Objective Week 3.1: Ratios, Proportions, and Rates
Unit 3 Benchmark Questions – Multiple Choice Question 1 Suppose you need to make a batch of purple clay. The recipe says you need to eight cups of red clay and twelve cups of blue clay. What is the simplest form of this ratio? a. 12:8 b. 8:12 c. 4:6 d. 2:3
Week 3.2: Operations with Integers
–6 + (–3) = a. 9 b. -‐9 c. 3 d. -‐3 Week 3.3: Read, Which algebraic equation matches write, and simplify this verbal phrase? algebraic equations 8 minus the product of 5 and a number is 23 a. 5n – 8 = 23 b. 8 – 5 – n = 23 c. 8 – 5n = 23 d. 8 – n5 = 23
Week 3.4: One-‐ step equations
Which step shows the correct inverse operations? x + (–3) = 24 a. x + (–3) – (–3) = 24 – (–3)
Question 2 Which proportion is correct? ! ! a. !" !! ! ! b. !!! c. !!!!! ! ! d. !" !! €
Question 3 Complete this proportion.
19 + (–19) = a. 0 b. -‐38 c. 38 d. -‐0 Which terms are like terms? 8c + 3d – 2c + 5d a. 8c, 3d, and 5d because they are positive b. 8c and 2c because they are both even c. 2c and 5d because they are next to each other d. 8c and 2c because they have the same variable Solve.
7 – (– 9) = a. 2 b. -‐2 c. 16 d. -‐16 Simplify: 2 (d – 4) a. 2d – 4 b. 2d – 8 c. 2d + 8 d. 2d + 4
–17 – a = 37 b. a = -‐44 c. a = 37
c. (–3) + 3 = 24 + 3
d. a = 17
d. x + (–3) = 24
=
25
a. 45 b. 29 c. 5 d. 1
–7 + (–3) -‐ 6 = a. 4 b. -‐4 c. 16 d. -‐16 Simplify: 14 + k – 7 + 8 = 1 a. 15 + k = 1 b. 16 + k c. k + 29 = k d. k = 16
In order to isolate the variable, what will you have to do?
Solve.
w =9 12
–3x = 45
a. a = 44
b. x – x + (–3) = 24
9 5
Question 4 Write as a unit rate. 240 miles in 6 hours a. 120 miles per two hours b. 4 miles per hour c. 40 miles per hour d. 236 miles per hour
a. multiply x by -‐3
a. w = 180
b. multiply x by 45
b. w = 3
c. divide x by -‐3
c. w = ¾
d. divide x by 3
d. w = 108
Week 3.5: Two-‐ step equations
€ Week 3.6: Complex Equations
Which step do you complete first? x 3 +13 = 21 a. divide by 3 on both sides b. subtract 21 from both sides c. subtract 13 from both sides d. multiply by 3 on both sides Solve: 45 + 9 = 3x + 21 a. x = 25 b. x = 11 c. x = 22 d. x = 99
To solve the equation 11x -‐ 9 = –4, which operation do you do second? a. add 9 b. subtract 9 c. multiply by 11 d. divide by 11
Solve for x: ½ x – 4 = 10 a. x = 6 b. x = 7 c. x = 28 d. x = 3
Solve for x: 3x + 6 = 21 a. x = 490 b. x = 910 c. x = 7.428 d. x = 4
Solve: 3x – 4 = 2 + x a. x = 3 b. x = ½ c. x = -‐2 d. x = 2
What equation represents the following problem? Vanessa went back to school shopping with $50. She needs to buy one sharpener and some pencils. If each pencil costs a quarter and one sharpener costs $2, how many pencils can she buy? a. $50 -‐ $2 = p + $0.25 b. p = $50 -‐ $0.25 c. 50 = $2 + $0.25 p d. $50 – p = $2
Monique went to Starbucks to do LW with some friends. She buys a cup of hot chocolate for each of her friends. The hot chocolate costs $3 a cup. If she starts out with $40 and leaves with $19, how many cups of hot chocolate did she buy? a. 7 cups of hot chocolate b. 63 cups of hot chocolate c. 16 cups of hot chocolate d. 0.5 cups of hot chocolate
Unit 3 Benchmark Questions – Constructed Response Objective Week 3.1: Ratios, Proportions, and Rates
Question The Fish Bowl store had a sale. During the sale, the store gave away two kinds of fish, goldfish and catfish. • Every 5th customer received a free goldfish. • Every 12th customer received a free catfish. There were 134 customers on the day of the sale. a. How many customers received a free goldfish? Show or explain how you got your answer. b. How many customers received a free catfish? Show or explain how you got your answer. c. How many customers received both a free goldfish and a free catfish? Show or explain how you got your answer.
Week 3.2: Operations with Integers
Roman Civilization began in 509 B.C. and ended in 476 A.D. 1. Draw a timeline to show the dates. 2. How long did Roman Civilization last? Explain how you got your answer. 3. Explain how you can check to know that your answer is correct. Week 3.3: Read, A coach is collecting a fee from each player on her soccer team. She collects the same amount of money from each player. The amount of money write, and simplify she collected over four days from some of the players is shown in the table below. algebraic equations Soccer Fees Collected Number of Amount Day Players Collected
1. 2. 3.
Week 3.4: One-‐ step equations
Monday
4
$ 88
Tuesday
7
$154
Wednesday
6
$132
Thursday
3
$ 66
Friday
2
?
On Friday, the coach will collect fees from 2 more players. What is the total amount of money the coach will collect from the 2 players? Show or explain how you got your answer. Use words or symbols to write or describe a rule that can be used to calculate the amount of money the coach will collect from p players. After every player on her team has paid the fee, the coach will have collected a total of $550. What is the total number of players on the soccer team? Show or explain how you got your answer.
At a recycling center in his state, Cody receives $0.05 for every can he returns. In the equation below, • m represents the total amount of money that Cody receives, and • c represents the total number of cans he returns. m = 0.05c a. What is the total amount of money that Cody receives for returning 10 cans? Show or explain how you got your answer.
Week 3.5: Two-‐ step equations
Cody received a total of $10 for the cans he returned last week. b. What was the total number of cans Cody returned last week? Show or explain how you got your answer. Cody's cousin lives in another state. She receives $0.05 more than Cody for every can she returns. c. Write a new equation to determine the total amount of money, m, Cody's cousin receives for returning c cans in this other state. Explain your reasoning. Here’s Ms. Joyce’s problem and work shown. 20 + 2w = 50 20 + 2w / 2 = 50 /2 20 + w = 25 20 – 20 + w = 25 – 20 w = 5 She got the problem wrong because she did not get w = 15. 4. Show your work to solve the problem correctly 5. Explain to Ms. Joyce what she did wrong in her first step.
Unit 3 Benchmark Questions – Multiple Choice – Review Standards
Objective Week 1.1: Reading and writing numbers
4 2 -‐1 Which number is the same as this power of ten form: 3 x 10 + 4 x 10 + 9 x 10 ? a. 30,400.9 b. 349 c. 3,409 d. 30,490 Week 1.2: Fractions, One KIPPster got the following answers correct on their tests this week. decimals, and ! percents Reading: of the questions correct !" Writing: 0.84 of the questions correct Math: 75% of the questions correct Science: 0.64 of the questions correct Which subject did this KIPPster get the least amount of questions correct? a. Reading b. Writing c. Math d. Science Week 1.3: Add and Simplify your answer. 1 + 3 = 8 4 subtract fractions a. 124 b.
1 2 7 c. 8 d. 97
Week 1.4: Exponents
Week 1.5: Add and subtract decimals
3
Simplify the expression: 28 -‐ 3 + 4 a. 27 b. 31 c. 55 d. 59 A KIPPster was measuring lengths of caterpillars in science. The lengths in millimeters were 9.18, 46.3, and 0.275. What is the total length that she measured? a. 55.755 mm b. .001656 mm c. 35.12 mm d. 34.845 mm
Week 1.6: Properties of operations
Week 2.1: Function Tables
To use either the associative or commutative property, the expression or equation must have: a. addition or subtraction only b. multiplication or division only c. addition or multiplication only d. subtraction or division only Harry made the input-‐output table shown below.
Input(x)
Output(y)
3
8
4
10
5
12
6
14
Which of the following expressions is true for all values in Harry’s input-‐output table? A. x + 5 = y B. x + 6 = y C. 2x + 2 = y D. 3x — 1 = y
Week 2.2: Multiplying decimals and fractions
What is the value of the expression below? A.
B.
C.
D.
Week 2.3: Models of Division Week 2.4: Divide decimals
Kim sold 315 boxes of cards. The cost of each box of cards was $2.90. Which of the following is the most reasonable estimate of the total cost of the boxes of cards Kim sold? A. $1300 B. $1200 C. $900 D. $600
Week 2.5: Divide fractions and mixed numbers
Unit 3 Benchmark Questions – For Weekly Assessments Objective Week 3.1: Ratios, Proportions, and Rates
Question 1
Question 2
Question 3
Question 4
Week 3.2: Operations with Integers
What is the value of the expression below?
The temperature at midnight was 2°F. At sunrise the temperature was 5°F lower.
What is the value of the expression below?
What was the temperature at sunrise?
2 + (−5)
A.
B.
C.
A. —7°F
A. 7
B. —3°F
B. 3
C. 3°F
C. −3
D. 7°F
D.
D. −7
Week 3.3: Read, write, and simplify algebraic equations
Ann Marie wants to buy a vase and some flowers. • •
What is the value of the expression below when
The vase costs $12. Each flower costs $2.
?
A. 55 B. 43
Which of the following expressions represents the cost, in dollars, of the vase and f flowers?
A carton contains 12 eggs. Which of the following expressions represents the total number of eggs that are contained in c cartons?
C. 23
A. c — 12
D. 16
B. c + 12
A.
C. c ÷ 12
B.
D. c × 12
C.
D.
Week 3.4: One-‐ step equations
What is the value of the expression below when
?
Maxine’s homework assignment is to determine the value of n that makes the equation below true. 26 + n = 78 Which of the following equations could Maxine use to determine the value of n? A. 78 – 26 = n
What is the value of the expression below when
= 3?
2 (
What is the value of n that makes the equation below true?
) + 5
B. 78 + 26 = n C. 26 – 78 = n D. 26 + 78 = n
A.
6
B.
7
C.
10
D.
11
A.
4
B.
9
C.
15
D.
36
Week 3.5: Two-‐ step equations
Paige, Rosie, and Cheryl each spent exactly $9.00 at the same snack bar. • • •
1.
2.
3.
The poster below shows the costs at a fall carnival.
Paige bought 3 bags of peanuts. Rosie bought 2 bags of peanuts and 2 pretzels. Cheryl bought 1 bag of peanuts, 1 pretzel, and 1 milk shake. What is the cost, in dollars, of 1 bag of peanuts? Show or explain how you got your Which of the following expressions represents answer. the total cost, in dollars, of 1 admission and r What is the cost, in rides, for any number of rides? dollars, of 1 pretzel? Show or explain how you got your answer. A. 10 + 2r What is the total number B. 10(r + 2) of pretzels that can be bought for the cost of 1 C. 10 − 2r milk shake? Show or explain how you got your D. 10 + r + 2 answer.
Karen purchased a new camera for $60. She also purchased 5 rolls of film. The total cost of the camera and the rolls of film was $90. Karen’s purchase is represented by the equation below. In the equation, f stands for the cost of each roll of film.
5f + 60 = 90 What was the cost of each roll of film that Karen purchased? A. $6 B. $12 C. $18 D. $30
Week 3.6: Complex Equations
The cost for labor at a car repair center is shown in the table below.
Car Repair Costs Hours
Total Cost
1
$ 60
2
$120
3
$180
A. $6
4
$240
B. $12
Based on the data in the table, which of the following expressions represents the total cost, in dollars, of a repair that requires h hours of labor?
C. $18
A. h + 60 B. h – 60 C. h × 60 D. h ÷ 60
Karen purchased a new camera for $60. She also purchased 5 rolls of film. The total cost of the camera and the rolls of film was $90. Karen’s purchase is represented by the equation below. In the equation, f stands for the cost of each roll of film. 5f + 60 = 90 What was the cost of each roll of film that Karen purchased?
D. $30