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Math 6
Spring Break
Review Packet
Name ______________________
Due ____________________
Integers
Integers- all whole numbers and their opposites […-3, -2, -1, 0, 1, 2, 3…]
NOT a fraction, decimal, or percent
-4.5, ¾, 85%
1. Compare the integers below using <,>, =
-19 ____ 5
-6 ____ -7
20 ____ -11
Graphing Inequalities
< Less than
> Greater than
≤ Less than or equal to
≥ Greater than or equal to
Open dot means < or >
“less than” or “greater than”
Closed dot means ≤ or ≥ “less than or equal to” or “greater than or equal to”
Always read the answer starting with the variable to find out which direction the arrow points.
2. Graph each inequality.
1.
r > -1
2.
p≤3
Measures of Central Tendency
Mean- the average (add up all of the numbers and divide by the number of items)
* Mean works well for sets of data with no very high or low numbers
Example: Test scores from the last unit test
82 95 73 100 85 79 64 88 91 76
Median- the middle number in a set of data
833
10
=
83.3 %
* Median is a good choice when data sets have a couple of values much higher or lower than
most of the others
Example: The number of fish in a pond:
Put the numbers in order:
3, 6, 1, 0, 5, 3, 4
0, 1, 3, 3, 4, 5, 6
3 is the median
Example: The number of cookies each student ate at lunch
Put numbers in order
4 1 5 2 0 8 4 3 0 6
0 0 1 2 3 4 4 5 6 8
3.5 is the median
Mode- the number that occurs most often
* There can be more than one mode or no mode at all
* If there are exactly two modes, it is called bimodal
* Mode is a good descriptor to use when the set of data has some identical values
Example: The number of points Victoria scores in each basketball game
12 5 18 10 12 9 18 12 7 15
Put numbers in order:
5 7 9 10 12 12 12 15 18 18
12 is the mode
3.Find the mean, median, and mode of the following sets of data.
Example: The number of hours kids watch TV per week
11
5
22
14
8
13
Mean =
6
16
Median-
Mode-
Mean as a balance point- the point on a number line where the data distribution is balanced
4. Find the mean as a balance point for the following set of data.
“Number of Siblings”
Multistep Word Problems
Six Step method to solving a word problem
1) The Question
3) The Plan
5) The Action
2)
4)
6)
The Facts
The Picture
The Check
Practice- Show all of your work and circle the best answer.
5.Martha is covering picture frames with ribbon. Each frame takes ¾ of a yard of ribbon. How
many frames can she cover with 6 yards of ribbon?
A. 7 yds.
B. 4 ½ yds.
C. 3/24 yds.
D. 8 yds.
6. Mr. Rico’s class decided to invite their parents to their National Hugging Day
party. Amber, Jordan, and Brian made the invitations.
Item
Cost
Package of Paper
$3.92
Package of Stickers
$3.42
Box of Envelopes
$5.13
Stamps
$0.32 each
It took one package of paper and one package of stickers to make the invitations. They used one
box of envelopes and twenty five stamps. About how much did it cost in all to make the
invitations?
Fractions
Numerator- the top number in a fraction
3
numerator
Denominator- the bottom number in a fraction
8
denominator
Improper Fraction- the numerator is greater than the denominator
Mixed Number- the combination of a whole number and a fraction
Adding Fractions- find a common denominator, make equivalent fractions, add the numerators
2/4 + 3/8
4/8 + 3/8 = 7/8
Subtracting Fractions- find a common denominator, make equivalent fractions, subtract the
numerators
2/4 – 1/3
6/12 – 4/12 = 2/12 = 1/6
Multiplying Fractions- multiply straight across, simplify your answer
4/5  2/3 = 8/15
Dividing Fractions- change the problem into multiplication, flip the second fraction (reciprocal),
multiply straight across (KFC)
1/5 ÷ 2/7
1/5  7/2 = 7/10
Always change mixed numbers into improper fractions when multiplying or dividing
Practice:
7. Change 18/5 into a mixed number _____
8. Change 3⅘ into an improper fraction _____
9. 1/3 + 4/5 = _____
10. 7/8 – 4/16 = _____
11. 1⅜ ● 2⅙ = _____
12. 4½ ÷ 3/5 = _____
13. Divide
2
3
by
and write in simplest form.
4
3
Modeling Multiplication and Division of Fractions
Modeling is a way of representing what happens when we multiply or dividing fractions. Modeling
can help you solve problems and determine how to solve a problem.
Multiplication
The diagram show ¼ of the columns are blue and
2/5 of the rows are green. The blue-green squares show the region
𝟏
𝟐
× 𝟓 or 1/10 of the diagram.
𝟒
𝟑
𝟏
14. Use the diagram to model 𝟒 × 𝟒
Division
15. When we divide, we find how
many ____ are in ____.
16. There are how many 2/3 in 2?
𝟐÷
𝟐
𝟑
Converting Fractions, Decimals, and Percents
Fraction


Decimal
if the denominator is 10 or 100, read the fraction as a decimal
reduce to simplest form and divide the numerator by the denominator
3 = 0.3
10
Decimal


10 (simplify to 5/6 and do long division) = 0.833
12
Percent
Dr. Pepper
.DP
move the decimal point two places to the right (multiply by 100)
0.82 = 82%
0.7 = 70%
Percent
94% = 0.94
Decimal move the decimal point two places to the left (divide by 100)
16.2% = 0.162
17-19. Find the percent of each grid
_____%
_____%
_____%
Comparing Fractions, Decimals, and Percents
Fractions
 find a common denominator
 change both fractions into decimals or percents
Decimals
 align decimal points
 add zeros to even up place values
 compare numbers according to their place values
Percents
 compare the whole numbers
Mixed Forms

change all numbers to the same form (percents are the easiest to compare)
20. Compare the following numbers using a <, >, or = sign.
0.9 ____ ½
82% ____ 1.4
2/3 ____ 5/6
21. Put the following numbers in ascending order.
0.64, 1/5, 43%, ½ ________________________________
22. Put the following numbers in descending order.
2/3, 0.09, 16%, 3/8 ________________________________
23. Which statement is true?
¼ ____ 2/7
A.
𝟏
𝟓
= 𝟎. 𝟎𝟐
𝟐
𝟑
3
2
B. 𝟑 =3.4% C. 150%=
D. 0.06= 0.06%
Patterns & Sequences
Sequence- a set of numbers that follows a numerical pattern
Term- any number in a sequence
Arithmetic Sequence- a sequence found by adding a fixed number to the previous term
Common Difference- the fixed number being added in an arithmetic sequence
4
6
+2
8
+2
10
+2
12
2 is the common difference
+2
Geometric Sequence- s sequence found by multiplying a fixed number to the previous term
Common Ratio- the fixed number being multiplied in a geometric sequence
2
6
x3
18
x3
54
3 is the common ratio
x3
24. Identify the common difference in the sequence and find the next three terms:
2, 5, 8, 11, 14, _____, _____, _____
common difference is _____
Perfect Squares & Square Roots
Perfect Square- the product of two equal whole numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
Square Root- a number multiplied by itself to equal a perfect square (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
25 = 5 (so 25 is a perfect square)
39 = 6.24 (so 39 is not a perfect square)
25. Circle ALL of the perfect squares in the following group of numbers:
4 6
9
10
12
16
25
30
35
42
64
100
26. What is the square root of 15? Round to the nearest hundredth. _____
Expressions, Equations, and Inequalities
Expression: a math phrase containing numbers, variables, and/or operations
What might you see: numbers, variables, operations
8 + 3  2a
Equation: a math sentence that states two expressions are equal
You must see an equal sign (=).
5x = 10
Coefficient- the number
being multiplied with a
variable
Constant- a
number by itself
Inequality: a math sentence that states one expression is greater than or less than another
expression
You must see an inequality symbol (<,>,≤,≥,≠)
4x + 7 > 3
Variable- a letter or
symbol that represents
a number (x)
Term- a number, a
variable, or the product
of a number and a
variable.
27. Identify what is circled in each
example.
Equation Expression Coefficient Term Variable –
If a math sentence contains more than one operation, you must complete the operations in a
certain order called the order of operations. (GEMDAS)Order of Operations
 evaluate exponents

20
–
8  2 + 32
 multiply and divide from left to right
20 – 8  2 + 9
 add and subtract from left to right
20 - 16 + 9
4+9
13*
if parentheses are involved, complete all operations inside the parentheses first.
42 ÷ (8 – 6)  3
42 ÷ 2  3
16 ÷ 2  3
83
2
*if a fraction bar is involved, complete the numerator, complete the denominator, then divide.
27. Simplify the following expressions:
1 + (19 – 3) ÷ 23
28. Simplify: 20 x 5^0 x 4 – (300 – 10 x 1
92  3(25) + 5
Coordinate Plane
Coordinate plane – the graph (grid) formed by the x and y axis
Quadrants – the four regions on a coordinate plane
Origin – the intersection of the x and y axis (the center of the coordinate plane)
x-axis – the horizontal number line
y-axis – the vertical number line
Ordered pair – the location of a point on the coordinate plane (x,y)
x-coordinate – the location of a point on the x-axis (2, -3)
y-coordinate – the location of a point on the y-axis (2, -3)
28.
Measurement:
Measurement Facts
30. 1 inch is about ___ centimeters
31. 1 meter is a little longer than a yard, or about ___inches
32. 1 mile is slightly farther than ___ kilometers
33. 1 kilogram is a little more than ___ pounds
34. 1 quart is a little less than ___ liter
35. 1 liter is a little more than 1 ______
Temperature Facts
36. Water freezes at _ _0C and ___0F
37. Water boils at ___0C and ____0F
38. Which shows units of weight and mass listed from least to greatest?
F gram, ounce, pound, kilogram, ton
G ounce, gram, kilogram, pound, ton
H gram, ounce, kilogram, pound, ton
J ounce, gram, pound, kilogram, ton
PROBABILITY
39. Jordan has 10 cards, two coins, and a spinner. Which of the following does not
represent a set of independent events?
A. Selecting one card and then selecting a second card without replacement
B. Tossing one coin and then another coin
C. Spinning the spinner and flipping one coin
D. Selecting one card, replacing the card in the deck, and then selecting a second card
40. Which of the following events is not dependent?
A. Selecting a marble from a bag, putting it your pocket, then selecting another marble.
B. Picking a heart from a deck of cards, placing it aside, and then picking another heart.
C. Choosing two different colored markers from a box, one after the other without
replacement.
D. Tossing a coin twice and observing a "tails" up both times.
EQUATIONS
Solving Equations
To solve an equation:



45.
A 16x = 4
B 4x = 16
C x + 4 = 16
D x – 4 = 16
46. Which is not a true statement?
A 25÷5= 5÷25
B 7+0 =7
C 5•6= 6• 5
D 5(4+6)= 20+30
Ex.
𝐲
𝟓
Find what operation is taking
place between the variable
and the numbers.
Use the inverse or opposite
operation on both sides of
the equation.
solve for the variable.
=𝟒
𝟓 𝒚
y is divided by 5
𝟓
(𝟏) 𝟓 = 𝟒 (𝟏)
𝒚=𝟓
Multiply by inverse of 5
Solve
47. Which property is shown in the following:
(
2
2
+4)• 1 = +4
5
5
F Multiplicative Inverse Property
G Additive Identity Property
H Multiplicative Identity Property
J Additive Inverse Property
Quadrilaterals
48. _________________- has only one set of parallel sides
49. _________________- has two sets of parallel sides





Parallelogram
Square
Trapezoid
Rectangle
Rhombus
50. _________________- has two sets of parallel sides and four congruent sides
51. _________________- has two sets of parallel sides and four right angles
52. _________________- has two sets of parallel sides, four congruent sides, and four right
angles
53. The angles of all quadrilaterals add up to 360°. What is the measure of angle
A below?
A
C=87°
B=85°
D= 135°