Illuminations: Six and Seven as Factors

# Six and Seven as Factors

## Finding Products

 Students examine the role of commutativity and the multiplicative identity, play a multiplication game, and explore products where one of the factors is 6. They also create a "My Personal Multiplication Chart" to record products.

### Learning Objectives

 Students will: find products where one factor is 6 or 7 use the commutative property explore the results of multiplying by 1 and by 0 practice the multiplication facts with factors of 6 and 7 create a learning tool for mastering products

### Materials

 Crayons Paper File Cards My Multiplication Chart Activity Sheet

### Questions for Students

 If you spin a 5, what would the product of 6 and that number be? What multiplication fact would show that? [30; 5 × 6 = 30.] If you spin a 1, what would the product of that number and 6 be? Why are you sure of that? [6; The multiplicative identity.] How could you model with streets and roads the multiplication facts 3 × 6 = 18 and 6 × 3 = 18? What is alike between these multiplication sentences? What is different? [Student responses may vary.] What numbers do you say when you skip count by 7's to 70? Which of these are even numbers? [7, 14, 21, 28, 35, 42, 49, 56, 63, 70; When the other factor is even, the product is even.]

### Assessment Options

 Distribute a copy of the My Multiplication Chart activity sheet to each student. Students should complete the chart for the facts they currently know. Collect the charts to assess student progress.

### Extensions

 What products can you get when you multiply by 7? How many are even? Will you get an even product when you multiply by 3? By 6? By 8? By 9? How can you tell if the product will be even? How many ways can you have a product of 6? Of 12? Of 25? Of 42? Of 1? Students who need additional practice may use the Times Table tool.

### Teacher Reflection

 Are some students reluctant to participate? How can I encourage their participation? Which students are able to identify with accuracy the facts they know by heart? How can the other students be helped to do this? Which students were able to stay on task while they played the game? Should some pairs be changed in the next lesson? What extension activities are appropriate for students who have memorized all their multiplication facts?

### NCTM Standards and Expectations

 Number & Operations 3-5Understand the effects of multiplying and dividing whole numbers. Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 3050. Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

### References

 Wirtz, Robert. Drill and Practice at the Problem Solving Level. Washington DC: CDA, 1976.
 This lesson was developed by Grace M. Burton.

1 period

### NCTM Resources

Principles and Standards for School Mathematics

### Activities

 More and Better Mathematics for All Students
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