Problems of the Week 19mathlearnnc.sharpschool.com/UserFiles/Servers... · problem yourself first.) 8 2 3 + 4 1 4 a. 12 3 7 b. 12 11 24 c. 4 5 12 d. 12 3 12 or 12 1 4 What solid figure

Grade 7 • Page 55

Geometry/Measurement

19Problems of the Week

Visual

Multi-Step

Make a Good"Expression"

Problem-SolvingStrategies

What Do You Say?

The triangles below are similar. Find themissing measurements: a, b, and c.

a10 20

4026 b

c

6550

Tommy was paid $5 an hour for washingcars. He worked 3 hours on Friday, 9hours on Saturday and 5 hours onSunday. Materials costs him $32.75.How much money did he make afterexpenses?

Write and solve an equation:

The product of –6 and a number is 42.

Solve a Simpler ProblemSolve the same problem but with smallernumbers. Then look for a pattern.

Eight people have entered a chesstournament. Each person is scheduled toplay every other person once. How manygames are scheduled for the tournament?

Explain why 4 is less than 5, and why –4is greater than –5.

If the height and the base measuresare halved, write a ratio in fractionform to show the new area comparedto the original area.

4 cm

12 cm

Grade 7 • Page 56

MentalMath

19

Keeping Skills Sharp

1. 5 × 14 ÷ 5

2. 381 + 562

3.9

11 – 6

11

4. 24 × (-15) × 0

5. .25

6. 514 × 10

7. 16 mL = ____ L

8. 75 – (3 × 25)

9. 560 ÷ ? = 8

10.12

2

1. 25 ÷ (5 + 20) × 2 =

2. 13.1 + 43.5 =

3. 7.5 × 105 =

4. 12% of 50 is what number?

5. Give the prime factorization of 28.

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.

*See answer key. The Mental Math section should not be duplicated for the students.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 57

19Visual

Multi-Step

Make A Good "Expression"


Problem-Solving Strategies

What Do You Say?

Mental Math1. 14

2. 943

3.3

11

4. 0

5. .5

6. 5,140

7. 0.016

8. 0

9. 70

10.14

Keeping Skills Sharp1. 2

2. 56.6

3. 750,000

4. 6

5. 22 × 7

6. 30

7. 12 cm

8. 26

9. 83,752,200

10. 90

Grade 7

Answer: a = 25; b = 20; c = 52

Answer: $52.25

–6n = 42n = –7

Answer: 28

A number’s value decreases the farther to theleft it appears on a number line.

Answer: 14

This section provides anoral drill for sharpeningone's mental computation.Before each session givethese directions, "Numberyour paper from 1 to 10.Write your answer as thequestions are called out.Each question will berepeated one time only."

Answer Key

Grade 7 • Page 58



Visual

Multi-Step



What Do You Say?

Complete the table:

(3 x ) – 2 =

4

10

3

7

10

28 19

John’s test grades were: 76, 82, 95, 82,78, 96, 91. His teacher will allow Johnto choose the central tendency measureto be used for his test grades? Whichmeasure should John choose?

Translate into an equation and solve:

Twenty-five is one sixth of this number.

Draw a DiagramA board is cut in half. Then each piece is cut inhalf again. Then each of these pieces is cut inhalf. How many pieces are there?

Look at the problem below and the multiplechoice answers to the problem. Explain why astudent might choose each of the wronganswers. (Hint: It might be helpful to work theproblem yourself first.)

823 + 4

14

a. 12 37 b. 12

1124

c. 45

12 d. 123

12 or 1214

What solid figure could be formedby using these shapes? (Note:figures not to scale)

Grade 7 • Page 59

MentalMath

20


1. (27 + 4) – (8 × 3)

2. 24 + 32

3. 25 × 10 × 125

4.481

5. -100 × -1

6.35

– 310

7. 15 × 2 − 45

8. –4(2)

9. 5 cm = _____ m

10. Estimate: What percent of 51 is 32?

1. 261 – 194 =

2. 9.73 – 2.41 =

3.57

14

× =

4. 110% of 99 is what number?

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?

8. Simplify: 7 + 49 ÷ 7

9. Round 0.619 to the nearest hundredth.

10. 42 + 9 × 6 – 4 =


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 60

20Visual

Multi-Step




What Do You Say?

Mental Math1. 7

2. 25

3. 10

4.29

5. 100

6.3

10

7. –15

8. –8

9. 0.05

10. 60%


2. 7.32

3.528

4. 108.9

5. 3 × 13

6. 140

7. 312 cm

8. 14

9. 0.62

10. 66

Answer: 7

Answer: mean (85.7)

Answer: 25 = 16 n

150 = n

Answer: 8

a. The student added numerators and addeddenominators and did not find a commondenominator.

b. The student found a common denominator, butthen incorrectly added denominators.

c. The student subtracted instead of added.

d. The student found a common denominator, butdid not convert the numerator part to findequivalent fractions.

Answer: cylinder


Answer Key

Grade 7 • Page 61



Visual

Multi-Step



What Do You Say?

If ■ + ■ + ● = 50 and ● = 10,then ■ = _____.

Jason bought a car for $3,500. He soldhis truck for $1,500 which he used as adown payment. The remainingamount was borrowed at 4.5% interestfor 9 months. How much will hismonthly payments be?

Similar triangles are shown. Findthe measure of x.

15 cm 12 c

x

12 cm

16 cm

If ■ ■ ● = 2x + 1, then what would■ ■ ■ ■ ■ ● ● equal?

Guess and Check or Make a ListOn a farm there were 36 heads and 104 legson the cows and chickens. How many of theanimals were cows and how many werechickens?

Tell about a real life situation where youshould use percents to compare datainstead of using fractions or decimals.Why does using percents result in a moremeaningful comparison than usingfractions or decimals?

Grade 7 • Page 62

MentalMath

21


1. ? – 9.5 = 10

2. ? – 3.4 = 5.6

3. =

4. 6 × ? = 420

5. 32 = 5

6.35

– 315

7. 32 + (9 × 5) + 4

8. –35 ÷ 5 – (–3)

9. What is the difference between 32 and 17?

10. 3L = _____ mL

1. 23 × 15 =

2. 38.2 × 0.015 =

3.57

914

÷ =

4. What number is 25% more than 65?



7. Find the circumference of the circle:

8. Simplify: 72 + 83 – 82


10. Estimate: 2214 × 4

13

16 cm


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

1028

?14

?

Grade 7 • Page 63

21Visual

Multi-Step




What Do You Say?

Mental Math1. 19.5

2. 9

3. 5

4. 70

5. 2

6.6

15 or 2

5

7. 58

8. -4

9. 15

10. 3,000


2. 0.573

3. 119

4. 80

5. 23 × 7

6. 14

7. 100.48 cm

8. -7

9. 1.92

10. 95 to 100

Answer: 20

Answer: $229.72

Answer: 20 cm

Answer: 5x + 2

Most will use guess, check or make a list.36 animals = 36 heads, so:

Cows Chickens Legs1 35 744 32 8810 26etc.

A clever approach is to reason that since there are atleast 2 legs for each animal, then 72 legs areaccounted for already. The number of legs leftover(104 – 72) is 32. These must belong to the 4-leggedanimals. That is 32 ÷ 2 = 16 pairs of legs for the 16cows. The rest: 36 – 16 = 20 chickens.

Students might mention the use of percents tocompare data when the base amounts are differentvalues. For instance, to compare 7 out of 20 and 9out of 25, change 7 out of 20 to 35% and 9 out of 25to 36%. It is now easy to see that 36% > 35%.


Answer Key

Grade 7 • Page 64



Visual

Multi-Step



What Do You Say?

If ■ ● ● = x + 2, then what does ■ ■ ●

equal?

Martha entered the elevator and wentdown 7 floors, up 10 floors, up 2floors, then down 5 floors. She wasthen on the eleventhfloor. On what floordid she enter theelevator?

If ★ ★ ★ ▲ ▲ ▲ = 3x + 3, then whatwould ★ ★ ▲ equal?

Draw a DiagramA survey was taken of 150 college freshmen.Forty of them were majoring inmathematics, 30 of them were majoring inEnglish, 20 were majoring in science, 7 hada double major of mathematics and English,and none had a double major with science.How many students had majors other thanmathematics, English, or science?

Write about the things you learned in mathclass this week. What did you learn that wasnew? Were the new concepts easy tounderstand? Is there anything you did notunderstand that you worked on this week?Do you need extra help on anything?

Use cubes to build the model pictured.Then draw the end, side, and top view.

Front

Grade 7 • Page 65

MentalMath

22


1. 16 4×

2. 32.9 – 9.2

3. 17 =

4. 7 – 315

5. ? + 105 = 215

6. 30 =

7. 4(3 + 9)

8. ? – 14 = 3

9. = 12

10.38

– 14

1. 459 ÷ 3 =

2. $1,912 ÷ 48 =

3.14

+ 38 =

4. Change 1316 to a percent.


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: 525 × 4

45


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

?17

? 5

? 12

Grade 7 • Page 66

22Visual

Multi-Step



What Do You Say?

Mental Math1. 8

2. 23.7

3. 289

4. 345

5. 110

6. 360

7. 48

8. 17

9. 60

10.18


2. $39.83

3.58

4. 81.25%

5. 2 × 3 × 13

6. 189

7. 600 cm2

8. 165

9. 0.9

10. 25

Answer: 2x + 1

Answer: 11th floor

Answer: 2x + 1

Problem-Solving StrategiesThere are 67 students who did not major in math,English or science.

M 33 23 E

20 S

7

Student answers will vary.

front or end view side view

top view


Answer Key

Grade 7 • Page 67



Visual

Multi-Step



What Do You Say?Similar rectangles are shown.What is the length of x?

x

20 cm

12 cm

8 cm

Write an equation and solve:

Three times the absolute value of a numberis fifteen. What two integers will be in thesolution set?

Look for a PatternFind the ones digit in 399.

Write a poem or a rap to help you rememberthe correct order of operations when solvingequations.

If the surface area of this cubeis 384 cm2, what is thelength of each side?

The surface area of this5 centimeter cube is _____cm2.

Grade 7 • Page 68

MentalMath

23


1. 4(.3 + 6)

2. 3.86 ÷ 0.01

3. = 12

4. 20 × ? = 400

5. 40 = ? – 40

6. (–4)3

7. 84 ÷ 12

8.227

3511

×

9.3

10 of 90

10.23

14

÷

1. 397 + 248 =

2. 4.2 + 7.9 + 3 =

3. 111332 – 3

232 =

4. 34% of 149 =



7. Find the area of this figure:

8. 937 + 17 – 17 =


10. Estimate: What percent of 52 is 10?

8.5 cm

8.5 cm


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

? 6

Grade 7 • Page 69

23Visual

Multi-Step




What Do You Say?

Mental Math1. 25.2

2. 386

3. 72

4. 20

5. 80

6. -64

7. 7

8. 10

9. 27

10.83 or 2

23


2. 15.1

3. 81132

4. 50.66

5. 2 × 3 × 19

6. 1

7. 72.25 cm2

8. 937

9. 0.42

10. 20%

Answer: 30 cm

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 amultiple of 4, the ones digit is 1. Since 100 has afactor 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.

3nnn n

= 15 5

= +5 or = 5=

–

Answers will vary.

Answer: 8 centimeters

Answer: 150 cm2


Answer Key

Grade 7 • Page 70



Visual

Multi-Step



What Do You Say?

Write the following:

Four is less than eight.

Solve AlgebraicallyA jar contains 48 marbles of differentcolors. There are twice as many yellow asred, twice as many blue as white. Thereare 6 more white than red. How many ofeach color are there?

Explain the relationship between thediameter of a circle and its circumference.How can you estimate the circumference ofa circle if you know its diameter? How canyou estimate the diameter of a circle if youknow its circumference?

If the volume of thiscylinder is 565.2 cm3,what is the height?

6 cm

5 cm

7 cm

4 cm

What is the volume of this triangularprism?

How much greater isthe volume of thelarger cone than thevolume of the othercone? Use 3.14 for π.

10 ft

20 ft

3 ft

6 ft

Grade 7 • Page 71

MentalMath

24


1. 5 × (–5) × ( –5)

2. 4.302 × 10

3. 802 ÷ 100

4. 8.6 × 0.1

5. =

6. –4 + (–7)

7. ? + 6 = 27

8. 61 × 100

9.23

14

×

10. – 625

1. 283 – 198 =

2. 2.18 – 1.019 =

3.8199

1127

× =

4. Change 0.008 to a percent.


6. Find the LCM of 39 and 65.

7. Find the area of the shaded region:(Right angles at all vertices)

8. 68 × 17 ÷ 168 =

9. Round 546.73856 to the nearest thousandth.

10. 212 – 2

110 =

3 m 12 m

12 m


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

? 21

5 7

Grade 7 • Page 72

24Visual

Multi-Step



Problem-Solving StrategiesLet x = number of red

2x = the number of yellowx + 6 = the number of white2x + 12 = the number of blues

So x + 2x + x + 6 + 2x + 12 = 48Simplify and solve for x. x = 5

So there are 5 red, 10 yellow, 11 white, 22 bluefor total 48 marbles.

What Do You Say?

Mental Math1. 125

2. 43.02

3. 8.02

4. 0.86

5. 15

6. –11

7. 21

8. 6,100

9. 212

or 16

10. –25


2. 1.161

3.13

4. 0.8%

5. 2 × 33

6. 195

7. 115.74 m2

8. 17

9. 546.739

10.25

Answer: 4 < 8

The circumference is approximately 3 times (π)

greater than the diameter. Cd≈ 3 14.

Divide the circumference by 3 to get diameter.Multiply the diameter by 3 to get circumference.

Answer: 5 cm

Answer: 70 cm3

Answer: 2198 ft3 or 8 times larger


Answer Key

Grade 7 • Page 73



Visual

Multi-Step



What Do You Say?

How many triangles are inthis figure?

A flagpole 5 meters high casts ashadow 2.5 meters long. Anearby pole that is 7 meters highwould cast a shadow that is howmany meters long?

Write an inequality:

Thirteen is less than fifteen.

Collecting DataHave students gather information about thesolar system and planets to solve this problem:

If all the planets wereplaced in a line, howlong would the line be orwhat is the total of allthe diameters of theplanets in our solarsystem?

What is absolute value? Describe how tofind the absolute value of any number.

Build a rectangular prism using cubes.The volume of the prism is 32 cubicunits. The surface area is 88 squareunits. Two faces have a perimeter of 24units.

Draw your solution from the end, top,and side.

Grade 7 • Page 74

MentalMath

25


1. (725)1

2. = 50

3. 60 × 45

4. -6 × -7

5. -3 + 69

6. 32 + 4 + 4

7. Estimate: 518 + 2

13

8. (4.32)0

9. 3,090 ÷ 3

10. 14 × 0 × 7

1. Determine the missing number: 1, 3, 7, ____, 31

2. 13.9 × 3.2 =

3.67 28

9÷ =

4. 30% of what number is 23.7?



7. Find the area of this figure:

8. 78 + 10 ÷ 5 =

9. Round 325 to the nearest ten.

10. Solve for n: 67

= 36n

8.5 cm

4 cm


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

? 5

Grade 7 • Page 75

25Visual

Multi-Step




What Do You Say?

Mental Math1. 725

2. 250

3. 48

4. 7 to 7

5. 66

6. 15

7. 42

8. 1

9. 1,030

10. 0


2. 44.48

3. 223

4. 79

5. 22 × 53

6. 15

7. 34 cm2

8. 80

9. 330

10. 42

Answer: 13

Answer: 3.5 meters

Answer: 13 < 15

Absolute value is the number of units from zero on anumber line. Students may also mention thatabsolute value is always positive.

Information from World Book Encyclopedia, 1990Mercury 3,031 milesVenus 7,520 milesEarth 7,926 milesMars 4,200 milesJupiter 88,700 milesSaturn 74,600 miles

(not including rings)Uranus 31,570 milesNeptune 30,800 milesTotal 248,347 miles


1 2

Answer Key

Grade 7 • Page 76



Visual

Multi-Step



What Do You Say?

If n is the length of each figure, thenfind an expression with n that willtell the area of the figure.

, , , , …

Casey is placing grass seed intocubical containers. If each sidemeasures 2.5 feet, how many cubicfeet of seed can the container hold?

Write an inequality and solve:

Twice a number is greater than six.

Work BackwardsA street vendor had a basket of apples.Feeling generous one day, he gave away one-half of his apples plus one to the first strangerhe met, one-half of his remaining apples plusone to the next stranger he met, and one-halfof his remaining apples plus one to the thirdstranger he met. If the vendor had one left forhimself, how many apples did he start with?

Wally the Weatherman said:

“There is a 25% chance of rain on Mondayand a 75% chance of rain on Tuesday, sothere is a 100% chance of rain for the week.”

Explain why Wally is wrong.

A science test has 2 parts. Themultiple choice part has 5 problemswith 4 choices per problem. The true-false section has 10 problems. Howmany sets of answers are possible?

Grade 7 • Page 77

MentalMath

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)

1. 8,048 ÷ 16 =

2. )0 5 2 25. .

3. 435 +

14 =

4. What number is 20% less than 121?


6. Find the GCF and LCM of 10 and 20.

7. Find the circumference of the figure:

8. 21 – (14 + 2) =

9. Round 216.098256 to the nearest ten-thousandth.

10. Estimate: 67

+ 12

9 cm


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 78

26Visual

Multi-Step




What Do You Say?

Mental Math1. 400

2. 12

3. 0

4. 6

5. 596,000

6. 112

7. 4

8. 11

9. –9

10. –3


2. 4.5

3. 41720

4. 96.8

5. 22 × 52

6. 10, 20

7. 28.26 cm

8. 5

9. 216.0983

10. 112

Answer: n2

Answer: 15.625 ft3

Answer: 2n > 6n > 3

The vendor ended up with 1 apple. In the previousstep, he gave away half of his apples plus 1 more.Thus he must have had 4 apples. 4 + 1 = 5 and2 • 5 = 10, thus he must have had 10 apples when hemet the second stranger. Repeat process once more,10 + 1 = 11 and 2 • 11 = 22. He had 22 apples.

Wally is wrong because 100% probability implies asure thing. Saying that there is a 100% chance ofrain for the week would mean that it woulddefinitely rain and there is no gurantee that this willhappen.

Answer: 1,048,576


Answer Key

Grade 7 • Page 79



Visual

Multi-Step



What Do You Say?

Figure 1 Figure 2 Figure 3

How many circles willbe in Figure 5?

A flower bed 2 yards long,16 feet wide and 3 inchesdeep would hold howmany cubic feet of pottingsoil?

Write an inequality and solve:A number plus fifteen is less than 20.

Draw a DiagramEvery Saturday, Ted and his brother canoefrom Murfree Landing, where the water is 1

foot deep, to a buoy 1 mile away. Every 16

of a mile, the water is 112 feet deeper. What

is the depth of the water at the buoy?

Read the following statement:

“When a negative number is subtractedfrom a negative number, the answer ispositive.”

Decide whether this statement is true orfalse. Explain your decision. You may useexamples to support your answer.

Eight friends always exchange birthdaygifts during the year. They have done itfor the past 3 years. How many giftshave been given?

Grade 7 • Page 80

MentalMath

27


1. Estimate: 9

10 3

8–

2.6

15 + 4

15

3.2015

= ?3

4. 20% of 40

5.7

11 3

22–

6. 15 – (–3)

7. 92 – 80

8.23

14

÷

9. 100% of 85

10. 4.86 × 10–1

1. 192 + 28 + 80 + 149 =

2. 8.41 + 6.92 =

3. Solve for n: 1135

= 350

n

4. 23% of what number is 28?


6. Find the GCF and LCM of 12 and 16.

7. Find the area of the triangle.

8. 8 + 2(15 – 7) ÷ 4 =

9. Round 4.8637 to the nearest tenth.

10. 23 + (–2) × (–2) + 24 =

4 dm

9.5 dm


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 81

27Visual

Multi-Step




What Do You Say?

Mental Math

1.12

2.1015

or 23

3. 4

4. 8

5.12

6. 18

7. 1

8.83

or 2 23

9. 85

10. 0.486


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

Answer: 17 circles

Answer: 24 ft3

n + 15 < 20n < 5

The statement is false. If the number being subtractedhas absolute value•smaller than the absolute value of the other number, theanswer is negative. ex. –3 – (–1) = –2•greater than the absolute value of the other number, theanswer is positive. ex. –3 – (–6) = 3•equal to the absolute value of the other number, theanswer is zero. ex. –3 – (–3) = 0

Answer: 7 × 8 = 56 gifts × 3 years = 168 gifts

Murfree Landing 1 mile Buoy

The depth of the water at the buoy is 10 feet.

06

16

26

36

46

56

66

1 ft2 ft

12

5 ft12

8 ft12

4 ft

7 ft

10 ft


Answer Key

Documents

Problems of the Week 19mathlearnnc.sharpschool.com/UserFiles/Servers... · problem yourself first.) 8 2 3 + 4 1 4 a. 12 3 7 b. 12 11 24 c. 4 5 12 d. 12 3 12 or 12 1 4 What solid figure