Using a Multiplication Table

In this lesson, students explore patterns on a multiplication table and use the patterns to complete the table.

Materials: partially completed multiplication tables from previous lesson

Preparation: none

Prerequisite Skills and Background: Students should know how to use a multiplication table to multiply.

• Display the multiplication table on the overhead projector. Point to the rows for 2 and 4.

• Ask: What number is the double of 2? (4)

• Say: Compare the products in the rows for 2 and 4. What do you notice?
  Elicit from students that the products in the row for 4 are double the products in the row for 2.

• Ask: What other row could you complete by using doubles? Explain.
  Students should realize that the products in the row for 6 are double the products in the row for 3.

• Have students use doubles to complete the row for 6 as you do it on the overhead. Then have them complete the column for 6.

• Ask: Is there another row you could complete by using doubles? Explain.
  Students should realize that the products in the row for 8 are double the products in the row for 4.

• Have students complete the row and column for 8 as you do it on the overhead. Then have them complete the column for 8.
  

• Say: We still have more spaces to fill in on our multiplication table. Let's count and skip count to fill in some of the remaining spaces.

• Ask: Which row and column can we complete by counting? (1) Which rows and columns can we complete by skip counting? (2, 3, 4, and 5)
  Write the numbers in these rows and columns on the overhead as students fill in their tables at their desks.
  

• Ask: How can we complete the remaining squares in our multiplication table?
  Elicit from students that they could also use skip counting to complete these rows. If they can't do this, suggest that they use repeated addition to complete the tables.

• Have a volunteer list the numbers that complete each remaining row and column. Write the numbers on the overhead.

• Say: Our multiplication table is complete. Let's see what other patterns we can discover.

• Write 3 3 = on the board.

• Ask: What is the product of 3 and 3? (9) Circle the product of 3 and 3 on your multiplication table.

• Say: Now shade the squares for all the products above the row for 3 and to the left of the column for 3.
  Do this on the overhead as students are working.

• Ask: What shape is formed by the shaded products? (a square)

• Say: The product of a number multiplied by itself is called a square number. 3 3 = 9, so 9 is a square number.

• Say: Find another square number on the table and circle it. Then shade all the products above the row and to the left of the column for the factors of the square number.

• Ask: Do the shaded squares form a square? What square number did you find? What number multiplied by itself is equal to your square number?
  On the overhead, circle all the square numbers students found as well as any they didn't find. (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100)

• Lead students to discover other number patterns on their multiplication tables with questions such as the following.
  Which rows and columns have products that alternate between even and odd numbers? (the rows and columns for 1, 3, 5, 7, and 9)
  What do you notice about the sum of the digits in the products for 9? (They equal 9.)

  Wrap-Up and Assessment Hints
  Have students explain in their own words how to find a product on a multiplication table. Offer clues that will lead them to discover a pattern and ask them how they could use the pattern to find the products of greater numbers.