Lesson 5

Completing the Table

Est. Class Sessions: 2–3

Developing the Lesson

Part 3. Completing the Table

Develop Strategies for Remaining Facts. Ask students to look at their My Multiplication Table and point out that they only have a few more multiplication facts to add to their table. When students begin this lesson, there should be 20 blank squares left (from the original 121) in their multiplication tables. Because of the turn-around facts, there are actually only 10 facts remaining. Ask students to discuss Question 1 in the Student Guide with their partner. Students discuss strategies they could use to figure out the remaining facts.

After students have talked with their partners, have students share and demonstrate some of the strategies with the class. To model two strategies, read and discuss the vignette on the Using Strategies to Complete the Table section of the Completing the Table pages in the Student Guide. Remind students that they can use the 200 Chart in the Student Guide Reference section, counters, number lines, grid paper, and other tools to develop strategies for these last 10 multiplication facts.

To generate discussion, ask questions similar to:

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  • What strategy could you use to figure out 8 × 7? (Possible response: I know the 5s and the 3s from my table. I could break apart an 8 × 7 rectangle into a 5 × 7 rectangle and a 3 × 7 rectangle. 5 × 7 + 3 × 7 = 56.)
  • Can anyone use a different strategy to solve that fact? (Possible response: I use a number line. Eight +7 hops is 7, 14, 21, 28, 35, 42, 49 and I land on 56. 8 × 7 = 56.)
  • What strategy could you use to figure out 4 × 7? (Possible response: Since one of the facts is even, I could use a halving strategy. I know the facts for the 2s. I can solve 4 × 7 by thinking about 2 × 7 + 2 × 7. 14 + 14 = 28.)
  • Use a second strategy to check that answer. (Possible response: I skip count by 7s on the 200 Chart: 7, 14, 21, 28.)
  • What strategy helps you solve 4 × 9? (Possible response: I know 4 × 9 means 9 fours. I know 10 fours is 40. I can reason from a known fact. 4 × 10 = 40 and 4 × 9 is one less 4. 40 − 4 = 36.)
  • Is there another way to solve 4 × 9? (Possible response: I used counters. 4 piles with 9 counters in each pile is 36 counters. I checked it with a calculator and got the same answer.)
  • Give an example of a fact that you need a strategy to solve.

Assign Question 2. Students will complete the remaining squares on their multiplication tables using any strategy they wish.

Identify Patterns in the Table. When students have completed their multiplication tables, display a completed table using the Multiplication Table Master. Assist students in checking their facts. Then, ask students to look for patterns in their tables. They have already looked for patterns in earlier lessons but will probably see new ones in the completed table.

In particular, they may notice that the diagonal line from the top left corner to the bottom right corner is a line of symmetry formed by the square numbers. To see this, students can circle a number above the line and connect it to its matching number on the bottom half, as in Figure 2.

Students may also see the pattern formed in the 9s column. As you go down the column, the digits in the tens place go up by one and the digits in the ones place go down by one.

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Use the Small Multiplication Tables Master to make two small multiplication tables for each student. (There are four tables on each page.) Students can tape one to their desk or notebook so they have ready access to all the facts while they are working on activities or playing games. They can take the other one home or attach it to a homework folder.

Student Guide: 205
Answers
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SG_Mini
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Student Activity Book:
Master:
Symmetry in the multiplication table
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