Illuminations: Multiplication: It's in the Cards

Multiplication: It's in the Cards

Looking for Calculator Patterns

Students use a web-based calculator to create and compare counting patterns using the constant function feature of the calculator. Making connections between multiple representations of counting patterns reinforces students understanding of this important idea and helps them recall these patterns as multiplication facts.

Learning Objectives
 
Students will:
  • skip count by twos, threes, fives, and tens
  • find products by adding equal sets
  • explore commutativity
  • practice the multiplication facts
  • record products on a multiplication chart

Materials
 
Counters or cubes
Playing cards
Crayons and Paper
Rules for Card Games
My Multiplication Chart Activity Sheet
Calculator and Hundred Boards Applet

Instructional Plan

To assess prior knowledge, invite groups of students to skip count in unison by 2's, 5's and 10's. As they do so, notice which students seem sure of the order of the numbers and which hesitate. Those students who are unable to skip count by these numbers fluently may need additional practice before attempting this lesson.

Next, assign the students to pairs and introduce the Calculator and Hundred Boards Applet.

Calculator and Hundred Board Applet Calculator and Hundred Board Applet

While using this applet, as the students enter repeated addition (3 + 3 =, =, =,) into the calculator, the squares on the hundred board that show the sums change color. Invite pairs of students to take turns using this site to count by twos, threes, fives, and tens.

Now call the class together and ask a volunteer to model repeated addition using counters and cubes and then go to the board, find the sum of 5 + 5 + 5, record it, add 3 + 3 + 3 + 3 + 3 and record that sum, and then compare the results. Encourage the students to try this with other pairs of numbers that represent the commutative property. Tell them to write what they notice in their own words. Finally, introduce them, if needed, to the formal term, "commutative." Ask them how knowing this can help them learn their number facts. If they know 3 × 4 = 12, they also know the product 4 × 3.

Next, assign the students to groups of three to five each, and distribute to each group a deck of playing cards from which the face cards have been removed. Display the Rules for Card Games of the game entitled Go Fishing. Tell them that this is a mathematically enhanced version of Go Fish. Allow the students to play several rounds.

Rules for Card Games

 

To end the lesson, ask the students to enter the multiplication facts that they are sure of on the My Multiplication Chart Activity Sheet.

My Multiplication Chart

A sample chart is shown below. Tell the students that they will be using this chart for several days.

 

 

Take note of which numbers students filled in on the chart. Although many numbers will not be filled in because students have not yet been exposed to those facts, others will not be filled in because students will not be comfortable with results already obtained. Make a note of the multiplication facts with which students need more practice, and look for opportunities to reinforce those facts during upcoming lessons.

Questions for Students
 

What is meant by the commutative property of multiplication?

[The order in which we multiply factors does not affect the product.]

Give an example of the commutative property of multiplication.

[Students examples may vary, but they should include some of the in-class examples.}

Assessment Options
 
  1. At this stage of the unit, it is important for students to know how to:

    • Skip count by twos, threes, fives, and tens
    • Find products by adding equal sets
    • Define and use the commutative property
  2. The guiding questions will help the students focus on the mathematics in this lesson. These questions will also aid you in assessing the students' level of knowledge and skill.
  3. Documenting information about students' understanding and skills throughout the unit by using the Class Notes may help you plan appropriate extension and remediation activities. You may also find this information useful when completing individual education plans.
  4. Collect students' My Multiplication Chart activity sheets and assess their recall of basic multiplication facts so far.

Teacher Reflection
 
  • Which students are able to skip count by 2, 3, 5, and 10 rapidly and correctly? What extension activities would be appropriate for those students?
  • Which students were able to identify the multiplication facts that they have at the immediate recall level? Which students were not able to do this? What instructional experiences do they need next?
  • What adjustments will I make the next time that I teach this lesson?

NCTM Standards and Expectations
 
Number & Operations 3-5
  1. Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems.
  2. Understand various meanings of multiplication and division.
  3. Recognize equivalent representations for the same number and generate them by decomposing and composing numbers.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

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