Reviewing The Greatest Common Factor

Reviewing The Greatest Common Factor

Which Tiles Will Exactly Cover the Grid?

Opening

Which Tiles Will Exactly Cover the Grid?

Suppose you want to cover a 12-unit by 18-unit rectangular grid exactly, without any gaps or overlaps. Can you do this using square tile stamps in the following unit sizes?

  • 1-unit square tiles? Explain why or why not.
  • 5-unit square tiles? Explain why or why not.

INTERACTIVE: Rectangular Grid

Math Mission

Opening

Investigate how to find the common factors of two numbers.

Square Tiles on the Grid

Work Time

Square Tiles on the Grid

  • Explore the interactive by trying square tiles of different sizes.
     
  • Answer these questions:
    • Which square tiles will exactly cover a 12 × 18 rectangular grid?
    • What do you notice about the square tiles that will exactly cover the 12 × 18 rectangular grid?
    • What is the largest square tile that will exactly cover the 12 × 18 rectangular grid?

INTERACTIVE: Rectangular Grid

Hint:

The numbers 12 and 18 are both even. Do you think 2-unit squares will exactly cover this rectangle?

Prepare a Presentation

Work Time

Prepare a Presentation

List all the tile sizes you were able to use to exactly cover the 12 × 18 rectangle. Explain what your findings tell you.

Challenge Problem

  • Predict what is the largest square you think will cover a 36 x 12 rectangular grid exactly. Then, test your prediction to see if it is correct.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Takes notes about your classmates’ approaches to finding the tile sizes that will cover a grid exactly.

Hint:

As your classmates present, ask questions such as:

  • How did you decide which squares to use to try to cover the grid?
  • Were there any square sizes that you knew right away would not cover the grid?
  • What are you finding when squares fit exactly along both the width and the length of the rectangular grid?
  • What does the largest square tile that covers the grid represent?

Greatest Common Factor

Work Time

Greatest Common Factor

Common factors are factors that are shared by two numbers. The greatest common factor of two numbers is the greatest number that is a factor of the two numbers.

  • Find the greatest common factor of 8 and 12.
  • Find the greatest common factor of 18 and 24.
  • Find the largest square tile that will cover a 27 × 63 rectangle.
  • What is the greatest common factor of 54 and 126?

Hint:

  • Find numbers that will divide evenly into both numbers. Which is the largest?
  • Find all the factors of both numbers. Look for the common factors.

All About Factors

Formative Assessment

All About Factors

Read and Discuss

  • A factor of a number is a whole number that divides a given quantity without a remainder. For example, 5 is a factor of 10 but not a factor of 8.
  • Common factors are factors that are shared by two numbers. For example, 2 is a common factor of 4 and 8.
  • The greatest common factor of two numbers is the greatest number that is a factor of the two numbers. So, the greatest common factor of 4 and 8 is 4.
  • When you can exactly fit congruent squares along the edge of a rectangular grid, the side length of the square is a factor of the side length of the rectangular grid.

Hint:

Can you:

  • Describe the relationship between the side length of the square and the side lengths of the rectangular grid?
  • Identify what the largest square that exactly covers the rectangular grid represents?
  • Use the terms factor ,common factor , andgreatest common factor appropriately?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

What I learned about common factors and greatest common factors is …