Curriculum / Math / 5th Grade / Unit 1: Place Value with Decimals / Lesson 2
Math
Unit 1
5th Grade
Lesson 2 of 13
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Use whole numbers to denote powers of 10. Explain patterns in the number of zeros when multiplying any powers of 10 by any other powers of 10.
The core standards covered in this lesson
5.NBT.A.2 — 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.
The foundational standards covered in this lesson
4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
a. How many do you see? How do you see them?
b. Instead of writing $$10 \times 10$$, we can write $$10^2$$, which we read “ten to the power of two.” The two is the exponent and tells us how many times we multiply 10 by itself. How would you represent the number of the smallest spokes in the image above as a power of 10?
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Grade 5 > Unit 6 > Lesson 2 > Warm-up, accessed on June 14, 2022, 5 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
a. Write each of the following as a product of tens and in standard form.
b. Write each of the following as a power of 10.
a. Solve.
b. How were powers of 10 useful in solving Part (a)?
Grade 5 > Unit 6 > Lesson 2 > Activity 2, accessed on June 14, 2022, 5:12 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Fill in the following chart.
What pattern do you notice between the standard form and repeated multiplication sentences in the table in #1?
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
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Explain patterns in the number of zeros of the product when multiplying a whole number by 10. Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right.
Topic A: Place Value with Whole Numbers
Build whole numbers to 1 million by multiplying by 10 repeatedly.
Standards
5.NBT.A.15.NBT.A.2
5.NBT.A.2
Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10.
Explain patterns in the number of zeros of the quotient when dividing a whole number by 10. Recognize that in a multi-digit whole number, a digit in any place represents $${\frac{1}{10}}$$ as much as it represents in the place to its left.
Explain patterns in the number of zeros of the quotient when dividing a whole number by powers of 10.
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Topic B: Place Value with Decimals
Build decimal numbers to thousandths by dividing by 10 repeatedly.
Explain patterns in the placement of the decimal point when a decimal is multiplied by any power of 10. Recognize that in a multi-digit decimal, a digit in any place represents 10 times as much as it represents in the place to its right.
Explain patterns in the placement of the decimal point when a decimal is divided by a power of 10. Recognize that in a multi-digit decimal, a digit in any place represents $${\frac{1}{10}}$$ as much as it represents in the place to its left.
Topic C: Reading, Writing, Comparing, and Rounding Decimals
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
5.NBT.A.3.A
Compare multi-digit decimals to the thousandths based on meanings of the digits using $${>}$$, $${<}$$, or $$=$$ to record the comparison.
5.NBT.A.3.B
Use place value understanding to round decimals to the nearest whole.
5.NBT.A.4
Use place value understanding to round decimals to any place.
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