Multiply and Conquer

This site provides a lesson plan that has students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and align paper-and-pencil calculations with the arrays. The lesson provides conceptual understanding of what occurs in a 2-digit multiplication problem. Partial product models serve as transitions to understanding the standard multiplication algorithm. This lesson will allow for a deeper understanding of the two-digit multiplication process beyond the algorithm itself. This lesson also helps to reinforce the relationship between area and multiplication. Several options for assessment are also included. This lesson also includes enrichment activities to further the learning.

Weblink address (URL):

Standards & Objectives

Learning objectives:

Learning Objectives

Students will:

Create and solve multiplication stories.
Practice selected multiplication facts.

Essential and guiding questions:

Questions for Students:

How does your model show the answer to your multiplication problem?
Why do we decompose a 2-digit number?
Is this method easier than the traditional way or harder?
What do the partial products show?

Lesson Variations

Blooms taxonomy level:

Applying

Extension suggestions:

Extensions:

This model of multiplication can be extended to 3-digit numbers although it becomes less efficient. Some students may enjoy the challenge of being given larger numbers to distribute and multiply. Three-digit numbers should be decomposed into hundreds, tens, and ones. Since three dimensions are required, they must be modeled with base ten blocks rather than paper grids.
Ask students to write journal entries comparing array models with the traditional algorithm. Ask them to determine what is happening when they use a regrouping method and how it works.
To practice the array models, play a game whose object is to color in as many squares as possible on a sheet of graph paper. Roll 3 dice, 2 of one color and 1 of another color. The same-color dice represent a 2-digit number and the other die represents a single-digit number. Students color in the partial product arrays. The first to correctly color in as much of their paper as possible is the winner. For an extra challenge, have students play in pairs, coloring the same grid. This adds strategy to the game.
Instead of giving students the factors to use in a model, have them discover the best strategy on their own. Students need to think flexibly about the factors as they develop strategies for multiplicative thinking. For example, ask students to compute 14 × 6, but let them discover other factors that work, such as 6 × (10 + 4), 6 × (9 + 5), 6 × (2 + 12), etc.Use questioning, discussions, and mathematical communication throughout the process.

Helpful Hints

Materials:

Base 10 blocks
2 × 1 Multiplication Activity Sheet
2 × 2 Multiplication Activity Sheet
Computers or tablets with internet access (optional)

References

Contributors:

Angela Collins

Originator:

Ayers Institute for Learning & Innovation