Lesson 1

The TIMS Candy Company

Est. Class Sessions: 2

Daily Practice and Problems

Teacher Notes
X

TIMS Bit

Use this DPP item C to practice the multiplication facts for the 9s by exploring patterns in the products.

  1. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

  2. Observing patterns helps students remember the facts for the nines. Patterns include:
    • When the products are listed in a column, the digits in the tens place count up by ones (0, 1, 2, 3, etc.) and the digits in the ones place count down by ones (9, 8, 7, etc).
    • The sum of the digits in each product is nine. For example, 36 is the product of 4 × 9. The sum of 3 and 6 is nine. This provides a strategy for checking multiplication by nine: Does 9 × 6 = 54 or 56? It must be 54 since 5 + 4 = 9, but 5 + 6 is not 9.
    • The nines can be easily derived from the tens. For example, 10 × 4 is 40. So, 9 × 4 is 4 less: 40 − 4 = 36.
  3. 8 × 10 = 80
    8 × 9 = 80 − 8 = 72

C. Patterns

  1. Complete:

    1 × 9 =

    2 × 9 =

    3 × 9 =

    4 × 9 =

    5 × 9 =

    6 × 9 =

    7 × 9 =

    8 × 9 =

    9 × 9 =

    10 × 9 =
  2. What patterns do you see in your answers to Question 1?
  1. John said, “I can use my multiplication facts for the 10s to learn the 9s, since 9 is one less than 10. See, to solve 6 × 9, I just think of an array for 6 × 10. That is 60. 6 × 9 will have one less row of sixes, so it is 60 − 6.”
  2. Fill in the second bubble to show how John would solve 8 × 9 in his head.