Curriculum / Math / 5th Grade / Unit 1: Place Value with Decimals / Lesson 7
Math
Unit 1
5th Grade
Lesson 7 of 13
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Lesson Notes
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Build decimal numbers to thousandths by dividing by 10 repeatedly.
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.
4.NF.C.5 — Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.6 — Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.C.7 — Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
As noted in the Progressions, “the power of the base-ten system is in repeated bundling by ten: 10 tens make a unit called a hundred. Repeating this process of creating new units by bundling in groups of ten creates units called thousand, ten thousand, hundred thousand… In learning about decimals, children partition a one into 10 equal-sized smaller units, each of which is a tenth” (NBT Progression, p. 3). While this idea of decimals being an extension of the place value system was explored a bit when decimals were first introduced in Grade 4, it is extended to further place values including thousandths and, optionally, ten thousandths.
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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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a. Here is a rectangle.
What number does the rectangle represent if each small square represents:
b. Use the value of the square and rectangle in Part (a-iii) to draw a model that represents 2.36.
c. Here is a square.
What number does each small rectangle represent if the square represents:
d. Use the value of the square and rectangle in Part (c-iii) to draw a model that represents 0.354.
Grade 6 Unit 5 Lesson 2 Teacher Version is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed June 1, 2018, 2:08 p.m..
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
Which digit is in the thousandths place of 4.5267?
Owen drew a picture to represent 0.035:
He said, “The small cubes represent tenths and the rods represent hundredths, which makes sense because ten small cubes make one rod, and ten times ten is one hundred.”
a. Explain why Owen’s reasoning is incorrect.
b. Determine two numbers that Owen’s model could represent. For each number, be sure to indicate what a small cube represents and what a rod represents.
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
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 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
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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