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This lesson provided by:
Author:Jessica Jeffers
System: Enterprise City
School: Hillcrest Elementary School
Lesson Plan ID: 24101

Area Model of Multiplication Using Base 10 Manipulatives


Students will use base 10 manipulatives to build a rectangular array to represent double digit multiplication. Students will make the connection between the standard algorithm and the rectangular array.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

Content Standard(s):
MA2015(4) 7. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4-NBT2]
MA2015(4) 10. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4-NBT5]
MA2015(5) 8. Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NBT5]
Local/National Standards:

Understand various meanings of multiplication and division; Understand the effects of multiplying and dividing whole numbers (NCTM National Standards 3rd -5th grade)

Primary Learning Objective(s):

Students will be able to solve double digit multiplication problems.

Additional Learning Objective(s):

Students will be able to manipulate base 10 blocks to build arrays.

Approximate Duration of the Lesson: 31 to 60 Minutes
Materials and Equipment:

Base 10 manipulatives, graph paper

Technology Resources Needed:

LCD or interactive whiteboard (optional)


Knowledge of basic multiplication facts and standard algorithm.

1.)Place students into academically diverse cooperative groups and pass out base 10 manipulatives.

2.)Ask students to build a 15 x 13 rectangle (see 15x13 attachment).

3.)Some students will try building their rectangle using only the small cubes. Walk the floor and ask questions such as: I wonder if there is something larger we could use, I see you built a 10x13 we want a 15x13; is there a way you could add more to one side?

4.)It is important for students to work with their group in order to find their own way of building the rectangle.

5.)Have groups share with the class how they built their rectangle using an interactive whiteboard to model for everyone in the class to see.
(Base 10 Blocks)
This website allows students to manipulate base ten blocks online.

6.)Show the class how to break the multiplication problem 15 x13 down into smaller multiplication problems (see partial products).

7.)Ask students if they see where the product 100 is located in their rectangle (students should recognize the 10x10).

8.)Ask students if they see where the products 50, 30, and 15 are located in their rectangle (students should be able to find each grouping within their rectangle).

9.)Now ask students to work together to build and solve the problem 14 x17.

10.)Ask students to draw a diagram of their rectangle on the graph paper and label the different products within the rectangle.

11.)This is a great time to also show the relationship between the area model(rectangle) and the traditional algorithm (ex. four times seven is twenty-eight, put down the eight and carry the two).

12.)In closing ask every group to make up a double digit multiplication problem to give to another group as a challenge (Limit the size of the double digit numbers to numbers less than 25).

13.)Groups must first build, graph, and solve their challenge problem correctly before passing their challenge on to another group.

14.)Allow groups an opportunity to share their strategy for solving the challenge problem on the interactive whiteboard (if available).

15.)Have student groups discover real life examples for using this two-digit multiplication problems (e.g. find area of a room to buy carpet, area of wall to buy paint, and how much grass seed to sow your yard).

Attachments:**Some files will display in a new window. Others will prompt you to download. Partial Products.JPG
15 x13.JPG
Assessment Strategies:

Self assessment as well as peer assessment can be used by giving another problem to build to his or her partner, graph and solve independently.


Students that have already mastered double digit multiplication can still benefit from seeing the link between the standard algorithm and the area model. Students may also be given larger numbers and small grid graph paper to draw rectangular arrays for these numbers.


Students that are still lacking basic facts will find double digit multiplication overwhelming. This site is useful for practicing basic math facts. Batter up

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

Hosted by Alabama Supercomputer Authority
The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
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