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Algebra 1 3-8 Complete Lesson: Unions and Intersections of Sets

By Matt Richardson
Last updated almost 3 years ago
35 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini-lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Fifty students were polled about their after-school activities. All said that they participate in one or more of three clubs: the Robotics Club (RC), the Student Council (SC), and the Theater Club (TC). How many students participate in the theater club only?
Enter only a number.

Problem 1 Got It? Match each set. Sets may be used more than once.

  • { 2, 4}
  • {0, 1, 2, 3, 4}
  • P = {x|x is a whole number less than 5}
  • Q = {y|y is an even natural number less than 5}
  • P Ï… Q

Problem 1 Got It? Reasoning: What is true about the union of two distinct sets if one set is a subset of the other?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? Draw a Venn diagram to represent the union and intersection of the following sets.

A = {x|x is one of the first five letters in the English alphabet}
B = {x|x is a vowel}
C = {x|x is a letter in the word VEGETABLE}

Problem 3 Got It?

Problem 4 Got It? Draw a Venn diagram to represent the scenario.

Of 30 students in student government, 20 are honor students and 9 are officers and honor students. All of the students are officers, honor students, or both.

Problem 4 Got It?

Problem 5 Got It?

Problem 5 Got It?

Vocabulary: Suppose A and B are nonempty sets. Which contains more elements: A ⋃ B or A ∩ B ? Explain your reasoning.

True or False: If x is an element of set A and x is not an element of set B, then x is an element of A ∪ B.

True or False: If x is an element of set A and x is an element of set B, then x is an element of A ∩ B.

Complete the Venn diagram using sets A and B. A = {1, 3, 5, 7, 9} B = {2, 3, 4, 5}

Review Lesson 3-7: Solve the equation.

Review Lesson 3-7: Solve the equation.

Review Lesson 3-7: Solve the equation.

Review Lesson 3-7: Solve the inequality.

Review Lesson 3-7: Solve the inequality.

Review Lesson 1-9: Categorize each ordered pair. Order ordered pairs may be used more than once.

  • (-1, 8)
  • (8, 11)
  • (1, 4)
  • (0, 0)
  • Solution of x + 3 = y
  • Solution of 2x - 5 = y
  • Solution of 0.5x + 7 = y
  • Not a solution of any of these equations

Review Graphing Ordered Pairs: Graph each point on the same coordinate grid.
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, and label points, as appropriate.

Vocabulary Review: Populate each set with its elements. Not all elements will be used.

  • -1
  • 0
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • whole numbers less than 4
  • even numbers between 1 and 9
  • odd numbers between 3 and 7, inclusive

Use Your Vocabulary: Is the set {apple, banana, cheese, milk, pear, yogurt} the union or intersection of the sets D and F below?

D = {cheese, milk, yogurt}
F = {apple, banana, pear}
M = {bread, cheese, egg}

Use Your Vocabulary: Is the set {cheese} the union or intersection of the sets D and M below?
D = {cheese, milk, yogurt}
F = {apple, banana, pear}
M = {bread, cheese, egg}

Use Your Vocabulary: Is the empty set the union or intersection of the sets F and M below?
D = {cheese, milk, yogurt}
F = {apple, banana, pear}
M = {bread, cheese, egg}

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success