End-of-Unit Assessment

1.

Clare has a recipe for yellow cake. She uses $9\frac13$ cups of flour to make 4 cakes. Noah will follow the same recipe. He will make $c$ cakes using $f$ cups of flour.

Which of these equations represent the relationship between $c$ and $f$ ?

A.

c=\frac{16}{3}f

B.

c=\frac{3}{16}f

C.

c=\frac{3}{7}f

✓

D.

c=\frac{7}{3}f

Answer: C

Teaching Notes

Students who select choice A may have subtracted

9\frac13-4=\frac{16}{3}

. Students who select choice D reversed the relationship between the variables. Students who select choice B may have reversed the variables while also making the mistake of subtracting to determine

\frac{16}{3}

.

2.

A graduated cylinder actually contains 7.5 milliliters of water. When Han measures the volume of the water inside the graduated cylinder, his measurement is 7 milliliters. Which of these is closest to the percent error for Han’s measurement?

A.

107.1%

B.

93.3%

C.

7.1%

D.

6.7%

Answer:

6.7%

Teaching Notes

Students who select choice A may be finding what percentage 7.5 is of 7. Students who select choice B may be finding what percentage 7 is of 7.5. Students who select choice C may be calculating the percent error relative to the measurement and not the actual value.

3.

It takes Diego $\frac{1}{24}$ of an hour to complete a lap on a circular bike track. The track is $\frac13$ mile long. What is Diego’s bike speed?

A.

$\frac18$ mile per hour

B.

$\frac18$ hours per mile

C.

8 miles per hour

D.

8 hours per mile

Answer:

8 miles per hour

Teaching Notes

Students who select choice A found how many hours per mile ( $\frac{1}{24}\div\frac13$ ). Students who select choice B, $\frac18$ hours per mile, divided correctly but found the pace and not the running speed. (It is for the teacher to decide if B will be an alternate correct answer, or if partial credit will be given.) Students who select choice D switched the order of the unit rate.

4.

A practice field is 250 feet long. The game field is 40% longer than the practice field. How long is the game field?

Answer:

350 feet

Teaching Notes

The most common error is students answering 100 feet by calculating 40% of 250 without adding 100 to 250. Students may also miss the fact that 40 is a percentage and compute $250+40$ feet. Students who miss this problem due to setting up a proportion incorrectly could benefit from using a double number line.

5.

Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

Noah paid $28 for the jeans after using the coupon. What is the regular price of the jeans?
The regular price of a hoodie is $27. What did Noah pay for the hoodie?
If the regular price of an item is $x$ dollars, what is the discounted price, in dollars?

Answer:

$40 ( $0.7x=28$ , so $x=40$ .)
$18.90 (70% of 27)
$0.7x$ or ( $x−0.3x$ ) or $\frac{7}{10}x$ (or equivalent)

Teaching Notes

The first part of this item can be answered in several different ways, including a double number line, a table, or solving an equation.

6.

Kiran’s mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20% as a tip.

What is the total after the discount and tip? Explain or show your reasoning.

Answer:

$25.50. Sample reasoning: The coupon takes away 15% of $25, which is $3.75. The cost after the coupon is $21.25. The added tip is $4.25 (20% of $21.25). The total is $25.50, the sum of $21.25 and $4.25.

Minimal Tier 1 response:

Work is complete and correct.
Sample: $25−3.75=21.25$ , and $21.25\boldcdot(1.20)=25.50$ .

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Calculating the tip to be $5 using $25 instead of $21.25; answering $4.25, using the amount of tip as the final answer; answering $25.50 without showing or explaining work; errors in computation but not in concept.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Ignoring the 15% discount or the 20% tip altogether; adding 15% to the total; using 15% of $25 as the amount before the tax; errors because of major misunderstandings about operations, such as subtracting $15 as the discount instead of 15%, or subtracting only $0.15.

Teaching Notes

Use this problem as a check on students’ ability to add and multiply with decimals, and as a check on their understanding of discounts and tips.

7.

Jada’s sister works in a furniture store.

Jada’s sister earns $15 per hour. The store offers her a raise—a 9% increase. After the raise, how much will Jada’s sister make per hour?
The store buys a table for $200 and sells it for $350. What percentage is the markup?
Jada’s sister earns a commission that is 3.5% of the amount she sells. Last week, she sold $7,000 worth of furniture. How much was her commission?

Answer:

$16.35. Because 9% of $15 is $1.35, Jada’s sister now makes $15+1.35$ dollars per hour.
75%. The markup is $150, and $150 is 75% of $200.
$245. The commission was $7,000\boldcdot(0.035)=245$ .

Minimal Tier 1 response:

Work is complete and correct, with complete explanation or justification
Sample:

$16.35. The raise is $1.35, because 9% of $15 is $1.35.
75%. The markup is $150, and $150 is 75% of $200.
$7,000\boldcdot(0.035)=245$

Tier 2 response:

Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
Sample errors: One or two calculation errors in executing the parts of the problem; stating 75 instead of 75% for the markup without a very clear description that the 75 refers to 75%; answering 1.35, the value of the raise, instead of the total after the raise.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: One major conceptual error, perhaps due to a misinterpretation of the meaning of one of the terms in the problem; omission of one part of the problem; repeated calculation errors in execution.

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: Two or more parts of the problem are omitted or with major conceptual errors.

Teaching Notes

While this problem does not require students to know the term “commission” from this unit, students who know the term will be more successful here. The term “markup” is required for the second part.