In Lessons 8 and 9, the class recorded and displayed multiplication strategies and methods on chart paper. Use these lists as the basis for Part 1 of this lesson in which the class builds a multiplication strategies menu.
Ask students to solve 59 × 4 using two different strategies. Refer students to the strategies collected and displayed on chart paper in Lessons 8 and 9. For one of their solutions, ask students to choose a strategy where students do as much work in their heads as possible.
Once students have been given a chance to solve the problem two ways, ask them to share their solutions. Have them record their solutions on the board or chart paper. If a student shares a mental strategy, indicate that by putting a cloud around the student's solution.
Looking at the many strategies devised by students, ask:
- Which of these strategies are similar? (Expanded form, all-partials, rectangles, and compact methods all solve the problem by breaking numbers into tens and ones, but use different ways of recording steps.)
- Which are different?
- Which strategies use tens and ones?
- Which strategies use simpler numbers?
- With which strategies did you do a lot of the work in your head?
Students may not be proficient enough with mental math strategies to solve the problem completely in their heads. To develop these mental strategies, students may need to record intermediate steps. Encourage students to identify strategies that use simpler numbers and that lead to a strategy that could be done mentally. See Figure 1 for examples.
Ask students to remove the Multiplication Strategies Menu from the Student Activity Book. See Figure 2. Compare the Multiplication Strategies Menu to the strategies the class has collected and discussed. Check to see if students came up with each of the strategies on the menu. If a strategy was not discussed by the class, ask students to solve 59 × 4 using that strategy. Label the strategies on the chart paper with the corresponding names from the menu.
Once you have compared each strategy on the menu to the strategies recorded and discussed on chart paper, ask:
- Are there any strategies we used that are not shown on the Multiplication Strategies Menu?
- Which ones?
- Do you think we should add this strategy to the menu?
- Is this new strategy a mental math strategy or a paper-and-pencil strategy?
Ask students to draw, reference, and/or describe another strategy in the blank box on the Multiplication Strategies Menu. Identify mental math strategies with a cloud.
- Allow students who still struggle with the multiplication facts to use their small multiplication tables or Multiplication Facts I Know charts. In this way they practice the facts while also practicing more complicated multiplication.
- Some students lose track of carries in the compact method or treat the parts of a number as digits rather than as tens and ones. Encourage these students to use expanded form to document the partitions of the factors and then the partial products. Once these students understand where the partial products come from, they can record them more efficiently using the all-partials method.
- Asking students to solve the same problem two ways encourages students who are still using repeated addition as their primary strategy to move to more efficient strategies.
- If choosing from six strategies is overwhelming to some students, limit their choices by blocking out some of the strategies on the menu. Using expanded form and a strategy that uses simpler numbers is sufficient to develop conceptual understanding of two-digit by one-digit multiplication. Once students are comfortable with these strategies, add other strategies to their menu of choices.
- Ask students who are ready for more of a challenge to solve the problems using mental math strategies.
The Multiplication Strategies Menu provides a collection of strategies that work well for two-digit by one-digit multiplication. What other strategies could students possibly come up with that are not already represented? Students may suggest repeated addition. Though common, it often produces errors and is inefficient. Doubling and halving is another strategy that students might want to include as an option.
Why many strategies? Some strategies are appropriate for some problems and not appropriate for others. Having more strategies available fosters flexibility, gives students a way to check for reasonableness, builds number sense, and encourages development of mental math skills.
