Lesson 4 | Decimal Fractions | 4th Grade Mathematics

Objective

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.

Common Core Standards

Core Standards

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.

Number and Operations—Fractions

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.

Number and Operations—Fractions

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.

Foundational Standards

The foundational standards covered in this lesson

4.NBT.A.2

Number and Operations in Base Ten

4.NBT.A.2 — Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
3.NF.A.2

Number and Operations—Fractions

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

Number and Operations—Fractions

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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Write a decimal value in fraction form, decimal form, unit form, and decimal and fraction expanded form for some number to hundredths.
Understand the value of each digit in a multi-digit decimal to hundredths, using pictorial base ten blocks to help (MP.7).
Understand that place value is symmetric about the ones place, as opposed to the decimal point.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

As mentioned in Lesson 3, there are many ways to read decimals aloud, but to help ensure students have a strong concept of the value of decimals, try to use place value language to read them for now. Further, for the sake of avoiding confusion, we recommend only using the word “and” in place of the decimal point and nowhere else. For example, 217.35 is read “two hundred seventeen and thirty-five hundredths,” not “two hundred and seventeen and thirty-five hundredths” or “two hundred and seventeen and thirty-five hundredths”. As time goes on, you can read them as “zero point _” or “point _”, as many mathematicians and scientists do. This will be especially helpful later in the unit, since “[d]ecimals with many non-zero digits are more easily read aloud in this manner. (For example, the number π, which has infinitely many non-zero digits, begins 3.1415…)” (NBT Progression, p. 14).

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Complete the following table. Draw models for each row if they will help you.

Fraction Form	Fraction Expanded Form	Decimal Expanded Form	Decimal Form
		$$1\times1+5\times0.1+7\times0.01$$
	$$(5\times 1)+\left(0 \times \frac{1}{10} \right) + \left(3\times\frac{1}{100}\right)$$
			$$98.30$$
$$623 \frac{46}{100}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Use the following numbers to answer each of the following questions:

1.57
5.03
98.30
623.46

a. What is the value of the digit 1 in (i)? The digit 5?

b. What is the value of the digit 3 in (ii), (iii), and (iv) above? How are those values related to one another?

c. What is the value of the digit in the hundreds place in (iv)? What is the value of the digit in the hundredths place in (iv)? How are these similar? How are they different?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How do the base ten blocks in #1 help to show the value of each digit?
In #2f, express this number in ones and tenths. Is this equivalent to 7 ones 70 hundredths? How do you know?
In #3, how did you determine the value of each digit? Did anyone draw base ten blocks to help?
Why is there one more item in the center column of #4 than in the other columns?
In #6, we can write the expanded notation of a number in different ways. What is similar about each of the ways? What is different?
Ten is found in the word “tenths,” and hundred is found in the word “hundredths.” We say that these place values are symmetric. What are they symmetric around?
Why is the number zero important? What role does it play in the number 100? The number 0.01? Based on that understanding, is 7 the same as 7.0? Why or why not?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Use the number below to answer the following questions.

268.39

a. What digit is in the hundreds place? What is its value?

b. What digit is in the tens place? What is its value?

c. What digit is in the ones place? What is its value?

d. What digit is in the tenths place? What is its value?

e. What digit is in the hundredths place? What is its value?

Student Response

Create a free account or sign in to view Student Response

Problem 2

Complete the following chart.

Fraction form	Fraction expanded form	Decimal expanded form	Decimal form
$$21\frac{9}{100}$$
			50.48

Student Response

An example response to the Target Task at the level of detail expected of the students.

Create a free account or sign in to view Student Response

Additional Practice

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

Extra Practice Problems

Answer Keys

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 3

Lesson 5

Lesson Map

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.

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.

4.NF.C.6

Topic B: Understanding Tenths and Hundredths

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.

4.NF.C.5 4.NF.C.6

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.

4.NF.C.5 4.NF.C.6

Regroup decimal numbers with more than 9 tenths or 9 hundredths into simplest unit form and vice versa.

4.NF.C.5 4.NF.C.6

Topic C: Decimal Comparison

Locate decimals on a number line and explain their placement.

4.NF.C.6

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.

4.NF.C.7

Topic D: Decimal Addition

Add tenths with hundredths written as decimal fractions.

4.NF.C.5

Add tenths with hundredths written as decimals.

4.NF.C.5

Solve word problems involving the addition of decimals and decimal fractions.

4.NF.C.5

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.

4.MD.A.2

Decimal Fractions

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Number and Operations—Fractions

Foundational Standards

Number and Operations in Base Ten

Number and Operations—Fractions

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy