a 7th grade mathematics 3:30-4:17

7th Grade Mathematics: My goal during this school closure is to help students maintain access to their education. I will include both worksheets and online-resources during this extended closure. Please know that I will be checking my email regularly in the event that you have any questions or concerns ([email protected]). Thank you. Students are certainly encouraged to use any notes they might have and a calculator while they work on these assignments. If students are confused, they are more than welcome to email me for help. I will respond as soon as I can. Schedule: Please use a calculator unless otherwise noted. (3/30/20-4/17/20) (15 school days)

*Days 1-3: Topics 1-6 Cumulative Benchmark Assignment. Students are expected to do their best to complete this 30-question assignment. They are welcome to use calculators. This assignment covers all of the lessons we’ve looked at thus far this year. There will certainly be things that you remember well and that are easy to do, but you will also encounter difficult problems that you may not remember. Again, do your best please. Problems: Topics 1-6 Cumulative Benchmark Assignment, questions 1-30.

*Days 4-5: Lesson 8-5 Finding the Circumference of a Circle. In this lesson you will be looking to find the circumference of a circle. First, we need to discuss the different parts of a circle. Circumference is the distance around the outside of the circle. The diameter is a straight line that goes from one side, through the middle of the circle, to the side directly opposite. Finally, the radius is the distance from one side to the middle of the circle. Use this diagram to help:

We have two formulas that we can use to find the circumference. One when you’re given the diameter (C=!") and another when you are given the radius (C=2!$). In the first formula (C=%&) the circumference C, is equal to pi (% =3.14) multiplied by our diameter (d). In the second formula (C=2%(), the circumference is equal to 2 multiplied by pi (% =3.14) multiplied by our radius (r). We also need to include our units. So I’ll give you two examples. Example 1, my diameter (d) is equal to 5 ft. I plug into our first formula because we’re given the diameter. So, C=%(5) or C=(3.14)(5), thus C=15.7, but we need to include units, so our answer would be 15.7 ft.

Example 2, my radius is 4 yards. So I now plug into our second formula because we are given the radius. So, C=2(%)(4) or C=(2)(3.14)(4), thus C=25.12, but we need to include our units and round, so our answer would be 25.1 yards. (Please round answers to the tenths place as

needed (only one number to the right of the decimal point). Problems: 8-5 Homework, questions 1-20

*Days 6-7: Lesson 8-6 Finding the Area of a Circle. In this lesson you will be looking to find the area of a circle. First, we need to discuss the different parts of a circle. Circumference is the distance around the outside of the circle. The diameter is a straight line that goes from one side, through the middle of the circle, to the side directly opposite. The radius is the distance from one side to the middle of the circle. Finally, the area of a circle is the two-dimensional space inside of the circle. Use this diagram to help:

We have one formula for area, but we will need more than one formula to solve for it at times. The main formula is A=!$2, where the area (A) is equal to pi (% =3.14) multiplied by the radius squared (the radius multiplied by itself). To solve you square the radius and then multiply by pi (% =3.14). With area our units need to be included, but they are units squared. So, if the example is using yards, we could say our answer and then “yards squared” or we could say our answer and yd2. The exponent of 2 shows that the units are squared. The only other formula you need is how to find the radius if you’re given the diameter. R=d/2, which means the radius (R) is equal to the diameter (d) divided by 2. ROUND ALL ANSWERS TO THE TENTHS PLACE.

Here are two examples, one when given radius and another when given diameter. Example 1, the radius is 4 cm. A=%(2, so A=(3.14)(42). A=(3.14)(16), A=50.24, so our final answer is A=50.2 cm2 or A=50.2 centimeters squared. Again, we need to round our answer to the tenths place and include our units. Since the number after the tenths place was less than 5, we rounded down and kept it as 50.2 cm2. Example 2, the diameter is 14 yards. We first need to find the radius. To do that we just need to divide the diameter by 2. So r=d/2, r=14/2, r=7 yards. Now we plug into the formula for area. A=%(2, so A=(3.14)(72). A=(3.14)(49), A=153.86, so our final answer is A=153.9 yd2 or A=153.9 yards squared. Again, we need to round our answer to the tenths place and include our units. Problems: 8-6 Homework, questions 1-20

*Days 8-9: Lesson 8-8 Find the Surface Area of Squares, Rectangles, and Triangles. In this lesson you will be working on finding the surface area of squares, rectangles, and triangles. As with our last lesson our units will need to be squared because we are finding area. We will need only two formulas for this lesson as squares and rectangles use the same formula. For rectangles and squares the formula is (L)(W)=A or in other words, the length (L) multiplied by the width (W) gives you the area (A). Please use the example that on the 8-8 Homework (Rectangles) for help. With triangles the formula is (b)(h)/2=A or in other words, you multiply the length of the base (b) by the height (h) and finally divide by 2. Again, we need to include units in our answers. Round answers to the nearest tenths place as needed. I’ll give you two examples, one with a square/rectangle and one with a triangle. Example 1 (square/rectangle).

In this example our length (L) is 11 inches and our width (W) is 7 inches. So, we plug into the formula for squares/rectangles. A=(L)(W), A=(11)(7). A=77, but we need to include our units, so we get an answer of A= 77 in2, or in other words the area is 77 inches squared. Example 2—triangles.

In this example our base length (b) is 10cm and our height (h) is 5cm. Now we plug into the formula for triangles. A=(b)(h)/2, so A=(10)(5)/2. A=(50/2), so A=25. However, our final answer is A= 25 cm2 or the area is 25 centimeters squared.

Problems: 8-8 Homework (2 sheets—total of 17 questions) Round answers to the

tenths place as needed.

Max Freeman

Max Freeman

Max Freeman

Max Freeman

*Days 10-11: Lesson 8-9 Volume of Rectangular and Triangular Prisms. In this lesson you will be working on how to find the volume of two different 3-D shapes. In this lesson we will need to include our units as part of our answer, but they will be cubed or have an exponent of 3. Volume is the space within a 3-D shape. We will need two formulas for this lesson. For rectangular prisms the formula is V=(L)(W)(H) or volume (V) is equal to the length (L) times the width (W) multiplied by the height (H). Basically, these problems will give you those three numbers and you will multiply them together and include your units as your answer. If there are no units included you should write your answer and u3, which stands for units cubed. For triangular prisms the formula is V=(b)(h)(L)/2 or volume (V) is equal to the length of the base (b) multiplied by the height (h) of the triangle, multiplied by the length (L) of the prisms and then finally divided by 2. Let’s look at an example for each type. Example 1: Rectangular Prisms .

In this example our length (L) is 3cm, our width (W) is 2cm, and our height (H) is 6cm. We multiply the three numbers together in the formula. V=(L)(W)(H), V=(3)(2)(6). V=36 cm3 or in others words volume (V) is equal to 36 centimeters cubed.

Example 2: Triangular Prisms In this example our base length (b) is 19 cm, our triangle height (h) is 24 cm and our prism length (L) is 47 cm. We plug into our formula, V=(b)(h)(L)/2. V=(19)(24)(47)/2, V=21,432/2. V=10,716 cm3 or in other words, the volume is equal to 10,716 centimeters cubed. The formula is set up this way because triangular prisms have half the volume that rectangular prisms do. Please round all answers to the tenths place as necessary. Problems: 8-9 Homework (2 sheets—total of 18 questions) Round answers to the

tenths place as needed.

*Days 12-15: Basic Operations Review and Multiplication Facts. For days 12-15 I expect that students will be doing their best to complete a basic operations review each day as well as spending 20-30 minutes working on their multiplication facts. Students can use the following link for multiplication facts: https://www.helpingwithmath.com/resources/online_flashcards/flashcard_multiplication03.htm I expect that students WON’T be using calculators for the basic operations review and that they will be showing their work as well.

Problems:

Basic Operations Review Day 12, questions 1-8 AND Multiplication Facts




Do your best with the work and as I’ve mentioned please ask for help when you

need it. I check my email very frequently and will get back to you as soon as possible. I

hope to see you all in the near future.

-Mr. Freeman

Copyright © by Savvas Learning Company LLC. All Rights Reserved. 7Topics 1–6 Cumulative/Benchmark Assessment

Topics 1–6Cumulative/

Benchmark Assessment Name

1. Which of the following expressions is

equivalent to -5

6

-13

? Select all that apply.

(-56) # (-3)

(-65) # (-3)

(-65) # (-1

3) (5

6) , (13)

56# (-3)

2. Owen and Jesse go to a restaurant for breakfast.

Part A

If the food and beverages cost $21.60 before a 7% meals tax is applied, what is the total cost of the bill?

Part B

If Owen and Jesse add a 15% tip after the tax is applied, what is the total cost, including tip?

3. A fruit stand sells mangoes for $3.49 per pound, papayas for $1.40 per pound, and coconuts for $1.24 per pound.

Part A

Write an expression to represent the total price of m pounds of mangoes, p pounds of papayas, and c pounds of coconuts.

Part B

What is the total cost of 3 pounds of mangoes, 4 pounds of papayas, and 6 pounds of coconuts?

4. Olivia has $240 in her bank account. Each month, her bank deducts a $12.50 fee for maintaining a balance below $250. If Olivia makes no other deposits or withdrawals, how much money will be in her account at the end of five months?

! $62.50

" $177.50

# $187.50

$ $302.50

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5. Does the equation y = 4.2x represent a proportional relationship? Explain.

6. At a flea market, used computer games are sold at the prices shown in the table below.

Number of Games Price ($)

2 9.00

5 22.50

7 31.50

Do the number of games and price form a proportional relationship? Explain.

7. Kaylee obtains a loan with simple interest to buy a car that costs $8,500. If Kaylee pays $1,020 in interest during the four-year term of the loan, what was the rate of simple interest?

8. Claire buys a jacket that originally cost $76. The price is marked down 25% for a sale, and Claire has a coupon to further reduce the marked down price by 10%. How much does Claire pay for the jacket?

! $49.40

" $51.30

# $57.00

$ $68.40

9. A community service group organizes a car wash that raises 7c - 18 dollars and a spaghetti dinner that raises 6s - 45 dollars. Which equation below represents the total amount of money raised?

! 13cs - 63

" 7c + 6s + 63

# 7c + 6s - 63

$ 7c + 6s - 27

10. Maxwell’s vegetarian tacos require 34 tablespoon of chili powder for every 12 pound of vegetables. How much chili powder will Maxwell need if he uses 13

4 pounds of vegetables?

! 214 tablespoons

" 212 tablespoons

# 258 tablespoons

$ 314 tablespoons

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11. Theo budgets $154 for karate classes. He buys a karate uniform, called a dogi, for $12. If it costs $8 to attend each karate class, which inequality below represents the number of classes, c, that Theo can take?

! 154 … 8c + 12

" 154 Ú 8c + 12

# 154 … 12c + 8

$ 154 Ú 12c + 8

12. Chloe compares the growth of plant species A and B.

4 5 98760 1 2 3

Plant A

Plant B

Growth (centimeters)

Part A

What do the box plots tell you about the growth of a typical plant of each species? Explain.

Part B

What do the box plots tell you about the variability of the data?

13. Which graph represents the solution of the inequality below?

-1.2x - 6.5x … 2.3x + 5

! 0212223 1 2 3

" 0212223 1 2 3

# 0212223 1 2 3

$ 0212223 1 2 3

14. Kai randomly surveys eighth graders at his school and learns that 7 of 35 respondents own a video gaming system. Based on these data, how many of the 150 eighth-grade students in Kai’s school would be expected to own a video gaming system?

! 15 students

" 25 students

# 30 students

$ 50 students

15. Solve the inequality below for x. -3.2(2x - 1) … 17.6

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16. A student council president wants to learn about the preferred theme for the upcoming spring dance. Which of the following samples are representative of the population? Select all that apply.

All students at her lunch table

Every fifteenth student who enters the school in the morning

All students on her bus

Every ninth student from an alphabetical list of students

All seventh graders

17. The seventh grade wants to break last year’s record of 78 coats collected for the annual clothing drive. They have already collected 13 coats.

Part A

Write and solve an inequality to represent the number of coats, c, that the seventh grade must still collect.

Part B

Graph the solution on a number line.

18. Paisley randomly surveys teachers about the type of car they drive.

Sedan TruckSUV

25

30

0

5

10

15

20

What inference can be made about the population based on Paisley’s data?

! Younger teachers drive trucks.

" Most teachers drive sedans.

# SUVs are driven by teachers with families.

$ Fewer teachers drive sedans than drive SUVs.

19. Find the solution of the equation below.

6(3x - 7.2) = 25.2

! x = -1

" x = 1

# x = 1.8

$ x = 3.8

20. Which of the following measures CANNOT be determined from a box plot? Select all that apply.

Interquartile range

Mean

Mean absolute deviation

Median

Mode

Range

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21. Find the solution of the following equation. 3.75x + 15 = 63.75

! x = 4

" x = 8

# x = 13

$ x = 17

22. Braden is comparing statistics about the prices of DVD players from two different stores.

Store A ($) Store B ($)Mean 61 58Median 57 56Range 11 7IQR 7 4MAD 4 2

Part A

Compare the measures of center of the data sets.

Part B

Compare the variability of the data of each store.

23. Solve the inequality 23x - 56 Ú 1

2 . Then graph the solution on a number line.

24. A grocery store buys oranges from two different farmers. The mean weight of farmer A’s oranges is 8 oz. The mean weight of farmer B’s oranges is 9.1 oz. The MAD of both data sets is 2. What can you infer about the two sets of oranges?

! The MAD is large.

" The data sets are very different.

# There is no difference between the sets of oranges.

$ The mean is small.

25. On a cross-country bicycle trip, participants ride about 75 miles per day. Approximately how many days, d, must they ride to travel at least 4,325 miles?

Part A

Write an inequality to represent the situation.

Part B

Solve the inequality. What does the solution represent in this situation?

0212225 2324 1 2 543

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26. Data from a random survey asking sixth and seventh graders about the number of siblings in their families are recorded in the dot plots below.

Number of Siblings

4 5 63210

Sixth Graders

Number of Siblings

4 5 63210

Seventh Graders

Compare the mean values of the data sets.

27. Solve the equation below.14x + 31

2 = 2(12x + 3

4)

28. Riley records the number of homework assignments completed by randomly selected students in her school on Monday in the table below.

Grade Assignments Completedeighth 5, 4, 5, 4, 4, 5, 4, 5seventh 6, 5, 5, 5, 6, 6, 5, 6sixth 5, 3, 4, 3, 5, 4, 4, 4

Make a comparative inference based on the mean values of each data set.

29. Lincoln is saving $360 to buy a new bike. He already has $85 and can earn $12 per hour at work. Which of the following equations describes the number of hours, h, for which Lincoln must work to earn enough money to buy the new bike?

! 360 - 12 = 85h

" 360h = 12 + 85

# 360 - 85 = 12h

$ 85 = 360 + 12h

30. Dave is 8 years younger than 4 times Julia’s age. If Dave is 16, how old is Julia?

! 6 years

" 24 years

# 32 years

$ 56 years

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Basic Pre-algebra Skill

Finding the Circumference of a CircleFind the circumference of each circle. Round to the nearest tenth.

1)

11 ft

2)

7 yd

3)

6.3 m

4)

11.8 ft

5)

2 km

6)

9 mi

7)

6 ft

8)

8.4 ft

9)

7.4 km

10)

8 m

-1-

11)

4 m

12)

22 mi

13)

5 m

14)

8 yd

15)

16.8 m

16)

6 cm

17)

14 in

18)

16 km

19)

10 in

20)

23.4 in

-2-

Basic Pre-algebra Skill

Finding the Area of a CircleFind the area of each. Round to the nearest tenth.

1)

12 mi

2)

5.2 km

3)

6.4 mi

4)

3 yd

5)

5 ft

6)

8.6 in

7)

10.3 km

8)

8 cm

9)

7 ft

10)

6 km

-1-

11)

20 m

12)

6.8 m

13)

22.6 yd

14)

18 ft

15)

16 mi

16)

13.8 mi

17)

22 yd

18)

6 m

19)

6.2 cm

20)

4 in

-2-

Name:

Super Teacher Worksheets - www.superteacherworksheets.com

Area of a Rectangle

Find the area of each rectangle.

To find the area of a rectangle, use the formula length x width = area.This formula is often written as l x w = A.

The rectangle pictured here has a length of 10 cm and a width of 8 cm.l = 10 cmw = 8 cm10 cm x 8 cm = 80 cm2

Note that the area’s unit is written as cm2.This is said as “square centimeters” or “centimeters squared”.

10 cm

8 cm

a.

9 cm

b.10 ft

3 ft

c.

4 km

2 km

d.

6 in.

12 in

.

e. 7 mm

6 m

m

f.

5 mi

8 m

i

Challenge: Find the area of the polygon. All corners are 90°. Use the back if you need workspace.

3 m

3 m

12 m

11 m

Super Teacher Worksheets - www.superteacherworksheets.com

Area of a Rectangle

Find the area of each rectangle.

To find the area of a rectangle, use the formula length x width = area.This formula is often written as l x w = A.

The rectangle pictured here has a length of 10 cm and a width of 8 cm.l = 10 cmw = 8 cm10 cm x 8 cm = 80 cm2

Note that the area’s unit is written as cm2.This is said as “square centimeters” or “centimeters squared”.

10 cm

8 cm

a.

9 cm

b.10 ft

3 ft

c.

4 km

2 km

d.

6 in.

12 in

.

e. 7 mm

6 m

m

f.

5 mi

8 m

i

Challenge: Find the area of the polygon. All corners are 90°. Use the back if you need workspace.

3 m

3 m

12 m

11 m

ANSWER KEY

81 cm2 30 ft2 8 km2

72 in.2 42 mm2 40 mi2

area of A =

area of B =

3 x 3 =

12 x 11 =

9 m2

132 m2

141 m2

+A B

1-10 90 80 70 60 50 40 30 20 10 0

1)

17 in

10 in

2)

15 mm

19 mm

3)

17 mm

13 mm

4)

2 km

9 km

5)

77 mm

24 mm

6)

19 m

11 m

7)

76 ft

82 ft

8)

18 m

19 m

9)

12 km

13 km

10)

100 ft

81 ft

1. 85 in2

2. 142.5 mm2

3. 110.5 mm2

4. 9 km2

5. 924 mm2

6. 104.5 m2

7. 3,116 ft2

8. 171 m2

9. 78 km2

10. 4,050 ft2

Find the area of each triangle. Units are not to scale.Finding Area of Triangles

Math www.CommonCoreSheets.com

Name:

Answers

1

1-10 90 80 70 60 50 40 30 20 10 0

1) 4

6

8

2) 4

6

2

3) 3

9

4

4) 8

9

4

5) 4

3

2

6) 3

3

2

7) 6

8

9

8) 8

3

6

9) 8

5

4

10) 3

8

9

1. 192

2. 48

3. 108

4. 288

5. 24

6. 18

7. 432

8. 144

9. 160

10. 216

Find the volume of each of the rectangular prisms. Measured in cm (not to scale).Finding Volume Of Rectangular Prisms

Math www.CommonCoreSheets.com

Name:

Answers

1

Printable Worksheets @ www.mathworksheets4kids.com

Name :

8) The base of a prism is a triangle with a base of 9 inches and a height of 5 inches. Determine the volume if itslength is 18 inches.

7) The base of a prism is a right triangle with legs measuring 16 feet and 4 feet. If the height of the prism is14 feet, find its volume.

7 in

5 in

12 in

1) 2) 3)

Volume = Volume = Volume =

4) 5) 6)

Volume = Volume = Volume =

Volume - Triangular Prism ES1

13 ft1

5 f

t2 ft

11 yd

4 y

d

6 yd

9 in

18

in

19 in

8 yd

10 yd17 yd

6 ft

14 ft 20 ft

Find the volume of each triangular prism.

Basic Operations Review Day 12 You may NOT use a calculator for this. Please show your work on a separate piece of paper and ONLY

answers go here. If you don’t show work you WILL NOT receive credit.

1.) 197.567 + 59.94=

2.) 56,235 + 98,976=

3.) 143.224 – 39.876=

4.) 197,445-187,978=

5.) 22 x 93 =

6.) 17 x 52 =

7.) 38/16=

8.) 48/5=


answers go here.

1.) -34 +147=

2.) -14-93=

3.) 13-493=

4.) 5.385 +19.83=

5.) 189,495 +769,439.385=

6.) -35 x 32=

7.) 17 x 19=

8.) 39 x 49=

9.) 145 x 17=

10.) 3.52 x 6.14=

11.) 195/3=

12.) 8845/4=

13.) 13.2/4=

14.) 143/8=

15.) 19/8=


answers go here.

1.) -34 +147=

2.) -14-93=

3.) 13-493=

4.) 5.385 +19.83=

5.) 189,495 +769,439.385=

6.) -35 x 32=

7.) 17 x 19=

8.) 39 x 49=

9.) 145 x 17=

10.) 3.52 x 6.14=

11.) 195/3=

12.) 8845/4=

13.) 13.2/4=

14.) 143/8=

15.) 19/8=


answers go here.

1.) -34 +19=

2.) -14-35=

3.) 13-93=

4.) 4.375 +19.23=

5.) 189,435 +789,419.345=

6.) -21 x 32=

7.) 14 x 19=

8.) 37 x 49=

9.) 145 x 12=

10.) 3.32 x 1.14=

11.) 189/3=

12.) 4356/4=

a 7th grade mathematics 3:30-4:17

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