Modeling factors through rectangles…. ….or another way to look at factor pairs

Example 1: Renting space at the annual Arts Festival Suppose you want to rent a space that is 12 square yards. Use 12 square tiles to represent the 12 square yards. Find all the possible ways that the renter can arrange the squares. Copy each rectangle into your spiral or on your grid paper. 1 x 12 2 x 6 3 x 4

Suppose you decided that you needed more space this time, 16 square yards.. Find all of the dimensions for rectangles that would provide the new area. Draw these in your spiral or on your grid paper. 1 x 16 2 x 8 4 x 4

Now it’s your turn…make rectangles for all of the whole numbers 1 to 30. Cut out a grid- paper model of each rectangle Write the number at the top of the paper and glue or tape all rectangles for that number to the paper.

Now look for patterns…. Which numbers have the most rectangles? What kind of numbers? Which numbers have the least rectangles? What kind of numbers are these?

Now look for patterns…. What numbers have squares on their posters? If you know the rectangles you can make for a number, how can you use this information to list the factors of the number?

Summarize……. Write a description, with examples, of numbers that have the given factors:  Exactly two factors  An odd number of factors

A mystery number…… I am thinking of a number…..It is larger than 12 and smaller than 40 and has exactly three factors. What is my number?