Place Value
These are the digits that make up numbers in our number
system.
0,1,2,3,4,5,6,7,8,9
5
,
5
5
5
ones
5
tens
5
hundreds
,
thousands
5
ten thousands
5
hundred thousands
5
millions
,
ten millions
billions
5
hundred millions
When these digits create a number, each digit sits in a
different place. Each place has a different value.
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.
Created by Mrs. M’s Style © 2017
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
left.
The digits move 1 space to the
right.
23 x 100 = 2,300
2,300 ÷ 100 = 23
The digits move 2 spaces to the
left.
The digits move 2 spaces to the
right.
23 x 1,000 = 23,000
23,000 ÷ 1,000 = 23
The digits move 3 spaces to the
left.
The digits move 3 spaces to the
right.
Do you notice a pattern?
When you multiply a number by
10, you add 1 zero to the
number you are multiplying.
When you multiply a number by
100, you add 2 zeros to the
number you are multiplying.
When you multiply a number by
1,000, you add 3 zeros to the
number you are multiplying.
What would happen if you
multiply a number by 10,000?
100,000? 1,000,000?
When you divide a number by
10, you remove 1 zero from the
number you are dividing.
When you divide a number by
100, you remove 2 zeros from the
number you are dividing.
When you divide a number by
1,000, you remove 3 zeros from
the number you are dividing.
What would happen if you divide
a number by 10,000? 100,000?
1,000,000?
Created by Mrs. M’s Style © 2017
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
the value of the
number
writing the number by
adding the value of
the digits
Expanded Notation
writing the number to
show the value of
each digit
Word Form
writing the number
using only words
6x100 + 3x10
+ 2x1
600 +
30 + 2
six hundred
thirty two
Created by Mrs. M’s Style © 2017
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
the value of the
number
writing the number by
adding the value of the
digits
Expanded Notation
writing the number to
show the value of
each digit
Word Form
writing the number
using only words
2x1 + 3x.1 +
5x.01
2 + .3 + .05
two and thirty
five
hundredths
Created by Mrs. M’s Style © 2017
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
the largest.
Start here
1=1
3=3
4 is less than 6
So……
13,453 is less than 13,623
13,453
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
Created by Mrs. M’s Style © 2017
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
1.
To round a number follow these steps.
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
Created by Mrs. M’s Style © 2017
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
1
$1.00
1 dollar
When an entire shape
is shaded in it
represents 1 whole.
This is one dollar. It is
made up of 10 dimes.
You can also make a
dollar with 100 pennies.
One Tenth
0.1
$0.10
1 dime
there are 10 tenths
in one whole
There are 10 columns
and 1 entire column is
shaded in. This
represents 1 tenth.
There are 10 dimes in
one dollar. One dime is
one tenth of a dollar.
One
Hundredth
0.01
$0.01
1 penny
there are 100
hundredths in one
whole
The square is split into
100 little square. One
of the squares is
shaded. This represents
1 hundredth.
There are 100 pennies
in one dollar. One
penny is one
hundredth of a dollar.
Created by Mrs. M’s Style © 2017
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
2=2
4 is more than 3
So……
12.4 is greater than 12.39
12.40
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
than 2 numbers.
Start here
3=3
4 is more than 3 (3.45 is the greatest)
9 is greater than nothing (3.39 is next
largest)
So……
3.45 is greater than 3.39 which is
greater than 3.3
3.45
3.39
3.30
Created by Mrs. M’s Style © 2017
Relating Decimals to
Fractions
Decimals and fractions both name a part
of a whole.
Decimals can be written as fractions.
𝟑
𝟒𝟓
.3 =
𝟏𝟎
and
.45 =
𝟏𝟎𝟎
Fractions can be written as decimals.
𝟔
𝟏𝟖
𝟏𝟎
= .6 and
𝟏𝟎𝟎
= .18
Decimals
Fractions
.2
2
10
25
100
6
10
68
100
.25
.6
.68
Created by Mrs. M’s Style © 2017
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.
F F
F F
F F
F F
F F
F F
This model shows squares divided into one-fourth sections.
Parts of a Fraction
There are specific terms to name
each part of a fraction.
•
•
•
The top number is called the
numerator
The bottom number is called
the denominator
The bar in the middle is called
the fraction bar
Improper Fractions
An improper fraction is a fraction
where the numerator is larger than
the denominator.
9
4
The model above shows an improper
fraction. Each square is divided into
fourths (denominator) and nine
(numerator) of them are shaded in.
Fractions as a Sum
You can represent fractions as
sum of smaller fractions. The
model can be represented as
different sums of fractions.
4
4
4
1
4
4
+ +
or
3
4
3
3
4
4
+ +
Mixed Numbers
A mixed number is a combination of
a whole number and a fraction.
2
1
4
The model above can be written as
a mixed number. Even though each
square is divided into fourths, there
are two whole squares shaded and
one fourth of another square.
Created by Mrs. M’s Style © 2017
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.
=
𝟑
𝟒
=
+
𝟐
𝟒
+
𝟏
𝟒
You can also decompose a fraction as a series of unit
fractions. A unit fraction will always have 1 in the
numerator.
=
𝟑
𝟒
=
+
𝟏
𝟒
+
+
𝟏
𝟒
+
𝟏
𝟒
Created by Mrs. M’s Style © 2017
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.
𝟏
𝟐
=
𝟐
𝟒
𝟒
𝟖
=
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
by Multiplying
𝟏
𝟐
x
𝟒
𝟒
=
𝟒
𝟖
You can find an equivalent
fraction by multiplying the
numerator and denominator
by the same number.
Find Equivalent Fractions
by Dividing
𝟐
𝟒
𝟐
𝟐
÷ =
𝟏
𝟐
You can find an equivalent
fraction by dividing the
numerator and denominator
by the same number.
Created by Mrs. M’s Style © 2017
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
𝟑
𝟒
>
𝟑
𝟔
The smaller denominator is the
greater fraction.
Same Denominator
𝟑
𝟓
<
𝟒
𝟓
The larger numerator is the
greater fraction.
Different Numerators and Denominators
If you are comparing two fractions with
different numerators and denominators,
find equivalent fractions with the same
denominator.
12 4
=
20 4
𝟑
𝟓
x >
𝟐
𝟒
x
5 10
=
5 20
3/5 is greater than 2/4 because when you
multiply to get the common denominator
of 20, 12 is greater than 10.
You can also use the butterfly method.
Cross multiply and then compare the
products. The larger product is the side
of the greater fraction.
5x2 = 10
𝟑
𝟓
>
𝟐
𝟒
3x4 = 12
12 is greater than 10 so 3/5 is greater
than 2/4.
Created by Mrs. M’s Style © 2017
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
F
F
F
F
4
4
1.
2.
3.
4.
+ 34 = 47 =
F
F
How To Subtract Fractions
F
F
O
O
3
4
5
6
1
Add the numerators.
Keep the denominators the
same.
Draw a model to check your
work.
If needed, convert the
fraction to a mixed number.
O
O
1.
2.
3.
O
O
- 36 = 26
Subtract the numerators.
Keep the denominators the
same.
Draw a model to check
your work.
Created by Mrs. M’s Style © 2017
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
¼
½
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
said the sum was 3/8.
Carrie added the fractions
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.
Created by Mrs. M’s Style © 2017
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
8
1
1
8
118
1
8
128
1
8
138
1
8
148
1
8
158
1
8
168
1
8
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.
1
4
1
4
1
114
1
4
1
4
124
134
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.
1
2
1
1
2
112
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?
Created by Mrs. M’s Style © 2017
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.
Step 2: Fill in a
zero as a place
-holder if
needed
Step 1: Line up
numbers
according to
place value
Adding
Step 4: Bring
down decimal
and check
Step 3: Solve.
Start with the
lowest place
value (right)
1
16.9
+ 4.62
16.90
+ 04.62
1
If you miss
this step, your
answer will
be incorrect.
Adding a zero
as a place
holder doesn’t
change the
value!
16.90
+ 04.62
21 52
Don’t forget
to carry the
one!
16.9
+ 04.62
21.52
Make sure
you check
your work!
Subtracting
16.9
- 4.62
16.90
- 04.62
You might be
tempted to line
up the 9 and
the 2, make
sure you line up
the decimals
instead.
Adding the zero
reminds you to
subtract the 2
rather than just
bring it down.
8 10
Since you can’t
subtract 2 from
zero, you have
to borrow from
the 9.
16.90
- 04.62
12.38
Make sure
you check
your work!
16.90
- 04.62
12 38
Created by Mrs. M’s Style © 2017
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
Created by Mrs. M’s Style © 2017
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.
Each row has the
same number of
circles.
⃝ ⃝ ⃝ ⃝ ⃝
⃝ ⃝ ⃝ ⃝ ⃝
⃝ ⃝ ⃝ ⃝ ⃝
⃝ ⃝ ⃝ ⃝ ⃝
This is a
column.
Each
column has
the same
number of
circles.
You can find the total of the array different ways.
You can count the
circles.
20
You can add up the
circles in each row.
5 + 5 + 5 + 5 = 20
You can add up the
circles in each column.
You can multiply the rows
by the columns.
4 + 4 + 4 + 4 + 4 = 20
5 x 4 = 20
Created by Mrs. M’s Style © 2017
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
the factors, and it won’t
change the answer.
You can change the
placement of the parenthesis
but it won’t change the
answer.
3 x 6 = 18
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
broken into (distributed) a sum
of two other multiplication
facts.
The product of any number
and 1 is always that number.
24 x 3 = ?
(20 + 4) x 3 = ?
(20 x 3) + (4 x 3) = ?
(80) + (12) = 92
4x1=4
32 x 1 = 32
The product of any number
and 0 is 0.
4x0=0
32 x 0 = 0
Created by Mrs. M’s Style © 2017
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.
Created by Mrs. M’s Style © 2017
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 +
20 x 40
40 = 800
+
2 20 x 2 =
40
3
3 x 40 =
120
3x2=
6
800 + 120 + 40 + 6 = 966
Step 1: Expand each of the
factors you are multiplying.
Step 2: Set up the numbers
above the boxes.
Step 3: Multiply the numbers
in the rows and columns.
Step 4: Add all of the
products found in each of
the boxes to get the total.
42 think (40 +2)
X 23 think (20 + 3)
6 (3 x 2)
120 (3 x 40)
40 (20 x 2)
+ 800 (20 x 40)
966
Step 1: Multiply by the ones.
Step 2: Multiply by the tens.
Step 3: List all the partial
products.
Step 4: Add all of the partial
products together to get
the total.
Created by Mrs. M’s Style © 2017
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
paper to help you find the quotient.
39÷3
Break 39 into two parts 30 + 9.
You can draw a rectangle to represent
each part.
The answer is 39÷3 = 13
10
3
3
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)
• 84 ÷ 6 = 10 + 4
• 84 ÷ 6 = 14
Think: 60 + 24 = 84
Think: 60 ÷ 6 = 10 and 24 ÷ 6 = 4
Think: 10 + 4 = 14
Created by Mrs. M’s Style © 2017
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
division
8,281 ÷ 7
Dad
divide
Mom
multiply
Sister
subtract
Brother
bring
down
Rover
repeat
1, 183
7 8,281
7
12
7
58
56
021
21
0
Set up for long division
7 8,281
Step 1: Divide 8 by 7.
8÷7 = 1
Step 2: Multiply 7 by 1.
7x1=7
Step 3: Subtract 7 from 8.
8–7=1
Step 4: Bring down the
next digit in the dividend
in this case it is the 2
Step 5: Repeat Steps 1-5
with the remaining digits
Created by Mrs. M’s Style © 2017
Compatible Numbers
You can use compatible numbers or rounding to help you
estimate solutions.
Compatible Numbers
Compatible numbers are
sometimes called friendly
numbers. These are numbers that
are easy to put together.
Numbers that
end in 0
Numbers that
end in 5
10, 100, 1000
5, 15, 105
Doubles Facts
Numbers that
Make 10
8+8 = 16
Rounding helps you estimate
numbers to the nearest group of
10. There are specific rules to
rounding.
Rules to Rounding:
1 + 9 = 10
20 + 20 = 40
Rounding
4 or less, let it rest
(stay the same)
5 or more, add 1 more
(add 1 to the place you
are rounding)
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
+ 65
140
76
+ 66
142
80
+ 70
150
For this set of numbers, which estimation strategy worked the best?
Why?
Created by Mrs. M’s Style © 2017
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.
Created by Mrs. M’s Style © 2017
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
Kelly is training for a race. She
runs 5 miles a day during the
week (Monday – Friday) and
runs 10 miles on Saturday. If she
wants to log 46 miles for the
week, how many miles does she
need to run on Sunday?
Think: In order to solve this
problem you need to multiply,
add, and subtract. You can
make a strip diagram for each
of these operations.
Step 1: Multiplication
m
5
5
5
5
5
Let’s have m represent the
number of miles Kelly ran
Monday – Friday.
m = 5x5
m = 25
Step 2: Addition
Step 3: Subtraction
n
46
25
(same as m)
10
Let’s have n represent the
number of miles Kelly ran during
the week (M – F) and on
Saturday. We know she ran 25
M – F and 10 on Saturday.
n = 25 + 10
n = 35
35 (same as n)
s
Let’s have s represent the number
of miles Kelly needs to run on
Sunday. We know her total
mileage for the week should be
46 and we know how much she
ran Monday - Saturday so we just
need to subtract to find s.
s = 46 – 35
s = 11
Created by Mrs. M’s Style © 2017
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
of soda
X
Y
input
output
4
11
25
5
8
15
35
7
1
2
2
4
3
6
12
19
65
13
4
8
16
23
80
16
The rule for this table
is X + 7 = Y. You can
use the same rule to
figure out future rows
added to the chart. If
X = 20 then Y = 27
(X+7 = 27)
The rule for this table
is kids x 2 = number
of cans of soda. You
can use the same
rule to figure out the
number of cans of
soda needed for 10
kids.
Set A
4
6
9
13
Set B
10
14
20
28
The rule for this table
is input ÷ 5 = output.
You can use the rule
and the inverse of
the rule to figure out
future rows of the
chart. If output = 20
then input = 100.
(20x5 = 100)
Sometimes input-output
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.
Created by Mrs. M’s Style © 2017
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
units inside the shape.
2. You can multiply the
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
Created by Mrs. M’s Style © 2017
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
is given you can add them up.
3
?
3
4
You can remember that opposite
sides are equal and you can add
using the information you are
given.
Perimeter =
3+3+4+3+4
= 17 units
6
4
?
Perimeter =
6+2+?+?=
6+2+6+2=
16 units
3
2
If you know a shape is made of
equal sides you just need the
length of one side to find the
perimeter.
?
5
?
Perimeter =5 + ? + ? =
5 + 5 + 5 =15 units
If you are given the perimeter,
you can work backwards to find
the length of each side.
?
?
?
?
Perimeter = 16 units ÷ 4 equal sides.
Each side = 4 units.
Created by Mrs. M’s Style © 2017
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
cross. They will always be
the same distance
apart. Think: Railroad
tracks
A line segment is part of
a line. It has a beginning
point and an end point.
Intersecting
Lines
Perpendicular
Lines
Intersecting lines are a
set of lines that meet at
one point.
Perpendicular lines are a
set of intersecting lines
that intersect at a right
angle.
Created by Mrs. M’s Style © 2017
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
symmetry
1 line of
symmetry
2 + lines of
symmetry
J
M
I
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
Right Triangle
Isosceles Triangle
All three angles are acute
(less than 90˚).
All three sides are
congruent (same size).
One of the angles is a
right angle (90˚).
Two sides are congruent
(same size).
Obtuse Triangle
Scalene Triangle
One of the angles is an
obtuse angle (greater
than 90˚).
No sides are
congruent(same size).
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
3 vertices
5 sides
5 vertices
6 sides
6 vertices
8 sides
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
parallel sides
4 right angles
4 equal sides
4 right angles
1 pair of
parallel sides
2 sets of
parallel sides
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
360
the circle.
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
÷
360
360
=1
360 ÷ 1 = 360
90˚ of the circle is shaded.
¼ circle is shaded.
90
360
÷
90
90
=
180
360
=
1
2
360 ÷ 2 = 180
120˚ of the circle is shaded.
1/3 of the circle is shaded.
1
120
4
360
360 ÷ 4 = 90
÷
180
180
÷
120
120
=
1
3
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.
T
S
Q
R
You can use what
you know about
one angle to find
the measurement
of an adjacent
angle without
using a protractor.
If you know…
∠QRS = 40˚
and
∠SRT = 80˚
If you know…
∠QRS = 40˚
and
∠QRT = 120˚
If you know…
∠QRT = 120˚
and
∠SRT = 80˚
Then you know…
∠QRT = 120˚
Then you know…
∠SRT = 80˚
Then you know…
∠QRS = 40˚
because…
40 + 80 = 120
because…
120 – 40 = 80
because…
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
It is about the length of a
paperclip.
It is about the width of the tip
on a sharp pencil.
A FOOT is the same as 12
inches.
A CENTIMETER is the same as
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
or 36 inches.
A METER is the same as 100
centimeters or 1,000
millimeters.
the customary system.
It is about the length of a
baseball bat.
unit in the metric system.
It is about the width of a door.
A MILE is the same as 1,760
yards or 5,280 feet or 63,360
inches
A KILOMETER is the same as
1,000 meters.
It is about the length of 17
football fields.
It is about the length of 11
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.
÷3
÷12
inches
feet
x12
÷1,760
yards
x3
miles
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
Think a gallon of
milk.
There are…
4 quarts in a
gallon
P = Pint
C = Cup
1 gallon =
4 quarts
8 pints
16 cups
1 pint =
2 cups
There are…
2 pints in a quart
8 pints in a gallon
1 quart =
2 pints
4 cups
There are…
2 cups in a pint
4 cups in a quart
16 cups in a
gallon
If you know the relationship between the different units of liquid
measure you can convert a variety of measurements.
If…
Then…
1 gallon = 4 quarts
3 gallons = 12 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
Red
Blue
Yellow
Orange
Tally Marks
Frequency
4
7
5
2
Keep in mind the following when you are making
a frequency table.
1.
2.
3.
4.
5.
Give the frequency table a title so you know what data
you are sharing.
Label the columns so you know what the information in
each column means.
As you are collecting data use tally marks to keep track of
your data points.
When you finish collecting all the data you can total up
the tally marks to find the frequency.
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
student
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0
1
2
3
4
5
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
in the stem
column
represents
the tens
place
The one in the tens
column doesn’t
represent a data point
by itself, but the digits in
the leaves column
represent the data
points 14 and 15
stem leaves
0 4 7 88
1 45
The numbers in
the leaves
column
represents the
ones place
This 8 represents one
of the 8s in the data
set
2
3 0 3 3 3 5
Each 3 listed in the leaves column
represents the data point 33.
Notice it appears 3 times in the
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
change. The amount is
the same each time it
occurs
Occurs regularly (weekly,
monthly, yearly)
• Easy to budget for
Amount can change
based on needs or wants
• Does not occur regularly
(it might be a one time
event or happens
infrequently)
• 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
time?
Yes
No
Is it a one-time expense?
No
Yes
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:
Lemons - $5
Glasses - $2
Pitcher - $3
Signs - $3
Stand - $10
Total: $23
You spent a total of $23 to set up your
lemonade stand.
After a week, you have sold 50 glasses
of lemonade. You charged $1.00 a
glass.
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
When you save your money at
home you put it in a piggy
bank or keep it hidden some
place safe.
Pros
Savings
Account
When you put money in a
savings account you let the
bank hold on to it. You earn
interest on the money you
save.
Cons
Pros
Cons
You have
It doesn’t
You don’t
It earns
immediate
earn
always have
interest.
Peopletosave
for a variety of reasons.
You can
access
it. money
interest.
immediate
save for a short-term goal or a long-term
goal.to it.
access
Short-Term Goals
•
•
•
•
Vacation
TV
New Clothes
Furniture
Long-Term Goals
•
•
•
•
Retirement
New Car
House
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
allowance should
be set aside for
your basic needs
and wants.
Make sure you pay
for your needs
before you start
buying things on your
wants list. Food, rent,
transportation and
bills get covered first.
If your monthly
income is $400 then
60% of that should
be used for your
basic expenses. This
equals $240 a month.
30% of your
allowance should
be set aside for
savings.
A good rule of
thumb is to put aside
30% of your income
to savings. This
includes saving for
both long-term and
short-term goals.
If your monthly
income is $400 then
30% of that should
be set aside for
savings. This equals
$120 a month.
10% of your
allowance should
be given away to
charity.
No matter how much
or how little you
make you always
want to give some
away to charity. 10%
is a pretty typical
amount.
If your monthly
income is $400 then
10% of that should
be given away to
charity. This equals
$40 a month.
When you stick to a budget it helps you be in control of your money.
Created by Mrs. M’s Style © 2017
Understanding
Financial Institutions
A financial institution is an organization that helps people
manage their money. A bank is an example of a
financial institution.
A bank has three basic purposes.
A bank keeps
money safe.
• A bank is FDIC
insured. This means
that the bank has
made a promise that
you will get your
money back.
•There are several
different types of
accounts you can open
at a bank. A checking
account allows you to
deposit and
withdrawal money
anytime you want. A
savings account has a
few more rules about
depositing and
withdrawing money.
A bank
borrows
money from
its customers.
• When you deposit
money into a longterm savings account,
banks will use that
money to lend out to
other customers in the
form of a loan.
• When banks borrow
money from their
customers they pay
them interest on the
money they borrow.
This means your
money is making
money while sitting in
the bank.
A bank lends
money to its
customers.
• A bank can lend
money to its
customers. This is
called a loan. People
often take out loans
for things like
purchasing a house, a
car, or paying for
college.
• When you take out a
loan from the bank
they will charge you
interest on the money
you borrow. When you
pay back the loan you
have to pay back more
than you borrowed.
Created by Mrs. M’s Style © 2017