Grade 7

Mid-Unit Assessment

Mid-Unit Assessment
1.
A standard number cube is rolled. What is the probability of rolling a number less than or equal to 2?
A.
16\frac16
B.
26\frac26
C.
25\frac25
D.

47\frac47

Answer: 26\frac26

Teaching Notes

Students who select choice A may have read the problem as “less than 2.” Students who select choice C may have miscounted the number of outcomes in the sample space. Students who select choice D may not understand how to calculate probability.

2.
Select all the events that have a probability of 0.
A.
A red block is chosen from a bag with 9 white blocks and 1 red block.
B.
A 6 is rolled three times in a row on a standard number cube.
C.
A 7 is rolled on a standard number cube.
D.
A 400-page book is opened to page 231.
E.

A 400-page book has a page number greater than 450.

Answer: C, E

Teaching Notes
Students who select choice A, choice B, or choice D may interpret an unlikely event as an event that is impossible.
3.

The basketball coach says that based on Noah's free throws this season, Noah has a 34\frac34 probability of making each free throw. Select all the ways Noah could accurately simulate the number of free throws he will make in his next 6 attempts.

A.
Flip a coin 6 times. Count the number of heads.
B.
Make a spinner with 6 equally-sized sections, labeled with the numbers 1 through 6. Spin the spinner 6 times and count how many times the spinner lands on 3 or 4.
C.
Put 3 red chips and 1 white chip in a bag. Draw a chip from the bag, record the result, and put it back in the bag. Do this 6 times and count the number of red chips drawn.
D.
Make a spinner with 4 equally-sized sections. Color 3 sections green and 1 section red. Spin the spinner 6 times and count the number of times the spinner lands on green.
E.

Put the numbers 1 through 6 in a bag. Pick a number from the bag.

Answer: C, D

Teaching Notes
Students who select choice A or choice B understand the general concept of simulations but not the correct probability. Students who select choice E are missing the concept that the outcomes are not equally likely, so a choice from 1 to 20 cannot be used.
4.

A furniture company sells 3 types of chairs: reclining, gliding, and standard. Each type of chair can be covered with 4 different colors of leather: black, brown, red, or white. How many different chairs can be made from these options?

Answer: 12

Teaching Notes
Students may choose to create a tree diagram or chart to represent all the choices.
5.

Imagine you flip a coin and roll a standard number cube. This is a situation that involves 2 parts (a coin and a cube) and has a total of 12 outcomes in the sample space. Describe a situation that involves 3 parts and has a total of 48 outcomes in the sample space.

Answer: Sample response: Flip a coin, roll a standard number cube, and spin a spinner divided into 4 equally-sized sections numbered 1 through 4.

6.

Tyler is about to spin a spinner like the one shown.

  1. Describe an event that is certain to happen on the next spin.

  2. Describe an event that is impossible on the next spin.

  3. Describe an event that is likely to happen, but not certain, on the next spin.
  4. Describe an event that is unlikely to happen, but possible, on the next spin.

A spinner

Answer:

Sample response:

  1. The color will be yellow, blue, or white.
  2. The spinner will land on 7.
  3. The color will be blue or white.
  4. The spinner will land on 1.

Minimal Tier 1 response:

  • Work is complete and correct.

  • Sample:

    1. The color will be yellow, blue, or white.
    2. The spinner will land on 7.
    3. The color will be blue or white.
    4. The spinner will land on 1.

Tier 2 response:

  • Work shows general conceptual understanding and mastery, with some errors.
  • Sample errors: One of the descriptions is incorrect or does not describe the event.

Tier 3 response:

  • Significant errors in work demonstrate a lack of conceptual understanding or mastery.
  • Sample errors: Two or more descriptions are incorrect or do not describe an event.

Teaching Notes
Use this problem to confirm that students understand how to find probability instead of just the numbers associated with a probability.
7.

You select a card from a deck that contains 25 red cards: 12 blue cards, 8 yellow cards, and 5 green cards.

  1. What is the probability of drawing a red card? Explain your reasoning.
  2. What is the probability of drawing a green card? Explain your reasoning.
  3. What is the probability of drawing a card that is not green? Explain your reasoning.

Answer:

  1. 2550\frac{25}{50} or 12\frac12. Sample reasoning: There are 25 red cards out of 50 total cards.
  2. 550\frac{5}{50} or 110\frac{1}{10}. Sample reasoning: There are 5 green cards out of 50 total cards.
  3. 4550\frac{45}{50} or 910\frac{9}{10}. Sample reasoning: There are 45 cards that are not green out of 50 total cards.

Minimal Tier 1 response:

  • Work is complete and correct.

  • Sample:

    1. 2550\frac{25}{50} or 12\frac12, because there are 25 red cards out of 50 total cards
    2. 550\frac{5}{50} or 110\frac{1}{10}, because there are 5 green cards out of 50 total cards
    3. 4550\frac{45}{50} or 910\frac{9}{10}, because there are 45 cards that are not green out of 50 total cards

Tier 2 response:

  • Work shows general conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
  • Sample error: Minor visible calculation errors cause one of the probabilities to be incorrect.

Tier 3 response:

  • Work shows a developing but incomplete conceptual understanding, with significant errors.
  • Sample errors: An error in calculating the total number of cards or in simplifying correctly.

Tier 4 response:

  • Significant errors in work demonstrate lack of conceptual understanding or mastery.
  • Sample errors: Two or more probabilities are incorrect and no explanations are provided.