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Third Grade Math Review
Know your multiplication and division facts, through memorization or other strategies!!!!
Remember, how many groups with how many in each group – multiply!
Always write (how many groups) x (how many in each group). If a bigger number is broken up into equal groups divide!
Use fact families to help you solve problems – 3x4=12, 4x3=12, 12÷3=4, 12÷4=3
For all word problems ask yourself: What do I know? What am I trying to find out?
Place Value:
F
 Place values: thousands, hundreds, tens, ones
 In the number 5,742: The value of the 7 is 700, but its place value
is the hundreds place
 Expanded Form: 4,000 + 600 + 20 + 3 =4, 623
 Know these signs: > greater than, < less than, = equal to
Rounding:
 Approximate, estimate, round, about. Look at the number to the
right: Numbers 0-4 stays the same
Numbers 5-9 round up
 Round first and then add or subtract – If there are 26 apples in
one bag and 52 in another, about how many apples are there?
30 + 50= about 80 apples
Addition and Subtraction:
 Adding – taking parts and combing them to find the total
 Subtracting – taking a total and finding one of the parts.
 If you use the traditional way, remember the steps and be careful
with your numbers (especially subtracting across zero).
Order of Operations:
 The order in which to solve problems
 Write PEMDAS to help you remember (parenthesis, exponents,
multiplication, division, addition, subtraction)
2+ (7-3) x6÷2 = 2+4x6÷2 = 2+24÷2 = 2+12 = 14
Properties:
 Commutative Property (order property – order doesn’t matter)
Addition: 3+4 = 4+3
Multiplication: 5x6 = 6x5
 Identity Property
Addition: 4+0=4
Multiplication: 8x1 = 8
 Associative Property (grouping property – use parenthesis)
Addition: (3+5) + 1= 9 and 3+ (5+1) = 9
Multiplication: (2x3) x 1 = 6 and 2x (3x1) = 6
 Zero Property (Multiplication Only)
Any number times zero equal zero 7x0=0
Fractions:
 A whole is broken into EQUAL parts
 Denominator: total number of parts
 Numerator: parts in question
 If comparing unit fractions (1 as the numerator and different
denominators) the smaller the number – the bigger the piece.
 If comparing fractions with the same denominators the bigger the
numerator the bigger the fraction.
 Cross multiply when comparing fractions that have different
denominators and numerators.
 Equivalent fractions: fractions that are equal
 Mixed numbers: Whole number & part of a whole (the extra) 4⅓
 Improper fraction gets changed to a mixed number or a whole
number 15/2 = 7 ½ Divide the numerator by the denominator
and the remainder is the fraction.
Time:
 Elapsed time: how much time as passed – Remember to write
SEE to help you solve. Mrs. Smith leaves for work at 4:00. Her
drive takes 45 minutes. What time does Mrs. Smith get home?
4:45 or Fred needs to be at school at 8:15. It takes him 20
minutes to get there and 30 minutes to get ready. What time
does Fred need to wake up? 7:25
 Quarter (1/4) of an hour is 15 minutes; half an hour is 30 minutes
Measurement:
 When given an item be able to identify the best unit to measure
the item. Think about what you know and compare.
 Length – customary and metric
Long distances: miles (m) and kilometers (km)
1 inch (in): the tip of your thumb to the first knuckle
1 foot (ft): length of a ruler or one of our tile squares
1 yard (yd): the width of our bookshelf
1 centimeter (cm): width of your pinky finger
1 meter (m): the length of two desks together
 When going from a small unit (in) to a bigger unit (ft) divide and
when going from a bigger unit (yd) to a smaller unit (in) multiply
 12 in = 1 ft
36 in= 1 yd
3 ft= 1yd. 5,280ft = 1 m
100cm = 1 m 10dm= 1 m 1,000km = 1 km
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Capacity - customary and metric
Be able to draw the Big G
1 gallon = 4 quarts = 8 pints = 16 cups
1 quart = 2 pints = 4 cups
1 pint = 2 cup
Metric - 1,000 mL = 1 liter (about a quart or the size of my water
bottle) 1 milliliter is about 20 drops from an eyedropper
Mass
1 pound (lb): your math textbook or a large soup can
1 ounce (oz): a large paperclip
1 gram (g): small paperclip
1 kilogram (kg): baseball bat
16 oz = 1lb – remember the 16 looks like the lb
1,000g = 1 kilogram
Temperature (Fahrenheit, Celsius)
Fahrenheit Temps.
Water freezes at 32
A warm room is 72
It is 98.6 inside of you
Water boils at 2-1-2
Celsius Temps.
30° is Hot
20° is Nice
10° is Cold
0° is Ice
 Look carefully at the side of thermometer to see if it is
Fahrenheit or Celsius. Also, determine what the pattern
between the numbers is (counting by 1’s, 2’s, 5’s)
Geometry
 2 – D figures - plane figures
 Polygons – closed figure with 2 or more straight sides – no
curves. Have the same number of angles as sides.
 Triangle: a three sided polygon
 Quadrilateral: a four sided polygon
Parallelogram – opposite sides are parallel
Rectangle – 4 right angles, opposite sides are the same
length and opposite sides are parallel
Square – 4 right angle, all sides are the same length and
opposite sides are parallel
Trapezoid – one pair of parallel sides
Rhombus – no right angle, all sides are the same length,
opposite sides are parallel.
 Other Polygons: Pentagon – 5, Hexagon - 6, Octagon – 8
 3-D figures – solid figures
 Most have edges (where 2 faces meet – sides), vertices (where
edges meet – points), and faces (flat surface)
Cube: 6 faces, 8 vertices, 12 edges
Rectangular Prism: 6 faces, 8 vertices, 12 edges
Pyramid: 5 faces, 5 vertices, 8 edges
Cylinder: 2 flat surfaces, 0 vertices, 0 edges
Sphere: 0 flat surfaces, 0 vertices, 0 edges
Cone: 1 flat surface, 0 vertices, 0 edges
Coordinate Points
 Ordered pair – gives the location on the grid – Over to the right
and up – a bird needs to walk before it can fly
 Point A is at ordered pair (0,3) – over zero and up 3 and Point C
is at ordered pair (5,4) over 5 and up 4
 To describe the path between two points on the grid you can
move in any order. Sometimes you will use up, down, left or right
or you can use directional words (north, east, south, west).
 To get from Point A to Point B go 4 to the right and 2 down. To
get from Point D to Point F go north 4 and east 2.
Patterns
 Find the rule of the pattern before extending it – check that rule
applies with all parts of the pattern.
1, 5, 9, 13 Rule is + 4
 Extend the pattern until the part that was asked about
Combinations, Permutations and Probability
 For combinations (order doesn’t matter) create an organized list
 For permutations (order matters – think numbers, letters) use
multiplication. If there are 3 choices then it is 3 x 2 x 1 = 6
 When finding probability, your answer is in the form of a fraction.
The denominator is the total number of items and the numerator
is how many of the item they are asking about.
Values of the Unknown
 Symbols are used in the place of unknown numbers – they can
be anything but all mean the missing number
8 x ☼ = 48 ☼ = 6 16 + x = 36
x=20
 Use the opposite operation to help you solve
35 ÷ ♥ = 5 you know 5x7=35
so ♥ = 7
23 + ■ = 45 you know 45-23= 22 so ■ = 22
N - 456 = 634 you know 456 + 634 = 1,120 so N = 1,120