5.NBT.2

Standard

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.


Student Language:

  • "I can explain patterns when multiplying a number by powers of 10."
  • "I can explain patterns when a decimal is multiplied or divided by a power of 10."

Explanation

About the Math, Learning Targets, and Rigor

This standard includes multiplying by multiples of 10 and powers of 10, including 10^2 which is 10 × 10 = 100, and 10^3 which is 10 × 10 × 10 = 1,000. Students should have experiences working with connecting the pattern of the number of zeros in the product when you multiply by powers of 10. (i.e. 10^4 has 4 zeroes. 10 x 10 x 10 x 10 = 10,000).


Example:

2.5 × 103 = 2.5(10 × 10 × 10) = 2.5 × 1,000 = 2,500. Students should reason that the exponent above the 10 indicates how many places the decimal point is moving (not just that the decimal point is moving but that you are multiplying or making the number 10 times greater three times) when you multiply by a power of 10. Since we are multiplying by a power of 10 the decimal point moves to the right.

This will relate well to subsequent work with operating with fractions. This example shows that when we divide by powers of 10, the exponent above the 10 indicates how many places the decimal point is moving (how many times we are dividing by 10 , the number becomes ten times smaller). Since we are dividing by powers of 10, the decimal point moves to the left.


NOTE: Provide students with many opportunities to explore this concept and come to this understanding; this should not just be taught procedurally.

Resources

Videos


EngageNY Lessons


Extra Practice


Released Assessment Questions

PARCC

Common Core State Standards

5.NBT.2-2

Use whole-number exponents to denote powers of 10.

      • For the explain aspect of 5.NBT.2, see 5.C.3.


Performance Indicators: 5.NBT.2-2

Level 5: Exceeds Expectations

In any multi-digit number, recognizes a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left and uses whole number exponents to denote powers of 10 and uses symbols to compare two powers of 10 expressed exponentially (compare 10^2 to 10^5 ).


Level 4: Meets Expectations

In any multi-digit number, recognizes a digit in one place represents 10 times as much as it represents in the place to its right or 1/10 of what it represents in the place to its left and uses whole number exponents to denote powers of 10.


Critiquing/Reasoning Standards

5.C.3

Reason about the place value system itself.

(Content Scope: Knowledge and skills articulated in 5.NBT.A)

    • Tasks do not involve reasoning about place value in service of some other goal (e.g., to multiply multi-digit numbers). Rather, tasks involve reasoning directly about the place value system, in ways consistent with the indicated content scope.


Performance Indicators: 5.C.3

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on place value system including:

    • a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
    • an efficient and logical progression of steps with appropriate justification
    • precision of calculation
    • correct use of grade-level vocabulary, symbols and labels
    • justification of a conclusion
    • evaluation of whether an argument or conclusion is generalizable
    • evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning, and providing a counterexample where applicable.

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on place value system including:

    • a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
    • a logical progression of steps
    • precision of calculation
    • correct use of grade-level vocabulary, symbols and labels
    • justification of a conclusion
    • evaluation of whether an argument or conclusion is generalizable
    • evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning.