Illuminations: All About Multiplication

All About Multiplication


Exploring Equal Sets

This lesson builds on the previous lesson and encourages students to explore another model for multiplication, the familiar set model. Students find products using equal sets and present results in the form of a table. The students apply their knowledge about multiplication in the creation of pictographs.

Learning Objectives

 
Students will:
  • explore the results of adding equal sets
  • construct a pictograph with icons representing multiple data points

Materials

 
Counters (such as chips)
Pieces of string or yarn
Equal Sets Activity Sheet
Bibliography of Books About Multiplication
Workmats (e.g. large construction paper)

Instructional Plan

To set the stage for this lesson, you may wish to read one of the books listed in the Bibliography of Books About Multiplication, What Comes in 2's, 3's, and 4's.

Bibliography of Books About Multiplication Bibliography of Books About Multiplication

You may also wish to discuss some examples from science such as:

  • If a starfish has 5 arms, how many arms will 2 starfish have?
  • If a spider has 8 legs, how many legs will 4 spiders have?

This is also a good time to relate multiplication to addition, in that multiplication is repeated addition. In the example, "If a starfish has 5 arms, how many arms will 2 starfish have?", students may recognize the mulitplication fact 5 × 2 = 10, and they may recognize the addition fact 5 + 5 = 10.

 

 

Provide students with counters, pieces of string or yarn, and a workmat (large construction paper). Tell them that they will be making equal sets and finding out how many counters there are in all. Ask them to make 5 sets of 4 counters, with each set inside its own yarn circle. Then tell them to determine in any way they wish how many counters they have used. Next display an empty table with several rows in which the three columns are labeled "Number of Sets, Number in Each Set, and Number in All". Have them suggest what will go in each column (5, 4, 20). Then have them work in pairs to create new equal set models for addition. When they have identified the product, help them enter their findings on their Equal Sets activity sheet.

Activity Sheet Equal Sets Activity Sheet

You may wish to review the terms factor, multiple, and product.

Allow the children time to make several entries, then ask them if they see any similarities among the entries. If examples of the order property are not mentioned, prompt them to notice such entries. Encourage students to also notice rows in which the last column shows the same number.

To provide an application for this model, have the children create pictographs of favorite fruit. If the children are not familiar with pictographs in which an icon stands for multiple data points, you might demonstrate one or find an example in their Social Studies textbook. Ask the students to vote for their favorite fruit, limiting the choices to a set number of possible selections. Then ask them to tally the collected data. Now assign them to groups and have each group construct a pictograph. Before they begin, you may wish to help the groups find an appropriate number for each icon to represent and also to decide what to do if the number choosing that fruit is not a multiple of the number they chose.

When the children are ready, call them together to share the pictographs and describe how each of the entries on it was constructed.

Questions for Students

 

Suppose you had 5 groups of 0. What would be the product? How about 0 groups of 5?

[0; 0]

Would you get the same product if you had 4 groups of 3 instead of 3 groups of 4?

[Yes, the product would be 12 in either case.]

Assessment Options

 
  1. At this stage of the unit, it is important for students to know how to:
    • model multiplication using the set model
    • construct a pictograph
    • recognize and use the order principle.
  2. These guiding questions may assist you in understanding the students’ level of knowledge, but others may seem appropriate as your dialogue with the students progresses. You may find it helpful add to your recordings on the Class Notes recording sheet you began earlier in this unit. This data may be helpful as you plan strategies for regrouping students and for remediation or extension activities.

Teacher Reflection

 
  • Which students met all the objectives of this lesson? What extension activities are appropriate for these students?
  • Which students did not meet the objectives of this lesson? What mathematical ideas need clarification? What misconceptions did they demonstrate?
  • What adjustments would I make the next time I teach this lesson?

NCTM Standards and Expectations

 
Number & Operations 3-5
  1. Develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
  2. Understand the effects of multiplying and dividing whole numbers.
  3. Understand various meanings of multiplication and division.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics


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