Grade 7

Mid-Unit Assessment

Mid-Unit Assessment
1.

Tiles with the numbers 1 through 9 are placed in a bag. What is the probability of choosing an even number that is greater than or equal to 4?

A.

19\frac19

B.

38\frac38

C.

39\frac39

D.

410\frac{4}{10}

Answer:

39\frac39

Teaching Notes

Students should count the number of outcomes in the event and divide by the number of outcomes in the sample space. Students who select choice A may not have counted all of the outcomes in the event. Students who select choice B may have incorrectly counted the number of items in the sample space.

2.

Select all of the events that are possible, but unlikely.

A.

A 300-page book is opened to page 143.

B.

A second-grade classroom contains some books.

C.

A 7 is rolled on a standard 6-sided number cube.

D.

Everyone in your school will get to school on time on the next school day.

E.

A triangle has 3 sides.

Answer:

A, D

Teaching Notes

Students who select choice B or choice E may not understand how to interpret “unlikely.” Students who select choice C may not have noticed that they were looking for events that are possible.

3.

Han heard that the school’s football team has a 13\frac13 probability of winning each of their next 5 games. Select all the ways Han could accurately simulate the number of games the football team will win.

A.

Roll a standard number cube 5 times. Count the number of 1s and 2s.

B.

Put the numbers 1 through 5 in a bag. Pick a number from the bag.

C.

Roll a standard number cube 5 times. Count the number of 1s.

D.

Mark a spinner with 3 equally-sized sections. Write “win” on 2 of the sections. Spin the spinner 5 times and count the number of times it lands on “win.”

E.

Put 2 white chips and 1 red chip in a bag. Draw a chip from the bag, record its result, and put it back in the bag. Do this 5 times and count the number of red chips drawn.

Answer: A, E

Teaching Notes

Students who select choice B are missing the concept that the outcomes are not equally likely, so a choice from 1 to 5 cannot be used. Students who select choice C understand the general concept but not the correct probability.

4.

A toy store sells different types of action figures based on a movie. The figures come in 3 sizes: small, medium, and large. There are also 3 characters to choose from: the main character, the friend, or the villain. How many different action figures are available if any combination could be made?

Answer:

9

Teaching Notes

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

5.

Imagine that there is a spinner with 5 equal sections, and there is also a standard number cube. You spin the spinner and roll the cube. This is a situation that involves 2 parts (the spinner and the cube) and has a total of 30 outcomes in the sample space.

Describe a situation that involves 3 parts and has a total of 36 outcomes in the sample space.

Answer:

Sample response: Flip a coin, roll a standard number cube, and choose one letter from the word “CAT.”

6.

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

A spinner

Answer:

Sample response:

  1. The color will be blue, white, or yellow.
  2. The color will be yellow.
  3. The color will be purple.
  4. The color will be blue or white.

Minimal Tier 1 response:

  • Work is complete and correct.
  • Sample:
    1. Priya spins a blue, white, or yellow.
    2. Priya spins a yellow.
    3. Priya spins pink.
    4. Priya spins blue or white.

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 an event.

Tier 3 response:

  • Significant errors in work demonstrate 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.

A game uses a special deck of cards with 40 cards numbered from 1 to 40. You draw a card from the shuffled deck.

  1. What is the probability of drawing a card that is divisible by 2? Explain your reasoning.
  2. What is the probability of drawing a card that is less than 50? Explain your reasoning.
  3. What is the probability of drawing a card that is greater than 50? Explain your reasoning.

Answer:

  1. 2040\frac{20}{40} or 12\frac12. Sample reasoning: There are 20 cards that would be divisible by 2.
  2. 4040\frac{40}{40} or 1. Sample reasoning: It is certain that this will happen.
  3. 0. Sample reasoning: It is impossible for this to happen.

Minimal Tier 1 response:

  • Work is complete and correct.
  • Sample:
  • 2040\frac{20}{40} or 12\frac12, because there are 20 cards that would be divisible by 2
  • 1, because it is guaranteed that this will happen
  • 0, because it is impossible for this to happen

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 counting the number of cards that are divisible by 2, but the probability is computed out of 40. The probabilities are given incorrectly, but with correct explanations.

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.