Review Outline: Math 6
Review Suggestions: - Review for 20-30 minutes each day, starting
TODAY.
- Try all the sample questions.
- Ignore the topics that you know you have already
mastered.
- Work with a friend or two to review the topics.
- Bring specific questions to class for discussion.
A. Develop Number Sense
A. Demonstrate an understanding of place value, including numbers
that are:
• greater than one million
• less than one thousandth.
Write each number in standard form.
1. 2 million 186 thousand 23
2. 50 000 000 + 5 000 000 + 70 000 + 2000 + 9
3. six billion two hundred seventeen million three thousand eleven
4. 1 856 374 021 356
Write each number in words.
5. 2 000 351 246
6.
7.
8.
9.
3.4715
0.003 025
1.250 4
0.005 3
Use a place-value chart to show each number.
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B. Solve problems involving whole numbers and decimal numbers.
1. Cecil planted 744 maple trees in 24 equal rows. How many trees were
planted in each row?
2. Shawn and his brothers went to the movie theatre. One ticket cost $7.75.
Estimate the cost of 3 tickets.
3. Shawn paid $10.75, including tax, for 3 containers of popcorn. Estimate
the cost of one container of popcorn, including tax.
4. Frank saved $4.35 each week for 8 weeks. He wants to buy a pair of
aluminum drumsticks that cost $35.65, including tax.
Does Frank have
enough money?
5. The decimal point in some of these products is in the wrong place.
Identify the mistakes, then write each product with the decimal point in
the correct place.
a) 3.984  3 = 119.52
b) 73.26  4 = 293.04
c) 3.001  5 = 150.05
d) 1.08  5 = 0.54
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C. Demonstrate an understanding of factors and multiples.
List the first 10 multiples of each number.
1. 4
2. 9
3. 25
Find the first 3 common multiples of each pair of numbers.
4. 2 and 3
5. 4 and 5
6. Circle the lowest common multiple for each question above.
Tell if each number is prime or composite.
7. 13
8. 48
9. 23
10. Lemons are packaged in bags of 6. Which of these numbers of lemons
can be packaged in full bags? How do you know?
46,
42,
60,
63
D. Relate improper fractions to mixed numbers and mixed numbers
to improper fractions.
1. Write each mixed number as an improper fraction.
a) 1 94 ______________________ b) 3 76 ______________________
c) 2 54 ______________________ d) 1 34 ______________________
3
2. Write each improper fraction as a mixed number.
a)
17
3
______________________ b)
29
9
c)
11
4
______________________ d)
7
2
______________________
______________________
Place the numbers in each set on the number line.
3.
4.
3
2
7
3
7
4
15
5
6
11
8
2
5. Write a fraction, a decimal, and a percent to name the shaded part of
each grid.
a)
b)
E. Demonstrate an understanding of ratio, concretely, pictorially and
symbolically.
1. Using the shapes above, write a ratio to show the number of:
4
a)
circles to squares
b)
_____________
c)
squares to triangles
_____________
triangles to circles
_______________
d)
circles to all shapes
_______________
2. Write 3 equivalent ratios for each ratio.
a) 3 : 5
__________________________________________________
b) 90 : 30
__________________________________________________
F. Demonstrate an understanding of percent.
1. Write each fraction as a percent and as a decimal.
a)
9
50
c)
3
4
= ________ = ________
= ________ = ________
b)
1
10
d)
2
5
= ________ = ________
= ________ = ________
2. Explain how you know the fraction or decimal is greater or less than 25%?
a) 0.17
______________________________________________________
b)
3
10
c)
1
5
_______________________________________________________
_______________________________________________________
d) 0.4
_______________________________________________________
3. Saul got 19 out of 25 on a test. Cindy got 79% on the same test.
Which student got the higher mark? Explain.
5
4. Write a percent that represents:
a) about
1
3
of something ____________
b) between 0.15 and 0.25 of something ____________
c) a little less than
9
10
of something ____________
G. Demonstrate an understanding of integers.
+1, –8, +9, –2, +8, –4, –1, +3, –7, +6, 0
1. Look at the above integers and list the ones that are:
a) less than 0
b) between –5 and +5
_______________________
________________________
2. Order these integers from least to greatest.
+15, +3, –18, –7, 0, –12, +7
___________________________________________________
H. Demonstrate an understanding of multiplication and division of
decimals.
1. Write each number in standard form.
a) 2 and 5 thousandths: ___________________________
b) 125 millionths: ___________________________
c) 17 hundred-thousandths: ___________________________
d) 1 and 34 ten-thousandths: ___________________________
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2. Estimate to replace each  with > or <. How did you decide which symbol
to use?
a) 4  2.12  10.68 _________________________________________
b) 3  0.97  29.1
_________________________________________
c) 6  5.215  30
_________________________________________
3. Estimate to place the decimal point in each product.
a) 3.4  8 = 272
b) 2.813  6 = 16878
c) 6.003  9 = 54027
4. Divide.
a)
14.6  4
b)
$2.57  9
c)
0.048  6
d)
0.0028  4
I. Explain and apply the order of operations, excluding exponents.
1. Evaluate each expression.
a) 48  (17 – 9)
____________
b) 26 + 2  3
c) 50  (6  3)
____________
____________
2. Use a calculator to evaluate each expression.
a)
(526 – 302)  28
____________
b) 385  48  12
____________
c) 726  142  (16  4)
____________
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J. Represent and describe patterns and relationships, using graphs
and tables.
1. Record this pattern in the table.
Fig.1 Fig.2
Fig. 3
Fig. 4
Fig. 5
2. Use grid paper. Draw a graph to represent the pattern.
3. Explain how the graph represents the pattern.
__________________________________________
__________________________________________________________
4. Write an expression to represent the pattern. ______________________
5. June is going to the amusement park with her friends. She will pay $8 for
admission, plus $2 for each ride she goes on.
a) Make a table to show how much June will pay if she goes on 1, 2, 3,
and 4 rides.
b) Write a pattern rule in words that relates the amount June pays
to the number of rides she goes on.
To find how much June pays for any number of rides, multiply
__________________________________________ and then add
_______________________________________________________
c) Write an expression to represent the pattern.
________________________
d) Suppose June goes on 8 rides. How much will she pay?
_______________________
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e) What strategy did you use to find out?
__________________________________________________________
f) Suppose June paid $30. How many rides did she go on?
_______________
g) How did you find out? _____________________________________
K. Express a given problem as an expression in which a letter
variable is used to represent an unknown number. Demonstrate
and explain the meaning of preservation of equality.
1. Write an expression with a variable to represent each pattern rule.
Let n represent the input.
a) Multiply the input by 10, then add 4. __________________________
b) Divide the input by 3, then add 4. ____________________________
c) Multiply the input by 7, then subtract 2. ________________________
2. Write an expression with 2 numbers and one operation to balance each
equation.
a) 5  7 = _______________
b)
18 – 9 = ______________
c) 32  8 = ______________
d) 11 + 11 = ______________
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Answer Key
A. Place Value (Page 1)
1. 2 186 023
2. 55 072 009
3. 6 217 003 011
4. One trillion, eight hundred fifty-six million, three hundred seventy-four million, twenty-one
thousand, three hundred fifty-six.
5. Two billion, three hundred fifty-one thousand, two hundred forty-six.
6.
One
Ten
Hundred
One
Ones
Tenths Hundredths
Thousandths Thousandths Thousandths Millionths
3
4
7
1
5
0
0
0
3
0
2
5
1
2
5
0
4
0
0
0
5
3
B. Solve whole and decimal number problems. (Page 2)
1. Total trees Cecil planted were 744 trees/row x 24 rows = 17 856.
2. All Tickets cost about $8.00 x 3 = $24.00 (rounding $7.75 up to $8.00).
3. One popcorn container cost about $3.50. (Using compatible numbers for 3, $10.75 rounds to
either $9 or $12, then dividing by 3 gives between $3 and $4.)
4. Frank does not have enough money. ($4.35 x 8 = $34.80, which is less than the price.)
5. a) 3.984  3 = 11.952
b) 73.26  4 = 293.04
c) 3.001  5 = 15.005
d) 1.08  5 = 5.4
C. Factors and Multiples (Page 3)
1. 4-8-12-16-20-24-28-32-36-40
2. 9-18-27-36-45-54-63-72-81-90
3. 25-50-75-100-125-150-175-200-225-250
4. 2: 2-4-6-8-10-12-18-20 } The first three Common Multiples are 6, 12, and 18.
3: 3-6-9-12-15-18
} The Lowest Common Multiple is 6.
4: 4-8-12-16-20-24-28-32-36-40-44-48-52-56-60} The first three Common Multiples are
20, 40, and 60.
5: 5-10-15-20-25-30-35-40-45-50-55-60
} The Lowest Common Multiple is 20.
7. 13 is Prime
8. 48 is Composite
9. 23 is Prime
10. Use divisibility rules: If the number can be divided by 2 and by 3, then is can be divided by
6 without a remainder. (E.g 63 is odd, so cannot be divided by 2, so cannot be divided by 6.)
D. Mixed Numbers and Improper Fractions (Page 3, 4)
1. a) 1 94 = 13
b) 3 76 = 27
c) 2 54 = 14
d) 1 34 = 7
9
7
5
4
(Multiply the whole number by the denominator [bottom number], and add the numerator [top
number] to your answer to find the new numerator. The denominator stays the same.)
2. a) 17 = 5 and 2
b) 29 = 3 and 2
c) 11 = 2 and 3
d) 7 = 3 and 1
3
3
9
9
4
4
2
2
(Divide the numerator [top number] by the denominator [bottom number] with pencil and paper.)
10
3.
3
2
4.
15
8
11
5
6
7
4
7
3
2
(extend line)
5.
a) 24 = 0.24 = 24%
100
b) 17 = 0.17 = 17%
100
E. Use Ratios (Page 5)
1.
a) 3:4 or 3 to 4 or 3/4
b) 2:3
2.
a) 3:5 = 6:10 = 9:15 = 12:20 = . . .
F. Use Percent (Page 5-6)
1. a) 18% = 0.18
b) 10% = 0.10
2. a) 0.17 < 25% because 0.17 = 17%
1
5
c) 4:2 (= 2:1)
d) 3:9 (=1:3)
b) 90:30 = 9:3 = 3:1 = 6:2 = . . .
c) 75% = 0.75
b)
3
10
> 25% because
d) 40% = 0.4
3
10
= 30/100 and 25% = 25/100
1
5
c) < 25% because = 2/10 = 20%
d) 0.4 > 25% because 25% = 0.25, and 0.40 > 0.25
3. (19 out of 25) x 4 = 76 out of 100, and 79% = 79 out of 100, so Cindy has the higher mark.
4. a) One third is about 33%.
b) 0.20 = 20% and is between 0.15 and 0.25
c) 9/10 = 90%, so 88% (or similar) is a little less than 9/10ths.
G. Integers (Page 6)
1. a) Less than 0 are:
b) Between (-5) and (+5) are:
(-8), (-7), (-4), (-2), (-1)
(-4), (-2), (-1), 0, (+1), (+3), (+6), (+8), (+9)
2. (-18), (-12), (-7), 0, (+3), (+7), (+15)
H. Decimal Multiplication and Division (Page 6-7)
1. a) 2.005 b) 0.000 125 c) 0.000 17 d) 1.003 4
2. a) 4  2.12 < 10.68 (4 x 2 = 8) b) 3  0.97 < 29.1 (3 x 1 = 3) c) 6  5.215 > 30 (6 x 5 = 30)
3. a) 3.4  8 = 27.2 b) 2.813  6 = 16.878 c) 6.003  9 = 54.027
4. a) 14.6  4 = 3.65 b) $2.57  9 = $0.29 c) 0.048  6 = 0.008 d) 0.002 8  4 = 0.000 7
I. Order of Operations (Page 7)
1. a) 48  (17 – 9) = 48  8 = 6
b) 26 + 2  3 = 26 + 6 = 32 c) 50  (6  3) = 50 x 2 = 100
2. a) (526 – 302)  28 = 224  28 = 8
b) 385  48  12 = 18 480  12 = 1540
c) 726  142  (16  4) = 726 x 142  4 = 103 092  4 = 25 773
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J. Patterns and Relations (Page 8)
Fig. #
1
2
3
4
5
Triangles
1
3
5
7
9
1.
2.
3. The graph shows that each time the figure number increases by 1, the number of triangles
increases by 2.
4. Let n be the Figure number. Then the number of triangles is 2 x n – 1.
5. a) Number of Rides:
1
2
3
4
What June Pays ($):
b)
c)
d)
f)
10
12
14
16
. . . multiply the number of rides by $2, and then add $8.
Let r be the number of rides. Then 2 x r + 8 is what June pays for any number of rides.
2 x $8 + $8 = $24.
e) I substituted 8 for n in my expression, then calculated.
11 rides g) By working backwards: 2 x n + 8 =30, so 2 x n = 30 – 8 or 2n = 22 and n = 11.
K. Using Variables and Recognizing Equality. (Page 8-9)
1. a) 10 x n + 4
b) n  3 + 4 c) 7 x n – 2
2. Similar to: a) 5  7 = 40 – 5 b) 18 – 9 = 27  3 c) 32  8 = 3 + 1
d) 11 + 11 = 11 x 2
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