Curriculum / Math / 4th Grade / Unit 6: Decimal Fractions / Lesson 3
Math
Unit 6
4th Grade
Lesson 3 of 13
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Represent decimals to hundredths less than one, understanding the equivalence of some number of tenths and ten times as many hundredths. Write a decimal value in fraction, decimal, and unit form.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.
4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
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. Fill in the following blanks to make true statements. Use base ten blocks to help you.
b. Below is an area model that represents 1 one. It is partitioned into tenths. Partition it to show what you would expect the next smallest unit to look like so that it continues the pattern in Part (a).
c. Use what you notice in Part (a) and (b) to write a similar sentence that starts “1 tenth is the same as…”
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The shaded part of this diagram represents 1 hundredth. We can write this as the fraction $$\frac{1}{100}$$ or as the decimal 0.01.
Fill out the following table to represent each given number.
a. Explain why $${{1\over10}={10\over100}}$$. Draw a picture to illustrate your explanation.
b. Explain why $${0.20 = 0.2}$$. Draw a picture to illustrate your explanation.
Fraction Equivalence, accessed on May 29, 2018, 11:07 a.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.
Jani and Kai are representing a decimal number. Here are the area models they drew:
a. What value do you think Jani and Kai are trying to model? How do you know?
b. Draw pictures to show what Kai might have drawn for each area model in Anchor Task 2.
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. Model 53 hundredths on the area model below.
b. What is 53 hundredths written as a decimal?
Damien says 0.78 is equivalent to 78 hundredths. Kelly says 0.78 is equivalent to 7 tenths and 8 hundredths. Who is right? Explain how you know.
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.
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Represent decimals to hundredths more than one. Write a decimal value in fraction, decimal, unit, and decimal and fraction expanded form for some number to hundredths.
Topic A: Understanding Tenths
Represent decimals to tenths less than or equal to one with area models. Write a decimal value in fraction, decimal, and unit form.
Standards
4.NF.C.6
Represent decimals to tenths greater than one with pictorial base ten blocks. Write a decimal value in fraction, decimal, unit, and fraction and decimal expanded form.
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Topic B: Understanding Tenths and Hundredths
4.NF.C.54.NF.C.6
Regroup decimal numbers with more than 9 tenths or 9 hundredths into simplest unit form and vice versa.
Topic C: Decimal Comparison
Locate decimals on a number line and explain their placement.
Compare two decimals, recording the result of a comparison with the symbol >, =, or <, and justify the conclusion.
4.NF.C.7
Compare two or more decimals written in various forms.
Topic D: Decimal Addition
Add tenths with hundredths written as decimal fractions.
4.NF.C.5
Add tenths with hundredths written as decimals.
Solve word problems involving the addition of decimals and decimal fractions.
Topic E: Money as a Decimal Amount
Find the value of some combination of dollar bills and coins.
4.MD.A.2
Solve word problems involving money.
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