Divi-Detectives: Cracking the Code of Unknown Numbers!

Mathematics Grades 3rd Grade 4:33 Video
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Lesson Description

Become a math detective and learn how to solve division problems with missing numbers! Discover fact families and use your division skills to find the hidden number.

Video Resource

How to Divide Unknown Numbers

Miacademy Learning Channel

Duration: 4:33
Watch on YouTube

Key Concepts

  • Fact Families (Multiplication and Division)
  • Inverse Operations (Multiplication and Division)
  • Solving for Unknowns in Division Problems

Learning Objectives

  • Students will be able to identify the fact family related to a given division problem.
  • Students will be able to use fact families to find the unknown number in a division equation.
  • Students will be able to solve division problems with unknowns using the 'switch' method.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of fact families with simple multiplication and division examples (e.g., 2 x 4 = 8, 4 x 2 = 8, 8 / 2 = 4, 8 / 4 = 2). Explain that they will be using fact families to solve division problems with a missing number, just like detectives!
  • Video Viewing (7 mins)
    Play the Miacademy Learning Channel video "How to Divide Unknown Numbers." Encourage students to pay attention to how Ashley uses fact families and the 'switch' method to solve for the unknown.
  • Guided Practice (10 mins)
    Work through several examples together on the board, modeling the 'switch' method. For example: 20 / ? = 4. Guide students to rewrite the problem as 20 / 4 = ?. Then, solve 20 / 4 = 5. Therefore, the unknown is 5. Start with simpler problems and gradually increase the difficulty.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing division problems with unknowns. Encourage them to use the 'switch' method and their knowledge of fact families to solve the problems independently. Circulate to provide support and answer questions.
  • Wrap-up and Assessment (8 mins)
    Review the answers to the independent practice problems. Discuss any common errors or misconceptions. Administer the multiple choice or fill-in-the-blank quiz to assess student understanding.

Interactive Exercises

  • Fact Family Flashcards
    Create flashcards with multiplication facts. Have students write the corresponding division facts (the fact family) on the back. This reinforces the relationship between multiplication and division.
  • Unknown Number Game
    Write division problems on the board with unknowns. Divide students into teams. The first team to correctly identify the unknown number earns a point. This is a fun way to practice solving for unknowns in a competitive setting.

Discussion Questions

  • What is a fact family, and how does it help us with division?
  • How does switching the numbers around help us find the unknown?
  • Can you think of a real-life situation where you might need to find a missing number in a division problem?

Skills Developed

  • Problem-Solving
  • Critical Thinking
  • Application of Mathematical Concepts

Multiple Choice Questions

Question 1:

What is the missing number? 12 / ? = 3

Correct Answer: 4

Question 2:

Which number sentence helps you solve 15 / ? = 5?

Correct Answer: 15 / 5 = ?

Question 3:

What is a fact family?

Correct Answer: A group of related math facts

Question 4:

What is the missing number? 24 / ? = 6

Correct Answer: 8

Question 5:

If 3 x 4 = 12, then 12 / 3 = ?

Correct Answer: 4

Question 6:

What is the missing number? ? / 4 = 5

Correct Answer: 20

Question 7:

If you know 18 / 6 = 3, which multiplication fact do you also know?

Correct Answer: 6 x 3 = 18

Question 8:

What is the missing number? 30 / ? = 5

Correct Answer: 6

Question 9:

What is the 'switch' method?

Correct Answer: Changing the numbers in a problem to help solve it

Question 10:

If 21 / 7 = 3, then 21 / 3 = ?

Correct Answer: 7

Fill in the Blank Questions

Question 1:

A fact family has related multiplication and ___________ facts.

Correct Answer: division

Question 2:

To find the unknown in 16 / ? = 4, you can switch it to 16 / 4 = ___________.

Correct Answer: 4

Question 3:

If 5 x 6 = 30, then 30 / 5 = ___________.

Correct Answer: 6

Question 4:

The missing number in 28 / ? = 4 is ___________.

Correct Answer: 7

Question 5:

Knowing your _____________ helps you solve division problems faster.

Correct Answer: facts

Question 6:

If 36 / 9 = 4, then 36 / 4 = ___________.

Correct Answer: 9

Question 7:

Using the 'switch' method can help you find the ___________ number.

Correct Answer: unknown

Question 8:

The missing number in ? / 8 = 2 is ___________.

Correct Answer: 16

Question 9:

Multiplication and division are _____________ operations.

Correct Answer: inverse

Question 10:

If 45 / 5 = 9, then 5 x ___________ = 45.

Correct Answer: 9

Educational Standards

3.A.2.1:Use number sense with the properties of addition, subtraction, and multiplication, to find unknowns (represented by symbols) in one-step equations. Generate real-world situations to represent number sentences. 3.N.2.7:Apply the relationship between multiplication and division to represent and solve problems. 3.N.2.6:Represent division facts and divisibility by modeling a variety of approaches (e.g., repeated subtraction, equal sharing, forming equal groups) to show the relationship between multiplication and division.

Teaching Materials

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