Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

 

Students are able to… 

  • Use manipulatives (base-ten blocks and coins), pictures, numbers, and words to explore multiplication of whole numbers and decimal numbers by powers of 10 (10; 100; 1,000; 10,000)
  • Engage in discussion describing patterns they have found and justify why those patterns work.
  • Understand and use exponential notation to write powers of ten.
  • Extend their knowledge of notation of exponents to express powers of ten to exploring what happens when they multiply a number times a power of ten written in multiple ways:
    • 5 x 10 x 10 = 500
    • 5 x 100 = 500
    • 5 x 102 = 500

 

Students are able to…because teachers:

  • Provide opportunities for to explore multiplying a number by a power of ten using concrete models, pictures, and words beginning with whole number examples and move to decimal numbers to the thousandths place.
    • For example: 5 x 10 = 50; 5 x 100 = 500; 5 x 1000 = 5000
    • 10 x $ .05 = $ 0.50; 100 x $ .05 = $ 5
  • Facilitate student discussions for students to justify patterns found and generalizations made.
  • Explain what happens with place value when describing patterns and relationships between the exponent and the number of times 10 is used as a factor.
    • 1,000 = 10 x 10 x 10 = 103

 

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Questions to ask students:

  • What do you notice about the product of 7 x 103?
    • Sample answer that indicates understanding: 103 can be represented by 10 x 10 x 10 or 10 groups of 100. The product represents 7 groups of 1,000, or 7,000.
    • Sample answer that indicates an incomplete understanding or a misconception: The product is 210 because 7 x 30 = 210. (Student sees 103 as 10 x 3)
  • Describe the pattern you see in the following:

10 = 101

100 = 10 x 10 = 102

1000 = 10 x 10 x 10 = 103

10,000 = 10 x 10 x 10 x 10 = 104

  • Sample answer that indicates understanding: The exponent tells me the number of times the base is used as a factor so if the base of 10 is used as a factor 4 times, for example, then I will need to multiply 10 by the factor 10, 4 times. The exponent increases in the pattern so the number of times we are multiplying 10 by the factor 10 increases, and the product becomes larger.
  • Sample answer that indicates an incomplete understanding or a misconception: The more zeroes in the number, the more tens. There are more zeroes added to the number as it gets larger.

 

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FSA Notes

Cognitive Complexity Level: 2 – Basic Application of Skills and Concepts

Achievement Level Descriptors: 

Level 2: recognizes patterns in the number of zeroes of products when multiplying a number by powers of 10; uses whole number exponents greater than zero to denote powers of 10

Level 3: explains patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explains patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10; uses whole number exponents to denote powers of 10

Level 4: interprets a multiplication problem to identify the factor of 10 by which one number is greater or lesser than another

Level 5: intentionally left blank

Assessment Limits: 

Items may contain whole number and decimal place values from millions to thousandths.
Items may contain whole number exponents with bases of 10.

 

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Additional Resources:

Additional in depth content knowledge:

Video:

 

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Sample Formative Assessment Tasks:

[divider] [/divider] Resources/Tasks to Support Your Child at Home:

0.04 x 10² = 40                        0.04 x 10³ = 400

             What was Maria’s error? Use pictures, words or number to explain.

  • Wayne was finding the quotients of decimals and powers of ten. He wrote:

0.9 ÷ 100 = 90                          0.09 ÷ 10 = 0.9

What was Wayne’s error? Use pictures, words or number to explain.

  • Create a 2-digit number. Write the result of multiplying or dividing by a power of 10 as shown below: