Grade 7 Test Questions by Standard 2013 – 2016
7NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers.
Skills Generalize rules for adding rational numbers with the same sign. Generalize rules for adding rational numbers with the opposite sign. Explain the additive inverse relationship between a rational number and its opposite.. Interpret sums of rational numbers by describing real-world contexts. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Illustrate subtraction of rational numbers using models and manipulatives. Calculate subtraction of rational numbers on a number line either horizontal or vertical.. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (– q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
Resources CMP: Accentuate the Negative Inv 1, 2, 4 Glencoe: Chapter 3: Lesson 2, 3 Chapter 4: Lesson 3, 4, 5 Common Core Mathematics: 1.6, 1.7, 3.2, 3.3, CC.1 Big Ideas Math: 1.1, 1.2, 1.3, 2.2, 2.3
7NS1a 1. Altitude above sea level is given in positive values and below sea level is given in negative values. Which situation describes a hiker in Death Valley stopping at an altitude of 0 feet? A. The hiker starts at -10 feet then increases altitude by 10 feet B. The hiker starts at -10 feet then decreases altitude by 10 feet C. The hiker starts at 10 feet then increases altitude by 10 feet D. The hiker starts at 0 feet then decreases altitude by 10 feet
7NS1b 1. Which phrase correctly describes the location on the number line of the opposite of -8?
A a point 8 units to the left of – 8 B a point 8 units to the right of - 8 C a point 8 units to the left of 0 D a point 8 units to the right of 0
2. What value of x makes the equation -3 + x = 0 true?
1 1 A -3 B - C D 3 3 3
7NS1c 1. Which expression is equivalent to 4 - (- 7)?
A 7 + 4 B 4 - 7 C -7 - 4 D -4 + 7
7NS1d 1. What is the value of the expression below? 3 4 3 5 + (- ) + (- ) + 8 5 8 4 1 9 4 A 0 B C D 2 20 20 5
2. Yesterday, the temperature at noon was 11.4°F. By midnight, the temperature had decreased by 15.7 degrees. What was the temperature at midnight?
A -4.3°F B -11.4°F C -15.7°F D -27.1°F
3. What is the value of the expression below? 2 3 -0.75 - (- ) + 0.4+ (- ) 5 4
A -1.5 B -0.7 C 0.8 D 2.3
4. From midnight to 7:00 a.m., the temperature dropped 1.35° each hour. If the temperature at midnight was 10°, what was the temperature at 7:00 a.m.?
Show your work.
Answer ______0C
5. Graham's monthly bank statement showed the following deposits and withdrawals:
-$25.20, $52.75, -$22.04, -$8.50, $94.11
If Graham's balance in the account was $47.86 at the beginning of the month, what was the account b a l a n c e at the end of the month?
Show your work
Answer $______
7NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Skills Fluently multiply and divide rational numbers. Apply the associative property of multiplication to multiplying rational numbers. Apply the commutative property of multiplication to multiplying rational numbers. Apply multiplicative inverse property to multiplying rational numbers. Apply properties of operations as strategies to multiply and divide rational numbers. Convert rational numbers to decimals through the process of long division dividing the numerator by the denominator. Differentiate between rational and irrational number. Calculate the remainder of each division as terminating or repeating using correct form. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Resources CMP: Accentuate the Negative Inv 3, 4 Glencoe: Chapter 3: Lesson 4, 5 Chapter 4: Lesson 1, 2, 6, 7, 8 Common Core Mathematics: 1.3, 1.4, 1.8, 2.6, 2.7, 3.4, 3.5, CC.2, CC.3 Big Ideas Math: 1.1, 1.4, 1.5, 2.1, 2.4
7NS2a 4 1. Yesterday, the temperature change for a 5-hour period of time was – degree per hour. Which 5 statement describes this change? 1 A The temperature rose 5 degrees. B The temperature rose by 4 degree 5 4 C The temperature fell by 4 degrees D The temperature fell by 5 degrees 5 5 1 2. What is the value of the expression? (- ) x (3 ) 8 2 5 3 3 5 A 3 B 2 C -2 D -3 16 16 16 16
1 3 3. What is the product of (- ) x (- ) ? 4 7
7 3 3 7 A - B - C D 12 28 28 12
7NS2b The elevation at ground level is 0 feet. An elevator starts 90 feet below ground level. After traveling for 15 seconds, the elevator is 20 feet below ground level. Which statement describes the elevator's rate of change in elevation during this 15-second interval?
A The elevator traveled upward at a rate of 6 feet per second. B The elevator traveled upward at a rate of 4 ~ feet per second. C The elevator traveled downward at a rate of 6 feet per second. D The elevator traveled downward at a rate of 4 ~ feet per second.
7NS2c 1. What is the value of the expression below? 1 3 4 . 2 2 4 3 3 A 2 B 3 C 8 D 12 8 8
5 2. A number, n, is multiplied by - . The product is - 0.4. What is the value of n? 8 16 1 1 16 A - B - C D 25 4 4 25
3. A company ordered 10 boxed lunches from a deli for $74.50. Each boxed lunch cost the same amount. Which equation represents the proportional relationship between y, the total cost of the boxed lunches, and x, the number of boxed lunches?
7.45 10 74.50 10 A 7.45x = y B = C 74.50x = y D = x y x y 4. What is the value of the expression?
8 ÷ (-0.35) 15
75 32 21 14 A - B - C - D - 14 21 32 75
7NS2d 1. When converted to a decimal, which fraction will result in a repeating decimal?
3 3 3 3 A B C D 6 9 12 15
7 2. What is the decimal equivalent of ? 8
A 0.780 B 0.870 C 0.875 D 0.885
3 3. Convert to a decimal equivalent using long division. 11
Show your work
Answer ______7NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
Skills Fluently add, subtract, multiply, and divide rational numbers. Construct and explain situations involving multiple operations involving rational numbers. Solve real world and mathematical problems involving rational numbers, including multi-step. Resources CMP: Accentuate the Negative: Inv. 1, 2, 3, 4; Stretching and Shrinking: Inv. 4 Filling and Wrapping: Inv 2, 3, 4 Glencoe: Chapter 1: Lesson 2 Chapter 3: Lesson 1, 2, 3, 4, 5 Chapter 4: Lesson 3, 4, 5, 6, 7, 8 Common Core Mathematics: 1.3, 1.4, 1.8, 3.4, 3.5, Big Ideas Math: 1.1, 1.2, 1.3, 1.4, 1.5, 2.2, 2.3, 2.4
1. The table shows prices for shoe rental, games, and snacks at the bowling a l l e y .
Gina rented shoes, bowled 3 games, and bought 1 order of nachos. She used a coupon for ½ off the price of her bowling games. What was Gina's total c o s t before tax was added? A $5.75 B $6.00 C $8.25 D $12.00
2. Gretchen makes pillows using 1⅝ yards of fabric per pillow. She has 8¼ yards of fabric. What is the greatest number of pillows Gretchen can make? A 4 B 5 C 6 D 8
3. The 90 members of a service club had the opportunity to vote for club officers on Tuesday or Wednesday. 3 of the members voted on Tuesday. 5 1 of the members who did not vote on Tuesday voted on Wednesday. 4 How many of the club members did not vote at all? A 36 B 27 C 22 D 9
4. The town council had a banquet as a fundraiser for new playground equipment. They sold 250 tickets for a total of $5,625. The expenses for the banquet were $6,182.50. What were the results of the town c o u n c i l ’ s banquet?
A They lost $2.23 per ticket sold. B They made $1.05 per ticket sold. C They lost a total of $307 .50. D They made a total of $557 .50.
0 5. Scientists determined that Antarctica’s average winter temperature was -34.44 C. The difference between this temperature and Antarctica’s highest recorded temperature was 49.44 degrees. What was Antarctica’s highest recorded temperature?
A -83.88°C B - 15°C C 15°C D 83.88°C
7 6. Evaluate (- + 0.15) ÷ (-0.125) 10
A -6.8 B -4.4 C 4.4 D 6.8
2 5 7. What is the value of the expression ( - ) 3 6 3
4
2 1 1 2 A - B - C D 9 8 8 9
1 1 4 8. What is the value of (- - ) ÷ (- ) 4 2 7 5 3 3 5 A -1 B - C D 1 6 7 7 6
9. Travis, Jessica, and Robin are collecting donations for the school band. Travis wants to collect 20% more than Jessica and Robin wants to collect 35% more than Travis. If the s t u d e n t s meet their goals and Travis collects $43, how much money did they collect in all?
A $1906.78 B $128.60 C $136.88 D $144.99
15 10. Amber determined that the expression i s e q u i v a l e n t t o . 82
Which statement describes the process Amber could have used?
1 A She divided - by -15 and then divided the result by 41 2 1 B She multiplied - by -15 and then divided the result by 41 2 1 C She divided - by -15 and then multiplied the result by 41 2 1 D She multiplied - by -15 and then multiplied the result by 41 2
3 11. A pile of newspapers in Ms. McGrath’s art class was 17 inches high. Each consecutive week, for 4 7 the next 5 weeks, the height of the pile of newspapers increased by 8 inches. What was the height, in 12 inches, of the pile after 3 weeks?
3 1 1 1 A 25 B 26 C 42 D 43 4 4 4 2 12. Three friends own a landscaping business. The number of hours each friend spent on the same project is shown in the table below.
HOURS WORKED ON LANDSCAPING PROJECT Name Hours worked Edgar 17¼ Kelly 18¼ Shawn 14½
In total, they earned $850 for the job. They put 15% of this amount into a joint savings account for future expenses. They then divided the rest proportionally based on the number of hours each worked. How much money did Shawn receive?
A $209.53 B $240.83 C $283.48 D $295.11
13. A pine tree m e a s u r e d 40½ feet tall. Over the next 7½ years, it grew to a height of 57 feet. During the 7½years, what was the average yearly growth rate of the h e i g h t of the tree?
Show your work.
Answer ______feet per year
14. On the first day camping, a group hiked at a rate of 2¼ miles per hour for 2½ hours before taking a break. How many miles had the group hiked before the break? Show your work.
Answer ______miles
The group hiked a total of 17.4 miles on the first day. On the second day, the group hiked a distance 12% more than the total distance hiked on the first day. To the nearest tenth of a mile, how many miles did the group hike on the second day? Show your work.
Answer ______miles 1 3 15. Maxine picked 7 pounds of blueberries, and Kodi picked 3 pounds of blueberries. They want to 4 4 1 package the blueberries into 1 pound bags to sell at their family fruit and vegetable stand. What is the 2 1 greatest number of 1 pound bags of blueberries that they can make? 2 Show your work
Answer ______bags
1 16. George hiked from the top of a hill to the valley floor. The elevation at the top of the hill is 127 2 1 feet above sea level. The valley floor is 52 feet below sea level. 2
George stopped at a rest stop that is at an elevation exactly halfway between the top of the hill and the valley floor. What is the elevation, in feet, of the rest stop?
Show your work Answer ______feet
3 17. Last week Rachel power walked 2 miles per day on each of the 7 days. During the same 5 3 week, she also jogged 5 miles per day on 4 days. What was the total number of miles Rachel power 4 walked and jogged last week?
Show your work
Answer ______miles 18. Explain the steps needed to determine the value of the expression shown below. Be sure to provide the correct value of the expression in your explanation.
1
2 1 2 + (- ) - 4 5
Answer ______
______
______
19. Ruby's Market sells smoked meats by the pound. The prices for several different meats are shown in the table.
RUBY'S MARKET PRICES Type of Meat Price per pound Beef $4.25 Chicken $2.50 Sausage $3.25 Turkey $2.85
How much more does 11 pounds of beef cost than 11 pounds of turkey? Show your work.
Answer $ ______
Brad has $10 to spend at Ruby's. He orders ~ pound of sausage and 11 pounds of chicken. How much money will Brad have left after he pays for this order?
Show your work.
Answer $ ______7RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units
Skills Identify ratios that compare two quantities. Show ways for expressing ratios. Solve problems using part to part and part to whole relationships. Compare part to part and part to whole relationships with and without models and pictures. Compute unit rates from given comparisons of quantities measured in like or different units (i.e. length, area, miles per hours, better purchase). Solve unit rates involving real world applications. Apply unit rate understanding to convert ratios. Apply unit rate understanding to compute equivalent measurements (i.e. area, length). Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
Resources CMP: Comparing and Scaling: Inv. 2 Glencoe: Chapter 1: Lesson 2 Common Core Mathematics: 5.1, 5.2,5.4, 5.5, CC.7 Big Ideas Math: 5.1 2 1. A crew of highway workers paved mile in 20 minutes. If they work at the same rate, what 15 portion of a mile will they pave in one hour?
1 2 2 5 A B C D 150 45 5 2
1 2. The label on a 1 pound bag of wildflower seeds states that it will cover an area of 375 square feet. 2 Based on this information, what is the number of square feet that 1 pound of wildflower seeds will cover?
1 1 A B 250 C 562 D 750 250 2 1 3. Ms Graves gave her class 12 minutes to read. Carrie read 5 pages in that time. 2 At what rate, in pages per hour, did Carrie read? 1 1 A 1 B 22 C 27 D 66 10 2
4. A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose 1 1 by degree every hour for a limited time. What was the rate, in degrees per hour that the 10 4 temperature of the compound rose?
1 2 5 40 A B C D 40 5 2 1
1 1 5. A recipe requires cup of milk for each cup of water. How many cups of water are needed 3 4 for each cup of milk? 1 3 11 1 A B C D 1 12 4 12 3
1 6. Gary buys a 3 pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food 2 each day. Which expression can Gary use to determine the number of pounds of cat food his cat eats each year? (1 year = 52 weeks)
7 52 7 3 1 3 1 52 A x B x C 3( x ) D 3( x ) 2 3 2 52 2 52 2 3
1 7. A recycling plant processes an average of ton of glass each minute. At approximately what rate 3 does the recycling plant process glass, in tons per day? (1 day = 24 hours)
A 20 B 180 C 480 D 4,320 3 4 8. Andrew walked mile in 10 minutes. Jill walked mile in 15 minutes. What was the difference in 4 5 their speeds, in miles per hour?
A 0.1 B 0.6 C 1.3 D 1.7
9. Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are shown below.
42 feet
25.5 feet
If the total cost of the wallpaper was $771.12, what was the cost, in dollars, of the wallpaper per square foot?
A $0.61 B $0.72 C $1.39 D $1.65
10. A pine tree measured 40½feet tall. Over the next 7½ years, it grew to a height of 57 feet. During the 7½ years, what was the average growth rate of the height of the tree?
Show your work
Answer ______feet per year 7RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Skills Define ratio and proportion. Compare two ratios to determine if they are proportional. Create a table of unit/rate values for a proportional relationship. Graph a set of unit/rate values for a proportional relationship on a coordinate grid Use tables and graphs to identify ordered pairs of proportional values. Compare proportional and non-proportional relationships on a graph. Define scale factor. Scale unit rates to correspond with given criteria (i.e. double, triple, half, etc.). Identify the constant rate of proportionality (unit rate) when given data in a table. Identify the constant rate of proportionality (unit rate) when given a diagram. Create algebraic equations that illustrates constant rate of proportionality. Predict outcomes from given proportional relationships, using tables, graphs, and equations. Write equations given a proportional relationship from tables and graphs. Graph proportional relationship using (x,y) values from function table. Explain the relationship between the x values and the y values in a table or on a graph. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation. Resources CMP: Stretching and Shrinking: Inv. 1, 2, 3,4 Comparing and Scaling: Inv. 1, 2, 3 Moving Straight Ahead: Inv. 1, 2 Glencoe: Chapter 1: Lesson 1, 3, 4, 5, 6, 7, 8, 9 Chapter 2: Lessons4, Common Core Mathematics: 5.2, 5.4, 5.5 Big Ideas Math: 5.2, 5.3, 5.4, 5.5, 5.6 7RP.2a 1. The table below shows the dimensions of several parallelograms.
Which pair of dimensions is in the same proportion as each of the pairs shown in the table?
A base of 30 inches and height of 20 inches B base of 40 inches and height of 30 inches C base of 45 inches and height of 27 inches D base of 48 inches and height of 32 inches
2. Jocelyn was shopping at a farmers' market. She observed the prices of cucumbers at several stands. Which sign shows a proportional relationship in the pricing of the cucumbers? 3. Which table below contains values that represent a directly proportional relationship between x and y?
X y x y x y x y A 9 12 B 10 16 C 10 15 D 14 16 24 32 25 36 15 24 34 40
4. Line KN represents a proportional relationship. Point N lies at (18, 12), as shown on the graph below.
Which ordered pair could represent the coordinates of point K?
A (6, 0) B (2, 3) C (1.5, 0) D (7.5, 5)
5. The lines graphed below show the amounts of water in two tanks as they were being filled over time.
For each tank, explain whether or not there is a proportional relationship between the amount of water, in gallons, and the time, in minutes. If there is a proportional relationship, identify the unit rate. Use specific features of the graph to support your answer. ______
7RP.2b 1. The table shows that the number of miles driven by Sandra is directly proportional to the number of gallons used.
What is the constant of proportionality for this relationship?
A 0.5 B 3 C 15 D 24.5
2. Last week Len spent $18 to bowl 4 games. This week he spent $27 to bowl 6 games. Len owns his bowling ball and shoes, so he only has to pay for each game that he bowls. If each of these bowling games costs the same amount of money, what is the constant of proportionality between the money spent and the number of games played?
A 1.5 B 2.0 C 4.5 D 9.0
3. The length of a shadow depends on the height of an object. The graph below represents this relationship. What is the ratio of shadow length to object height?
A 1: 2 B 2:1 C 3:2 D 2:3
4. Mr. Lesko compared the cost of bottles of cranberry juice in three stores.
• At Store 1 the total cost, C of b bottles is given by the equation C = 2.89b • At Store 2, Mr. Lesko bought 5 bottles of cranberry juice for $13.75. • The graph below represents the cost at Store 3
Which of the three stores had the lowest unit rate, in dollars, for a bottle of cranberry juice? Include the unit rate in your answer. Show your work
Answer Store ___
Unit rate______
5. At every game, a school buys bottles of water for its basketball team. The table shows the relationship between the number of bottles bought and the total cost. If C = kN, where C is the cost of N bottles and k is the constant of proportionality, what is the value of k?
Answer ______In October, the school bought 150 bottles of water for the basketball team. What was the total cost? Show your work.
Answer $______
6. A convenience store sells two brands of orange juice. Brand A contains 8 fluid ounces and costs $1.28. Brand b contains 12 fluid ounces and costs $1.68.
What is the difference in cost, in dollars, per fluid ounce between the two brands of juice?
Show your work
Answer ______per fluid ounce.
7. The table shows the prices of different numbers of cards on a web site. COST OF CARDS Number of Price cards (dollars) 20 13 40 26 60 39 100 65 For each order, the web site applies a 7.7% sales tax to the price of the cards, plus a one-time mailing fee of $5.95. Based on the information in the table, what will be the total cost for an order for 280 cards? Show your work Answer $______
7RP2c 1. The cost of oranges in a grocery store is directly proportional to the number of oranges purchased. Jerri paid $2.52 for 6 oranges. If p represents the cost, in dollars, and n represents the number of oranges purchased, which equation best represents this relationship?
A p = 0.42n B p = 2.52n C p = 6n D p = 15.12n
2. Bananas cost $0.45 per pound. What equation is used to find C the total cost of p pounds of bananas?
A C = 0.45p B C = p + 0.45 C 0.45C = p D 0.45 + C = p
3. A rhombus with side length s is shown below
The perimeter, P, of a rhombus is proportional to the length of each side, s. Which equation r e p r e s e n t s this relationship? A P = 4s B s = 4P C P = 4 + s D s = 4 + P
7RP2d 1. The relationship between the number of songs downloaded, x, and the total cost, in dollars, of the downloads, y, is represented by a graph drawn in an xy-plane. Points (1, 3) and (4, 12) lie on the graph. What does the ordered pair (4, 12) indicate?
A 12 downloads that cost $4 each B 4 downloads that cost $12 each C 12 downloads that cost a total of $4 D 4 downloads that cost a total of $12
2. The relationship between the length of one side of a square, x, and the perimeter of the square, y, can be represented in an xy-plane by a straight line. Which of the points with coordinates ( x, y) lie on the line?
A (2, 6) B (2, 8) C (6, 2) D (8, 2) 3. The graph below shows the relationship between the number of people in a group and the total cost of admission tickets for, a circus.
What point on the graph represents the unit rate?
A (0,0) B (1,15) C (15,1) D (8,120)
7RP.3 Use proportional relationships to solve multistep ratio and percent problems
Skills Convert between fractions, decimals, and percent equivalents. Solve percent problems: o Find part of a number when given whole and percent. o Find percent when given part and whole. o Find whole when given part and percent. Define tax, commission, and gratuity Calculate o Discount on purchased items. o Percentage of discount. o Tax/gratuities added to a purchase. o Commission on transactions. o Percent of increase or decrease. o Simple interest. Percent of error Use the formula (difference/original x 100 = percent) to calculate the percent of change in a number. Use real world situations to show application a variety of proportional relationships.
Resources CMP: Stretching and Shrinking: Inv. 3 Comparing and Scaling: Inv. 1, 2, 3 What Do You Expect?: Inv. 1, 2, 3, 4, 5 Glencoe: Chapter 1: Lesson 3, 6 Chapter 2: Lesson 1, 2, 3, 4, 5, 6, 7, 8 Chapter 4: Lesson 7 Common Core Mathematics: 6.7, 6.8, 9.7 Big Ideas Math: 5.1, 5.3, 6.3, 6.4, 6.5, 6.6, 6.7
1. The Lions won 16 games last year. This year the Lions won 20 games. What is the percent increase in the number of games the Lions won from l a s t year to this year?
A 20% B 25% C 80% D 125%
2. Suzanne bought a sweater at the sale price of $25. The original cost of the sweater was $40. What percent represents the discount that Suzanne received when buying the sweater?
A 15% B 37.5% C 60% D 62.5%
3. Ashley completed reading a history assignment in 4 days. On Monday, she read 16 pages. For each of the next 3 days, the number of pages she read increased by 50% over the number of pages she read on the previous day. Greg read the same history assignment, but he read an equal number of pages per day from Monday through Friday. How m a n y p a g e s did Greg read per day for t h e 5 days?
A 12.8 B 20 C 26 D 32.5
4. Julia's service charge at a beauty salon was $72.60, before tax. The sales tax rate was 8%. If she added 20% of the amount before tax as a tip: how much did she pay for the service at the salon?
A $87.12 B $92.93 C $100.60 D $145.20
5. On Mother's Day, Mr. Olson took Mrs. Olson a n d their daughter, Diane, t o a restaurant for d i n n e r . All three ordered the Mother's Day Special, regularly priced at $24.80. Mrs. Olson received a 40% d i s c o u n t for h e r dinner. Diane’s dinner was half price for a child's portion.
What was the total amount of the bill for the three meals after the discounts but before tax and tip were added?
A $74.40 B $52.08 C $49.60 D $47.12
6. A store sold 650 bicycles last year. This year the store sold 572 bicycles. What is the percent decrease in the number of bicycles sold from last year to this year?
A 12% B 14% C 78% D 88%
7. A dealer paid $10.000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction price. The salesperson received a commission of 25% of the difference b e t w e e n the auction price and the dealership price. What was the salesperson's commission?
A $750 B $1,750 C $3,250 D $5,500
8. Charis invested $140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
A $4.20 B $6.00 C $8.40 D $12.60
9. A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price. The customer was charged a 7% tax when the DVD was sold. What was the customer's total cost for the DVD? A $12.84 B $18.42 C $18.84 D $19.26
10. Lehana and Marty each opened a savings account with a deposit of $100.
• Lehana earned 2.5% simple interest per year. • Marty earned 2% simple interest per year. • Neither of them made additional deposits or withdrawals.
How much more did Lehana receive in interest than Marty after three years?
A $0.50 B $1.50 C $5.00 D $15.00
11. During a sale, a store offered a 40% discount on a particular camera that was originally priced at $450. After the sale, the discounted price of the camera was increased by 40%. What was the price of the camera after this increase?
A $252 B $360 C $378 D $450
12. Each sales associate at an electronics store has a choice of the two salary options shown below.
• $115 per week plus 9.5% commission on the associate's total sales • $450 per week with no commission
The average of the total sales amount for each associate last year was $125,000. Based on this average, what is the difference between the two salary options each year? (52 weeks = 1year)
A $4,262.11 B $5,545.00 C $10,956.90 D $11,525.00
13. Dimitri wants to use his 18% employee discount to buy a video game that is priced at $69.99. A 6.5% sales tax is applied to the discounted price. What will be the total cost of the video game, including the sales tax?
A $55.37 B $56.54 C $61.12 D $61.94 14. The price of a computer that was originally $374.99 was reduced to $299.50. What was the percent decrease of the price of the computer? Round your answer to the nearest tenth of a percent.
A 20.1% B 25.2% C 75.5% D 79.9%
15. A rectangular brick walkway has a length of ten feet and a width of four feet. The length and the width of the walkway will each be expanded by 25%. What will be the increase in the area, in square feet, of the walkway?
A 2.5 B 10 C 12.5 D 22.5
16. Last week, Burton paid $36.80 for 11½ gallons of gas. This week, he bought 9¼ gallons of gas. The cost per gallon of gas increased by 5% between last week and this week. How much did Burton pay for the 9¼ gallons of gas this week?
A $28.12 B $31.08 C $38.64 D $44.40
17. A clothing store used the sign shown below to advertise a discount on shirts.
DISCOUNT
Buy Two Shirts
Ky wants to buy three shirts, which were originally priced $49.96 each. The store will discount the price of the third shirt and then apply a 7.1% tax to the total cost of all three shirts. Including the tax, what will be the mean cost of each shirt?
A $41.99 B $42.70 C $44.59 D $45.18
18. Last year 950 people attended a town's annual parade. This year 1,520 people attended. What was the percent increase in attendance from last year to this year?
A 37.5% B 57.0% C 60.0% D 62.5%
19. A group of friends went to lunch. The bill, before sales tax and tip was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added. What w a s the amount, in dollars, of the sales tax? Show your work. Answer $ ______
What was the total amount the group paid, including tax and tip? Show your work.
Answer $ ______
20. The local library raised money by having a used book sale. Rebecca volunteered to help. Her task was to stick price labels on each of the 198 books on a bookshelf. In 5 minutes, Rebecca had labeled 18 books. At this rate, what was the total number of minutes Rebecca needed to label all 198 books? Show your work.
Answer ______minutes
All 198 books Rebecca labeled were priced at $1.75 per book. By 4:00 p.m., all but 80 of those books had been sold. What was the total amount of money collected from the sale of these books?
Show your work.
Answer $ ______
21. Patel bought a model rocket kit from a catalog. The price of the kit was $124.95. The state sales tax of 7% was added, and then a $10 charge for shipping was added after the sales tax. What was the total amount Patel paid, including tax and shipping cost? Show your work.
Answer $ ______
Patel received an allowance of $15 per week. How many weeks will it take him to purchase the kit? Show your work. Answer ______weeks
22. Kelsie sold digital cameras on her web site. She bought the cameras for $65 each and included a 60% markup to get the selling price, To the nearest dollar, what was the selling price for one camera?
Show your work
Answer $______
23. Mrs. Hamilton worked for a real estate agency. She sold a house for $175,000. The agency's fee for the sale was 4% of the sale price. Mrs. Hamilton received $4,725 of the agency's fee as her commission. What percent of the agency's fee did Mrs. Hamilton receive? Round your answer to the nearest tenth of a percent.
Show your work
Answer ______%
24. Daniel bought a new car for $15,000. He also paid two fees for the car dealership: $450 for an extended warranty $275 for a stereo upgrade In addition, he paid sales tax, which was 8.75% of the total cost, including the purchase price and fees. Daniel initially gave the dealership 8% of the total amount, including sales tax, as a down payment. What was the amount of the down payment? Show your work
Answer $ ______
25. A home-improvement store sold wind chimes for $30 each. A customer signed up for a free membership card and received a 5% discount off the price. Sales tax of 5% was applied after the discount. What was the final price of the wind chime?
Show your work.
Answer $ ______
26. The coach for a basketball team wants to buy new shoes for her 12 players.
Super Sports is offering a 20% · discount on each pair of shoes, which were originally priced $72.50. A 6.5% sales tax will be applied to the discounted price.
The same shoes are also available on Double Dribble's web site for $54.75. A 9% processing fee will be applied to the cost of the shoes, plus a shipping fee of $5.99 for each pair.
What is the difference in the total costs of the 12 pairs of shoes between the two stores? Show your work.
Answer $______
7EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Skills Recall mathematical properties of operations as they apply to rational numbers (integers) Recognize terms (like/unlike) Use properties of operations to combine like terms Explain the application of the commutative property to solve different types of problems. Explain the application of the distributive property to solve different types of problems. Explain the application of the associative property to solve different types of problems. Simplify, expand, and combine like terms of linear expressions with Rational Coefficients. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Resources CMP: Moving Straight Ahead: Inv. 4 Glencoe: Chapter 5: Lesson1, 2, 3, 4, 5, 6, 7, 8 Common Core Mathematics: CC.4 Big Ideas Math: 3.1, 3.2
1. Which expression is equivalent to (7x -5) – (3x – 2)?
A 10x -7 B 10x -3 C 4x – 7 D 4x -3
2. Which expression is equivalent to 2(3n – 4) – 2(n – 2)?
A 4n - 4 B 4n + 4 C 8n - 4 D 8n + 4
3. Which expression represents the sum of (2x – 5 y ) and (x + y)?
A 3x – 4y B 3x – 6y C x – 4y D x – 6y
4. The three steps shown below were used to find an expression equivalent to 2 (15x - 30y) + 10x. 5 Step 1:_?_ Step 2: 16x - 12y Step 3: 4(4x - 3y)
Which expression could be used as Step 1? 2 A (25x – 30y) B 6x - 12y + 10x C 6x - 30y + 10x D 15(x - 2y) + 10x 5
5. The expression below was simplified using two properties of operations.
5(11z + 29 + 6z) Step 1 5(11z + 6z + 29) Step 2 5(17z + 29) Step 3 85z + 145
Which properties were applied in Steps 1 and 3, respectively?
A commutative property, then distributive property B commutative property, then identity property C associative property, then distributive property D associative property, then commutative property
6. Which expression is equivalent to 4.8 + 2.2w - 1.4w + 2.4?
A 0.4(6 + 2w) B 0.8(9 + w) C 1.6(3 + 2w) D 3.6(2 + w)
7. If the perimeter of a square is 14g + 28 inches, what is the length, in inches, of each side of the square?
A 0.5g + 1 B g+2 C 2g + 4 D 3.5g + 7
8. The expression below is equal to -20g plus a constant term.
-8(2.5g – 4.25) + 5.25
What is the value of the constant term?
A -28.75 B -8 C 34 D 39.25
1 1 1 1 1 9. Which expressions below is equivalent to 2 (2 a) + 2 (1 a) + 2 (2a) 4 2 4 2 4
1 1 1 1 1 1 1 1 A 2 . (2 a) + 1 a + 2a B 2 (2 a + 1 a + 2a) C 2 (6 + a3) D 2 x 6 + a3 4 2 2 4 2 2 4 4 10. Which expression represents a factorization of 32m + 56mp?
A 8(4m + 7p) B 8(4 + 7)mp C 8p(4 + 7m) D 8m(4 + 7p)
11. Which expression is equivalent to 8c + 6 – 3c -2?
A 5c + 4 B 5c + 8 C 11c + 4 D 11c + 8
12. Which expression is equivalent to 6m + 9q - 3mq + 4m?
A 2m + 9q - 3mq B 7m + 6q C 10m + 9q - 3mq D 16mq
5 13. Which expression represents the product of 3 and ( n + 1.8)? 4
A 5.55n B 9.15n C 3.75n + 1.8 D 3.75n + 5.4
3 14. Which expression is equivalent to x + 9y? 5
3 3 3 3 A x(9y) B (9xy) C (x + 15y) D x(1+15y) 5 5 5 5
15. Which expression is equivalent to the expression - 3(4x - 2) - 2x?
A -8x B -16x C -14x - 2 D -14x + 6
16. Rewrite in simplest form.
5(4c -2d) + 2d - 6(d - 3
Simplified form ______
Write the simplified expression in factored form. Factored form ______
7EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related
Skills Recall mathematical properties of operations as they apply to rational numbers (integers) Explain that expressions in different forms can be equivalent, and rewrite an expression to represent a quantity in a different way. Generate equivalent forms of the same expression given a word problem (a 20% discount = 80% of the cost). Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related Resources CMP: Shapes and Designs: Inv 2 Moving Straight Ahead: Inv. 3, 4 Glencoe: Chapter 2: Lessons 6 Chapter 5: Lesson1, 2, 3, 4, 5, 6, 7, 8 Common Core Mathematics: 6.4, 6.6, 6.7, 9.8 Big Ideas Math: 3.1, 3.2
1. The population o f a city is expected to increase by 7.5% next year. If p represents the current population, w h i c h expression represents the expected population next year?
A 1.75p B 1.075p C p + 0.075 D 1 + 0.075
2. The expression 1.08(0.6p) represents the total amount Naomi paid for a jacket originally priced p dollars. Which changes to the original price could have resulted in this expression?
A The original price was reduced by 40% and then increased by 8%. B The original price was reduced by 40% and then increased by 108%. C The original price was increased by 60% and then increased by 8%. D The original price was increased by 60% and then increased by 108%.
3. Leo bought a used car for x dollars. One year later the value of the car was 0.88x. Which expression is another way to describe the change in the value of the car?
A 0.12% decrease B 0.88% decrease C 12% decrease D 88% decrease
4. The population of a city is expected to increase by 7.5% next year. If p represents the current population , which expression represents the expected population next year?
A 1.75p B 1.075p C p + 0.075 D 1 + 0.07 5. Sammy drew a rectangle that was w inches wide. The expression 2(2w) + 2(w) represents the perimeter of the rectangle that Sammy drew. Which statement relates the perimeter to the width of the rectangle?
A The perimeter is 6 inches more than the width. B The perimeter is 6 times the width. C The perimeter is 2 inches more than the width. D The perimeter is 2 times the width. 6. Sally has a discount card that reduces the price of her grocery bill in a certain grocery store by 5%. If c represents the cost of Sally’s groceries which expression represents Sally's grocery bill?
A 0.05c B 0.95c C c - 0.05 D c + 0.95
7. The value of x is decreased by 40%. Which expression can be used to represent this situation?
A 0.4x B 0.6x C 1- 0.4x D 1- 0.6x
8. The original selling price of a share of stock was d dollars. The selling price for a share of the same stock at a later date was represented by the expression 1.150(0.95d). Which description could explain what happened to the price of the share of stock?
A The price decreased by 5% and then increased by 0.15% B The price decreased by 95% and then increased by 0.15% C The price decreased by 5% and then increased by 15% D The price decreased by 95% and then increased by 15%
9. Cal had 52 pieces of wood to make frames. He used four pieces of wood to make each frame. Which pair of expressions both represent the number of pieces of wood Cal had left after making x frames?
A 52-4x and 4(13-x) B 52 - 4x and 4(13 - 4x) C 52x - 4x and 4(13x - x) D 52x - 4x and 4(13x - 4x)
10. Lance bought n notebooks that cost $0.75 each and p pens that cost $0.55 each. A 6.25% sales tax will be applied to the total cost. Which expression represents the total amount Lance paid, including tax?
A 0.0625(n + p) + 0.0625(0.75n + 0.55p) B (0.75n + 0.55p) + 0.0625(0.75n + 0.55p) C 0.75(0.0625n) + 0.55(0.0625n) D 0.75(1.0625n) + 0.55(1.0625n) 7EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Skills Convert among fractions, decimals, and percents. Apply properties of operations to solve real-world problems involving rational numbers in expressions and equations. Apply number sense to understand, perform operations, and solve problems with rational numbers of equations and expressions in any form. Assess the reasonableness of answers using mental computation and estimation strategies. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Resources CMP: Moving Straight Ahead: Inv. 1, 2 What Do You Expect?: Inv. 1, 2, 3, 4, 5 Glencoe: Chapter 2: Lesson 1, 2, 4, 5, 6, 7, 8 Chapter 3: Lesson 2, 4 Chapter 4: Lesson 1, 2, 3, 4, 5, 6, 8 Chapter 6: Problem solving Investigation Common Core Mathematics: 1.2, 1.3, 1.4, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8 Big Ideas Math: 6.1, 6.2, 6.4
1. David bought a computer that was 20% off the regular price of $1,080. If an 8% sales tax was added to the cost of the computer, what was the price David paid for it?
A $302.40 B $864.00 C $933.12 D $1382.40
1 2. Mark has a collection of 1,200 music CDs. He considers 6 of his collection rock music. 2 Of the rock music CDs, 20% are by s o l o artists. Of the s o l o artists, 5 are by female artists. Exactly how many of Mark's CDs are by female solo rock artists?
A 4 B 16 C 740 D 920 3 1 3. Doug earns $10.50 per hour working at a restaurant. On Friday he spent 1 hours cleaning, 2 4 3 5 hours doing paperwork, and 1 hours serving customers. What were Doug’s earnings? 12
A $46.97 B $47.25 C $53.00 D $57.75
4. Salid bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including sales tax. If Sal id paid with a $100.00 bill, how much change should he have received?
A $20.00 B $38.75 C $61.25 D $80.00
5. What is the value of the expression below? 1 3 (3 - 9 2 4 ) ÷ (-2.5)
A -2.5 B -2.3 C 2.3 D 2.5
6. What is the value of the expression below?
1 3 (3 - 9 ) ÷ (-2.5) 2 4
A -2.5 B - 2.3 C 2.3 D 2.5
7. A corporation had $125,000 in a bank account on March 1. On April 1, the amount of money in the account had decreased by 8%. On May 1, the amount of money in the account was half of the amount that was in the account on April 1. How much money was in the account on May 1?
A $52,500 B $57,500 C $62,500 D $67,500
1 8. Ms. Donaldson earns $18.80 per hour for the first 40 hours she works in a week. She earns 1 2 times that amount per hour for each hour beyond 40 hours in a week. Last week Ms. Donaldson worked 45.5 hours. How much money did she earn? Show your work
Answer $______
A health insurance payment of $34.55 was deducted from Ms. Donaldson's earnings for the week. After the insurance deduction, payroll taxes equal to 28% of the balance were deducted. What was the amount that Ms. Donaldson received? Show your work
Answer $______
9. A scientist uses a submarine to study ocean life She begins at sea level, which is at an elevation of 0 feet She travels straight down for 90 seconds at a speed of 3.5 feet per second She then travels directly up for 30 seconds at a speed of 2.2 feet per second. After this 120-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at the submarine’s maximum speed of 4.8 feet per second? Round your answer to the nearest tenth of a second.
Show your work
Answer ______seconds
10. Trent is fishing from a pier.
3 • The tip of his fishing rod is 53 feet above the surface of the water. 4 2 • The hook on the end of the fishing line is directly below the tip of the fishing rod 12 3 feet below the surface of the water.
Trent estimates that the distance between the tip of his fishing rod and the hook isless than 65 feet. Is Trent's estimate reasonable? Explain your answer. Answer ______
______
______Trent lets his hook drop another 10 inches. What is the distance, in feet, between the tip of the fishing rod and the hook? Do not round your answer. Show your work.
7EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
Skills Select appropriate variables to represent unknown quantities. Identify the correct operation used to write and solve for unknown values. Identify the correct sequence of the operations used to solve an algebraic equation. Evaluate, simplify, and solve equations. Construct algebraic equations from real-world problems by reasoning. Graph solutions of inequalities on a number line. Interpret solutions of inequalities from graphs. Model real-world problems using graphs to demonstrate inequalities including negative coefficients. Graph the solution set of the inequality and interpret it in the context of the problem Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach Resources CMP: Shapes and Designs: Inv 2, 3 Stretching and Shrinking: Inv. 4 Moving Straight Ahead: Inv. 1, 2, 4 Glencoe: Chapter 6: Lesson1, 2, 3, 4, 5, 6, 7, 8, Common Core Mathematics: 4.1, 4.2, CC.5, CC.6 Big Ideas Math: 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, 4.4
7EE.4a 1. Carmine paid an electrician x dollar per hour for a 5-hour job plus $70 for parts. The total charge was $320. Which equation ca n be used to determine h o w much the electrician charged per hour?
A 5x = 320 + 70 B 5x = 320 - 70 C (70 + 5)x = 320 D (70 - 5)x = 320
2. Katie bought 4 sweaters that each cost the same amount and 1 skirt that cost $20. The items she bought cost a total of $160 before tax was added. What was the cost of each sweater?
A $20 B $35 C $40 D $45
3. Which steps can be used to solve for the value of y? ⅔ (y + 57) = 178
A divide b o t h sides by ⅔, then subtract 57 from both sides B subtract 57 from both sides, then divide both sides by ⅔ C multiply both sides by ⅔, then subtract 57 from both sides D subtract ⅔ from both sides, then subtract 57 from both sides
4. Roberto bought snacks to take to his soccer team's practice. He bought a bag of oranges for $5.65, and he bought a 12-pack of water bottles. The total cost was $12.13 before tax was added. Which equation can be used to determine b, the price for each bottle of water?
A 12(b + 5.65) =12.13 B 5.65b + 12=12.13 C 5.65(12)+ b =12.13 D 12b + 5.65 = 12.13 5. Solve for x : 0.5 x + 78.2 = 287
A x = 104.4 B x = 417.6 C x = 495.8 D x = 730.4
6. Katie bought 4 sweaters that each cost the same amount and 1 skirt that cost $20. The items she bought cost a total of $160 before tax was added. What was the cost of each sweater? A $20 B $35 C $40 D $45
7. . Ruby bought 6 magazines that cost $4.44 each. She also bought a paperback book. The total price for these items before tax was $33.96. What was the price of the book?
A $4.92 B $5.66 C $7.32 D $10.10
8. The perimeter of a certain pentagon is 10.5 centimeters. Four sides of this pentagon have the same length, in centimeters, h, and the other side has a length of 1.7 centimeters, as shown below.
What is the value of h?
A 2.2 B 3.7 C 4.8 D 8.8
9. Dustin bought three shirts and a belt. Each shirt cost the same amount of money, and the belt cost $22.50. If the total amount Dustin paid was $69.75 before tax, what was the price of each shirt before tax?
A $15.75 B $17.44 C $23.06 D $23.25 10. Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6 plus $3 per mile. The total fare was $24, not including the tip. How many miles did Mike travel by taxi on this ride?
A 2 B 6 C 8 D 10
11. When Keisha installed a fence along the 200-foot perimeter of her rectangular back yard, she left an opening for a gate. In the diagram below, she used x to represent the length, in feet, of the gate.
What is the value of x?
A 10 B 20 C 25 D 30 12. Mr. Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some bracelets that cost $4.50 each, including tax. Write an equation to determine x, the maximum number of bracelets Mr. Gonzales could buy. Equation ______
Solve the equation to determine the number of bracelets Mr. Gonzales could buy.
Show your work
Answer ______bracelets
13. Jackie bought 2 packages of paper for $5.80 each and 4 notebooks for d dollars each. She spent a total of $32 for the packages of paper and the notebooks. Write an equation, using d that represents the situation above.
Equation______Solve your equation and write the cost of 1 notebook in the answer blank. Show your work. Answer $______Jackie returned to the store later that day and bought n more notebooks at the same price. This time she used a store coupon for $3.50 off her entire purchase. The total she spent was more than $18. Write an inequality to represent this situation. Inequality______What was the least number of notebooks that Jackie could have bought this time?
Answer______notebooks
14. Members of a baseball team raised $967.50 to go to a tournament. They rented a bus for $450.00 and budgeted $28.75 per player for meals. They will spend all the money they raised.
Write and solve an equation that models this situation and could be used to determine the number of players, p, the team could bring to the tournament.
Show your work
Answer ______players
15. Keith and Jolene raised $152.75 to buy shirts for new players on their softball teams. Jolene needs to buy four shirts for her team. Each shirt will cost $11.75. Write an equation that can be used to determine the maximum number of shirts Keith can buy for his team in addition to the four shirts Jolene needs to buy.
Equation ______What is the maximum number of shirts Keith can buy for his team in addition to the four shirts Jolene needs to buy?
Show your work Answer _____shirts
16. Ms. Hernandez has $100 to spend on parking and admission to the zoo. The parking will cost $7, and admission tickets will cost $15.50 per person, including tax. Write and solve an equation that can be used to determine the number of people that she can bring to the zoo, including herself.
Show your work.
Answer ______people
7EE.4b 1. Craig went bowling with $25 to spend. He rented shoes for $ 5.25 and paid $ 4.00 for each game. What was the g r e a t e s t number of games Craig could have played? A 4 B 5 C 6 D 7
2. For her cell phone plan, Heather pays $30 per month plus $0.05 per text. She wants to keep her bill under $60 per month. Which inequality represents the number of texts, t, Heather can send each month while staying within her budget? A t < 600 B t > 600 C t < 1,800 D t > 1,800
3. Jaime's summer homework assignment is to read more than 500 pages of books or magazines. He read a book that had 282 pages. He plans to complete the rest of the assignment by reading 20 pages a day. Which inequality can be used to determine t, the number of days Jaime needs to read to complete his assignment?
A 20t + 282 < 500 B 20t + 282 > 500 C 282t + 20 < 500 D 282t + 20 > 500
4. Ben earns $9 per hour and $6 for each delivery he makes. He wants to earn more than $155 in an 8-hour workday. What is the least number of deliveries he must make to reach his goal?
A 11 B 12 C 13 D 14
5. Addison wants to ride her bicycle more than 80 miles this week. She has already ridden her bicycle 18 miles. Which inequality could be used to determine the mean number of miles, m, she would need to ride her bicycle each day for six more days to achieve her goal?
A 6m + 18 < 80 B 6m - 18 < 80 C 6m + 18 > 80 D 6m - 18 > 80
6. A trailer will be used to transport several 40-kilogram crates to a store. The greatest amount of weight that can be loaded onto the trailer is 1,050 kilograms. An 82-kilogram crate has already been loaded onto the trailer. What is the greatest number of 40-kilogram crates that can also be loaded onto the trailer?
A 24 B 25 C 26 D 27
7. Harper has $15.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 eacn and one box of crackers that costs $3.50.
Write and solve an inequality that models this situation and could be used to determine the maximum number of bags of fruit, b, Harper can buy. Show your work
Answer ______bags of fruit.
6SP2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
1. The test scores of the students in Mr. Duffy's class are shown on the line plot below.
Most of the students in Ms. Guzman's class scored higher than most of the students in Mr. Duffy's class on the same test. Which line plot could represent the test scores of the students in Ms. Guzman's class?
6 SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
1. Jared surveyed the students in his class to determine how they scored in a game. He displayed his results in the table shown below.
GAME SCORES
Score (points) Number of students
0 to 4 5
5 to 9 10
10 to 14 3
15 to 19 Which histogram represents the data in the table?
7SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
Skills Identify correct population sector for taking a given sample population Demonstrate examples of representative bias and insufficient samples. Infer valid statistics about a population based on random sampling. Draw conclusions about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Resources CMP: Samples and Populations: Inv. 2 Glencoe: Chapter 10: Lesson1, 2, 3 Common Core Mathematics: 11.4 Big Ideas Math: 10.6 1. Cassie rolls a fair number cube with 6 faces labeled 1 through 6. She rolls the number cube 300 times. Which result is most likely?
A Cassie will roll a 1 or a 2 about 50 times. B Cassie will roll a 1 or a 2 exactly 50 times. C Cassie will roll an even number about 150 times. D Cassie will roll an even number exactly 150 times.
2. The junior h i g h school principal designed a survey to find o u t which new foods students would b u y in the cafeteria. Which method of sampling will h e l p the principal make a valid decision about which foods to add to the lunch menu?
A Give the survey to every student in the eighth grade. B Give the survey to every student taking a science class after lunch. C Give the survey to every student who walks or rides a bicycle to school. D Give the survey to every third student entering the building in the morning.
3. A school principal wants to determine which type of speaker the students prefer to invite to an assembly for the entire student population. , Which survey method would produce the best representative sample?
A survey every fifth person who shops at a mall B survey all of the students on the student council C survey every tenth student entering the school one morning D survey all of the students who went to the last basketball game
4. Carol is planning her company's holiday party. She wants to survey a small group of her coworkers to determine the favorite type of food among all the employees at the company. Which method would result in a sample that is not representative of the population?
A Select every fourth employee that enters the company's building one day. B Select 45 randomly chosen employees exercising at the company's gym one day. C Select every fifth employee on an alphabetical list of all employees at the company. D Select 80 names from a jar that contains the names of all employees at the company 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
Skills Explain variation in random samples. Make predictions based on possible outcomes and from compiled data.. Apply the principles of probability to solve problems in real world contexts. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Resources CMP: Samples and Populations: Inv. 2 Glencoe: Chapter 10: Lesson1, 2 Common Core Mathematics: 11.5, CC.13 Big Ideas Math: 10.6 1. Laticia randomly selected 25% of the seventh-grade students in her school and asked them their favorite s e a s o n . Of the students surveyed, 51 chose summer as their favorite season. Based on the data, what is the most reasonable prediction o f the number of seventh-grade students in her school who would choose summer as their favorite season?
A 15 B 75 C 150 D 200 2. Brendan surveyed a group of students selected at random from the 420 students in his high school. He asked them to pick one favorite indoor gym activity from four choices. The table shows the survey results.
Based on the data recorded in the table above, which of the following can most likely be the number of students in his school who prefer kickball
A 70 B 110 C 130 D 150 3. To select a new school mascot, 20 randomly selected students in each grade were asked to choose between the two finalists: tiger and eagle. The results are shown below.
PREFERRED MASCOT
Grade Tiger Eagle 5 14 6 6 13 7 7 8 12 8 5 15
Which statement is best supported by the results? A The preferred mascot is a tiger. B The preferred mascot is an eagle. C Fifth and sixth grade students at the school preferred an eagle mascot. D Seventh and eighth grade students at the school preferred an eagle mascot.
4.The student council is holding elections for seventh-grade class president. Virginia surveys a representative sample of seventh-grade students at her school to determine for which candidate each student will vote. The results are in the table below.
STUDENT VOTES Candidate Number of votes Jeanette 5 Raymond 8 Shay 14 Charles 7 Use the results of Virginia’s sample to predict which candidate will receive the most votes during the actual election. Justify your answer.
Answer
5. Two math classes took the same quiz. The scores of 10 randomly selected students from each class are listed below. • Sample of Class A: 75, 80, 60, 90, 85, 80, 70, 90, 70, 65 • Sample of Class B: 95, 90, 85, 90, 100, 75, 90, 85, 90, 85 Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in Class A compared to all the students in Class B? Explain your reasoning to justify your answer. ______
______7SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
Skills Represent and draw conclusions for 2 data sets using a table, graph, dot plot, and box plot. Calculate, compare, and interpret the mean, median, upper quartile, lower quartile, and inter- quartile range for two sets of data. Calculate Mean Absolute Deviation Analyze and summarize data sets, including initial analysis of variability. Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Resources CMP: Samples and Populations: Inv. 1, 3 Glencoe: Chapter 10: Inquiry Lab Common Core Mathematics: CC.12 Big Ideas Math: 10.7
1. Two schools used can recycling as a school project last year. They both recorded the number of cans recycled per week for 20 weeks. The data is displayed in the box-and-whisker plots below. Which conclusion is best supported by the data?
A The range of the Lincoln School data was 40 greater than the range of the Adams School data. B The median numbers of cans collected at both schools was approximately the same. C Adams School had the least and the greatest number of cans recycled per week
D Lincoln School recycled more cans per week than Adams School for more than half of the weeks in the 20-week period
2. Ms. Andrews made the line plots below to compare the quiz scores for her first-period math class and her second-period math class. She gave the same quiz to each class.
What conclusion can Ms. Andrews make about the performance of her first- and second- period classes?
A The first period class had a higher median score than the second period class B The second period class scores had a higher mean than the first-period class scores. C The first period class scores had a greater range than the second period class scores. D The second-period class scores had a greater mean absolute deviation than the first period class scores.
3. An electronic sign that showed the speed of motorists was installed on a road. The line plots below show the speeds of some motorists before and after the sign was installed.
Based on these data, which statement is true about the speeds of motorists after the sign was installed?
A The mean speed and the range of the speeds of the motorists decreased. B The median speed and the range of the speeds of the motorists increased. C The mean speed of the motorists decreased and the range of the speeds increased. D The median speed of the motorists increased and the range of the speeds decreased. 7SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Skills Compare two sets of data using measures of center and variability Draw informal comparative inferences about two populations Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book Resources CMP: Samples and Populations: Inv. 1 Glencoe: Chapter 10: Lesson 4 Common Core Mathematics: Activity Lab 1.10b Big Ideas Math: 10.7
1. The Grant family had a garage sale. The prices, in dollars, of the items that were sold are shown below. $12 $17 $32 $8 $22 $5 $38 $42 $11 $12 $27 $25 $35 $55 $13 $5 $3 $26 $47 $61 Which graph represents the data?
2. The box plots below show the scores on last week's test for 10 randomly selected students from each of Mr. Brenner's two mathematics c l a s s e s .
Which statement about the performance of the students in the two classes is best supported by the data from these samples?
A The two classes performed e q u a l l y well because the range of each class is the same. B The two classes performed equally well because the greatest s c o r e in each class is the same. C The students i n Class Y generally performed b e t t e r t h a n the students i n Class X because most students i n Class Y had a score greater than 70. D The students i n Class Y generally performed b e t t e r t h a n the students i n Class X because the median of Class Y is greater than that of Class X. 3. A regional manager of a tire distributor is collecting information to compare the sales of tires in two stores. The numbers of tires sold weekly by each store for five randomly selected weeks are shown in the table below.
What comparison can the regional manager make from the sales data for the two stores?
A The range of the number of tires sold weekly by Store M was greater than the range of the number of tires sold by Store N. B The range of the number of tires sold weekly by Store N was greater than the range of the number of tires sold by Store M. C The median of the number of tires sold weekly by Store M was greater than the median of the number of tires sold by Store N. D The median of the number of tires sold weekly by Store N was greater than the median of the number of tires sold by Store M.
4. A random sample of the numbers of miles that two people drove each day last month is shown below. Martina: 32, 41, 36, 54, 32, 12, 24 William: 26, 24, 10, 18, 40, 21, 15
Which of these statements is best supported by these data?
A William has the greater median and mean, so he generally drove farther last month than M a r t i n a . B Martina has the greater median and mean, so she generally drove farther last month than William. C William has the greater median and Martina has the greater mean, so William generally drove farther last month than Martina. D Martina has the greater median and William has the greater mean, so Martina generally drove f arther last month than William. 5. Malika and Adrian prepared containers of potato salad at a deli. Each container was supposed to h a v e a mass of one pound. The manager selected a random sample of containers prepared by each employee to check the mass of each container. The results are shown in the table below.
MASS OF EACH CONTAINER Malika’s Container Adrian’s Container (pounds) (pounds) 1.10 1.30 1.08 1.21 1.05 0.79 0.95 0.90 0.98 0.88
Which inference is best supported by these data? A Malika will produce more containers with a mass of exactly one pound than Adrian will. B Adrian will produce more containers with a mass of exactly one pound than Malika will. C Most of Malika's containers will have a mass closer to one pound than most of Adrian’s containers. D Most of Adrian's containers will have a mass closer to one pound than most of Malika's containers.
6. The lists below show the number of points scored by Lin and Vivi in five randomly selected basketball games this season.
Lin: 2, 3, 7, 8, 8 Vivi: 3, 5, 6, 9, 11
Which statement is best supported by the data?
A Vivi tends to score more points because her mean score is greater than Lin's. B Vivi tends to score more points because the range of her scores is greater than Lin's. C Lin tends to score more points because the median of her scores is greater than Vivi's. D Lin tends to score more points because the interquartile range of her scores is greater than Vivi's. 7SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Skills Explain how the probability of an event is expressed as a fraction. Represent the probability of events that are impossible, unlikely, likely and certain using rational numbers from 0 to 1. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Resources CMP: What Do You Expect?: Inv. 2, 4, 5 Glencoe: Chapter : Lesson 1, 5 Common Core Mathematics: 12.1 Big Ideas Math: 10.1, 10.2, 10.3
1. A box contains congruent c o l o r e d cubes. 6 9 of the cubes are blue of the cubes are green 24 24 7 2 of the cubes are red of the cubes are yellow 24 24
Dina will choose a cube from the box without looking. Which color cube is Dina most likely to choose?
A blue B green C red D yellow 1 2. Sara is playing a board game. The probability that Sara will score a point on her next turn is 3 Which statement describes the probability that Sara will score a point on her next turn?
A likely B certain C unlikely D impossible
1 3. Sara is playing a board game. The probability that Sara will score a point on her next turn is . 3 Which statement describes the probability that Sara will score a point on her next turn?
A likely B certain C unlikely D impossible
4. Which event is most likely to occur?
A flipping a fair coin, with sides labeled heads and tails, and the coin landing on tails B choosing a marble out of a bag, with nine blue marbles and one red marble, and the marble being red C rolling a fair number cube, with faces labeled one to six, and the cube landing on a number less than six D spinning the arrow on a spinner, with four equal sectors labeled one to four, and the arrow landing on a number greater than one 7SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
Skills Define theoretical probability and proportions Design, perform, and collect data on a chance event Analyze data from tables (frequency), graphs and plots to determine probabilities of an event Use probability to predict outcomes of long-run or repeated/ larger events Organize collected data from experiments performed in tables, graphs, and plots. Compare theoretical and experimental probability using the “Law of Large Numbers.” Use theoretical probability and proportions to make approximate predictions. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Resources CMP: What Do You Expect?: Inv. 1, 2, 3, 4 Glencoe: Chapter 9: Inquiry Lab Common Core Mathematics: 12.1, 12.2. Activity Lab 12.2a Big Ideas Math: 10.3
1. The spinner below has 8 sectors labeled with letters. Each sector of the spinner below is the same size, as shown.
If the arrow is spun 400 times, how many times would it be expected to land on a sector labeled B?
A 50 B 100 C 150 D 25
2. A storeowner made a list of the number of greeting cards sold last month. The store sold 167 thank-you cards, 285 birthday cards, and 56 blank cards. Based on these data, which number is closest to the probability that the next customer will buy a blank card?
A 0.11 B 0.33 C 0.56 D 0.89
3. An owner of a small store knows that in the last week 54 customers paid with cash, 42 paid with a debit card, and 153 paid with a credit card. Based on the number of customers from last week, which fraction is closest to the probability that the next customer will pay with cash?
1 1 1 1 A B C D 5 4 3 2 4. An online flower service sells boxes of roses. Each box contains one dozen roses of only one color-either red, white, or pink. The colors chosen for the last 1,000 orders are shown in the table below.
COLOR OF ROSES SOLD
Color Frequency Red 677 Pink 109 White 214
Based on the last 1,000 orders, about how many boxes out of the next 100 orders will be for white or pink roses?
A 11 B 21 C 32 D 48
5. Julia has a jar that contains a mixture of dimes and pennies. She reaches into the jar without looking and selects a coin. She repeats this process 14 times, which results 8 dimes and 6 pennies. Based on these results, about how many pennies can she expect if she randomly selects a total of 70 coins?
A 24 B 30 C 40 D 53
6. The school bus Evie rides is scheduled to arrive at her stop at 8:20 a.m. each day. The table b e l o w shows the actual arrival times of the bus for several days that were randomly selected over t h e past few months.
BUS ARRIVAL TIMES (a.m.) 8:21 8:21 8:19 8:20 8:23 8:22 8:20 8:18 8:20 8:18 8:21 8:20 8:19 8:19 8:25 8:20 8:20 8:18 8:17 8:24
Based on these data, what is the probability that the bus will arrive at Evie's stop before 8.20 a.m. tomorrow?
3 1 7 13 A B C D 10 3 20 20 7. The results of a survey of 120 students who were selected randomly are listed below:
60 students have a cell phone plan with company X 36 students have a cell phone plan with company Y 24 students do not have a cell phone The total population of students was 380. Based on the data, what is the best approximation for the total number of students who have a cell phone plan with company Y?
A 114 B 127 C 143 D 163
8. An after-school program offers tutoring for different subjects. During the last month, a teacher recorded the number of students who participated in tutoring in each subject, as shown in the table below.
TUTORING PARTICIPATION Subject Number of students Math 40 Science 55 English 47 History 58
Explain how the teacher could use these data to predict about how many of the next 100 students will participate in math tutoring.
______
______
______7SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
Skills Predict frequencies of outcomes based on theoretical probability Recognize an appropriate design to conduct an experiment with simple probability events. Develop a probability model to predict outcomes based on a series of random events (experimental probability). Use a variety of experiments to explore the relationship between experimental and theoretical probabilities and the affect of sample size on this relationship. Recognize the frequency of outcomes based on theoretical probability. Compare outcomes from theoretical to experimental probability. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected Resources CMP: What Do You Expect?: Inv. 3,5 Glencoe: Chapter : Lesson 1, 2 Common Core Mathematics: 12.2. Activity Lab 12.2a Big Ideas Math: 10.2, 10.3
1. Cynthia conducted an experiment with a spinner that contained only 4 sectors: F, G, H, and J. She spun the arrow 40 times and recorded the frequencies in the table below.
Based on the data, what is the probability that the next spin will land on H?
1 1 3 3 A B C D 4 3 8 5 2. A cereal company puts a colored ring in each box of cereal. There are 6 different ring colors. The colors of the rings in each of 50 cereal boxes are shown in the table below.
RING COLORS IN CEREAL BOXES Color Number of rings Red 7 Blue 15 Green 8 Purple 10 Yellow 5 Orange 5
Based on the data, what is the probability that the next cereal box will contain a blue or a yellow ring?
1 2 3 2 A B C D 6 5 5 3 7SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events.
Skills Compare frequency of events based on a mode. Develop a uniform probability model by assigning equal probability to all outcomes and use it to determine probability of events. Develop a non-uniform probability model by assigning unequal probability to all outcomes Explain and justify discrepancy of events from observed frequencies. Compare probability from models to observed frequencies Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Resources CMP: What Do You Expect?: Inv. 1, 2, 3, 4, 5 Glencoe: Chapter : Lesson 3, 4, 5, 6, 7 Common Core Mathematics: 12.3, 12.4 Big Ideas Math: 10.4, 10.5
1. Which tree diagram shows all of the possible outcomes for tossing a coin and rolling a fair number pyramid that has four sides labeled 1 through 4? 2. Henry has a fair number pyramid with four faces and a spinner with three equal-sized colored sections. The possible outcomes for each are shown below.
What is the probability that the number pyramid will land on three and the spinner will stop on blue?
1 3 4 7 A B C D 12 12 12 12 7G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Skills Calculate scale factor between corresponding lengths in similar objects. Calculate actual lengths of corresponding sides when given a scale factor. Create a similar drawing through enlarging or shrinking by incorporating the scale factor. Calculate area of actual shape when given scale drawing.. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Resources CMP: Stretching and Shrinking, Inv. 1, 2, 3, 4 Glencoe: Chapter 7: Lesson Common Core Mathematics: 5.5, 5.6 Big Ideas Math: 7.5 1. The scale drawing below represents the side of a ramp. In the scale drawing, one inch equals three feet.
What is the actual area, in square feet, of the side of the ramp?
A 0.5 B 3 C 4.5 D 9
2. The drawing below represents a rectangular garden. In the scale drawing, one inch equals 30 yards.
What is the actual area of the garden?
A 3 sq yd B 90 sq yd C 210 sq yd D 2,700 sq yd 3. The drawing of a road around a lake, shown below, has a scale of 1 inch to 4 kilometers.
What is the total distance, in kilometers, of the actual road?
A 12 B 24 C 48 D 96
4. The drawing of a building, shown below, has a scale of 1 inch to 30 feet.
What is the actual height, in feet, of the building?
A 22.5 B 24 C37.5 D 40
5. An artist is making a mural by reproducing a painting at a different scale. The original painting is 10½ inches long and 4 inches wide. The mural will cover an entire wall that is 52.5 feet long and 20 feet wide. What will be the scale that relates the original painting to the mural?
A inch = 1 foot B inch = 5 feet C inch = 25 feet D inch = 60 feet 6. A scale drawing of a rectangular park has a scale of 1cm = 120 m.
What is the actual perimeter of the park in meters? Show your work
Answer ______meters 7G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Skills Recall that the combined angle measures of a triangle equals 180 degrees. Construct shapes, focusing on the drawing of triangles with given measurements. Distinguish between different types of angles. Apply knowledge of geometric terms to draw geometric shapes with given conditions, which should include: Parallel lines, angles, perpendicular lines, line segments, etc. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle Resources CMP: Shapes and Designs: Inv. 1, 2, 3 Stretching and Shrinking: Inv. 3 Glencoe: Chapter 7: Lesson 3 Common Core Mathematics: CC.8 Big Ideas Math: 7.3, 7.4
7G.3 Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids
Skills Examine parallel and perpendicular cross sections of three-dimensional figures. Slice (dissect) 3-dimensional figures into 2-dimensional cross sections Evaluate the two-dimensional cross sections that result from the dissecting of the three- dimensional shape. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Resources CMP: Filling and Wrapping: Inv. 2 Glencoe: Chapter 7: Lesson 5, 6 Common Core Mathematics: CC.9 Big Ideas Math: Extension 9.5 7G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Skills Show the relationship between the circumference and the diameter expressed as pi Derive the formula for the area of a circle and the circumference of circle. Determine the relationship between the circumference and area of a circle. Determine the area of complex or composite figures Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Resources CMP: Filling and Wrapping: Inv. 3 Glencoe: Chapter 8: Lesson1, 2, 3, Common Core Mathematics: 8.5 Big Ideas Math: 8.1, 8.2, 8.3, 9.3
1. A circle has a radius of 2.6 centimeters. What is the circumference, in centimeters, of the circle?
A 2.6 π B 5.2 π C 6.76 π D 13.52 π
2. What is the area, in square centimeters, of a circle with a diameter of 12 centimeters?
A 12 π B 24 π C 36 π D 144 π
3. The circumference of a circle is 18π centimeters. What is the area, in square centimeters, of this circle?
A 9 π B 36 π C 81 π D 324 π
4. What is the radius, in centimeters, of a circle that has a circumference of 16 centimeters?
A 8 B 16 C 32 D 64
5. The mean radius of Earth is 6,371.0 kilometers and the mean radius of Earth's Moon is 1,737.5 kilometers. What is the approximate difference in the mean circumferences, in kilometers, of Earth and Earth's Moon? Round your answer to the nearest tenth of a kilometer.
A 40,030.2 B 29,113.1 C 14,556.6 D 10,917.0 6. Kevin made a round pizza that fit in the square box as shown below.
What is the area, rounded to the nearest tenth of a square inch, of the pizza?
A 50.3 B 201.1 C 402.1 D 804.2
7. A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 18 centimeters. The blueprint has a scale of three centimeters to four feet. What will be the actual area of the base of the fountain, in square feet, after it is built? Round your answer to the nearest tenth of a square foot.
Show your work.
Answer ______square feet
8. The circumference of a circle is 11π inches. What is the area, in square inches, of the circle? Express your answer in terms of π
Show your work
Answer ______square inches 7G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Skills Interpret facts about angles that are created when a transversal cuts parallel lines. Explain why the sum of the measures of the angles in a triangle is 180 degrees. Apply knowledge about triangles to find unknown measures of angles. Identify and draw complementary angles, supplementary angles, vertical angles, and adjacent angles. Apply algebraic concepts to solve for unknown measures. Interpret information in a word problem about angles to write and solve equations Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Resources CMP: Shapes and Designs: Inv. 1, 2, 3 Glencoe: Chapter 7: Lesson 1,2 Common Core Mathematics: 7.2 Big Ideas Math: 7.1, 7.2
7G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Skills Recall the formulas for area, surface area and volume of two and three-dimensional figures. Apply the understanding of two- and three-dimensional figures to solve real-world problems. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Resources CMP: Filling and Wrapping: Inv. 1, 2 Glencoe: Chapter 8: Lesson 3, 4, 5, 6, 7, 8 Common Core Mathematics: 8.2, 8.3, 8.4, 8.9, 8.10 Big Ideas Math: 8.4, 9.1, 9.2, 9.4, 9.5