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Multiplication and Division: Patterns, Algebra, and Strategies

Learn about patterns, algebra, and strategies for multiplication and division. Explore the concepts of doubling, halving, partitioning, and using the distributive property. Practice skip counting and repeated addition or subtraction. Enhance your problem-solving skills!

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Multiplication and Division: Patterns, Algebra, and Strategies

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  1. $2 $4 $8 $16 $32 $64 $108 $2 $4 $6 $8 $10 $12 $14 skip counting is repeatedly adding 2 repeatedly multiplying by 2 Multiplication and Division 10 Patterns and Algebra 18

  2. 2 x 7 = x 2 = double 5 + 2 distributive property distribute multiplication 
over addition 2 x 5 = 10 2 x 2 = 4 10 + 4 = 14 2 x 7 = 14 Multiplication and Division 10 Patterns and Algebra 18

  3. $80 $40 $20 $10 $5 $2.50 $1.25 $80 $78 $76 $74 $72 $70 $68 repeatedly 
dividing by 
2 skip counting backwards is repeatedly subtracting 2 Multiplication and Division 10 Patterns and Algebra 18

  4. 1 of 16 = 16 ÷ 2 = ÷ 2 = halve 2 ÷ 2 = 10 + 6 10 + 6 1 of 10 = 5 of 6 = 3 10 ÷ 2 = 5 6 ÷ 2 = 3 5 + 3 = 8 2 1 2 5 + 3 = 8 partition and divide by 2 partition and halve 1 of 16 = 8 16 ÷ 2 = 8 2 Multiplication and Division 10 Patterns and Algebra 18

  5. 15 ÷ 2 = 1 ÷ 2 = halve of 15 = 2 ÷ 2 = 10 + 5 10 + 5 4 + 1 4 + 1 1 10 ÷ 2 = 5 4 ÷ 2 = 2 5 + 2 = 7 of 10 = 5 of 4 = 2 2 1 2 5 + 2 = 7 partition and divide by 2 partition and halve 15 ÷ 2 = 7r1 of 15 = 7r1 1 2 Multiplication and Division 10 Patterns and Algebra 18

  6. 2 x 17 = x 2 = double 10 + 7 distributive property distribute multiplication 
over addition 2 x 10 = 20 2 x 7 = 14 20 + 14 = 34 2 x 17 = 34 Multiplication and Division 10 Patterns and Algebra 18

  7. 1 36 ÷ 2 = ÷ 2 = halve of 36 = 2 1 ÷ 2 = 30 + 6 30 + 6 2 1 of 30 = 15 of 6 = 3 30 ÷ 2 = 15 6 ÷ 2 = 3 15 + 3 = 18 2 1 2 15 + 3 = 18 partition and divide by 2 partition and halve 1 36 ÷ 2 = 18 of 36 = 18 2 Multiplication and Division 10 Patterns and Algebra 18

  8. 35 ÷ 2 = ÷ 2 = halve of 35 = 1 2 ÷ 2 = 1 30 + 5 30 + 5 2 4 + 1 4 + 1 30 ÷ 2 = 5 4 ÷ 2 = 2 15 + 2 = 7 1 of 30 = 5 of 4 = 2 2 1 2 15 + 2 = 7 partition and divide by 2 partition and halve of 35 = 17r1 35 ÷ 2 = 17r1 1 2 Multiplication and Division 10 Patterns and Algebra 18

  9. 2 x 27 = x 2 = double 20 + 7 2 x 20 = 2 x 10 x 2 2 x 2 = 4 4 x 10 = 40 2 x 20 = 40 2 x 7 = 14 40 + 14 = 54 associative property we can multiply in any order distributive property distribute multiplication 
over addition 2 x 27 = 54 Multiplication and Division 10 Patterns and Algebra 18

  10. 136 ÷ 2 = ÷ 2 = halve of 136 = 1 2 ÷ 2 = 100 +30 + 6 100 +30 + 6 1 100 ÷ 2 = 50 30 ÷ 2 = 15 6 ÷ 2 = 3 50 + 15 + 3 = 68 of 100 = 50 2 of 30 = 15 of 6 = 3 1 2 1 2 50 + 15 + 3 = 68 partition and halve partition and divide by 2 136 ÷ 2 = 68 of 136 = 68 1 2 Multiplication and Division 10 Patterns and Algebra 18

  11. 135 ÷ 2 = 1 ÷ 2 = halve of 135 = 2 1 ÷ 2 = 100 +30 + 5 100 +30 + 5 2 4 + 1 4 + 1 1 100 ÷ 2 = 50 30 ÷ 2 = 15 4 ÷ 2 = 2 50 + 15 + 2 = 67 of 100 = 50 2 1 of 30 = 15 of 4 = 2 2 1 2 50 + 15 + 2 = 67 partition and halve partition and divide by 2 of 35 = 17r1 1 135 ÷ 2 = 67r1 Multiplication and Division 10 Patterns and Algebra 18 2

  12. 2 x 87 = x 2 = double 80 + 7 2 x 80 = 160 2 x 7 = 14 160 + 14 = 174 2 x 80 = 2 x 10 x 8 2 x 8 = 16 16 x 10 = 160 associative property we can multiply in any order distributive property distribute multiplication 
over addition 2 x 87 = 174 Multiplication and Division 10 Patterns and Algebra 18

  13. 2 x 287 = x 2 = double 200 + 80 + 7 2 x 80 = 2 x 10 x 8 2 x 8 = 16 16 x 10 = 160 2 x 200 = 400 2 x 80 = 160 2 x 7 = 14 400 + 160 + 14 = 574 associative property we can multiply in any order distributive property distribute multiplication 
over addition 2 x 287 = 574 Multiplication and Division 10 Patterns and Algebra 18

  14. What number are we multiplying by 2? How could we multiply this number by 2? How could we use the distributive property? How could we double? What number are we dividing by 2? What number are we halving? How could we divide this number by 2? How could we halve this number? How could we partition the number? How could we divide the parts? How could we add the quotients? The number I selected is ... I multiplied … by 2 by ... I partitioned the number into … I multiplied the parts … I added the products … I doubled by … The number I selected is ... I divided … by 2 by ... I halved this number by … I partitioned the number into … I divided the parts … I added the quotients … What is multiplication? How could we multiply by 3? What is the distributive property? What is division? How could we divide by 2? What fraction do we get when we divide by 2? Multiplication and Division 10 Patterns and Algebra 18

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