Grade 6

End-of-Unit Assessment

There are 15 pieces of fruit in a bowl and 6 of them are apples. What percentage of the pieces of fruit in the bowl are apples?

0.06%

0.4%

40%

Answer:

40%

Teaching Notes

This problem is possible to solve without any calculations: 6 is a bit less than half of 15, and choice D is the only answer choice that is reasonably close. Students who select choice A or C are using the given information of “6 apples” without calculating the percentage of the whole. Students who select choice B have correctly divided 6 by 15, but have not multiplied by 100.

Select all of the trips that would take 2 hours.

Drive 60 miles per hour between Buffalo and Seneca Falls, which are 120 miles apart.

Walk 3 miles per hour to school, which is 1.5 miles away.

Take a train going 80 miles per hour from Albany to New York City, which are 160 miles apart.

Answer: A, C

Teaching Notes

Students who incorrectly select choice B are reversing the ratio, dividing speed by distance or noticing that the speed is twice the distance. In choices A and C, the distance is twice the speed, which means that a person traveling at that rate would cover the distance in two hours.

Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?

24.5 miles

50 miles

59.5 miles

200 miles

Answer:

50 miles

Teaching Notes

Students are not expected to take an algorithmic approach to find $B$ in “ $A\%$ of $B$ is $C$ .” They may use a double number line diagram or table to keep track of values.

Students who select choice A are computing 70% of 35, rather than using the information that 35 miles is 70% of the trip. Students who select choice C are calculating 70% of 35, and then are adding 35 more miles (because that distance is already traveled). Students who select choice D may be calculating 200 as the solution to “35% of what is 70?”, reversing the 35 and 70.

Lin runs 5 laps around a track in 6 minutes.

How many minutes per lap is that?
How many laps per minute is that?
At that rate, how long does it take Lin to run 21 laps?

Answer:

$\frac{6}{5}$ or 1.2 minutes per lap
$\frac{5}{6}$ laps
25.2 minutes ( $21 \boldcdot (1.2)= 25.2$ )

Teaching Notes

This problem has students calculate both unit rates that describe a situation. In the third part, students need to decide which of the two unit rates makes sense to use.

A car is traveling at a constant speed. The table shows how far it travels in some amounts of time.

What is the speed of the car?

time (hours)	distance (miles)
2	84
3	126

Answer:

42 miles per hour

Teaching Notes

To answer this question, students need to recognize speed as distance traveled per unit of time and express it in miles per hour.

Students may create a double number line diagram or extend the table to find the number of miles that correspond to 1 hour. They may also divide a given distance by its corresponding time. Some students may observe the difference in time and in distance shown in the two rows—the distance traveled increases 42 miles with 1 additional hour of travel—and conclude that this is the speed.

Which weighs more: a watermelon that weighs 7.5 kilograms or a baby that weighs 12 pounds? Explain your reasoning.

Note: 1 pound is about 0.45 kilograms.

Answer:

The watermelon weighs more. Sample reasoning:

12 lbs is about 5.4 kg.
Without computing anything, it can be reasoned that $12 \boldcdot (0.45)$ is less than 6, so the baby must weigh less than the watermelon.

Minimal Tier 1 response:

Work is complete and correct.
Sample: A 12-pound baby weighs less than 6 kilograms, so the watermelon weighs more.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Correct unit conversion with incorrect interpretation; unit conversion multiplies kilograms by 0.45 or otherwise “goes the wrong way”; arithmetic errors in unit conversion.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Work does not involve unit conversion, either through estimation (as in the minimal Tier 1 response) or explicitly; unit conversion is attempted but with an incorrect conversion factor.

Teaching Notes

This problem can be solved quickly using estimation, though students may do computations to convert pounds to kilograms or kilograms to pounds.

On Saturday, Elena read 40% of a 225-page book. That day, Jada read 45% of a 200‑page book.

Who read more pages that day? Explain or show your reasoning.

Answer:

They read the same number of pages (90). Sample reasoning:

Calculate $\frac{P}{100}$ times the number of pages for each reader.
Create tables, double number line diagrams, or tape diagrams to find the pages read for an intermediate percentage (5%, 10%, or 20% for Elena, and 1% or 5% for Jada), and then scale those numbers to 40% and 45%, respectively.

Minimal Tier 1 response:

Work is complete and correct, with complete explanation or justification.
Sample: $\frac{40}{100} \boldcdot 225=90$ , so Elena read 90 pages. $\frac{45}{100} \boldcdot 200 = 90$ , so Jada read 90 pages.

Tier 2 response:

Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
Sample errors: Work uses a valid representation or sequence of calculations but contains one error that propagates. A written-only response is reasoned correctly but contains arithmetic errors.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: A representation is used to keep track of the information but contains flawed reasoning. Calculations show incorrect values being associated with 100% or misinterpretation of the values to be found and compared.

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: No visual representation or written explanation. Explanation does not involve reasoning about ratios and rates.

Teaching Notes

This problem prompts students to compare percentages of two different values. Students can find each percentage in a variety of ways, with or without using representations such as tables, double number line diagrams, or tape diagrams. Because 100% corresponds to different values for each reader in the problem, students will need to create two representations (either of the same kind or different kinds) if they choose to use them.