Numbers
Standard
Written
5,421
five thousand,
four hundred
twenty-one
Expanded
Visual Model
5,000+400+20+1
Addition
Identity
The sum of a number and zero is that number.
15+0=15
Commutative
You can add numbers in any order, and the sum
will be the same.
2+3=3+2
Associative
No matter how you group numbers, the sum is
the same.
(2+3)+1=2+(3+1)
( ) ( ) Multiples of Ten
4x30=
4 groups of 30
30+30+30+30=120
(4x3)x10=120
Multiplication
Grouping Model
Repeated
Addition
3x4=
4+4+4=12
Array
Number
Line
Division
Grouping Model
Repeated 15÷3=
Subtraction
15-3-3-3-3-3
Array
Number
Line
Word Problems
Addition
all together
plus
total
both
sum
join
increase
combined
add
Multiplication
equal groups
total
triple
product
how many left
minus
remove
fewer decrease
take away
difference
in all
by
Subtraction
twice
double
times
multiplied by
Division
share equally
each
half
parts
quotient
split equally
divided by
Word Problems
Joining Problems
Result Unknown
3+4=?
Change Unknown
3+?=7
Three boys were playing
outside. Four more boys
came to join them. How
many boys are playing
outside now?
Start Unknown
?+4=7
Three boys were playing
Some boys were playing
outside. Some more boys outside. Four more boys
came to join them. Now
came to join them. Now
there are seven boys
there are seven boys
playing outside. How many playing outside. How many
boys joined the first
boys were first outside?
three?
Separating Problems
Result Unknown
6-2=?
Change Unknown
6-?=4
There were six pieces of
There were six pieces of
gum. Sally ate some
gum. Sally ate two pieces
pieces of the gum. There
of gum. How many pieces
were four pieces of gum
of gum were left?
left. How many pieces of
gum did Sally eat?
Start Unknown
?-2=4
There were some pieces
of gum. Sally ate two
pieces of the gum. There
were four pieces of gum
left. How many pieces of
gum were there to begin
with?
Comparing Problems
Difference Unknown
8-3=? 3+?=8
Quantity Unknown
8-5=?
5+?=8
Referent Unknown
8-3=? ?+3=8
Mark collected 8 rocks.
Jen collected three rocks.
How many more rocks did
Mark collect than Jen?
There are eight rocks.
Mark found 5 rocks and
Jen found the other
rocks. How many rocks
did Jen find?
Mark has three more
rocks than Jen. Mark has
8 rocks. How many rocks
does Jen have?
Number
?+15=25
25-15=10
?=10
?-10=15
15+10=25
?=25
15+?=25
25-15=10
?=10
?x3=15
15÷3=5
?=5
15-?=25
25-15=10
?=10
?÷3=5
5x3=15
?=15
3x?=15
15÷3=5
?=5
15÷?=3
15÷3=5
?=5
Multiplication
Identity
Commutative
Associative
Distributive
Changing the order
The multiplicative
of addends or
identity is one. If you
factors does not
multiply a factor by
one, the product will affect the product.
equal that factor.
3x5=15
5x3=15
5x1=5
1x5=5
The order in which
Multiplying a sum by
numbers are
a number is the
grouped does not
same as multiplying
affect the product. each addend by the
number and then
(3x5)x4=60
adding the products.
3x(5x4)=60
3x15=45
(3x10)+(3x5)=45
Division
35÷7=?
7x?=35
?=5
32÷4=?
4x?=32
?=8
54÷9=?
9x?=54
?=6
Facts
x0-always equals zero
x1-equals that number
x2-double that number
x3-double and 1 more
x4-double, double
x5-count by fives
x6-count by fives and
add 1 more
x7-count by fives and
add the double
x8-double, double, double
x9-count by tens, take
away a group
x10-count by tens
Word Problems
1. Read and reread
the problem.
2. Break the
problem into
parts.
3. Decide what
each part is
asking.
4. Step-by-step
solve the
problem.
5. Double-check
your answer.
Patterns
Input
Output
Input
Output
2
4
2
6
3
6
3
9
4
8
4
12
5
10
5
15
Input
Output
Input
Output
2
10
2
20
3
15
3
30
4
20
4
40
5
25
5
50
Fractions
A fraction shows equal parts of a whole.
Numerator-the number of
parts counted
Denominator-the total
number of parts
Unit Fraction-a fraction with a
numerator of one.
Number Line
Fractions
Equivalent fractions are fractions
that are the same size or are on the
same point on a number line.
=
=
=
=
Time
The amount of time that
passes between one time
and another time.
Start: 7:30
1 hour
Stop: 9:15
30 min.
15 min.
7:30
9:00
9:15
8:30
Elapsed Time: 1 hour and 45 minutes
Start: 3:20
Stop: 5:45
2 hours
3:20
20 min.
5:20
5 min.
5:40 5:45
Elapsed Time: 2 hours and 25 minutes
and Mass
Volume-the amount of space
an object takes up
Beaker A
Beaker B
There are 70
more milliliters
in Beaker A
than Beaker B.
150 ml
80 ml
Mass-the measure of the
amount of matter in an object
The lighter
side rises.
The heavier
side lowers.
Bar Graphs
Collect Data
Favorite Food
pizza
chicken
hotdog
taco
5511
5111
55
55 1111
Bar Graph
Picture Graph
pizza
✖✖✖✖✖✖
chicken ✖✖✖✖
hotdog ✖✖✖✖✖
taco
✖✖✖✖✖✖✖
✖=2 votes
14
12
10
8
6
4
2
pizza
chicken
hotdog
taco
Ruler to ¼ Inch
• Circle the number before the
whole number line.
• Write down that whole number.
• Find the line halfway between
the circled whole number and the
next whole number-that line
shows ½.
• The line before the ½ mark is ¼.
• The line after the ½ mark is ¾.
The bar is 5 ¾ inches long.
Area
Area is the measure of the
surface of an object. It is
measured in square units.
A=5 square units
Count the
boxes.
A=5 square units
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
A=25 sq. units
The Area
To find the area, multiply
length by width.
A=3x6 sq. ft.
3 ft.
A=18 sq. ft.
6 ft.
Area is additive.
2 ft.
5 ft.
A=(5x2)+(2x6)=22
sq. feet
2 ft.
6 ft.
Perimeter
Perimeter is the distance
around an object. Count or add
all of the sides together.
p=12 units
P=12 units
6 ft.
4 ft.
P=3+3+3=9 in.
P=6+6+4+4=20 ft.
Polygons
Quadrilaterals
Parallelogram
Non Parallelogram
Other
Rhombus
Kite
Rectangle
Trapezoid
Square
Shapes
All parts must be equal