Download 4th Grade Math Study Guide

NAME ______________________________
FOURTH GRADE MATH REVIEW
GEOMETRY
LINES/POINTS:
 Line: a line that continues forever
 Point: a point on a line
 Line Segment: a part of a line
 Ray: a line that ends on one side and continues forever on the other
YOU NAME A LINE WITH 2 LETTERS. IF IT IS A RAY, NAME IT WITH THE POINT END FIRST.*



Parallel Lines: 2 lines that will never intersect, even if you continue the line forever
Intersecting Lines: lines that intersect at any point and at any angle
Perpendicular Lines: intersecting lines that form 4 right angles when they cross
Closed Figure: a figure that is completely closed (sealed at all points)
Open Figure: a shape that is open at some spots and doesn’t close
ANGLES:
 Acute Angle: and angle that is between 0 and 90 degrees
 Right Angle: a 90 degree angle
 Obtuse Angle: an angle that is between 90 and 180 degrees
 Straight Angle: an angle that is 180 degrees; looks like a straight line
TWO DIMENSIONAL SHAPED (2-D) PLANE FIGURES- LENGTH AND WIDTH
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
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Polygon: a two dimensional closed shape formed from 3 or more line segments
Congruent: polygons that are exactly the same size and shape
Similar: polygons that are exactly the same shape, but are different sizes
*ALL POLYGONS THAT ARE CONGRUENT ARE ALSO SIMILAR*
THREE SIDED FIGURES: TRIANGLES
 Triangle: polygons that have 3 sides and 3 angles
 Equilateral Triangle: triangle that has all sides the same length
 Isosceles Triangle: triangle with 2 sides the same length
 Scalene Triangle: triangle with no sides equal
 Acute Triangle: triangle with all acute angles
 Right Triangle: a triangle that has one right angle
 Obtuse Triangle: a triangle with one obtuse angle
NAME ______________________________
TWO DIMENSIONAL SHAPED (2-D) PLANE FIGURES- CONTINUED
Scalene Triangle
Acute Triangle
Right Triangle
Equilateral Triangle
Acute Triangle
Isosceles Triangle
Acute Triangle
Obtuse Triangle
FOUR SIDED FIGURES: QUADRILATERALS
 Quadrilaterals: polygons that have 4 sides and 4 angles
 Parallelogram: quadrilaterals that have parallel line segments in both pairs of opposite sides
 Rectangles: parallelograms that have 4 right angles
 Squares: rectangles that have all sides that are equal in length
 Rhombus: parallelograms that have all sides equal in length but no right angles
 Trapezoid: quadrilaterals that have 1 pair of opposite sides parallel
FIVE SIDED FIGURES:
 Pentagons: polygons that have 5 sides and 5 angles
SIX SIDED FIGURES:
 Hexagons: polygons that have 6 sides and 6 angles
SEVEN SIDED FIGURES:
 Heptagons: polygons that have 7 sides and 7 angles
EIGHT SIDED FIGURES:
 Octagons: polygons that have 8 sides and 8 angles
NINE SIDED FIGURES:
 Nonagons: polygons that have 9 sides and 9 angles
TEN SIDED FIGURES:
 Decagons: polygons that have 10 sides and 10 angles
Regular Shape:
All sides the same length
Irregular Shape:
The sides are not all the same
length
NAME ______________________________
PERIMETER
 The distance around a 2-D figure (fence around a yard)
 Find by adding up the length of every side
 Answer is given in units (feet, inches, miles, etc.)
AREA
 The number of squares in a 2-D figure (amount of grass in the yard)
 Find by multiplying length times width
 Answer is given in units squared or units 2
TERMS TO KNOW
Addends: the numbers you add together in an addition problem
Sum: answer to an addition problem
Factors: the number you multiply together in a multiplication problem
Product: the answer to a multiplication problem
Dividend: the number you are dividing (large #)
Divisor: the number you are dividing by
Quotient: the answer to the division problem
Odd number: ends with 1,3,5,7, or 9
Even number: ends with 0,2,4,6, or 8
Factors: the numbers that can be multiplied together to reach the same number
For example: factors of 24: 2, 12, 1, 24, 3, 8, 4, 6
Prime Numbers: a number whose factors are itself and one
For example: 5: 5, 1
11: 11, 1
29: 29, 1
Composite Numbers: a number that has more than two factors
For example: 12: 2, 6, 1, 12, 3, 4
Multiples: the numbers found in the center of a multiplication chart…
For example: the multiples of 3 are: 0, 3, 6, 9, 12, 15, 18, 21, etc.
COMPARING SYMBOLS
Less than <
Greater than >
Equal to =
Always circle the smaller number and make sure you point
to it.
NAME ______________________________
MULTIPLICATION AND DIVISION
Area Array
Partial Product
DIVISION (TRADITIONAL)
1 20 5R1
4 4, 8 2 1
4
0 8
- 8
02
0
21
- 20
1
PROPERTIES OF ADDITION
Commutative Property: switch the numbers around, and they still add up to the same amount
Example: 2 + 3= 3 + 2
Associative Property: grouping in parenthesis can be different
Example: (3 + 1) + 2 = 3 + (1 + 2)
Identity Property: any number plus zero is itself
NAME ______________________________
PROPERTIES OF MULTIPLICATION
Commutative Property: switch the numbers around, and they still multiply to the same amount
Example: 5 x 3 = 3 x 5
Associative Property: grouping in parenthesis can be different
Example: (2 x 3) x 4= 2 x (3 x 4)
Identity Property: any number times one is itself
Example: 6 x 1 = 6
Zero Product Property: any number times zero is zero
Example: 4 x 0 = 0
PROPERTY OF MULTIPLICATION AND ADDITION
Distributive Property: you can multiply then add, or add then multiply = same answer; the only
property that contains addition and multiplication in the same problem.
23 X 5
(20 X 5) + (3 X 5)
100 + 15
115
34 X 23
(30 X 20) + (30 X 3) + (4 X 20) + (4 X 3)
600 + 90 + 80 +12
690 + 92
782
NAME ______________________________
Length:
STANDARD/CUSTOMARY MEASUREMENT
Inch: width of a bandage
Foot: length of a piece of paper
Yard: height of a table
Mile: you can walk it in 15-20 minutes
1 foot = 12 inches
1 yard = 3 feet
1 mile = 5, 280 feet
1 pound = 16 ounces
1 ton = 2,000 pounds
Capacity:
Teaspoon: small spoon
Tablespoon: serving spoon
Cup: amount of milk you drink at lunch
Pint: about a soda bottle
Quart: small container of milk
Gallon: large plastic container of milk
1 tablespoon = 3 teaspoons
1 cup = 16 tablespoons
1 fluid cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
Weight:
Degrees Fahrenheit
Freezing = 32 F
Ounce: weight of a slice of bread
Pound: regular size stapler
Ton: weight of a car
Length:
Inch (in.)
Feet (ft.)
Yard (yd.)
Mile (mi.)
Ounce (oz.)
Pound (lb.)
Ton (T.)
Teaspoon (tsp.)
Tablespoon (tbsp.)
Cup (c.)
Pint (pt.)
Quart (qt.)
Gallon (gal.)
Degree Fahrenheit ( F)
METRIC MEASUREMENT
Millimeter – the thickness of a penny
Centimeter: width of a paperclip
Decimeter: length of a already sharp pencil
Meter: length of a baseball bat
Kilometer: a little shorter than a mile
1 centimeter = 10 millimeters
1 decimeter = 10 centimeters
1 meter = 10 decimeters
1 kilometer = 1,000 meters
Capacity (Volume):
Mass (Weight):
1 kilogram = 1,000 grams
Milliliter: rain drop
Liter: carton of orange juice
Kiloliter – the capacity of a large kids plastic
pool
Capacity:
1 liter = 1,000 millimiters
Weight (Mass):
Milligram – Mass of a speck of dirt
Gram: weight of a dollar bill
Kilogram: Mass of a pineapple
Degrees Celsius
Freezing = 0 C
Millimeter (mm.)
Centimeter (cm.)
Decimeter (dm.)
Meter (m.)
Kilometer (km.)
Gram (g.)
Kilogram (kg.)
Milliliter (mL.)
Liter (L.)
Degrees Celsius ( C)
NAME ______________________________
FRACTIONS
3
5
Numerator
Denominator
Mixed Number: whole number and a fraction
5
310
Improper to Mixed: Divide the denominator into the numerator…quotient becomes whole number,
remainder is numerator, denominator stays the same (ex:
22 would be 5 2
4
4
).
Mixed to Improper: Multiply the whole number times the denominator, add the numerator. New
number becomes new numerator, denominator stays the same (ex.
3105 =
35
10
Simplify (Reduce to lowest terms): Taking a fraction to its lowest terms means that the numerator and
denominator cannot be divided evenly by any other number except 1.
3
6
=
1
2
Because 3 and 6 can both be divided by
3. 1 and 2 cannot be divided evenly by
any other number, therefore 3/6 = ½
and it is reduced to lowest terms
Equivalent Fractions: fractions that are equal to each other
1
3
=
2
6
1
2
1
6
1
6
1
2
1
6
1
6
1
6
1
6
Adding/Subtracting Fractions: Add or subtract only the numerators if you have like denominators. The
denominators stay the same.
Subtracting with regrouping
2
7
+
6
7
=
8
7
or
1
13cross out and make into 12 10
1 7
-
5
10
Multiplying Fractions: Multiply across; put the whole number over 1
6
24
3
4 x 7 = 7 or 3 7
1 (a one should go here…any number over 1 represents a whole number)
10
NAME ______________________________
FRACTIONS OF A CIRCLE
2
+
10
30
=
100
**You must make 2/10 equivalent to 30/100 by multiplying the
numerator and denominator by 10. You can then add or subtract
the fractions.
**On the fraction circle, you would shade in 50/100 or 5/10 because
they are equivalent. 50/100 would be half of the circle shaded.
PLACE VALUE
____
____
____
____
____
____
____
____
____
.
____
____
Hundredths
Tenths
Decimal (say
“and”)
Ones
Tens
Hundreds
Thousands
Ten Thousands
Hundred
Thousands
Millions
Ten Millions
Hundred Millions
Place Value of a digit: give what place value it sits in
Value of a digit: give how much it is worth, like 3 hundreds or 300
Expanded form: add together the value of each digit in the number
For example: 6, 432.34 would be 6,000 + 400 + 30 + 2 + .3 + .04
Word Form: write out the number in words; For example: 31,645.98 would be thirty one thousand,
six hundred forty five and ninety eight hundredths
ADDITION/SUBTRACTION
2,308.21
-1, 239.32
3, 091.9
+2, 821.23
**Adding and subtracting decimals: line up the decimals, fill in zeros where necessary**
NAME ______________________________
ESTIMATION
Remember: When you round, underline the named place. look to the right, and circle that space.
If the circled
number is 5 or even
more, add 1 to the
place you underlined
before.
If the circled
number is 1, 2, 3, or 4,
keep the underlined
number
the same as it was
before.
3,459,983 If rounding to the hundred thousands place, the answer would be 3,500,000
3,459,983 If rounding to the millions place, the answer would be 3,000,000
For example:
3,238 – 2,032 = Could be estimated as 3,000 – 2,000 if rounded to the nearest thousand
3,238 – 2,032 = Could be estimated as 3,200 – 2,000 if rounded to the nearest hundred
Measuring Angles
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Protractors usually have two sets of numbers going in opposite
directions.
Be careful which one you use!
When in doubt think "should this angle be bigger or smaller than
90°?
Complimentary: Two angles are
complementary if the sum of their
angles equals 90o. If one angle is
known, its complementary angle can
be found by subtracting the measure
of its angle from 90o.
Supplementary: Two angles are supplementary if the
sum of their angles equals 180o. If one angle is known,
its supplementary angle can be found by subtracting the
measure of its angle from 180o.