Curriculum / Math / 5th Grade / Unit 1: Place Value with Decimals / Lesson 9
Math
Unit 1
5th Grade
Lesson 9 of 13
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Lesson Notes
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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.
The core standards covered in this lesson
5.NBT.A.1 — Recognize that in a multi-digit number, 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.
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
Suggestions for teachers to help them teach this lesson
You might decide to include a Do Now/Warm-Up exercise at the beginning of the lesson that asks students to solve division equations with single decimal units (as either the dividend or the quotient), e.g., $$0.1\div10$$ and $$10\div1,000$$.
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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. Solve.
b. What do you notice about Part (a)? What do you wonder?
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c. Solve.
d. What do you notice about Part (c)? What do you wonder?
e. Use your conclusions from Parts (b) and (d) to find the solutions below.
Write a number in which the value of the digit 5 is $$\frac{1}{1000}$$ the value of the digit 5 in 5.26. Explain how you know the number you wrote is correct.
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
A number is given below.
605.49
In a different number, the 5 represents $$\frac{1}{10}$$ of the value of the 5 in the number above. What value is represented by the 5 in the other number?
Explain why $$ 56 \div 1,000 = 0.056$$.
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
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Next
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
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
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.
5.NBT.A.2
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.
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.
Topic C: Reading, Writing, Comparing, and Rounding Decimals
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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