Accelerated 7th Grade Summer Math Letter
Accelerated 7th Grade Summer Math Dear Accelerated 7th Grade Parents: The attached summer coursework consists of two sections. (1) The first section contains a packet of 45 problems covering material that most students should be familiar with from earlier math courses. This packet of problems is to serve as a review of those topics that your child may have previously learned. Clearly, if there are areas that he/she has not covered in earlier math classes, it is recommended and absolutely acceptable that you allow your child to skip these problems. We do not expect your child to learn new material during the summer months. Please be assured that after your child’s summer packet is reviewed, we will address and teach to your child those topics that correspond to his/her skipped problems. An item analysis is included at the end of the packet and may be used to identify topics that correspond to each problem. The directions for completing the packet are as follows: Show all work in the space provided next to or below each problem. Work should be completed neatly in pencil. Draw a circle around your final answer. Should you need additional space for your work, please clearly label your work on additional paper and staple the paper to the packet. (2) The second section contains word problems. Your child should choose and solve four of the six problems in the space provided below each problem. Work should be completed neatly in pencil. Draw a circle around your final answer. Should you need additional space for your work, please clearly label your work on additional paper and staple the paper to the packet. Completed packets are due by August 3. If you have any questions about the packet or the 6th grade curriculum over the summer, please contact accelerated 7th grade math teacher Marybeth Paolino at [email protected]. Packets should be mailed to: De LaSalle Middle School Attn: Alana Parenteau Principal 612 Academy Avenue Providence, RI 02908 !
Name _________________________________________________________
7 t h Grade Directions: Show all work for each problem in the space provided next to or below each problem. Do your work neatly in pencil. Draw a circle around your final answer. Multiply or divide. 1. 4.5 ÷ 0.9
2. 34.1 ÷ 5.5
3. 2.7(7.8)
6 5 • 9 4. 7
5.
4 8 ÷ 5 11
6.
3 4 • 8 9
7.You need to buy 5 notebooks for your classes at school. Each notebook costs $2.79. What is the
total cost of 5 notebooks before tax?
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Complete the statement using < , > , or = . 8.
4 tables 3 groups
6 tables 5 groups
9.
66 pages 2 hours
99 pages 3 hours
10. You have $50 in your savings account. Each week you deposit
$5 in your account. Write an expression that models the situation.
Solve the equation. 11. x + 5 = 10
12.
x−2 = 6
13.
x −1 = 9
14.
7 + x = 13
15. 5 x = 65
x = 11 16. 3 2
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17. What
is the surface area of a rectangular prism with length 5 centimeters, width 2 centimeters, and height 3 centimeters?
Tell whether the two expressions are equivalent. 18. 5 + 3b; 3b + 5
19. 5(h + 7); 5h + 35
20. (2 − c)4; 2 − 4c
Find the area of the figure. 21.
22.
23. What is the circumference
of the circle? Use 3.14 for π .
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Write the decimal as a percent. 24. 0.89
25. 2.37
26.0.0029 Write the percent as a decimal. 27.3%
28.78%
29.500%
17 of the people surveyed have a cat. What percent 25 of the people surveyed have a cat? 30.In a survey,
Order the numbers from least to greatest.
5 8
31. , 60%, 0.64
32. 34%,
4 , 0.3 15
33. 0.57, 5.8%,
14 25
Estimate the sum or product. 4
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34. 1.52(98)
35. 2.04(3.97)
36. 4.42 + 5.91
Find the mean, median, mode(s), and range of the data set. 37. 5, 9, 12, 3, 4, 5, 7, 14, 13
38.1, 7, 2, 3, 9, 4, 6, 10
39.The following data are the numbers of customers at a coffee shop
over a 10-day period. 135, 124, 140, 122, 409, 132, 119, 128, 136, 125 Which measure of center best represents the daily average number of customers at the coffee shop? Explain your reasoning.
Multiply or divide. 40. 56 × 18 Copyright © Big Ideas Learning, LLC
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41. 656 ÷ 41
42. 184 ÷ 23
Write the fraction as a decimal. 43.
13 20
44.
3 8
45.
21 40
6
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7 t h Grade Item Number
Item Analysis Skills
Item Number
1
dividing decimals
24
2
dividing decimals
25
3
multiplying decimals
26
4
multiplying fractions
27
5
dividing fractions
28
6
multiplying fractions
29
7
multiplying decimals
30
8
comparing rates
31
9
comparing rates
32
10 11 12 13 14 15 16 17 18 19 20 21 22 23
writing expressions to represent situations solving one-step equations solving one-step equations solving one-step equations solving one-step equations solving one-step equations solving one-step equations finding the surface area of a rectangular prism applying the comm. property applying the distributive property applying the distributive property finding the area of a parallelogram finding the area of a triangle finding the circumference of a circle
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33 34 35 36 37 38 39 40 41 42 43 44 45
Skills
converting decimals to percents converting decimals to percents converting decimals to percents converting percents to decimals converting percents to decimals converting percents to decimals converting fractions to percents ordering rational numbers ordering rational numbers ordering rational numbers estimating product of decimals estimating product of decimals estimating sum of decimals finding measures of center and range finding measures of center and range determining measures of center multiplying whole numbers dividing whole numbers dividing whole numbers converting fractions to decimals converting fractions to decimals converting fractions to decimals
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Word Problems for Accelerated Grade 7 Mathematics (Source: Socially Conscious Word Problems for the Algebra Curriculum Created by Deborah Gordon-Goodrich & Gary Kaufman, Montclair Kimberly Academy https://sociallyconsciousmath.wordpress.com)
Directions: Solve four problems from those listed below. Show each step of your solution. 1. Budgeting Question: Suzannah can spend up to ⅝ of her salary on rent. If she earns $1900 per month entering data for a company, how much does she have to spend on insurance, car payments and utilities – assuming those are her only other monthly expenses? 1a. What is her monthly rent? The average rent for a studio apartment in Montclair is $950 per month and $1250 per month for a one-bedroom. Knowing the average rents, what type of apartment would you assume Suzannah rents? 1b. If she spends $850 on her other expenses a month, will she have enough money to put $200 a month away in her saving account? 1c. How much more a month would Suzannah need to earn in order to rent a 1-bedroom apartment, continue spending the same on other monthly expenses and put $200 into a savings account each month? (zillow.com)
2. Environment/Sustainability & Budgeting Question: A typhoon is what a Northwest Pacific cyclone is called. In the Northeastern Pacific and Northern Atlantic, these events are called Hurricanes. In November 8, 2013, Typhoon Yolanda hit the Philippines, killing over 5,000 people. Typhoon Yolanda’s 165 knots of wind speed made it a Super Typhoon. 2a. In 2005, Hurricane Katrina swept through New Orleans flooding it and causing $125 billion in damage. It swept its path with 175 mile per hour winds. Since a Hurricane is just a different name for a Typhoon, convert the 175 miles per hour to knots and state what type of Typhoon it would have been if it had been in the Northwest Pacific. (http://en.wikipedia.org/wiki/Typhoon_Haiyan, http://www.jma.go.jp/jma/jma-eng/jma-center/rsmc-hp-pubeg/RSMC_HP.htm)
3. Health and Nutrition Question: A Starbucks grande Caramel Frappuccino has 410 calories. The average active 7th grader should have a diet of 2,000 calories per day. 3a. Assuming there is a need to average 2000 calories per day, how many calories would be consumed by other foods/drinks at the end of a week if such a diet were followed with 4 Frappuccinos being were consumed in a week? (www.starbucks.com)
4. Environment/Sustainability Question: In 1996, U.S. mills recycled 34.3 million tons of paper. This represents about 45% of the total paper produced. 4a.How much paper was produced in 1996? 4b. If a single pine tree can produce 80,500 sheets of paper, and a ream (package) of photocopier paper contains 500 sheets, how many reams of paper does a single pine tree provide? 4c. Suppose that the number of pieces of paper in a recycling bin at school is 135. What percentage of a ream of paper is in the recycling bin? How does that percentage compare with the national percentage of 45% of paper recycled? http://www.ecology.com/2011/09/10/paper-chase
5. Environment/Sustainability: By law, toilets must use no more than 1.6 gallons of water per flush. Prior to this law in 1995, toilets on average used 3.5 gallons of water per flush. 5a. What was the percent decrease in water usage per flush, due to this 1995 law? 5b. If a person were born after 1995, toilet trained at age 3, and had a life expectancy of 85 years, how much less water would that person use in their lifetime if the government changed the law to 1.4 gallons per flush compared with 1.6 gallons per flush? What would be the percent decrease in water usage for that person’s lifetime? 5c. The average household uses 300 gallons of water a day, 46 of which are flushing toilets. What percentage of the gallons used a day are for flushing the toilet? motherearthnews.com,
6. Budgeting: Costco is a popular place to buy things, mostly in bulk (look up “bulk” if you don’t know what it means). A pack of 80 rolls of toilet paper costs $74.99 at Costco and 27 rolls of the same toilet paper costs $27 at Stop & Shop. 6a. Use ratios to determine which is the better deal. Show the work that justifies your answer so that someone simply looking at your work would know the better place to purchase toilet paper in bulk. 6b. If Stop & Shop is having a sale on toilet paper for 10% off, does that change which one is the better deal? (www.costco.com, www.stopandshop.com)
Name _________________________________________________________
7 t h Grade Directions: Show all work for each problem in the space provided next to or below each problem. Do your work neatly in pencil. Draw a circle around your final answer. Multiply or divide. 1. 4.5 ÷ 0.9
2. 34.1 ÷ 5.5
3. 2.7(7.8)
6 5 • 9 4. 7
5.
4 8 ÷ 5 11
6.
3 4 • 8 9
7.You need to buy 5 notebooks for your classes at school. Each notebook costs $2.79. What is the
total cost of 5 notebooks before tax?
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Big Ideas Math Red
1
Complete the statement using < , > , or = . 8.
4 tables 3 groups
6 tables 5 groups
9.
66 pages 2 hours
99 pages 3 hours
10. You have $50 in your savings account. Each week you deposit
$5 in your account. Write an expression that models the situation.
Solve the equation. 11. x + 5 = 10
12.
x−2 = 6
13.
x −1 = 9
14.
7 + x = 13
15. 5 x = 65
x = 11 16. 3 2
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17. What
is the surface area of a rectangular prism with length 5 centimeters, width 2 centimeters, and height 3 centimeters?
Tell whether the two expressions are equivalent. 18. 5 + 3b; 3b + 5
19. 5(h + 7); 5h + 35
20. (2 − c)4; 2 − 4c
Find the area of the figure. 21.
22.
23. What is the circumference
of the circle? Use 3.14 for π .
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Big Ideas Math Red
3
Write the decimal as a percent. 24. 0.89
25. 2.37
26.0.0029 Write the percent as a decimal. 27.3%
28.78%
29.500%
17 of the people surveyed have a cat. What percent 25 of the people surveyed have a cat? 30.In a survey,
Order the numbers from least to greatest.
5 8
31. , 60%, 0.64
32. 34%,
4 , 0.3 15
33. 0.57, 5.8%,
14 25
Estimate the sum or product. 4
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34. 1.52(98)
35. 2.04(3.97)
36. 4.42 + 5.91
Find the mean, median, mode(s), and range of the data set. 37. 5, 9, 12, 3, 4, 5, 7, 14, 13
38.1, 7, 2, 3, 9, 4, 6, 10
39.The following data are the numbers of customers at a coffee shop
over a 10-day period. 135, 124, 140, 122, 409, 132, 119, 128, 136, 125 Which measure of center best represents the daily average number of customers at the coffee shop? Explain your reasoning.
Multiply or divide. 40. 56 × 18 Copyright © Big Ideas Learning, LLC
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5
41. 656 ÷ 41
42. 184 ÷ 23
Write the fraction as a decimal. 43.
13 20
44.
3 8
45.
21 40
6
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7 t h Grade Item Number
Item Analysis Skills
Item Number
1
dividing decimals
24
2
dividing decimals
25
3
multiplying decimals
26
4
multiplying fractions
27
5
dividing fractions
28
6
multiplying fractions
29
7
multiplying decimals
30
8
comparing rates
31
9
comparing rates
32
10 11 12 13 14 15 16 17 18 19 20 21 22 23
writing expressions to represent situations solving one-step equations solving one-step equations solving one-step equations solving one-step equations solving one-step equations solving one-step equations finding the surface area of a rectangular prism applying the comm. property applying the distributive property applying the distributive property finding the area of a parallelogram finding the area of a triangle finding the circumference of a circle
Copyright © Big Ideas Learning, LLC
33 34 35 36 37 38 39 40 41 42 43 44 45
Skills
converting decimals to percents converting decimals to percents converting decimals to percents converting percents to decimals converting percents to decimals converting percents to decimals converting fractions to percents ordering rational numbers ordering rational numbers ordering rational numbers estimating product of decimals estimating product of decimals estimating sum of decimals finding measures of center and range finding measures of center and range determining measures of center multiplying whole numbers dividing whole numbers dividing whole numbers converting fractions to decimals converting fractions to decimals converting fractions to decimals
Big Ideas Math Red
7
Word Problems for Accelerated Grade 7 Mathematics (Source: Socially Conscious Word Problems for the Algebra Curriculum Created by Deborah Gordon-Goodrich & Gary Kaufman, Montclair Kimberly Academy https://sociallyconsciousmath.wordpress.com)
Directions: Solve four problems from those listed below. Show each step of your solution. 1. Budgeting Question: Suzannah can spend up to ⅝ of her salary on rent. If she earns $1900 per month entering data for a company, how much does she have to spend on insurance, car payments and utilities – assuming those are her only other monthly expenses? 1a. What is her monthly rent? The average rent for a studio apartment in Montclair is $950 per month and $1250 per month for a one-bedroom. Knowing the average rents, what type of apartment would you assume Suzannah rents? 1b. If she spends $850 on her other expenses a month, will she have enough money to put $200 a month away in her saving account? 1c. How much more a month would Suzannah need to earn in order to rent a 1-bedroom apartment, continue spending the same on other monthly expenses and put $200 into a savings account each month? (zillow.com)
2. Environment/Sustainability & Budgeting Question: A typhoon is what a Northwest Pacific cyclone is called. In the Northeastern Pacific and Northern Atlantic, these events are called Hurricanes. In November 8, 2013, Typhoon Yolanda hit the Philippines, killing over 5,000 people. Typhoon Yolanda’s 165 knots of wind speed made it a Super Typhoon. 2a. In 2005, Hurricane Katrina swept through New Orleans flooding it and causing $125 billion in damage. It swept its path with 175 mile per hour winds. Since a Hurricane is just a different name for a Typhoon, convert the 175 miles per hour to knots and state what type of Typhoon it would have been if it had been in the Northwest Pacific. (http://en.wikipedia.org/wiki/Typhoon_Haiyan, http://www.jma.go.jp/jma/jma-eng/jma-center/rsmc-hp-pubeg/RSMC_HP.htm)
3. Health and Nutrition Question: A Starbucks grande Caramel Frappuccino has 410 calories. The average active 7th grader should have a diet of 2,000 calories per day. 3a. Assuming there is a need to average 2000 calories per day, how many calories would be consumed by other foods/drinks at the end of a week if such a diet were followed with 4 Frappuccinos being were consumed in a week? (www.starbucks.com)
4. Environment/Sustainability Question: In 1996, U.S. mills recycled 34.3 million tons of paper. This represents about 45% of the total paper produced. 4a.How much paper was produced in 1996? 4b. If a single pine tree can produce 80,500 sheets of paper, and a ream (package) of photocopier paper contains 500 sheets, how many reams of paper does a single pine tree provide? 4c. Suppose that the number of pieces of paper in a recycling bin at school is 135. What percentage of a ream of paper is in the recycling bin? How does that percentage compare with the national percentage of 45% of paper recycled? http://www.ecology.com/2011/09/10/paper-chase
5. Environment/Sustainability: By law, toilets must use no more than 1.6 gallons of water per flush. Prior to this law in 1995, toilets on average used 3.5 gallons of water per flush. 5a. What was the percent decrease in water usage per flush, due to this 1995 law? 5b. If a person were born after 1995, toilet trained at age 3, and had a life expectancy of 85 years, how much less water would that person use in their lifetime if the government changed the law to 1.4 gallons per flush compared with 1.6 gallons per flush? What would be the percent decrease in water usage for that person’s lifetime? 5c. The average household uses 300 gallons of water a day, 46 of which are flushing toilets. What percentage of the gallons used a day are for flushing the toilet? motherearthnews.com,
6. Budgeting: Costco is a popular place to buy things, mostly in bulk (look up “bulk” if you don’t know what it means). A pack of 80 rolls of toilet paper costs $74.99 at Costco and 27 rolls of the same toilet paper costs $27 at Stop & Shop. 6a. Use ratios to determine which is the better deal. Show the work that justifies your answer so that someone simply looking at your work would know the better place to purchase toilet paper in bulk. 6b. If Stop & Shop is having a sale on toilet paper for 10% off, does that change which one is the better deal? (www.costco.com, www.stopandshop.com)
