1. Math State Assessment Review
Use this to help you review for the upcoming state assessment in math.

2. Adding & Subtracting Decimals
Remember to align (line up) the decimals.
Then fill in the zeros.
Then add or subtract.
Drop the decimal straight down.
3.431 _ 00 =
15 931 .

3. Multiplying Decimals 432.1 x 0.03 432.1 x 0.03 = 12 963 .
Do NOT line up the decimals.
Multiply as usual.
However many digits to the right of the decimal in problem. That’s how many should be behind the decimal in the answer.
432.1 x
432.1 x 0.03 =
12 963 .

4. Dividing Decimals
The first number should go on the inside.
Move the decimal on the outside number to make it a whole number.
Move the decimal on the inside number the same number of times.
Move the decimal straight up into the answer.
Divide.
9 2 .
7.36 ÷ 0.8 = . .

5. Adding & Subtracting Fractions
Convert each fraction to a common denominator.
Convert the numerators.
Add or subtract.

6. Multiplying Fractions
Cross-simplify if possible.
Multiply across. 1 2

7. Dividing Fractions 2 1 Flip the second fraction.
Cross-simplify if possible.
Multiply across. 2 1

8. Fractions Review
On the sheet of paper your teacher gave you, work out each problem.
1. 𝟑 𝟒 + 𝟒 𝟕 = 𝟏 𝟐 × 𝟐 𝟑 =
3. 𝟒 𝟓 − 𝟓 𝟖 = 𝟒 𝟓 ÷ 𝟐 𝟏𝟓 =

9. Multiplying by 10, 100, 1000
When multiplying by 10, move the decimal 1 place to the right.
When multiplying by 100, move the decimal 2 places to the right.
When multiplying by 1000, move the decimal 3 places to the right.
765432 .

10. Dividing by 10, 100, 1000
When dividing by 10, move the decimal 1 place to the left.
When dividing by 100, move the decimal 2 places to the left.
When dividing by 1000, move the decimal 3 places to the left.
765432 .

11. 6 4 3 . 0 0 6.43 x 104 = Scientific Notation
Move the decimal to the right as many places as the exponent.
Fill in the zeros.
6.43 x 104 =
6 4 3 .
0 0

12. Evaluating Expressions
Plug in the numbers for their variables.
Simplify using your calculator or the order of operations.

13. Converting Between Decimals & Fractions
Sometimes you will need to convert all your numbers to fractions or all to decimals.
To convert fractions to decimals, take the top number divided by the bottom number.
Ex. 3/5 = 3÷5 = 0.6
To convert decimals to fractions, put the number over the place value and simplify.
Ex = 45/100 = 9/20

14. Common Fractions & Decimals
Cover up the decimals and see if you can guess them. Then cover up the fractions and do the same.
Fraction
Decimal
1/2
0.5
1/4
0.25
3/4
0.75
1/10
0.1
3/10
0.3
7/10
0.7
9/10
0.9
Fraction
Decimal
1/5
0.2
2/5
0.4
3/5
0.6
4/5
0.8
1/3
0.3
2/3

15. Powers of 10 and S.N. Review 0.07 x 0.005?
1. What is the sum of 3.4 x 104 and 5,630?
2. What is 𝟓 𝟔 as a decimal and a percent?
3. How many zeros are between the decimal and the first non zero digit:
0.07 x 0.005?

16. Writing Equations
Addition
Subtract (and switch)
Multiplication
Greater than
Less than Of
More than
Fewer than
Per
Older than
Younger than
Each/Every
Times
Times more
Ex: Mary has 3 fewer cousins than 2 times how many Steve has. The equation would be m = 2s – 3.
If a number is listed as a fixed rate or a price only paid once, it must stand alone. If cannot be in parentheses or multiplied by another number.

17. Proportions Proportions are made up of two ratios (fractions).
A ratio is a comparison of two numbers. It can be shown in three ways: 13/14, 13:14, 13 to 14.

18. To solve a proportion…
1. Multiply the two numbers that are diagonal from each other (circled below).
2. Take that number and divide it by the third number.
Ex.: ● 56 ÷ 14 = 52

19. Proportions (cont.) Remember that in a proportion:
1. Whatever you do to the top, you do to the bottom.
2. Whatever you do to the bottom, you do to the top.
3. Whatever you do the left, you do to the right.
4. Whatever you do the right, you do to the left.
Example: Find the relationship between 6 and x.
Which is bigger, 6 or x?
5 times bigger
So x is 5 times as great as 6.
5 times bigger

20. Proportions (cont.) Draw an arrow from one letter to the other.
Draw another arrow in the same direction.
If a is 4 times greater than c, then:
A. b is also 4 times greater than d.
B. d is also 4 times greater than b.
C. c is also 4 times greater than a.
D. a is also 4 times greater than d.

21. Percents
Convert the percent to a decimal by moving the decimal point two places to the left.
Multiply it by the number given.
Ex. What is 3% of 240?
0.03 ● 240 = 7.2
Percent
23% 4%
370%
900% 6%
Decimal to Multiply
0.23
0.04
3.7 9
0.06

22. Scale Maps & Drawings x = 40 in y = 5 in
Use the key to set up the left side of the proportion.
Put the number from the map or drawing on the right side of the proportion while matching up the labels (ex. inches with inches, hours with hours, etc.).
Solve the proportion(s).
x = 40 in
y = 5 in

23. Patterns
The pattern is either adding, subtracting, multiplying, or dividing by the same number each time.
To find the next term, continue the pattern.
The exceptions are the squares (1, 4, 9, 16, 25…) and the cubes (1, 8, 27, 64, 125).
3, 5.5, 8, 10.5, 13, _________
15.5
40, 20, 10, 5, 2.5, _________
1.25

24. 4, 7, 10, 13… 10, 8, 6, 4… Finding the nth Term nth term 3n + 1 -2n
Look at how much the numbers are increasing/decreasing each time.
That number is paired with n.
Take that number and ask yourself, “How do I get from that number to the first term?” You will need to add or subtract that number.
+ 3
+ 3
+ 3
nth term
4, 7, 10, 13… 3n
+ 1 -2 -2 -2
10, 8, 6, 4…
-2n
+ 12

25. Proportions and nth term Review
1. Find the actual height of the house.
2. If Mrs. Landon eats 7 cookies to Mrs. Ayers 5 cookies, how many cookies did Mrs. Landon eat if Mrs. Ayers ate 40?

26. Proportions and nth term con’t
3. What is 125% of 75?
4. What is the nth term of this sequence?
12, 7, 2, –3, –8, –13, –18

27. Properties of Triangles & Quadrilaterals
How many degrees are in a triangle? _____
How many are in a quadrilateral? _____
What is the measure of each angle in a rectangle? _____
What is the measure of each angle in a square? _____
180°
360°
90°
90°

28. Properties of Quadrilaterals
Four sides
Parallelogram: Both pairs of opposite sides parallel
Trapezoid:
Exactly one pair of parallel lines
Rectangle:
Parallelogram with four right angles
Rhombus: Four equal sides
Square: Four right angles and four equal sides

29. Properties of Quadrilaterals (cont.)
Quad Shape
Figure
A. Only 1 pair of parallel lines
B. 2 pairs of parallel lines
C. All sides congruent
D. Opposite sides congruent
E. All angles are right angles
1. Trapezoid
2. Parallel-ogram
3. Rhombus
4. Rectangle
5. Square x
x x
x x x
x x x
x x x x

30. Area & Perimeter Area of a Parallelogram = base x height
Area of a Triangle = base x height ÷ 2
Base and height must meet at a 90° angle
Perimeter  add all the sides
13 cm
13 cm
A = 15●6 = 90 sq. in
11 in
10 cm
7 in
6 in
A = 10●11÷2
= 55 sq. cm
15 in

31. Area & Perimeter area perimeter Perimeter  add all the sides
When you are asked to find the space inside a shape and the labels are in units squared, you are being asked to find ________________.
When you are asked to find the distance around a shape and the labels are not in units squared, you are being asked to find ________________.
area
perimeter

32. Composite Figures
For area, break the shape into rectangles and triangle. Find the area of each and add them together.
For perimeter, find the lengths of the missing sides, and add all lengths together.
18 in
5 in
40 in2
7 in
7 in
4 in
4 in
4 in
4 in
48 in2
6 in
9 in
9 in
10 in
8 in
Perimeter = 68 in
Area = = 88 in2

33. Circles
The diameter is all the way across. The radius is half way across.
Circumference = π●d
Area = π●r2 or π●r●r
5 cm
radius
C = 3.14 ● 10 = 31.4 cm
12 cm
A = 3.14 ● 5 ● 5 = 78.5 cm2
diameter
C = 3.14 ● 12 = cm
A = 3.14 ● 6 ● 6 = cm2

34. Surface Area of Cubes
The formula for surface area of a cube is S.A. = 6s2 or 6●s●s. This means that you take the area of the front square and multiply it by 6.
11 cm
8 cm
S.A.= 6●8●8 = 384 cm2
S.A.= 6●11●11 = 726 cm2

35. Volume of Rectangular Prisms
The formula for volume of a rectangular prism is V=lwh (length times width times height).
10 in
4 cm
3 cm
9 cm
6 in
7 in
V = 9●3●4 = 108 cm3
V = 7●6●10 = 420 in3

36. Geometry Review 1. Find the surface area and volume of the cube.
2. Find the circumference and area of the circle.

37. Geometry Review con’t
3. Find the perimeter and area of the figure.

38. Frequency Tables Intervals must be even. They cannot overlap.
Numbers should match the data items.
Range
Freq.
70-74 3
75-79 4
80-84
85-89
Range
Freq.
70-75 3
75-80 4
80-85
85-90
Range
Freq.
70-74 3
75-79
80-89 6
90-99
Range
Freq.
70-74 3
75-79
80-84
85-89

39. Circle Graphs
Sections must be proportionate to the percent of the whole.
All percents must add to 100%.

40. Venn Diagrams Make sure the entire diagram matches all the data.
Understand the relationships that can be shown with Venn diagrams.
Rectangles
Parallelograms
All rectangles are parallelograms, but not all parallelograms are rectangles.

41. Graphs Make sure the data matches the graph.
Make sure that the numbers on the vertical and horizontal axis increase by the same amount.

42. Graphs
Make sure you understand the difference between horizontal axis (x-axis) and vertical axis (y-axis).
The horizontal (x) axis is flat like the horizon.
The vertical (y) axis runs up and down.
vertical (y-axis)
horizontal (x-axis)

43. Stem-and-Leaf Plots All numbers should be represented.
If a number is represented twice in list, it should be represented twice in the plot.
The stem for single-digit numbers is 0.
The leaves are the last digit of every number.

44. Scatter Plots increases up decreases down
Positive trend: as one increases, the other ________________. The points on the plot with a positive trend will go __________ as you go to the right.
Negative trend: as one increases, the other _________________. The points on the plot with a negative trend will go __________ as you go to the right.
Age (in years)
Value ($)
increases up
Age (in years)
Value ($)
decreases
down

45. Box-and-Whisker Plots
Make sure you put the numbers in order from least to greatest before you find the least, greatest, and median values.
Be able to identify the following characteristics of the plot: 48 52 56 60 64 68 72 76 80 84
Lowest Value
Lower Quartile
Median
Upper Quartile
Highest Value

46. Misleading Representations of Data
Look at the numbers on the both axes. They need to be evenly spaced (same interval).
You need to recognize that the graph may be misleading if you look at the height of the bars or dots rather than the values on the vertical axis.
The interval on the y-axis is not consistent.

47. Misleading Representations of Data (cont.)
Look at the numbers on the both axes. They need to be evenly spaced (same interval).
You need to recognize that the graph may be misleading if you look at the height of the bars or dots rather than the values on the vertical axis.
The interval on the y-axis is not consistent.

48. Misleading Representations of Data (cont.)
Sometimes the graph is misleading because the numbers don’t start at zero. See below.
It appears as though Brand Z lasts three times longer than Brand W,, but it doesn’t. Use the numbers to help you get the correct information.

49. Changes in Scale Interval of 5 Interval of 10
If the interval on an axis increases (from 5 to 10), the appearance of the graph gets smaller.
Interval of 5
Interval of 10 90 80 70 60 50 40 30

50. Changes in Scale Interval of 5 Interval of 2
If the interval on an axis decreases (from 5 to 2), the appearance of the graph gets larger.
Interval of 5
Interval of 2 42 40 38 36 34 32 30

51. Changes in Scale (cont.)
Vertical (y-axis) Scale/Interval
Horizontal (x-axis) Scale/Interval
Vert. Scale Decreases
Graph Stretches Toward the Top of the Graph
Vert. Scale Increases
Graph Shrinks Toward Bottom of Graph
Horiz. Scale Decreases
Graph Stretches Toward the Right of the Graph
Horiz. Scale Increases
Graph Shrinks Toward Left of Graph

52. Graphs Review
Answer the following questions on the assignment sheet. This is your last assignment. Turn in your paper tomorrow.
1. Explain how this bar graph is misleading.

53. Graphs Review con’t
2. What would happen if the the vertical axis was changed from intervals of 1 to intervals of 2?
3. Make a stem and leaf plot using this data.