Download math eog review - Mrs. Campbell`s 5th Grade Class

5th Grade
Math EOG Study Guide
Place Value
1, 234, 567. 891
Rounding
“Don’t forget the Poem” 5 and more add 1 more, 4 or less just ignore.
Ex. Round 482 to the nearest tens place.
1.
482
480
Circle the digit in the tens place and write down any numbers before it.
2. Look to the right of your circled number.
3. Since I see a number that is four or below, I will let it go, meaning I will keep my eight and change the rest
of the numbers to zeros. (if the number to the right had been five or higher, I would have given my 8 a
shove and turned it into a 9).
Fractions

⅝ *Remember that the numerator is the number on the top (5) and the denominator is “da” number on “da”
bottom (8).

When comparing fractions, use Shoot for the Stars or benchmarks (0, ½, 1, +1).
o

½<⅝ * remember that the crocodile’s mouth is always open to the biggest number
When ordering fractions, remember these rules:
o
If the denominators are the same, use the numerator to put them in order:

o
⅛<⅜<⅝<⅞
If the numerators are the same, look at the denominator. The denominator that is the biggest is
actually the smallest fraction.

o
⅛<¼<½
You can also use benchmarks to compare and order fractions.

11 1
5 12
12 10 8 7
1

0 ½ +1
When adding or subtracting fractions, remember to find a common denominator.
o
Ex. ½+¼

Write down your denominators and list their multiples:


2, 4, 6, 8, 10
4, 8, 12, 16, 20
Find the least common multiple (in this case it is 4) and change any fractions to fourths
using equivalent fractions.

½=


Then add your new fractions and reduce if needed.
When reducing fractions, list the FACTORS of the numerator and denominator. Find the greatest common
factor and divide the numerator and the denominator by that number.
o
10
10: 1, 2, 5, 10
10÷5= 2
15
15: 1, 3, 5, 15
15÷5= 3
Order of Operations
Please Excuse My Dear Aunt Sally
Parenthesis
Exponents
Multiplication OR Division (whichever comes first when working left to right)
Addition OR Subtraction (whichever comes first when working left to right)
Area and Perimeter

Perimeter: the distance around a figure; add up all the sides

Area: the number of square units needed to cover a flat surface; Length X Width (LxW)
Measurement
-
*Big to small: MULTIPLY
-
1 in = 2.5 cm
-
1 ft = 12 in
*Small to big: DIVIDE
-
1 yard = 3 ft
-
1 yard = 36 in
-
1 kg = 2.2 lbs (a kg is bigger than a pound)
-
1 lb (pound) = 16 oz (ounces)
-
1 ton = 2,000 lbs
-
1 mile = 1.6 km
-
1 meter is about the same as 1 yard ( a meter is a little bit bigger than a yard- think of a meter stick vs. a
yard stick OR Mr. Yardly vs. Mr. Meter)
1,000
Kilo
kg
km
kl
100
Hecto
hg
hm
hl
King
Milk
The Land of “G”
10
Deka
dKg
dKm
dKl
Henry
1
Gram(g)
Meter(m)
Liter(l)
Doesn’t
0.1
Deci
dg
dm
dl
Usually
0.01
Centi
cg
cm
cl
Drink
Geometry

Angles: right angle is exactly 90° (use the corner of a piece of paper)
acute angle is less than 90° (the paper will cover the other ray)
0.001
Milli
mg
mm
ml
Chocolate
obtuse angle is greater than 90° but less than 180° (the paper won’t cover the
other ray)
straight angle is exactly 180° (a straight line)


Lines:
o
Intersecting lines: two lines that cross at exactly one point
o
Parallel lines: lines that go in the same direction and stay exactly the same distance apart.
o
Perpendicular lines: two lines that intersect to form right angles
Polygons:
o
Regular shape: all sides and all angles are equal
o
Irregular shapes: sides are different lengths and angles are different sizes
o
Types of polygons:
-
Triangles= 3 sides, 3 angles, 180°
- Quadrilaterals= 4 sides, 4 angles, 360°
-
Pentagons= 5 sides, 5 angles, 540°
- Hexagons= 6 sides, 6 angles, 720°
-
Septagons= 6 sides, 6 angles, 900°
- Octagons= 8 sides, 8 angles, 1080°
-
Nonagons= 9 sides, 9 angles, 1260°
- Decagon= 10 sides, 10 angles, 1440°
o
Remember that you can figure out how many degrees are in a polygon by triangulating, since we
know that there are 180° in a triangle.
Ex.
o
Line symmetry: a figure has line symmetry when it can be folded about a line so that its two parts
are identical
o
Rotational symmetry: a figure has rotational symmetry when it can be turned about a central point
and still look the same in at least two positions

Triangles: 3 sides, all angles add up to be 180°

Quadrilaterals:
o
Square: 4 equal sides, 4 right angles, 2 pairs of parallel sides, equal and perpendicular diagonals
o
Rectangle: 2 pairs of equal sides, 2 pairs of parallel sides, 4 right angles, equal diagonals
o
Trapezoid: 1 pair of parallel sides, diagonals are sometimes congruent
o
Parallelogram: 2 pairs of parallel sides, 2 obtuse angles, 2 acute angles
o
Rhombus: 4 equal sides; 2 pairs of parallel sides, 2 acute angles, 2 obtuse angles, perpendicular
diagonals
Graphing

Median: the middle number in an ordered series of numbers (one for you, one for me…)
5, 6, 7, 10, 12

7 is the median
Mode: the number listed most often in a set of data
6, 7, 8, 8, 8, 9, 10

Range: the difference between the greatest and least numbers in a set of data.
2, 3, 4, 7

8 is the mode
7-2=5, therefore, 5 is the range
Mean: the average of a set of numbers; to find the average add all the numbers and divide by the number
of numbers added (add it all up and divide it all up)
5 + 5 + 7 + 9 + 9 = 30
30÷5=6

X-axis: the horizontal axis

Y-axis: the vertical axis
The mean is 6.
Algebra
>
-
Greater than
-
Greater than or equal to
- less than
≥
<
- equal to
- less than or equal to
≤
=
- not equal to
≠
Formulas:
1. Perimeter of a rectangle: Add all sides or p= (2l + 2w) 2 times the length plus 2 times the width
2. Area of a rectangle: A= (l x w) length times width
3. Perimeter of a polygon: add the length of all sides
4. Area of a parallelogram: A= (b x h) base times height
5. Area of a triangle: A= (½ b x h) one half base times height
Important Facts about Perimeter and Area:
 The unit of measurement for perimeter does not have an exponent.
o For example:
5 cm
P= 14 cm
2 cm
2 cm
5 cm

The unit of measurement for area does have an exponent. It should be square units
o For example:
5 cm
2 cm
2 cm
A= 10 cm 2



Perimeter is the distance around a figure. The fence that goes around your yard
Area is the amount of space a figure takes up. The grass that covers the area inside your yard
When finding the area or perimeter of an irregular figure, be sure to break the figure into
known parts like squares, and rectangles.
o For example: you can break this L shape into two rectangles and calculate the
perimeter and area based on the known facts.
Perimeter: add all sides
P= 44 m
Area: find the area of each rectangle, then add them together. A= 54m
2
9m
To find this missing side you
should take the opposite side
of 9 m and subtract the part
that is cut out which is 2 m.
9m – 2m = 7m
4m
4m
7m
13 m
9m
To find this missing side
you should take the
opposite side of 13 m
and subtract the part that
is cut out which is 4 m.
13m – 4m = 9m
9m
2m
To find this
missing side
you must know
that opposite
sides of
rectangles are
equal
Side - one of the line segments that make up the polygon.
Vertex - point where two sides meet. Two or more of these points are called vertices.
Diagonal - a line connecting two vertices that isn't a side.
Interior Angle - Angle formed by two adjacent sides inside the polygon.
Exterior Angle - Angle formed by two adjacent sides outside the polygon.
Fractions: Adding, Subtracting and Multiplying.

When adding or subtracting fractions you must find the Least Common Multiple (LCM) to get a
common denominator before you can add or subtract. Remember to change improper
fractions to mixed numbers and reduce your final answer. Also “Watch the sign”, many
students get these questions incorrect because they add when they should subtract or
subtract when they should add.
o For example:
Find the LCM (least common
multiple) of the denominators 2
and 5.
2) 2, 4, 6, 8, 10, 12
1
2
+
2
=
5
?
Get a Common
Denominator
Make
Equivalent
fractions
Add the top
keep the
denominator the
same, and reduce
if possible
Fractions: Multiplying Fractions, and changing improper fractions to mixed numbers, and mixed
numbers to improper fractions.
You do not need a common
denominator to multiply fractions,
so you simply multiply:
Numerator
1X2= 2
Denominator 2 X 5= 10
Use GCF (Greatest Common Factor) to
reduce the fraction:
2 is a prime number. Its factors are 1,
and 2. 10 is a composite number its
factors are 1, 10, 2, and 5. The GCF is 2,
so divide by 2.
Numerator
2 divide by 2 = 1
Denominator 10 divided by 2 = 5
1
2
x
2
2
=
5
2
10
1
=
10
Multiply across
the top and
bottom
5
Reduce the
fraction
Note: If you are multiplying mixed numbers you must first change them into improper
fractions.
Changing an Improper Fraction to a Mixed Number:
1. Divide the numerator by the denominator.
11
2. The quotient becomes the whole number and
the remainder becomes the numerator.
The denominator stays the same.
5
2
5 11
- 10
1
1
2
5
Changing a Mixed Number to an Improper Fraction:
1. Multiply the whole number and the
denominator.
2. Add the product to the numerator.
The sum becomes the new numerator.
The denominator stays the same.
1
2
11
2 x 5 = 10 +1 = 11
5
5
Metric
Customary
Measurement:
length
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
1 mile (mi) = 1,760 yards (yd)
1 mile (mi) = 5,280 feet (ft)
Weight
1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2,000 lbs
1 ton (T) = 32,000 oz
capacity
1 pint (pt) = 2 cups (c)
1 quart (qt) = 2 pints (pt)
1 quart (qt) = 4 cups (c)
1 gallon (gal) = 4 quarts (qt)
1 gallon (gal) = 8 pints (pt)
1 gallon (gal) = 16 cups (c)
1
1
1
1
1 kilogram (kg) = 1,000 grams (g)
1 Liter (l) = 1,000 milliliters (mL)
Big G:
centimeter (cm) = 10 millimeters (mm)
decimeter (dm) 10 cm or 100 mm
meter (m) = 10 dm / 100 cm / 1,000 mm
kilometer (km) = 1,000 m
Remember: when you go from a
larger unit to a smaller unit you should
multiply “horse to fly multiply”
but when you go from a smaller unit to
a larger unit you should divide “fly to
horse divide of course”
Polygon Names and properties
Sample questions about polygons and their properties can be found on pages 206-211 of your math
text book.
Number
of Sides
3
Polygon
Name
Triangle
3 sides
3 angles
Sum of
interior
angles
180
4
Quadrilateral
4 sides
4 angles
360
5
Pentagon
5 sides
5 angles
540
6
Hexagon
6 sides
6 angles
720
7
Heptagon
7 sides
7 angles
900
8
Octagon
8 sides
8 angles
1080
These are regular polygons,
that means that all the sides
and angles are equal, the
shapes will not always look
this way. You will need to
learn the # of sides to identify
the name of a polygon.
Triangles: Triangles can be identified by the kind of angles and the lengths of its sides.
Right Triangle:
contains 1 angle
that is equal to
90 degrees
Obtuse Triangle:
contains 1 angle
is greater than
90 degrees
Isosceles Triangle:
two sides are the
same length
Acute Triangle:
all angles are
less than 90
degrees
Equilateral Triangle:
all sides are the
same length
Scalene Triangle: no
sides are the same
length
Special quadrilaterals (4 sided figures)
Trapezoid: 1 pair of parallel sides
Parallelogram: opposite sides are equal
and parallel
Rectangle: a parallelogram with 4 right angles,
Rhombus: a parallelogram with all sides
the same length
Square: a rectangle with all sides the same length
Right Angle:
measures exactly
90 degrees
Obtuse Angle:
measures more
than 90 degrees
Straight Angle:
measures exactly 180
degrees, can be made
when two right angles
are put together
Acute Angle:
measures less than
90 degrees
Math Vocabulary
Numbers and Operations













Place value of numbers one through hundred millions (1-100,000,000)
Standard (number), word, and expanded form ex: 324= 300 + 20 + 4
NEW Expanded form ex: 324= 3 x 100 + 2 x 10 + 4 x 1
Rounding numbers: Slip to the side and look for a FIVE! If it's 5 or more we go up one more,
4 or less we AVOID the mess (stay the same)! Numbers in front stay the same and numbers
behind turn to ZEROS!
Decimals: standard, word, and NEW expanded form ex: 2.45= 2 x 1 + 4 x .1 + 5 x .01
Rounding decimals
Comparing and ordering decimals
Adding and Subtracting decimals- Line up the DOT and give it all ya GOT!
Estimating Products (rounding and multiplying numbers)
Multiplying two by two and three by three digit numbers
Dividing by one divisor (Does McDonald's Serve Cheese Burgers?)- Divide, Multiply, Subtract,
Check, Bring down!
Estimating Division (finding compatible numbers and changing the rest to zeros!)
Dividing by two digit divisors
Measurement





Length: centimeter, inch, yard, meter, kilometer, mile
Customary: system used here in the United Stated
Metric: system used in most other countries
Mass/Weight: grams, ounces, pounds, kilograms
Capacity: The big "G" and A Liter is a little bit more than a Quart
Data Analysis









Stem and Leaf Plot: used to organize a set of data (after it has been collected)
Pictograph: graphs using pictures to display data
Bar Graph: Display data by category
Circle Graph: Graphs that show parts of a WHOLE
Line Graph: Shows change over time
Range (take the highest # in a set of data and lowest #, stack 'em, and subtract 'em)
Median (number in the middle of a set of data- you may have to average the two in the middle
to find this)
Mode (The number that occurs the most in a data set- there may be more than one- or none
at all)
Midpoint (The exact # in the middle of a data set- only available with an odd # of data
collected)
Geometry
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
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








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
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






Polygon: A closed figure made my joining line segments.
Regular Polygon: A polygon with all equal sides and angles.
Irregular Polygon: A polygon with one or more different sides or angles.
Right Angle: An angle measuring exactly 90 degrees.
Acute Angle: An angle measuring less than 90 degrees.
Obtuse Angle: An angle measuring more than 90 degrees but less than 180 degrees.
Straight Angle: An angle measuring exactly 180 degrees- also a straight line.
Triangle: A 3 sided polygon
Right Triangle: A triangle with one right angle and two acute angles.
Acute Triangle: A triangle with three acute angles. (MUST have 3)!
Obtuse Triangle: A triangle with one obtuse angle and two acute angles.
Scalene Triangle: A triangle with no equal sides.
Isosceles Triangle: A triangle with two equal sides.
Equilateral Triangles: A triangle with ALL equal sides.
Perimeter: distance around an object
Area: space inside an object (Length X Width)
Quadrilaterals: A four sided polygon
Line Symmetry: When a figure can be folded ona line and match exactly on both sides.
Rotational Symmetry: The figure can be rotated less than 360 degrees around a central point
and still match the original figure.
Pentagon: A five sided polygon
Hexagon: A six sided polygon
Octagon: An eight sided polygon
Decagon: A ten sided polygon
Dodecagon: A twelve sided polygon
Supplementary angles: two angles that add up to 180 degrees or form a straight line
Complementary angles: two angles that add up to 90 degrees or a right angle
Fractions










Fraction: Part of a whole
Numerator: The top number in a fraction
Denominator: The bottom number in a fraction
Common or like Fractions: These are two or more fractions that may look different but
represent the same amount. ex: 1/2 is 2/4 which is also 4/8
Common Denominators: Two or more fractions with the same number in the denominator
spot. When adding fractions with like denominators, just add the numerator and the
denominator STAYS THE SAME!
Factors: The two numbers you multiply together to get a larger number. Ex: the factors of 6
are: 1,2,3,6 (1 x 6) and (2 x 3)
Greatest Common Factor (GCF): The largest factor that both the numerator and the
denominator have in common.
Equivalent Factions: Fractions that share the same value but have different numerators and
denominators.
Simplest Form: When a fraction can not be reduced any further. This is the form that all
answers will be in on the EOG!
Improper Fractions: A fraction that has a larger numerator than denominator.





Mixed Number: A value that includes a whole number and a fraction.
Prime Number: A number that only has two factors- one and itself. (ex: 2, 3, 5, 7, 11)
Composite Number: A number that has more than two factors.
"big brother": The little brother (smaller denominator) always looks up and wants to be just
like the BIG brother (larger denominator)- so we do whatever we need to to the little brother
to make him the big brother! Then, whatever we did to the bottom, we must do to the top!
In 5th grade we will only be adding and subtracting unlike denominators through our "fraction
families" (halves, thirds, and fifths) so this concept will work every time!
Adding mixed numbers with unlike denominators: Students will learn to "Prepare the Patient"
(find common denominators), "Operate" (add or subtract mixed numbers- fractions first of
course), and then "Recovery" (simplify)!
***Please remember that Geometry is the strand most heavily tested on the 5th grade Math EOG.
The key to Geometry is mastering the vocabulary and being able to apply the terms to different
scenarios.