Problems of the Week
19
Visual
The triangles below are similar. Find the
missing measurements: a, b, and c.
65
50
c
26
10
40
b
20
Make a Good
"Expression"
a
Write and solve an equation:
Multi-Step
The product of –6 and a number is 42.
Tommy was paid $5 an hour for washing
cars. He worked 3 hours on Friday, 9
hours on Saturday and 5 hours on
Sunday. Materials costs him $32.75.
How much money did he make after
expenses?
Geometry/
Measurement
Problem-Solving
Strategies
Solve a Simpler Problem
Solve the same problem but with smaller
numbers. Then look for a pattern.
Eight people have entered a chess
tournament. Each person is scheduled to
play every other person once. How many
games are scheduled for the tournament?
4 cm
What Do You Say?
12 cm
If the height and the base measures
are halved, write a ratio in fraction
form to show the new area compared
to the original area.
Explain why 4 is less than 5, and why –4
is greater than –5.
Grade 7 • Page 55
*See answer key. The Mental Math section should not be duplicated for the students.
19
1.
5 × 14 ÷ 5
2.
381 + 562
3.
9
6
–
11
11
4.
24 × (-15) × 0
5.
Mental
Math
.25
6.
514 × 10
7.
16 mL = ____ L
8.
75 – (3 × 25)
9.
560 ÷ ? = 8
10.
 1
 2
2
Keeping Skills Sharp
1.
25 ÷ (5 + 20) × 2 =
2.
13.1 + 43.5 =
Write answers here:
1. ___________
2. ___________
5
3.
7.5 × 10 =
4.
12% of 50 is what number?
3. ___________
5.
Give the prime factorization of 28.
4. ___________
6.
Find the GCF of 30 and 90.
7.
What is the perimeter of a 4 cm × 2 cm rectangle?
8.
Simplify: 62 – 4 × 3 + 2
9.
Round 83,752,245 to the nearest hundred.
10.
Estimate: 62% of 151.
5. ___________
6. ___________
7. ___________
8. ___________
9. ___________
10. __________
Grade 7 • Page 56
Answer Key
Visual
Mental Math
Answer: a = 25; b = 20; c = 52
1.
14
2.
943
Multi-Step
3.
3
11
Answer: $52.25
4.
0
5.
.5
6.
5,140
7.
0.016
8.
0
9.
70
10.
1
4
Geometry/Measurement
1
Answer:
4
19
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
Make A Good "Expression"
1.
2
–6n = 42
n = –7
2.
56.6
3.
750,000
4.
6
5.
22 × 7
6.
30
7.
12 cm
8.
26
9.
83,752,200
10.
90
Problem-Solving Strategies
Answer: 28
What Do You Say?
A number’s value decreases the farther to the
left it appears on a number line.
Grade 7
Grade 7 • Page 57
Problems of the Week
20
Visual
Complete the table:
(3 x
)–2=
4
3
10
10
7
28
19
Make a Good
"Expression"
Multi-Step
Translate into an equation and solve:
John’s test grades were: 76, 82, 95, 82,
78, 96, 91. His teacher will allow John
to choose the central tendency measure
to be used for his test grades? Which
measure should John choose?
Geometry/
Measurement
What solid figure could be formed
by using these shapes? (Note:
figures not to scale)
Twenty-five is one sixth of this number.
Problem-Solving
Strategies
Draw a Diagram
A board is cut in half. Then each piece is cut in
half again. Then each of these pieces is cut in
half. How many pieces are there?
What Do You Say?
Look at the problem below and the multiple
choice answers to the problem. Explain why a
student might choose each of the wrong
answers. (Hint: It might be helpful to work the
problem yourself first.)
2
1
8 +4
3
4
3
11
a. 12
b. 12
24
7
5
3
1
c. 4
d. 12
or 12
12
12
4
Grade 7 • Page 58
*See answer key. The Mental Math section should not be duplicated for the students.
20
1.
(27 + 4) – (8 × 3)
2.
24 + 32
3.
25 × 10 ×
4.
Mental
Math
1
25
4
81
5.
-100 × -1
6.
3
3
–
5
10
7.
15 × 2 − 45
8.
–4(2)
9.
5 cm = _____ m
10.
Estimate: What percent of 51 is 32?
Keeping Skills Sharp
Write answers here:
1. ___________
1.
261 – 194 =
2.
9.73 – 2.41 =
2. ___________
3.
5
1
×
=
7
4
3. ___________
4.
110% of 99 is what number?
4. ___________
5.
What is the prime factorization of 39?
6.
Find the least common multiple of 28 and 70.
7.
What is the perimeter of a regular hexagon whose sides are 52 cm? 6. ___________
8.
Simplify: 7 + 49 ÷ 7
9.
Round 0.619 to the nearest hundredth.
10.
42 + 9 × 6 – 4 =
5. ___________
7. ___________
8. ___________
9. ___________
10. __________
Grade 7 • Page 59
Answer Key
Visual
Mental Math
Answer: 7
1.
7
2.
25
3.
10
4.
2
9
5.
100
6.
3
10
7.
–15
8.
–8
9.
0.05
10.
60%
Multi-Step
Answer: mean (85.7)
Geometry/Measurement
Answer: cylinder
Make A Good "Expression"
1
n
6
150 = n
20
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Answer: 25 =
Keeping Skills Sharp
1.
67
2.
7.32
3.
5
28
4.
108.9
What Do You Say?
5.
3 × 13
a.
6.
140
7.
312 cm
8.
14
9.
0.62
10.
66
Problem-Solving Strategies
Answer: 8
b.
The student added numerators and added
denominators and did not find a common
denominator.
The student found a common denominator, but
then incorrectly added denominators.
c.
The student subtracted instead of added.
d.
The student found a common denominator, but
did not convert the numerator part to find
equivalent fractions.
Grade 7 • Page 60
Problems of the Week
21
Visual
■ + ■ + ● = 50 and ● = 10,
then ■ = _____.
If
Make a Good
"Expression"
Multi-Step
Jason bought a car for $3,500. He sold
his truck for $1,500 which he used as a
down payment. The remaining
amount was borrowed at 4.5% interest
for 9 months. How much will his
monthly payments be?
Geometry/
Measurement
15 cm
If ■ ■ ● = 2x + 1, then what would
■ ■ ■ ■ ■ ● ● equal?
Problem-Solving
Strategies
Guess and Check or Make a List
On a farm there were 36 heads and 104 legs
on the cows and chickens. How many of the
animals were cows and how many were
chickens?
What Do You Say?
12 c
x
12 cm
16 cm
Similar triangles are shown. Find
the measure of x.
Tell about a real life situation where you
should use percents to compare data
instead of using fractions or decimals.
Why does using percents result in a more
meaningful comparison than using
fractions or decimals?
Grade 7 • Page 61
*See answer key. The Mental Math section should not be duplicated for the students.
21
1.
? – 9.5 = 10
2.
? – 3.4 = 5.6
10 = ?
3.
4.
14
28
6 × ? = 420
5.
32 = ?
6.
3
3
–
5
15
7.
32 + (9 × 5) + 4
8.
–35 ÷ 5 – (–3)
9.
What is the difference between 32 and 17?
10.
3L = _____ mL
Mental
Math
5
Keeping Skills Sharp
Write answers here:
1. ___________
1.
23 × 15 =
2.
38.2 × 0.015 =
3.
5
9
÷
=
7
14
4.
What number is 25% more than 65?
5.
What is the prime factorization of 56?
6.
Find the GCF of 98 and 112.
7.
Find the circumference of the circle:
2. ___________
3. ___________
4. ___________
5. ___________
6. ___________
16 cm
7. ___________
8. ___________
8.
Simplify: 72 + 83 – 82
9.
Round 1.915 to the nearest hundredth.
10.
Estimate: 22
9. ___________
10. __________
1
1
×4
4
3
Grade 7 • Page 62
Answer Key
Visual
Mental Math
Answer: 20
1.
19.5
2.
9
3.
5
Multi-Step
4.
70
Answer: $229.72
5.
2
6.
6
2
or
15
5
7.
58
8.
-4
9.
15
10.
3,000
Geometry/Measurement
Answer: 20 cm
Make A Good "Expression"
21
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Answer: 5x + 2
Keeping Skills Sharp
Problem-Solving Strategies
Most will use guess, check or make a list.
36 animals = 36 heads, so:
Cows
Chickens
Legs
1
35
74
4
32
88
10
26
etc.
A clever approach is to reason that since there are at
least 2 legs for each animal, then 72 legs are
accounted for already. The number of legs leftover
(104 – 72) is 32. These must belong to the 4-legged
animals. That is 32 ÷ 2 = 16 pairs of legs for the 16
cows. The rest: 36 – 16 = 20 chickens.
1.
120
2.
0.573
3.
1
4.
80
5.
23 × 7
6.
14
7.
100.48 cm
8.
-7
9.
1.92
10.
95 to 100
What Do You Say?
Students might mention the use of percents to
compare data when the base amounts are different
values. For instance, to compare 7 out of 20 and 9
out of 25, change 7 out of 20 to 35% and 9 out of 25
to 36%. It is now easy to see that 36% > 35%.
Grade 7 • Page 63
1
9
Problems of the Week
22
Visual
If ■ ● ● = x + 2, then what does ■ ■ ●
equal?
Make a Good
"Expression"
Multi-Step
If ★ ★ ★ ▲ ▲ ▲ = 3x + 3, then what
would ★ ★ ▲ equal?
Martha entered the elevator and went
down 7 floors, up 10 floors, up 2
floors, then down 5 floors. She was
then on the eleventh
floor. On what floor
did she enter the
elevator?
Problem-Solving
Strategies
Geometry/
Measurement
Use cubes to build the model pictured.
Then draw the end, side, and top view.
Draw a Diagram
A survey was taken of 150 college freshmen.
Forty of them were majoring in
mathematics, 30 of them were majoring in
English, 20 were majoring in science, 7 had
a double major of mathematics and English,
and none had a double major with science.
How many students had majors other than
mathematics, English, or science?
What Do You Say?
Front
Write about the things you learned in math
class this week. What did you learn that was
new? Were the new concepts easy to
understand? Is there anything you did not
understand that you worked on this week?
Do you need extra help on anything?
Grade 7 • Page 64
*See answer key. The Mental Math section should not be duplicated for the students.
22
1.
16 ×
2.
32.9 – 9.2
3.
17 = ?
17
1
7–3
5
4.
5.
6.
7.
8.
9.
10.
Mental
Math
4
? + 105 = 215
30 = ?
12
4(3 + 9)
? – 14 = 3
? = 12
5
3
1
–
8
4
Keeping Skills Sharp
Write answers here:
1. ___________
1.
459 ÷ 3 =
2.
$1,912 ÷ 48 =
3.
1
3
+
=
4
8
4.
13
Change
to a percent.
16
2. ___________
3. ___________
4. ___________
5. ___________
5.
What is the prime factorization of 78?
6.
Find the lowest common multiple of 21 and 27.
7.
Find the surface area of a cube with 10 cm sides.
8.
Simplify: 132 – 8 × 2 ÷ 4
9.
Round 0.862 to the nearest tenth.
10.
Estimate: 5
6. ___________
7. ___________
8. ___________
9. ___________
2
4
×4
5
5
10. __________
Grade 7 • Page 65
Answer Key
Visual
Mental Math
Answer: 2x + 1
1.
8
Multi-Step
2.
23.7
Answer: 11th floor
3.
289
Geometry/Measurement
4.
3
5.
110
6.
360
7.
48
8.
17
9.
60
10.
1
8
front or end view
side view
top view
4
5
22
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
1.
153
Make A Good "Expression"
2.
$39.83
Answer: 2x + 1
3.
Problem-Solving Strategies
5
8
4.
81.25%
There are 67 students who did not major in math,
English or science.
5.
2 × 3 × 13
6.
189
7.
600 cm2
8.
165
9.
0.9
10.
25
M
33
7
20
S
23
E
What Do You Say?
Student answers will vary.
Grade 7 • Page 66
Problems of the Week
23
Visual
The surface area of this
5 centimeter cube is _____cm2.
Make a Good
"Expression"
Write an equation and solve:
Three times the absolute value of a number
is fifteen. What two integers will be in the
solution set?
Multi-Step
If the surface area of this cube
is 384 cm2, what is the
length of each side?
Problem-Solving
Strategies
Look for a Pattern
Find the ones digit in 399.
Geometry/
Measurement
What Do You Say?
Similar rectangles are shown.
What is the length of x?
Write a poem or a rap to help you remember
the correct order of operations when solving
equations.
x
20 cm
8 cm
12 cm
Grade 7 • Page 67
*See answer key. The Mental Math section should not be duplicated for the students.
23
1.
4(.3 + 6)
2.
3.86 ÷ 0.01
3.
? = 12
4.
6
20 × ? = 400
5.
40 = ? – 40
6.
(–4)3
7.
84 ÷ 12
8.
22
35
×
7
11
9.
3
of 90
10
10.
2
1
÷
3
4
Keeping Skills Sharp
Mental
Math
Write answers here:
1. ___________
1.
397 + 248 =
2.
4.2 + 7.9 + 3 =
3.
11
4.
34% of 149 =
5.
Give the prime factorization of 114.
6.
Find the GCF of 45 and 77.
7.
Find the area of this figure:
2. ___________
13
2
–3
=
32
32
3. ___________
4. ___________
5. ___________
8.5 cm
6. ___________
8.5 cm
7. ___________
8. ___________
8.
937 + 17 – 17 =
9.
Round 0.421 to the nearest hundredth.
10.
Estimate: What percent of 52 is 10?
Grade 7 • Page 68
9. ___________
10. __________
Answer Key
Visual
Mental Math
Answer: 150 cm2
1.
25.2
2.
386
3.
72
4.
20
5.
80
6.
-64
7.
7
8.
10
9.
27
10.
8
2
or 2
3
3
Multi-Step
Answer: 8 centimeters
Geometry/Measurement
Answer: 30 cm
23
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
Make A Good "Expression"
1.
645
2.
15.1
n = +5 or n = – 5
3.
8
Problem-Solving Strategies
4.
50.66
31 = 3, 32 = 9, 33 = 27, 34 = 81, 35 = 243, 36 = 729,
37 = 2187, 38 = 6561. The pattern of ones digits is 3,
9, 7, 1, 3, 9, 7, 1. When the exponent of 3 is a
multiple of 4, the ones digit is 1. Since 100 has a
factor of 4, 3100 must have a ones digit of 1.
Therefore, the ones digit of 399 must be 7 , since 399
precedes 3100 and 7 precedes 1 in the sequence.
5.
2 × 3 × 19
6.
1
7.
72.25 cm2
8.
937
9.
0.42
10.
20%
3 n = 15
n= 5
What Do You Say?
Answers will vary.
Grade 7 • Page 69
11
32
Problems of the Week
24
Visual
20 ft
10 ft
6 ft
3 ft
How much greater is
the volume of the
larger cone than the
volume of the other
cone? Use 3.14 for π.
Make a Good
"Expression"
Multi-Step
Write the following:
If the volume of this
cylinder is 565.2 cm3,
what is the height?
Four is less than eight.
Problem-Solving
Strategies
6 cm
Solve Algebraically
A jar contains 48 marbles of different
colors. There are twice as many yellow as
red, twice as many blue as white. There
are 6 more white than red. How many of
each color are there?
Geometry/
Measurement
What is the volume of this triangular
prism?
4 cm
What Do You Say?
7 cm
5 cm
Explain the relationship between the
diameter of a circle and its circumference.
How can you estimate the circumference of
a circle if you know its diameter? How can
you estimate the diameter of a circle if you
know its circumference?
Grade 7 • Page 70
*See answer key. The Mental Math section should not be duplicated for the students.
24
1.
5 × (–5) × ( –5)
2.
4.302 × 10
3.
802 ÷ 100
4.
6.
8.6 × 0.1
? = 5
21
7
–4 + (–7)
7.
? + 6 = 27
8.
61 × 100
9.
2
1
×
3
4
10.
– 625
5.
Keeping Skills Sharp
Mental
Math
Write answers here:
1. ___________
1.
283 – 198 =
2.
2.18 – 1.019 =
3.
81
11
×
=
99
27
4.
Change 0.008 to a percent.
5.
What is the prime factorization of 54?
6.
Find the LCM of 39 and 65.
7.
Find the area of the shaded region:
2. ___________
3. ___________
4. ___________
5. ___________
6. ___________
(Right angles at all vertices)
3m
12 m
7. ___________
8. ___________
12 m
8.
68 × 17 ÷ 168 =
9.
Round 546.73856 to the nearest thousandth.
10.
2
1
1
–2
=
2
10
Grade 7 • Page 71
9. ___________
10. __________
Answer Key
Visual
Mental Math
Answer: 2198 ft3 or 8 times larger
1.
125
2.
43.02
3.
8.02
Multi-Step
4.
0.86
Answer: 5 cm
5.
15
6.
–11
7.
21
8.
6,100
9.
2
1
or
12
6
10.
–25
Geometry/Measurement
Answer: 70 cm3
24
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
Make A Good "Expression"
1.
85
2.
1.161
Problem-Solving Strategies
3.
1
3
Let x = number of red
2x = the number of yellow
x + 6 = the number of white
2x + 12 = the number of blues
4.
0.8%
5.
2 × 33
6.
195
So x + 2x + x + 6 + 2x + 12 = 48
Simplify and solve for x. x = 5
7.
115.74 m2
8.
17
So there are 5 red, 10 yellow, 11 white, 22 blue
for total 48 marbles.
9.
546.739
10.
2
5
Answer: 4 < 8
What Do You Say?
The circumference is approximately 3 times (π)
C
greater than the diameter. ≈ 3.14
d
Divide the circumference by 3 to get diameter.
Multiply the diameter by 3 to get circumference.
Grade 7 • Page 72
Problems of the Week
25
Visual
How many triangles are in
this figure?
Make a Good
"Expression"
Multi-Step
Write an inequality:
Build a rectangular prism using cubes.
The volume of the prism is 32 cubic
units. The surface area is 88 square
units. Two faces have a perimeter of 24
units.
Draw your solution from the end, top,
and side.
Geometry/
Measurement
A flagpole 5 meters high casts a
shadow 2.5 meters long. A
nearby pole that is 7 meters high
would cast a shadow that is how
many meters long?
Thirteen is less than fifteen.
Problem-Solving
Strategies
Collecting Data
Have students gather information about the
solar system and planets to solve this problem:
If all the planets were
placed in a line, how
long would the line be or
what is the total of all
the diameters of the
planets in our solar
system?
What Do You Say?
What is absolute value? Describe how to
find the absolute value of any number.
Grade 7 • Page 73
*See answer key. The Mental Math section should not be duplicated for the students.
25
1.
(725)1
2.
? = 50
3.
60 ×
4.
-6 × -7
5.
-3 + 69
6.
32 +
7.
Estimate: 5
8.
(4.32)0
9.
3,090 ÷ 3
10.
14 × 0 × 7
Mental
Math
5
4
5
4 +4
1
1
+2
8
3
Keeping Skills Sharp
1.
Determine the missing number: 1, 3, 7, ____, 31
2.
13.9 × 3.2 =
3.
6
9
÷
=
7
28
4.
30% of what number is 23.7?
5.
Give the prime factorization of 500.
6.
Find the GCF of 75 and 105.
7.
Find the area of this figure:
Write answers here:
1. ___________
2. ___________
3. ___________
4. ___________
5. ___________
8.5 cm
4 cm
6. ___________
7. ___________
8.
78 + 10 ÷ 5 =
9.
Round 325 to the nearest ten.
8. ___________
9. ___________
6
36
=
10. Solve for n:
n
7
10. __________
Grade 7 • Page 74
Answer Key
Visual
25
Mental Math
Answer: 13
Multi-Step
Geometry/Measurement
Answer: 3.5 meters
Make A Good "Expression"
1.
725
2.
250
3.
48
4.
7 to 7
5.
66
6.
15
7.
42
8.
1
9.
1,030
10.
0
1
2
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
Answer: 13 < 15
1.
15
Problem-Solving Strategies
2.
44.48
Information from World Book Encyclopedia, 1990
Mercury
3,031 miles
Venus
7,520 miles
Earth
7,926 miles
Mars
4,200 miles
Jupiter
88,700 miles
Saturn
74,600 miles
(not including rings)
Uranus
31,570 miles
Neptune
30,800 miles
Total
248,347 miles
3.
2
4.
79
5.
22 × 53
6.
15
7.
34 cm2
8.
80
9.
330
10.
42
What Do You Say?
Absolute value is the number of units from zero on a
number line. Students may also mention that
absolute value is always positive.
Grade 7 • Page 75
2
3
Problems of the Week
26
Visual
,
,
,
If n is the length of each figure, then
find an expression with n that will
tell the area of the figure.
,…
Make a Good
"Expression"
Write an inequality and solve:
Twice a number is greater than six.
Multi-Step
A science test has 2 parts. The
multiple choice part has 5 problems
with 4 choices per problem. The truefalse section has 10 problems. How
many sets of answers are possible?
Geometry/
Measurement
Casey is placing grass seed into
cubical containers. If each side
measures 2.5 feet, how many cubic
feet of seed can the container hold?
Problem-Solving
Strategies
Work Backwards
A street vendor had a basket of apples.
Feeling generous one day, he gave away onehalf of his apples plus one to the first stranger
he met, one-half of his remaining apples plus
one to the next stranger he met, and one-half
of his remaining apples plus one to the third
stranger he met. If the vendor had one left for
himself, how many apples did he start with?
What Do You Say?
Wally the Weatherman said:
“There is a 25% chance of rain on Monday
and a 75% chance of rain on Tuesday, so
there is a 100% chance of rain for the week.”
Explain why Wally is wrong.
Grade 7 • Page 76
*See answer key. The Mental Math section should not be duplicated for the students.
26
1.
1,600 – 1,200
2.
24 – (6 × 2)
3.
143 × 0
4.
17 – 5 – (18 ÷ 3)
5.
596 × 1,000
6.
12 + (10 × 10)
7.
10 × 10 × 10 × 10 = 10?
8.
121
9.
–17 + 8
10.
–9 – (–6)
Keeping Skills Sharp
Write answers here:
1.
8,048 ÷ 16 =
1. ___________
2.
0.5) 2.25
2. ___________
3.
4
4.
What number is 20% less than 121?
5.
What is the prime factorization of 100?
6.
Find the GCF and LCM of 10 and 20.
7.
Find the circumference of the figure:
3 1
+ =
5 4
3. ___________
4. ___________
5. ___________
6. ___________
7. ___________
9 cm
8. ___________
8.
21 – (14 + 2) =
9.
Round 216.098256 to the nearest ten-thousandth.
10.
6
1
+
Estimate:
7
2
9. ___________
10. __________
Grade 7 • Page 77
Mental
Math
Answer Key
Visual
Mental Math
Answer: n2
1.
400
2.
12
3.
0
Multi-Step
4.
6
Answer: 1,048,576
5.
596,000
6.
112
7.
4
8.
11
9.
–9
10.
–3
Geometry/Measurement
Answer: 15.625 ft
3
Make A Good "Expression"
Answer:
26
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
2n > 6
n>3
Problem-Solving Strategies
The vendor ended up with 1 apple. In the previous
step, he gave away half of his apples plus 1 more.
Thus he must have had 4 apples. 4 + 1 = 5 and
2 • 5 = 10, thus he must have had 10 apples when he
met the second stranger. Repeat process once more,
10 + 1 = 11 and 2 • 11 = 22. He had 22 apples.
What Do You Say?
Wally is wrong because 100% probability implies a
sure thing. Saying that there is a 100% chance of
rain for the week would mean that it would
definitely rain and there is no gurantee that this will
happen.
1.
503
2.
4.5
3.
4
4.
96.8
5.
22 × 52
6.
10, 20
7.
28.26 cm
8.
5
9.
216.0983
10.
1
17
20
1
2
Grade 7 • Page 78
Problems of the Week
27
Visual
Figure 1
Figure 2
Figure 3
How many circles will
be in Figure 5?
Make a Good
"Expression"
Multi-Step
Eight friends always exchange birthday
gifts during the year. They have done it
for the past 3 years. How many gifts
have been given?
Write an inequality and solve:
A number plus fifteen is less than 20.
Problem-Solving
Strategies
Geometry/
Measurement
Draw a Diagram
Every Saturday, Ted and his brother canoe
from Murfree Landing, where the water is 1
1
foot deep, to a buoy 1 mile away. Every
6
1
of a mile, the water is 1 feet deeper. What
2
is the depth of the water at the buoy?
What Do You Say?
Read the following statement:
A flower bed 2 yards long,
16 feet wide and 3 inches
deep would hold how
many cubic feet of potting
soil?
“When a negative number is subtracted
from a negative number, the answer is
positive.”
Decide whether this statement is true or
false. Explain your decision. You may use
examples to support your answer.
Grade 7 • Page 79
*See answer key. The Mental Math section should not be duplicated for the students.
27
9
3
–
10
8
1.
Estimate:
2.
6
4
+
15
15
3.
20
?
=
15
3
4.
20% of 40
5.
7
3
–
11
22
6.
15 – (–3)
7.
92 – 80
8.
2
1
÷
3
4
9.
100% of 85
10.
4.86 × 10–1
Keeping Skills Sharp
1.
192 + 28 + 80 + 149 =
2.
8.41 + 6.92 =
3.
11
n
=
Solve for n:
35
350
4.
23% of what number is 28?
5.
What is the prime factorization of 78?
6.
Find the GCF and LCM of 12 and 16.
7.
Find the area of the triangle.
Write answers here:
1. ___________
2. ___________
3. ___________
4. ___________
5. ___________
6. ___________
4 dm
7. ___________
9.5 dm
8.
8 + 2(15 – 7) ÷ 4 =
9.
Round 4.8637 to the nearest tenth.
10.
23 + (–2) × (–2) + 24 =
8. ___________
9. ___________
10. __________
Grade 7 • Page 80
Mental
Math
Answer Key
27
Mental Math
Visual
Answer: 17 circles
Multi-Step
Answer: 7 × 8 = 56 gifts × 3 years = 168 gifts
Geometry/Measurement
Answer: 24 ft3
Make A Good "Expression"
n + 15 < 20
n<5
1.
1
2
2.
10
2
or
15
3
3.
4
4.
8
5.
1
2
6.
18
7.
1
8.
8
2
or 2
3
3
9.
85
10.
0.486
This section provides an
oral drill for sharpening
one's mental computation.
Before each session give
these directions, "Number
your paper from 1 to 10.
Write your answer as the
questions are called out.
Each question will be
repeated one time only."
Keeping Skills Sharp
Problem-Solving Strategies
0
6
Murfree Landing
1 ft
1
6
2
6
3
6
4
6
5
6
6
6
1 mile
Buoy
1
2 ft
2
4 ft
The depth of the
water at the buoy is
10 feet.
5
1
ft
2
7 ft
1
8 ft
2
10 ft
What Do You Say?
1.
449
2.
15.33
3.
110
4.
121.7
5.
2 × 3 × 13
6.
GCF = 4, LCM = 48
7.
19 dm2
8.
12
9.
4.9
10.
36
The statement is false. If the number being subtracted
has absolute value
•smaller than the absolute value of the other number, the
answer is negative. ex. –3 – (–1) = –2
•greater than the absolute value of the other number, the
answer is positive. ex. –3 – (–6) = 3
•equal to the absolute value of the other number, the
answer is zero. ex. –3 – (–3) = 0
Grade 7 • Page 81