Please Note: this material was created for use in a classroom but can be easily modified for homeschooling use.
Introduction
This lesson will help students understand the role of the decimal point and the relationship between tenths, hundredths, and thousandths.
Prepare to teach your students about decimal points with this outline of a detailed lesson which includes steps to follow, guided practice, assessments, and extension activities. By the end of the lesson, students will understand the role of the decimal point and the relationship between tenths, hundredths, and thousandths.
Lesson Objectives
In this lesson, students will:
- explore decimal place value
- read and write decimals using tenths, hundredths, and thousandths
- compare decimals using greater-than and less-than notation.
Common Core Standards
This lesson plan appears to align with several Common Core Standards for Mathematics, particularly those related to understanding fractions and decimals. Below are some of the relevant standards:
For Grade 4:
- CCSS.MATH.CONTENT.4.NF.C.6: Understand decimal notation for fractions, and compare decimal fractions.
For Grade 5:
- CCSS.MATH.CONTENT.5.NBT.A.3: Read, write, and compare decimals to thousandths.
- CCSS.MATH.CONTENT.5.NBT.A.3.A: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
- CCSS.MATH.CONTENT.5.NBT.A.3.B: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Please note: You should cross-check with your state or school district's specific standards to ensure full alignment.
Lesson Details
Suggested time allowance: This lesson can be divided into two or three smaller lessons, each lasting about 20-25 minutes or it can be completed in one longer lesson.
Materials
- Grid Paper
- Teacher Guided Practice Questions
- Guided Practice Worksheet [ Answer Key]
- Independent Practice Worksheet [ Answer Key]
- Extension Worksheet, [ Answer Key]
- Homework Worksheet [ Answer Key].
What Is Decimal Place Value?
Before we dive into our lesson, let's familiarize ourselves with some important terms we'll be using. These terms are crucial for understanding decimal place values.
Decimal: A number system based on tens. The numbers to the left of the decimal point represent whole numbers, and as we move to the right of the decimal point, each number place represents a fraction of a whole.
Decimal Point: The dot in a decimal number. The decimal point separates the whole number from the fractions of a whole.
Tenths Place: The first place to the right of the decimal point. For example, in the number 0.1, the number 1 is in the tenths place, representing one-tenth of a whole.
Hundredths Place: The second place to the right of the decimal point. For example, in the number 0.01, the number 1 is in the hundredths place, representing one-hundredth of a whole.
Decimal place value refers to the position of a digit in a number and indicates its value. Each place to the right or left of the decimal point represents a different power of 10. For instance, the first place to the right of the decimal point represents tenths (1/10), the second place represents hundredths (1/100), and so on.
In the next section, we will explore these concepts in more detail and learn how to work with numbers in decimal form.
Teaching Steps
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Introduce key vocabulary: decimal, decimal point, tenths place, hundredths place.
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Display or share a 10 x 10 grid (you could use this grid paper).
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Have students examine the 10 x 10 grid. Ask:
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How many small boxes make up the whole grid? (100)
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Have a student come to your whiteboard where the grid is projected, count out a row or column (10 squares), and shade it. Alternatively, all students could try this on handouts.
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What does the shaded part represent? (one-tenth of a whole)
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Explain, or ask students to explain, ways to read and write this decimal (one-tenth, 0.1, or 1/10). The first place to the right of the decimal point is the tenths place.
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Have a second student come to your whiteboard and shade in only one square on the grid. Alternatively, have all students shade it on their handouts (in a different color). Ask:
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What does the shaded part represent? (one hundredth)
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What are ways to read and write this decimal? (one hundredth, 0.01, or 1/100)
The second place to the right of the decimal point is the hundredths place.
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Ask students:
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Is 0.1 greater or less than 0.01? (greater)
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How much greater? (10 times)
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Explain that one tenth (0.1) and ten hundredths (0.10) have the same value. Clean the overhead, and have a third student shade both values to illustrate that they are the same.
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If the first place to the right of the decimal is called the tenths place, and the second place to the right of the decimal is called the hundredths place, what do you think the third place to the right of the decimal point is called? (the thousandths place)
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What are ways to read and write one thousandth? (one thousandth, 0.001, or 1/1,000)
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Ask students to name instances when it is important to calculate and record numbers less than 1 (Possible answers: time, money, scientific measurements). Use instances from life to show the class how each of the following decimals is written and read.
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Marcel’s slice of pizza cost $1.35.
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In the 1988 Summer Olympics, Carl Lewis won the gold medal for running the 100-Meter Dash in 9.92 seconds.
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An inch is equal to 2.54 centimeters.
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The average body temperature is 98.6° Fahrenheit.
How to Use Decimal Place Value
How to Write a Fraction into a Decimal
- First, make a chart that has places for ones, tenths, hundredths, and more.
- Next, divide the top number of the fraction (the numerator) by the bottom number (the denominator).
- Write the answer on your chart. The first number after the decimal point is in the tenths place, the second number is in the hundredths place, and so on.
How to Write the Value of a Number in a Decimal
- Find the number in the decimal you want to write about.
- Figure out the place value of that number (like ones, tenths, hundredths, etc.).
- Now, write the value of that number based on its place value.
Teaching Steps
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Start by explaining what a fraction is and the terms 'numerator' and 'denominator'. Use visual aids if possible.
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Show the students how to convert a fraction into a decimal. Use a simple fraction like 1/2 or 3/4 for this demonstration.
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Draw a place value chart on the board and explain how each place represents ones, tenths, hundredths, etc.
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Divide the numerator by the denominator and fill in the chart. Explain that the first digit after the decimal point is in the tenths place, the second is in the hundredths place, and so on.
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Give the students a decimal number and ask them to identify the number in each place.
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Once they've identified the number, guide them to figure out the place value of that number.
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Ask the students to write the value of the decimal number based on its place value.
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Repeat these steps with a few more examples to ensure students understand the concept. Encourage students to ask questions if they're unsure about any step.
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Distribute the Guided Practice Worksheet and have students work in pairs or independently to practice using decimal place value.
How to Compare the Value of a Number in Two Decimals
When comparing decimals, begin on the left and compare the digits in each place. Example: Compare 0.11 and 0.12.
In the tenths place the digits are the same. Look at the hundredths. 2 is greater than 1, so 0.12 > 0.11.
Compare 0.02 and 0.120.
The ones are the same. 1 is greater than 0 in the tenths place, so 0.120 > 0.02.
Compare 2.17 and 0.99.
The ones are different. Since 2 is greater than 0, 2.17 > 0.99.
Teaching Steps
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Remind students that when there are non-zero digits on both sides of the decimal point, they should say, "and," where they see the decimal point. For example, 2.17 is read, "two and seventeen hundredths."
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Use models on a 10 x 10 grid as necessary to guide the class in comparing decimals numbers using > and <.>
1. 0.1 (>) 0.01
2. 0.2 (
3. 0.999 (
4. 0.13 (
5. 0.51 (>) 0.509
6. 0.183 (>) 0.083
7. 1.460 (
8. 0.005 (
9. 1.003 (>) 0.339
10. 1.06 (>) 1.007
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To help students compare the value of decimals, see Teacher Guided Practice Questions .
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Distribute the Independent Practice Worksheet and have students complete independently.
Assessment
Use these Assessment Questions to evaluate student knowledge.
Students should be able to:
- read and write decimals accurately, moving between the written, spoken, and symbolic forms of decimals.
- understand the role of the decimal point and the relationship among tenths, hundredths, and thousandths.
- complete and explain grids to form a picture of a decimal value.
- compare and order decimals and use this skill to solve basic word problems.
Extension Activities
- Distribute the Extension Worksheet and have students complete them independently.
- Distribute theHomework Worksheet and have students complete it. You may want to reinforce the lesson by discussing the answers as a class.
