1. 6th Grade Math Study Guide for Final Exam
Exam: Week of May 20th
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2. Prepared for you by: Mrs. Hunger Riverdale Middle School
Overview of Skills to be tested: Numbers in parenthesis represent pretest numbers.
Adding and Subtracting Fractions (1)
Workbook pages 61 – 64
Chapter 4 Lessons 3 and 4
Decimals (27)
Chapter 1 Lesson 2 Workbook p. 3-4
(35) Ch. 1 Lesson 3 Work book p. 5-6
(41) Not in workbook
(44) Multiplying and Dividing Decimals
Workbook p 13 – 18 Ch. 1 Les 7
(48) Adding and Subtracting Decimals
Ch. 1 Lesson 5 Workbook pages
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Study Guide for Final Exams Geometry
(66) Classify Angles: Workbook: ch 8 Les 2 p
(69) Classifying Triangles: Workbook ch. 8 Les 4 p. 129 – 130
(75) Classifying Polygons: Workbook ch. 8
Les 5 p. 131 – 132
(79 ) Area and Perimeter: Wb. 145 – 148
Ch. 9 Les 3
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Study Guide for Final Exams: Integers
(91) Operations with integers
Wb. P. 161 – 175
(141) Perfect Squares Ch. 12 Les 5
Wb. P – 202
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Study Guide for Final Exam
(151) Solving One – Step Equations
Ch. 2 Les. 5 p. 29 – 30
(156) Exponents Ch. 2 Les 8 p 35 – 36
(157) Number Patterns Ch. 2 Les. 4
(160 – 172) Order of Operations
Not in workbook
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Study Guide for Final Exam
( 173 – 178) Evaluate Expressions Not in Workbook
means to solve them or compare them.
(179 – 187) Graphing Coordinate Pairs
Ch. 10 Lesson 6 p
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Practice Activities from Workbook:
Fractions: See Workbook p. 61 – 64 for extra practice.
To add or subtract fractions with unlike denominators, you can use equivalent fractions
Example 1 : Find 5/6 + ½
Find the least common denominator of 6 and Count by 2’s
Six is the first number 6 can go into. So the LCD is 6
Write equivalent fractions using the LCD /6 = 5/ ½ = 1 x 3 = 3, 2 X 3 = 6, so ½ = 3/6
Add. Write the sum in simplest form. 5/ /6 = 8/6 = 1 2/6 = /3
Example 2: Find 4/ /3
Find the least common denominator of 5 and 3 Count by 3’s
15 is the first number the 5 can go into. So the LCD is 15
Write equivalent fractions using the LCD 4/5 = 4 X 3 = 12, 5 X 3 = /5 = 12/15
1/3 = 1X 5 = 5, 3 X 5 = so 1/3 = 5/15
Subtract:. Write the difference in simplest form / /15 = 7/15
Practice: ½ + ¾ = _____ / /16 = _____ 7/ /3 = ______
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Practice Activities from Workbook: Decimals Chapter 1
Reading and Writing Decimals: See Workbook p for extra practice.
Standard form:
To find the value of a digit, multiply the digit by its place value.
9 stands for 9 X or .009
Expanded form: =
Comparing and Ordering Decimals: Use >, <, or = to compare
Write the numbers on grid paper with the decimal points lined up.
Compare digits in the greatest place. Move to the right until you find digits that are
not the same.
4 ones = 4 ones
0 tenths = 0 tenths
9 hundredths > 8 hundredths
So, >
To order from least to greatest:
Write the numbers on grid paper (decimal points lined up) and compare.
Then arrange the numbers from least to greatest. 4 . 9 2 8
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9. Prepared for you by: Mrs. Hunger Riverdale Middle School
Practice Activities: Decimals
Adding and Subtracting Decimals See Wb p for extra practice.
Add
First Estimate: 35
Then follow these steps.
Line up the decimal points Add as you would add Place the
Write in any needed zeros whole numbers Decimal
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Practice Activities: Multiplying and Dividing Decimals
See Workbook pages 13 – 18 for extra practice.
When multiplying or dividing decimals, simply perform the operation pretending the decimals are not there. Then count the total digits to the right of all of the decimals. That is the number of digits you need after the decimal in your answer. You may have to add a zero to hold the place open.
Example:
X X 02
68246
5 digits are after So place the decimal
the decimals in front of the six.
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Study Guide for Final Exam 6th Grade Math
Classifying Angles: Wb p. 125 – Ch. 8 Les 2
When two lines cross perpendicularly, they form right angles. Any angle that opens wider than a right angle is called obtuse. Any angle that opens smaller than that is called acute. An angle that is 180 degrees is a straight angle.
Complementary Angles: the sum of two angles measures 90 degrees
Supplementary Angles: the sum of two angles measures 180 degrees.
Congruent Angles: two angles that have the same measures.
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Study Guide for Final Exam:
Classifying Triangles: Chapter 8 Lesson 4
See Workbook p 129 – 130 for extra practice.
The sum of all angles in any triangle is 180 degrees.
Triangles can be classified by the measures of their angles.
Acute: has 3 acute angles
Right: has 1 right angle
Obtuse: has 1 obtuse angle
Triangles can be classified by the number of congruent sides.
Equilateral: all congruent sides
Isosceles: 2 congruent sides
Scalene: no congruent sides
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Study Guide for Final Exam: 6th Grade Math
Classifying Polygons: Ch. 8 Les 5
See Workbook p for extra practice
A polygon is a closed figure formed by three or more line segments that do not cross.
Polygons can be named according to the number of sides:
3: Triangle
4: Quadrilateral
5: Pentagon
6: Hexagon
7: Septagon
8: Octagon
9: Nonagon
10: Decagon
12: Dodecagon
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Study Guide for Final Exam: 6th Grade Math
Area and Perimeter: Ch. 9 Les 3 Wb. p
Perimeter:
The perimeter of a figure is the sum of the lengths of
Its sides. Opposite sides of a rectangle are equal. To
Find the perimeter, add the 2 lengths ( L) and the 2
widths (W).
4 inches
10 inches
= 28 inches
Area:
The area of a figure is the number of square units
Needed to cover the figure. To find the area of a
Rectangle, multiply the length (L) and the width (W)
The area of the rectangle above is
4inches X 10 inches = 40 inches squared
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Study Guide for Final Exam
Operations with Integers
See Workbook p. 161 – 175 for extra practice.
Using a number line:
The absolute value of a number is its distance from zero.
Written l -4 l = or l 4 l = 4
Opposite integers like -4 and 4 are the same distance from 0.
For two integers on a number line, the greater integer is farther to the right.
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Study Guide for the Final Exam
Adding Integers See Workbook p. 163 – 164 for extra practice.
You can add integers on a number line.
Example 1: Find
Start at zero and move 4 digits to the right, then 3 digits to the right.
= 7
Example 2: Find
Start at zero and move 3 digits to the left, then 2 digits to the left.
= - 5
Example 3: Find 5 + (-3)
Start at zero and move 5 digits to the right, and then 3 digits left.
5 + (-3) = 2
Example 4: Find
Start at zero and move 4 digits to the left, and then 1 digit to the right.
= -3
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Study Guide for Final Exam
Subtracting Integers: See Workbook pages 165 – 166 for extra practice.
To subtract an integer, add the opposite.
Example 1: Subtract 5 – 8
Add the opposite: (-8)
5 -8 = -3
Example 2: Subtract (-4)
Add the opposite:
= 6
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Study Guide for Final Exam
Multiplying Integers: See Workbook pages for extra practice.
When two integers have like signs, the product will always be positive.
Examples:
Both integers are positive: 3 X 4 = 12
Both integers are negative: -3 X ( -4) = 12
When two integers have unlike signs, the product will always be negative.
One integer positive, one negative 3 X (-4) = -12
One integer negative, one positive X 4 = -12
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Study Guide for Final Exam:
Dividing Integers: See workbook p. 169 – 179 for extra practice.
When two integers have like signs, the quotient will always be positive.
Examples:
Both integers are positive: 8 ÷ 2 = 4
Both integers are negative: -8 ÷ -2 = 4
When two integers have unlike signs, the quotient will always be negative.
One integer positive, one negative: 8 ÷ (-2) = -4
One integer negative, one positive: -8 ÷ 2 = -4
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Study Guide for Final Exam:
Graphing in the Coordinate Plane: See Workbook p for extra practice.
The X axis is the horizontal line on a coordinate plane. The first number in a coordinate pair tells its position on the X axis.
The Y axis is the vertical line on a coordinate plane. The second number in a coordinate pair tells its position on the Y axis.
The origin is the 0 point where the X and Y axis cross.
Positive numbers move to the right of 0 on the X axis, or up on the Y axis.
Negative numbers move to the left of 0 on the X axis, or down on the Y axis.
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Study Guide for the Final Exam:
Graphing Functions. See Workbook p. 175 – 176 for extra practice.
A table or a graph can show how the input and output of a function are related.
An input / output chart can give you the values for plotting points on a graph.
Think of the input as the first coordinate, ( X axis) and the output as the second coordinate, ( Y axis). This data can show a trend in your data.
Practice plotting coordinate points from Workbook p. 175.
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Study Guide for Final Exam:
Perfect Squares: See Workbook pages for extra practice.
A perfect square is the square of a whole number. The number 81 is a perfect square because it is the square of 9.
You could also say that 9 is the square root of 81, or = 9
The square root of a given number is a number that, when multiplied by itself, is the given number.
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Study Guide for Final Exam:
(151) Solving One – Step Equations See Workbook p. 29 – 30
for extra practice.
One way to solve some equations is to use mental math.
Example 1: Find the solution to the equation a = 10
What you think:
If I add 5 to 5, the sum is = So, a = 5
Example 2: Find the solution to the equation. Y = 15
If I subtract 9 from 24, the answer is 15, = So, y = 24
Example 3: Find the solution to the equation. W ÷ 5 = 100
W ÷ 5 means w divided by 5. I know that 500 ÷ 5 = So, w = 500
Example 4: Find the solution to the equation. 4w = 24
4w means 4 times w. I know that 4 X 6 = So, w = 6
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Study Guide for Final Exam:
Exponents See Workbook page for extra practice.
An exponent tells how many times a number is used as a factor.
3 X 3 X 3 X 3 shows the number 3 is used as a factor 4 times.
3 X 3 X 3 X 3 can be written 3 ⁴. In 3 ⁴, 3 is the base and
4 is the exponent.
To simplify a power, first write it as a product.
2⁵ = 2 X 2 X 2 X 2 X 2 = 32
When you simplify expressions with exponents,
do all operations inside parentheses first. Then simplify the powers.
Example: 30 – ( ) = =
= 5
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Study Guide for Final Exam:
(157)Number Patterns See Workbook page 27 for extra practice.
Stony Hollow School District has a softball playoff
Each spring for its 8 schools. Each school plays
1 game against every other school. The winner
Is the school with the greatest number of victories.
How many playoff games are played in all?
Problem Solving: Make a table and look
for a pattern.
Read and Understand:
Plan and Solve
Make a table. Look for a pattern.
Look back and Check.
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# of
schools
# of games 2 1 3 4 6 5 10 15 7 21 8 28 +2 +3 +4 +5 +6 +7
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Study Guide for Final Exam:
(160 – 172) Order of Operations Not in Workbook
Operations need to be performed in this order:
1. Addition Subtraction Multiplication Division
When you need to solve an equation that does not have parentheses, you must first complete the addition or subtraction, then do the multiplication or division.
Example 1: 2 X = ________ First add = 8 Then multiply 8 X 2 = 16
Example 2: ÷ 2 = _________ First add = 10, Then divide 10 ÷ 2 = 5
Now try a few on your own:
÷ 2 = _______ X 3 = ____________
X ( 3 + 1) X 4 = _______ ÷ 2 = ___________
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Study Guide for Final Exam:
Evaluate Expressions not in work book
(173 – 178) Evaluate Expressions simply means to solve them.
Graphing Coordinate Pairs See Workbook p. 171 – 172
Coordinate Pairs are always written in this order:
1st number is the number that is placed on the graph first. It is placed on the X axis. If it is positive, you start at zero and move to the right. If it is negative you start at zero and move to the left.
2nd number is the number that is placed on the graph second. It is placed on the Y axis. If it is positive, you start at the 1st number’s place and move up. If it is negative, you start at first number’s place and move down.
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Study Guide for Final Exam:
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30. Prepared for you by: Mrs. Hunger Riverdale Middle School
Study Guide for Final Exam:
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