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Looking for Calculator Patterns

Number and Operations
Location: Unknown

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.

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.

appicon Calculator and Hundred Board 

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.

pdficon 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.

pdficon My Multiplication Chart Activity Sheet 

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

LookingForCalculatorPatterns IMAGE SampleChart 

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.

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.
    pdficon My Multiplication Chart Activity Sheet 
Move on to the next lesson, More Patterns with Products.

Questions for Students 

1. What is meant by the commutative property of multiplication?

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

2. Give an example of the commutative property of multiplication.

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

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?
Number and Operations

Looking for Patterns

Students skip count and examine multiplication patterns. They also explore the commutative property of multiplication.
Number and Operations

More Patterns with Products

After using an interactive Web site to find patterns in the multiplication tables, the students practice multiplication facts and record their current level of mastery of the multiplication facts on their personal multiplication chart.
Number and Operations

Keeping It All Together

By playing card games and using the The Product Game applet, students practice the multiplication facts. As students continue to master their facts, the teacher closely monitors their progress.

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.

NCTM Standards and Expectations

  • Recognize equivalent representations for the same number and generate them by decomposing and composing numbers.
  • Understand various meanings of multiplication and division.
  • Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems.

Common Core State Standards – Mathematics

Grade 3, Algebraic Thinking

  • CCSS.Math.Content.3.OA.A.1
    Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

Grade 3, Algebraic Thinking

  • CCSS.Math.Content.3.OA.B.5
    Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)

Grade 3, Algebraic Thinking

  • CCSS.Math.Content.3.OA.C.7
    Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Grade 4, Num & Ops Base Ten

  • CCSS.Math.Content.4.NBT.B.5
    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.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP6
    Attend to precision.