Mathematics Pacing Resource Document
5.NS.4
Standard: 5.NS.4: 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.
Teacher Background Information:
The student will:
*Understand the way places shift and the zeros pattern that results when the multiplier is 0.1; 0.01; 0.001.
*Solve multiplication problems with decimal multipliers when the other factor is either a whole number or a decimal number.
*Use money examples to see the way places shift to the right
*Understand and apply shift patterns when multiplying by 10; 100; 1,000; 0.1; 0.01; or 0.001
*Solve multi-digit multiplication problems when one or both factors are decimal numbers
Lesson Plans/Print Activities:

Math Expressions:
*Unit 7, Lessons 8 and 9 (Note: TE p. 701: Teaching Note: Math Background—
Introduce the list called “the powers of 10.”)

Learnzillion: Go to www.learnzillion.com and enter the following quick code.
o Explain and represent patterns in zeros when multiplying or dividing by a
power of 10: LZ2471, LZ2583, LZ2762, LZ2836
o Explain the effect of multiplication and division by a power of ten on the
number of zeroes: LZ2835, LZ2730, LZ2805, LZ2806, LZ2808
o Explain patterns in zeros and decimals when multiplying and dividing by
powers of 10: LZ434, LZ435, LZ436, LZ437, LZ438, LZ439, LZ440, LZ1874

http://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/mult-div-by10-dec-pre-alg/v/multiplying-a-decimal-by-a-power-of-10 Khan academy: Moving
the decimal to multiply and divide by 10

http://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place-valuedecimals-top/cc-5th-mult-powers-of-10/v/powers-of-10 Khan Academy:
Multiplication by powers of 10
Indianapolis Public Schools
Web-based Practice:

https://www.mangahigh.com/en/maths_games/number/calculations_wit
h_whole_numbers_integers/multiply_and_divide_whole_numbers_by_10
_100_and_1000 Manga High tutorial: Multiply and divide whole numbers
by 10, 100 and 1000

http://braingenie.ck12.org/skills/101866 Brain Genie: online video and
practice
Curriculum and Instruction
Mathematics Pacing Resource Document

https://www.engageny.org/resource/grade-5-mathematics-module-2-topiclesson-2 Engage NY: Estimate multi-digit products by rounding factors to a basic
fact and using place value patterns

https://www.engageny.org/resource/grade-5-mathematics-module-1-topiclesson-3 Engage NY: Use exponents to name place value units and explain
patterns in the placement of the decimal point.
Item Bank:
1) Write 61, 204 in expanded form using exponents. Use what you know about powers of ten and exponents to explain your answer. [Howard County Public
Schools, Maryland] Sample Answer: (6 × 104) + (1 × 103) + (2 × 102) + (4 × 100) The 6 in this number is worth 60,000, which is 6 × 104. A pattern continues with the
exponent decreasing by one each time. Notice that 101 does not appear since a zero holds the tens place.
2) Which is another name for: (7 × 103) + (4 × 102) + (2 × 101) + (9 × 1)
Use what you know about powers of ten and exponents to explain your answer. [Howard County Public Schools, Maryland] Sample Answer: 7,429 See answer
above for a similar explanation.
3) Explain the pattern you can use to find the product when multiplying a whole number by a power of 10.
Will this pattern be the same when multiplying a decimal by a power of 10? Explain with examples. [Howard County Public Schools, Maryland] Sample Answer:
The pattern you use when multiplying whole numbers by powers of ten depends on the power of 10. The exponent will tell you how many time bigger than the
other factor the product is. In other words it will tell you how many zeros to add to the right of the factor to get the product. (13 x 104 = 130,000)
The pattern will be similar when multiplying a decimal by a power of 10. In this case, however, instead of adding zeros, it may be necessary to move the decimal
point to the right to get a product that is 10, 100, 1,000 times larger than one factor.
4) How can you use what you know about multiplying by powers of 10 to help you find 4 x 23 x 25? Explain your thinking. [Howard County Public Schools,
Maryland] Sample Answer: I look for two factors that will give a product that is a power of 10. In this case, 25 x 4 is 100, so I will do that first. Then I take 100 x 23
to get 2,300.
Performance Tasks from www.illustrativemathematics.org:
https://www.illustrativemathematics.org/illustrations/1524 Marta’s Multiplication Error
https://www.illustrativemathematics.org/illustrations/1620 Multiplying Decimals by 10
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.4
Standard: 5.NS.4: 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.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.NS.4
Standard: 5.NS.4: 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.
Indianapolis Public Schools
Curriculum and Instruction