

Kelly is training for a race. She m
runs 5 miles a day during the
week (Monday – Friday) and 55555
runs 10 miles on Saturday. If she
wants to log 46 miles for the Let’s have m represent the
week, how many miles does she number of miles Kelly ran

need to run on Sunday? Monday – Friday.
Think: In order to solve this m = 5x5
problem you need to multiply, m = 25
add, and subtract. You can
make a strip diagram for each

of these operations.

Step 2: Addition Step 3: Subtraction

n 46

25 (same as m) 10 35 (same as n) s

Let’s have n represent the Let’s have s represent the number
number of miles Kelly ran during of miles Kelly needs to run on
Sunday. We know her total
the week (M – F) and on
Saturday. We know she ran 25 mileage for the week should be
46 and we know how much she
M – F and 10 on Saturday. ran Monday - Saturday so we just
n = 25 + 10
n = 35 need to subtract to find s.
s = 46 – 35
s = 11

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Input-Output Tables

Input-output tables are sometimes called function tables or pattern
tables. The function or pattern is the rule. The rule helps you

understand the relationship between the two columns or rows. If
you know the rule you can complete any input-output table.

Kids Cans XY input output
of soda 4 11 25 5
8 15 35 7
12 12 19 65 13
16 23 80 16
24
The rule for this table The rule for this table
36 is X + 7 = Y. You can is input ÷ 5 = output.
use the same rule to You can use the rule
48 figure out future rows and the inverse of
added to the chart. If the rule to figure out
The rule for this table X = 20 then Y = 27 future rows of the
is kids x 2 = number (X+7 = 27) chart. If output = 20
of cans of soda. You then input = 100.
can use the same (20x5 = 100)
rule to figure out the
number of cans of
soda needed for 10
kids.

Set A 4 6 9 13 Sometimes input-output
Set B 10 14 20 28 tables have a two part rule.
Can you figure out what the
rule is for this function table?

When you think you have figured out the rule for the function
table, you want to make sure it works with every set of
numbers! Make sure you always double check each set.

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AREA

The area of a shape is the total number of square
units inside that shape.

There are different ways to find the area of a shape.

1. You can count the square 2. You can multiply the

units inside the shape. length times width. You can

use the formula A = LxW

4

Area = 16 square units 4

Area = 4x4 = 16 square units

You can use the same strategies to find the area of irregular
shapes. You just have to be creative.

1. You can count the square units in this shape.
Area = 12 square units

2. You can use the formula A = LxW to find the
area of the yellow square and red rectangle
and then add them together.

A=2x2=4
A=2x4=8
8 + 4 = 12 square units

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PERIMETER

The perimeter of the shape is the measurement of the
distance around the shape. To find the perimeter you

need to add the length of ALL the sides.

You can find the perimeter of a shape in many ways.

If the measurement of each side You can remember that opposite
is given you can add them up. sides are equal and you can add

3 3 Perimeter = using the information you are
3+3+4+3+4
= 17 units ? given.

44 Perimeter =

6 ? 6+2+?+?=
6+2+6+2=

16 units

3
2

If you know a shape is made of If you are given the perimeter,
equal sides you just need the you can work backwards to find
length of one side to find the
the length of each side.
perimeter.
?

?5 ??

? ?
Perimeter =5 + ? + ? = Perimeter = 16 units ÷ 4 equal sides.

5 + 5 + 5 =15 units Each side = 4 units.

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Types of Lines

A line is a straight route. All lines extend in two directions
and have no end. There are different types of lines.

Parallel Lines Line Segment

Parallel lines will never A line segment is part of
cross. They will always be a line. It has a beginning
point and an end point.
the same distance
apart. Think: Railroad

tracks

Intersecting Perpendicular

Lines Lines

Intersecting lines are a Perpendicular lines are a
set of lines that meet at set of intersecting lines
that intersect at a right
one point. angle.

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Lines of Symmetry

A line of symmetry divides a shape
into two congruent parts. Congruent
means the parts are both the same
size and the same shape.

Lines of symmetry can be vertical, horizontal, or diagonal.

Shapes can have different numbers of lines of symmetry.

The number of congruent sides a
shape has tells you the number of
lines of symmetry a shape has. A
square has four congruent sides so it
has four lines of symmetry.

O lines of 1 line of 2 + lines of
symmetry symmetry symmetry

JMI

Created by Mrs. M’s Style © 2017

Types of Triangles

There are many different types of triangles. Triangles
can be classified by their angles or by their sides.

Acute Triangle Equilateral Triangle

All three angles are acute All three sides are
(less than 90˚). congruent (same size).

Right Triangle Isosceles Triangle

One of the angles is a Two sides are congruent
right angle (90˚). (same size).

Obtuse Triangle Scalene Triangle

One of the angles is an No sides are
obtuse angle (greater congruent(same size).

than 90˚).

Created by Mrs. M’s Style © 2017

Classify Two-Dimensional

Shapes

Two-dimensional shapes are flat figures that have a length and a
width. Two-dimensional shapes can also be called a plane figure

or polygon. They can be classified by the number of sides and
vertices (corners) they have. You can also classify shapes by the

types of lines and angles they have.

Triangle Pentagon Hexagon Octagon

3 sides 5 sides 6 sides 8 sides
3 vertices 5 vertices 6 vertices 8 vertices

Quadrilaterals are shapes that have 4 sides and 4 vertices. There
are many different names for quadrilaterals.

Rectangle Square Trapezoid Parallelogram

2 sets of 4 equal sides 1 pair of 2 sets of
parallel sides 4 right angles parallel sides parallel sides
4 right angles

Some quadrilaterals can have multiple names.

Example: A square can also be called a parallelogram
because it has two sets of parallel sides.

Created by Mrs. M’s Style © 2017

Illustrating Angles

An angle is part of a circle. Think of each circle being cut into
360 small pieces. An angle can be as small as 1 of those 360
pieces (it would have a measurement of 1˚) and as large as all

360 pieces (it would have a measurement of 360˚) .

This angle shows 1˚.

It is 1 of the circle.

360

We can use equivalent fractions to help us convert angles to

fractions.

360˚ of the circle is shaded. 180˚ of the circle is shaded.

1 whole circle is shaded. ½ of the circle is shaded.

360 ÷ 360 = 1 180 ÷ 180 = 1
360 180 2
360 360

360 ÷ 1 = 360 360 ÷ 2 = 180

90˚ of the circle is shaded. 120˚ of the circle is shaded.
¼ circle is shaded. 1/3 of the circle is shaded.

90 ÷ 90 = 1 120 ÷ 120 = 1

360 90 4 360 120 3

360 ÷ 4 = 90 360 ÷ 3 = 120

Created by Mrs. M’s Style © 2017

Measuring Angles

You can use a protractor to help you find the
measurement of any angle.

1. Line up the vertex of the angle at the center point of the
protractor.

2. Make sure the bottom ray of the angle goes through the
zero. You can measure angles using either side of the
protractor.

3. Count up from the zero until the other ray intersects. This is
the measurement of your angle.

This angle has a measurement of 55˚.

BE CAREFUL!

If you don’t measure correctly, you might think this angle has
a measurement of 125˚. Make sure you always count up
starting from the zero.

Created by Mrs. M’s Style © 2017



Adjacent Angles

The term adjacent angles is used to describe two angles
that share one ray. The angles shown here are adjacent

angles.

S You can use what
Q
T you know about

one angle to find
the measurement

of an adjacent
angle without
using a protractor.

R

If you know… If you know… If you know…
∠QRS = 40˚ ∠QRS = 40˚ ∠QRT = 120˚
and and and
∠SRT = 80˚ ∠QRT = 120˚ ∠SRT = 80˚

Then you know… Then you know… Then you know…

∠QRT = 120˚ ∠SRT = 80˚ ∠QRS = 40˚

because… because… because…
40 + 80 = 120 120 – 40 = 80 120 – 80 = 40

Think of fact families when you are working with
adjacent angles!

Created by Mrs. M’s Style © 2017

Measuring Length

There are two different systems for measuring length. You can use
the customary system or the metric system. Learning the two
systems are important. You want to be able to select the

appropriate unit of measurement for the length you are measuring.

CUSTOMARY METRIC

An INCH is the smallest unit in A MILIMETER is the smallest

the customary system. unit in the metric system.

It is about the length of a It is about the width of the tip
paperclip. on a sharp pencil.

A FOOT is the same as 12 A CENTIMETER is the same as
inches. 10 millimeters.

It is about the length of a ruler. It is about the width of your
pinky finger.

A YARD is the same as 3 feet A METER is the same as 100
or 36 inches. centimeters or 1,000
millimeters.
It is about the length of a
baseball bat. It is about the width of a door.

A MILE is the same as 1,760 A KILOMETER is the same as
yards or 5,280 feet or 63,360 1,000 meters.

inches It is about the length of 11
football fields.
It is about the length of 17
football fields. Created by Mrs. M’s Style © 2017

CUSTOMARY

CONVERSIONS

You can multiply or divide to convert measurements within the
same system. You can use this chart to help you make your
conversions.

÷12 ÷3 ÷1,760

inches feet yards miles

x12 x3 x1,760

Example:

If you have a rope that is 72 inches long and you wanted to
know how many feet that is you would use the following
equation.

72 inches ÷12 = 6 feet

You know that the rope is 6 feet long. If you wanted to convert
that rope into yards you would use the following equation.

6 feet ÷3 = 2 yards.

You know that 72 inches = 6 feet = 2 yards.

Created by Mrs. M’s Style © 2017



Liquid Volume

Liquid volume is the measurement of the amount of liquid in a
contained space. The basic units of liquid volume in the
customary system are gallons, quarts, pints, and cups.

G = Gallon Q = Quart

1 gallon = 1 quart =
4 quarts 2 pints
8 pints 4 cups
16 cups
There are…
Think a gallon of 4 quarts in a
milk.
gallon

P = Pint C = Cup

1 pint = There are…
2 cups 2 cups in a pint
4 cups in a quart
There are…
2 pints in a quart 16 cups in a
8 pints in a gallon gallon

If you know the relationship between the different units of liquid
measure you can convert a variety of measurements.

If… Then…
3 gallons = 12 quarts
1 gallon = 4 quarts

1 quart = 2 pints 4 quarts = 8 pints

1 pint = 2 cups 2 pints = 4 cups

Created by Mrs. M’s Style © 2017

Frequency Table

A frequency table is one way you can collect
and show data.

My Classmate’s Favorite Colors

Color Choices Tally Marks Frequency

Red 4
Blue 7
Yellow 5
Orange 2

Keep in mind the following when you are making
a frequency table.

1. Give the frequency table a title so you know what data
you are sharing.

2. Label the columns so you know what the information in
each column means.

3. As you are collecting data use tally marks to keep track of
your data points.

4. When you finish collecting all the data you can total up
the tally marks to find the frequency.

5. Use the data you collect to make an informed decision.

Created by Mrs. M’s Style © 2017

Dot Plot

A dot plot is a way to display data. You place a dot above
a number on a number line to represent one data point. A

dot plot can also be known as a line plot.

Number of Cookies Eaten at Lunch

X X=1
XX student
XXX

XXXX

XXXXXX

012345

Cookies packed in student lunches

This dot plot can give us a lot of information. We can count the
total number of dots to find out that 16 students were part of this
survey. We can also tell that the majority of students either bring

1 or 2 cookies for lunch.

When you make a dot plot remember the following:
1. Give it a title.

2. Include a key so you know what the dot or X represents.
3. Be sure to label the number line so you know what you

are measuring.

Created by Mrs. M’s Style © 2017

Stem & Leaf

Plot

A stem and leaf plot is a way to show the frequency of
a set of data. A stem and leaf plot is different from other
graphs because the data is organized by place value.

Data Set: 4, 7, 8, 8, 14, 15, 30, 33, 33, 33, 35

The numbers stem leaves The numbers in
in the stem the leaves
0 4 7 88 column
column 1 45
represents represents the
ones place
the tens
place This 8 represents one
of the 8s in the data
The one in the tens 2
column doesn’t 3 set

represent a data point 03335
by itself, but the digits in
Each 3 listed in the leaves column
the leaves column represents the data point 33.
represent the data
Notice it appears 3 times in the
points 14 and 15 data set

A stem and leaf plot can show you the total number
of data points collected as well as the frequency of
each data point. It is another way to organize data!

Created by Mrs. M’s Style © 2017

Expenses

An expense is anything you spend money on.
There are two types of expenses.

Fixed Expenses Variable Expenses

• Amount does not • Amount can change
change. The amount is based on needs or wants
the same each time it • Does not occur regularly

occurs (it might be a one time
• Occurs regularly (weekly, event or happens
infrequently)
monthly, yearly)
• Easy to budget for • Can be more challenging
to budget for
EXAMPLES: rent, car
payments, membership fees EXAMPLES: clothes,
entertainment, gifts,

vacations

If you aren’t sure if your expense is fixed or variable, you can ask
yourself these questions. To help you budget, it’s important to
know the type of expenses you have each month.

Question FE VE

Is the expense always the same amount? Yes No

Does the payment always happen at the same Yes No
time? No Yes

Is it a one-time expense?

Created by Mrs. M’s Style © 2017

Calculating Profit

Profit is the amount of money someone makes off of a
good or service after they have accounted for all of

their expenses.

Example: Lemonade Stand

You want to set up a lemonade stand. Before you start selling
lemonade you need to purchase some materials for your stand.

Expenses: You spent a total of $23 to set up your
Lemons - $5 lemonade stand.
Glasses - $2
Pitcher - $3 After a week, you have sold 50 glasses
Signs - $3 of lemonade. You charged $1.00 a
Stand - $10 glass.
Total: $23
How much is your profit?

Profit = Income – Expenses

We know that your income is $50 and we know that your
expenses are $23. Since we know both of these amounts, we can
plug them into the profit equation to figure out how much profit

you made.

Profit = $50 - $23

Profit = $27

You profited $27 from selling 50 glasses of lemonade.
How much would your profit be from 100 glasses? 200 glasses?

Created by Mrs. M’s Style © 2017

Savings Options

When you save money you set it aside to use for a later
date. You wait to spend the money you are saving.
You can save money in different ways.

Home Savings

Savings Account

When you save your money at When you put money in a
home you put it in a piggy savings account you let the
bank hold on to it. You earn
bank or keep it hidden some interest on the money you
place safe.
save.

Pros Cons Pros Cons

You have It doesn’t varieiInttyteeoarefrnsrtes. asonasimYl.wYomaouyeudsdcohiaanat’nvete
immediate earn
aPcecoepssletosaitv. e
moinnteeyrefsot.r a

save for a short-term goal or a long-termacgcoeassl.to it.

Short-Term Goals Long-Term Goals

• Vacation • Retirement
• TV • New Car
• New Clothes • House
• Furniture • College Tuition

Created by Mrs. M’s Style © 2017

Budgeting an

Allowance

When you have an allowance or an income you should
create a budget for it, no matter how much it is.

A budget is a plan for how you will spend your money.

Budget Explanation Example

60% of your Make sure you pay If your monthly
allowance should for your needs income is $400 then
be set aside for before you start 60% of that should
your basic needs
buying things on your be used for your
and wants. wants list. Food, rent, basic expenses. This
transportation and equals $240 a month.
30% of your bills get covered first.
allowance should
be set aside for A good rule of If your monthly
thumb is to put aside income is $400 then
savings. 30% of your income 30% of that should

10% of your to savings. This be set aside for
allowance should includes saving for savings. This equals
be given away to both long-term and
short-term goals. $120 a month.
charity.
No matter how much If your monthly
or how little you income is $400 then
make you always 10% of that should
be given away to
want to give some charity. This equals
away to charity. 10%
$40 a month.
is a pretty typical
amount.

When you stick to a budget it helps you be in control of your money.

Created by Mrs. M’s Style © 2017