AUSD Grade 6
1
Benchmark 1 Study Guide
Determine the Greatest Common Factor:
1´
40 and 96
Prime Factor Method
40
96
4
10 8
12
You try: Find the Greatest Common Factor:
75 and 90
List Method
All factors of 40:
1, 2, 4, 5, 8, 10,
20, 40
22 2 5 222 4 3
2 2
40 = 2 • 2 • 2 • 5
96 = 2 • 2 • 2 • 2 • 2 • 3
All factors of 96:
1, 2, 3, 4, 6, 8, 12,
16, 24, 32, 48, 96
Common Factors:
1, 2, 4, 8
The Greatest Common
The Greatest
Factor is the product
Common Factor is
of the primes that are
the largest number
in both numbers.
that appears in
GCF(40,96) = 2 • 2 • 2 both lists.
GCF(40,96) = 8
ஃ The Greatest Common Factor of 40 and
96 is 8.
2
Determine the Least Common Multiple:
2´
24 and 36
24 = 2 • 2 • 2 • 3
LCM =
=
You try: Find the Least Common Multiple:
18 and 42
36 = 2 • 2 • 3 • 3
ஃ The Least Common Multiple of 24 and
36 is 72.
Page 1 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
3
Simplify:
a. 5.39 + 6.7
Traditional
Benchmark 1 Study Guide
3´
a. 8.25 + 4.8
Place Value Decomposition
1
You try: Simplify:
5.39 + 6.7
= 5.0 + 0.3 + 0.09 + 6.0 + 0.7
5.39
+ 6 .7
12.09
= 5.0 + 6.0 + 0.3 + 0.7 + 0.09
= 11.0 + 1.0 + 0.09
= 12.09
b. 19.4 − 8.8
b. 12.3 − 4.7
Open Number line
What is the difference between 12.3 and 4.7?
+ 0.3
+7
+ 0.3
4.7 5.0
=> total = 7.6
12.3
12.0
6.NS.1
4
Find the product of 2.4 • 0.15 four
different ways.
Convert to Fraction
2.4 • 0.15
24 15
=
•
10 100
2 • 2 • 2 • 3• 3• 5
=
2 • 5• 2 • 2 • 5• 5
9
=
25
= 0.36
Traditional
2.4
× 0.15
120
240
0.36
4´
You try: Find the product of 2.42 • 1.2 two
different ways.
Partial Products
2.4
× 0.15
0.020
0.10
0.04
0.2
(0.4 × 0.05)
( 2 × 0.05)
(0.4 × 0.1)
( 2 × 0.1)
0.36
Area Model Using A
Generic Rectangle
0.1
.05
2
0.4
0.2
0.04
0.1
0.02
= 0.2 + 0.1 + 0.02 + 0.04
= 0.36
6.NS.3
Page 2 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
5
Benchmark 1 Study Guide
Find the quotient three different ways.
624 ÷ 8
Traditional
Partial
Convert to a
Quotients
Fraction
78
8 624
8 624
− 400 50
224
− 56
64
− 160 20
64
− 64 8
0€
= 78
− 64
0
5´
You try: Find the quotient.
468 ÷ 6
6´
You try: Divide:
624 ÷ 8
624
=
8
2 • 2 • 2 • 2 • 3•13
=
2•2•2
= 78
6.NS.2
6
Divide:
a. 276 ÷ 12
Partial Quotients
12 276
- 120 10
156
− 120 10
36
− 36 3
0
= 23
b. 1680
÷
a. 589 ÷ 31
Traditional
23
12 276
− 24
36
− 36
0
b. 2496 ÷ 48
28
1680 ÷ 28
1680
=
28
2 • 2 • 2 • 2 •3•5• 7
=
2•2•7
= 60
6.NS.7D
Page 3 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
7
Divide:
Benchmark 1 Study Guide
33.6 ÷ 0.21
7´
You try: Divide:
3.5 ÷ 0.45
8´
You try: What is a unit rate? Write the
definition. Then, make up and write at least
two unit rates of your own. Include one about
money, and one about distance.
Estimate first: About how many groups of
0.21 are in 33.6? Round 0.21 to 0.20, and
33.6 down to 30.0. Thinking about money, I
ask how many groups of 20 cents are in 30
dollars. That would be 150. So my answer
must be around 150.
Traditional
0.21 33.6 multiply both divisor and dividend
by 100 to move the decimal two
21. 3360. place values to the right
160.
21 3360.
- 2100.
1260.
− 1260.
0
6.NS.3
8
What is a unit rate?
Answer: A unit rate is a rate that is simplified
so that it has a denominator of one unit.
Which of the following are unit rates?
Select Yes or No for each.
1. Bananas cost $0.20 per pound.
2. I made $50 for 2 hours of work.
3. The car traveled 65 mph.
4. For every 6 cats at the Animal Shelter,
there are 2 dogs.
Answers:
1. Yes, it is units per one pound
2. No, the rate is given in two hours
3. Yes, 65 mph means 65 miles in one hour
4. No, there are six cats and two dogs.
6.NS.6
Page 4 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
Bobby is helping collect money for the
basketball team. The team decided to sell
sweatshirts. When they sold 20 sweatshirts
they earned $300.
a) Fill in the ratio table for the missing
values.
Number of $Money
sweatshirts earned
20
$300
9´
You try: Alana is helping to raise money for
her leadership class. The class decided to sell
bobble heads of the P.E. teachers. When they
sold 12 bobble heads they earned $240.
a) Fill in the ratio table for the missing
values.
Number of
$
bobble
Money
heads
earned
12
$240
10
?
?
$75
3
?
3
1
?
1
$120
0
Missing Values: $150, 5, $45, $15
b) What is the unit price for the
sweatshirts?
Answer: Each sweatshirt was sold for $15.
c) Label your axis. Then, plot the five
points on the coordinate below.
b) What is the unit price for the bobble
heads?
c) Label your axis. Then, plot the five
points on the coordinate below.
300
280
260
240
220
Money Earned
9
Benchmark 1 Study Guide
200
180
160
140
120
100
80
60
40
20
2
4
6
8
10
12 14
16
18 20
Number of Sweatshirts
6.EE.3
Page 5 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
Benchmark 1 Study Guide
10 Solve the percent problems:
10´ You try: Solve the percent problems:
a. What is 20% of 300?
Reasoning with 10%
20% of 300 is the
same as 10% of 300 +
10% of 300
I know 10% of 300 is
30.
Therefore, 30 + 30
represents 20% and
that equals 60.
a. What is 30% of 400?
Direct Translation
x is 20% of 300
20
• 300
100
20
x =
• 300
100
20 • 3 • 100
x=
100
x = 60
x =
b. 28 is 35% of what number?
?
28
0
0%
35%
!"
!"
50%
b. 11 is 22% of what number?
100%
?
= !""
4⋅7
?
=
5 ⋅ 7 100
5 times 20 makes 100. So, I
know multiplying 4 and 20
keeps it equivalent.
Therefore, 28 is 35% of 80.
4
?
=
5 100
c. 15 is what percent of 90?
c. 68 is what percent of 272?
68
x
=
272 100
2 ⋅ 2 ⋅17
x
=
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅17 100
1
x
=
4 100
1 25
x
× =
4 25 100
25
x
=
100 100
ஃ 68 is 25% of 272.
6. RP.3c
6. RP.3c
Page 6 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
Benchmark 1 Study Guide
11 Read the ratio relationship and write 3 true
statements that can be made using the
relationship.
The ratio of buttons to sweaters at the
clothing factory is 18:3.
11´ You try: Read the ratio relationship and write
3 true statements that can be made using the
relationship.
The ratio of legs to trunks in the Elephant
area at the zoo is 4:1.
1. Each sweater needs 6 buttons.
2. 10 sweaters would need 60 buttons.
3. For every 18 buttons there are 3 sweaters.
6.EE.1
12 Read the problem, show your work neatly and
explain how you got the answer.
It took 8 hours to clean 5 busses. If busses
are cleaned at the same rate, how many
busses can be cleaned in 56 hours?
Number of busses
Time in hours
5
8
10
16
25
40
35
56
12´
You try: Read the problem, show your work
neatly and explain how you got the answer.
It took 4 hours to wash 14 cars. If cars
continue to be washed at the same rate,
how many cars could be washed in 48
hours?
Using the table I reasoned that cleaning 10
busses would take 16 hours. Then, I noticed
that every 8 hours the number of busses
cleaned increased by 5. Because 56 divided
by 8 is 7, then 7 times 5 gives me the answer
of 35. 35 busses can be cleaned in 56 hours.
6.RP.3b
13 Gecko Mart offers 2 bags of 30 crickets for
$6.48. Forest Friends also sells crickets.
They are selling 5 bags of 30 crickets for
$16.60. Which store has the better price?
Gecko Mart
$6.48
2 𝑏𝑎𝑔𝑠 𝑐𝑟𝑖𝑐𝑘𝑒𝑡𝑠
$3.24
=
1 𝑏𝑎𝑔 𝑐𝑟𝑖𝑐𝑘𝑒𝑡𝑠
13´ You try: The cost of 4 pedicures is $24.80
at Quick Clips. The cost of 5 pedicures is
$30.50 at Fancy Feet. Which store has the
better price for pedicures?
Forest Friends
$16.60
5 𝑏𝑎𝑔𝑠 𝑐𝑟𝑖𝑐𝑘𝑒𝑡𝑠
$3.32
=
1 𝑏𝑎𝑔 𝑐𝑟𝑖𝑐𝑘𝑒𝑡𝑠
Gecko Mart has the better price for
crickets. It is $0.08 cheaper per bag.
6.RP.3a
Page 7 of 11
End of Study Guide
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
Benchmark 1 Study Guide
You Try Solutions:
1´
3´
Determine the Greatest Common Factor:
a. 8.25 + 4.8
75 and 90
Partial Sums
Prime Factor Method
90
75
9
10 5
15
33 2 5
You try: Simplify:
8.25
+ 4 .8
0.05
5 3
1 .0
12 .0
90 = 2 • 3 • 3 • 5
75 = 3 • 5 • 5
13 .05
b. 19.4 − 8.8
The Greatest Common Factor is the
product of the primes that are in both
numbers.
8
− 8 .8
10 .6
GCF(75,90) = 3 • 5
GCF(75,90) = 15
The Greatest Common Factor of 75 and
90 is 15.
2´
You try: Determine the LCM of 18 and 42.
4´
You try: Find the product of: 2.42 • 1.2
two different ways.
Convert to Fraction
2.42 • 1.2
242 12
=
•
100 10
2 • 11 • 11 • 2 • 2 • 3
=
2• 2•5•5•2•5
363
=
125
= 2.904
Use Bubble Method:
18 = 2 • 3• 3
1
19 .4
42 = 2 • 3• 7
€
Partial Products
2.42
× 1.2
0.004 (0.2 × 0.02 )
0.08 (0.2 × 0.4 )
0.4
0.02
0.4
(0.2 × 2.0)
(1 × 0.02 )
(1 × 0.4)
2.00 (1 × 2)
2.904
ஃ The Least Common Multiple of 18 and
42 is 126.
Page 8 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
5´
Benchmark 1 Study Guide
You try: Find the quotient.
7´
468 ÷ 6
Tradition
78
6 468
− 42
48
− 48
0
Partial
Quotients
6 468
− 300 50
168
− 120 20
48
− 48 8
0.45 3.5 multiply both divisor and dividend
Convert to a
Fraction
by 100 to move the decimal two
45. 350. place values to the right
468 ÷ 6
468
=
6
2 • 2 • 3 • 3 • 13
=
2•3
= 78
7.77
45 350.00
- 315.
35.0
- 315.
0
35
= 78
6´
You try: Divide:
3.5 ÷ 0.45
ஃ The number repeats.
You try: Divide:
a. 589 ÷ 31
8´
31 589
- 310 10
279
You try: What is a unit rate? Write the
definition. Then, make up and write at least
two unit rates of your own. Include one about
money, and one about distance.
What is a unit rate?
Answer: A unit rate is a rate that is simplified
so that it has a denominator of 1 unit.
− 155 5
124
- 124 4
0
= 19
The macaroni and cheese cost $.0.25 per
ounce.
b. 2496 ÷ 48
52
48 2496
I ride my bike 14 miles per hour.
− 240
96
− 96
0
Page 9 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
You try: Alana is helping to raise money for
her leadership class. The class decided to sell
bobble heads of the P.E. teachers. When they
sold 12 bobble heads they earned $240.
a) Fill in the ratio table for the missing
values.
Number of
$
bobble
Money
heads
earned
12
$240
6
$120
3
60
1
20
0
0
10´
You try: Solve the percent problems:
a. What is 30% of 400?
30% of 400
= (10% + 10% + 10%) of 400
= 40 + 40 +40
= 120
ஃ 120 is 30% of 400
b. 11 is 22% of what number?
11 is 22% of x
22
• x
100
22 x
11 =
100
11 11x
=
1
50
1 x
=
1 50
x=50 ஃ 11 is 22% of 50.
11 =
b) What is the unit price for the bobble
heads?
Answer: Each bobble head was $20.
c) Label your axis. Then, plot the five
points on the coordinate below.
300
280
260
c. 15 is what percent of 90?
240
220
15
x
=
90 100
3⋅5
x
=
2 ⋅ 3 ⋅ 3 ⋅ 5 100
1
x
=
6 100
x
0.16 =
100
x
0.16(100) =
(100)
100
16.6 = x
ஃ15 is 16.6% of 90.
200
180
Money Earned
9´
Benchmark 1 Study Guide
160
140
120
100
80
60
40
20
2
4
6
8
10
12 14 16 18 20
Number of Bobble Heads
Page 10 of 11
MCC@WCCUSD (AUSD) 12/21/15
AUSD Grade 6
Benchmark 1 Study Guide
11´ You try: Read the ratio relationship and write
3 true statements that can be made using the
relationship.
The ratio of legs to trunks in the Elephant
area at the zoo is 4:1.
1. For every 4 legs there is one trunk.
2. If there are 3 elephant trunks, then there
are 12 legs.
3. Each elephant trunk has 4 legs.
12´
Your try: Read the problem, show your work
neatly and explain how you got the answer.
13´ You try: The cost of 4 pedicures is $24.80
at Quick Clips. The cost of 5 pedicures is
$30.50 at Fancy Feet. Which store has the
better price for pedicures?
Quick Clips
Fancy Feet
$24.80
4 𝑝𝑒𝑑𝑖𝑐𝑢𝑟𝑒𝑠
$6.20
=
1 𝑝𝑒𝑑𝑖𝑐𝑢𝑟𝑒
$30.50
5 𝑝𝑒𝑑𝑖𝑐𝑢𝑟𝑒𝑠
$6.10
=
1 𝑝𝑒𝑑𝑖𝑐𝑢𝑟𝑒
Fancy Feet has the better price for
pedicures. It is $0.10 cheaper per pedicure.
It took 4 hours to wash 14 cars. If cars
continue to be washed at the same rate,
how many cars could be washed in 48
hours?
Number of cars
Time in hours
7
2
14
4
28
8
140
40
Using the table I reasoned that washing cars
for 40 hours would be 10 times as many cars,
or 140 cars. I also noticed that 8 hours would
be twice as many cars, which is 28 cars. So,
adding 140 and 28 is the number of cars that
can be washed in 48 hours. 168 cars can be
washed in 48 hours.
Page 11 of 11
MCC@WCCUSD (AUSD) 12/21/15