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Keeping It All Together

Number and Operations
Location: Unknown

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.

Assign the students to pairs, and ask each student to select three multiplication facts that he or she wants to work on. Have the students cut two triangles from each of two file cards. Demonstrate how to make a triangular flash card by putting the two factors in two of the corners and the product in the other corner. Ask them to make triangle fact cards for the facts they chose, then trade them with their partner. Ask each student to cover the product on one card with his or her thumb, show the card to the other student, and ask him or her to tell the product.

1276 cards triangle 

When the students have had a chance to try all the cards, distribute the Rules for Card Games.

pdficon Rules for Card Games 

Students will then play a new card game, Climb the Ladder.

Next, show the students how to play The Product Game.

appicon The Product Game

Initially, you may choose two students to play the game as the rest of the class watches. You may need to call their attention to the oval-shaped markers at the end of the number bar. As students begin to understand the rules for play, other pairs may work together at their computers to play the game.

To conclude the lesson, have students complete their My Multiplication Chart activity sheet. At this point, you should see significant progress in their mastery of multiplication facts.

pdficon My Multiplication Chart

Alternatively, or in addition to the above activities, students can work (either individually or in pairs) to review the multiplication facts by using the Concentration applet.

appicon Concentration

To do so, students should select the multiplication facts under Levels, and either 1 or 2 players. In this activity, students match the factors with their associated products (shown in various representations explored in this unit.)

Assessment Options

  1. At this stage of the unit, it is important for students to:
    • Describe the effects of the commutative property.
    • Identify the multiplication facts that they can immediately recall.
    • Choose strategies to help them learn multiplication facts.
  2. Your notes on the students' progress will be helpful as you plan ways to ensure that each student has mastered the multiplication facts. Use the Class Notes recording sheet to document student progress.
  3. Collect the students' My Multiplication Chart Activity sheets.

Questions for Students 

  1. What numbers did you say when you skip counted by ___? How can knowing this help you learn the multiplication facts?
  2. What strategies do you use when you set out to learn a multiplication fact?

Teacher Reflection 

  • Which students have only a few multiplication facts left to learn? What activities should I plan for them?
  • What activities are appropriate for students who have several facts left to learn?
  • 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

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.
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.

Learning Objectives

Students will:

  • Practice reciting multiplication facts.
  • Discuss the effects of the commutative property.
  • Choose strategies to help them learn multiplication facts.

Common Core State Standards – Mathematics

Grade 3, Algebraic Thinking

  • CCSS.Math.Content.3.OA.A.3
    Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

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 3, Algebraic Thinking

  • CCSS.Math.Content.3.OA.D.8
    Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Grade 4, Algebraic Thinking

  • CCSS.Math.Content.4.OA.A.2
    Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Grade 4, Algebraic Thinking

  • CCSS.Math.Content.4.OA.A.3
    Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP6
    Attend to precision.