In this lesson plan, your learner will make sense of tenths and hundredths in decimal notation. They will rely on their knowledge of fractions to express tenths and hundredths as decimals, seeing connections between fraction notation, names of fractions in words, and decimal notation.
Key Concepts for Writing Tenths and Hundredths as Decimals
Here are a few concepts and vocabulary terms that are important to know for the lesson:
Tenths: These are fractions with a denominator of 10. They can be written as fractions (e.g., 1/10), decimals (e.g., 0.1), and represented on grids. Each square in a 10-by-10 grid can represent 1/10 if ten squares are shaded.
Hundredths: These are fractions with a denominator of 100. They can be written as fractions (e.g., 1/100), decimals (e.g., 0.01), and represented on grids. Each square in a 10-by-10 grid represents 1/100.
Decimal Notation: The decimal point separates the whole number part from the fractional part of a number. Digits to the left of the decimal point are whole numbers. If the decimal is less than 1, there is a leading zero (e.g., 0.7).
Place Value: The first place to the right of the decimal point is the tenths place, and the second place is the hundredths place. For example, in the number 0.56, 5 is in the tenths place, and 6 is in the hundredths place.
10-by-10 Square Grid: A 10-by-10 square grid, also known as a 100-square grid, is a useful tool for visualizing decimals and relating them to fractions. Each small square in the grid represents 1/100 or 0.01. When 10 squares are shaded, they represent 1/10 or 0.1.
Teaching Plan
The activities in this lesson plan will help your learner develop confidence in writing tenths and hundredths as decimals.
Examples and visuals to support the lesson:
1. Exploring 10-by-10 Grids
The purpose of this activity is to introduce the use of a square grid to represent fractions in hundredths. While your learner explores the diagram, focus on expressing the fractions of the large square that are shaded and unshaded.
Display a 10-by-10 square grid with 6 squares shaded.
Ask: “What do you notice? What do you wonder?”
Your learner might respond by saying: There is a 10-by-10 square grid with some part of it shaded, there are 100 small squares in a large square, six of the little squares are shaded and 94 are not, or 6/100 of the square is shaded.
They might also wonder: What does the shaded portion represent or mean? Does the large square represent 1? Why is most of the grid not shaded? How many different ways are there to show 6/100 on the grid?
Skill Check
I can look at a 10-by-10 square grid and identify how much of it is shaded and unshaded.
2. Connecting Fractions to Decimals
In this activity, your learner will begin to make connections between the familiar representations of a fraction—using a diagram, fraction notation, and words—and the newly introduced decimal notation.
Display diagrams of various 10-by-10 square grids with different amounts of squares shaded. Ask your learner: “What notation can we write to show each fraction? How do we say the fraction in words?” Write their responses in both notation and words.
Next, use grids and fractions to show connections between fraction notation and decimal notation. Guide your learner in writing decimal numbers to represent the grids from the first part of the activity.
Remember to consistently read numbers as decimals, for example, 1.7 as "one and seven tenths" and not "one point seven." This will help your learner connect decimal notation to visual representations and fraction notation.
To reinforce the connections between fractions and decimals, create a two-column table with examples of tenths and hundredths in both decimal and word form.
Have your learner describe any patterns that they notice.
To check their understanding, ask how they would write 7 hundredths, 70 hundredths, and 7 tenths in decimal notation. (0.07, 0.70, 0.7)
Skill Check
I know that tenths and hundredths fractions can be written as decimals.
3. Representing Decimals
In this activity, your learner will practice representing and writing decimals given another representation (fraction notation or a diagram).
Provide your learner with 10-by-10 square grids that are partially shaded.
Have them write a fraction and a decimal that represent the shaded parts of each diagram, then write each amount in words.
Provide various fractions or decimals and have your learner use colored pencils to shade a grid to represent the numbers.
Challenge your learner with numbers that represent more than one whole, such as 1.6, which requires using two square grids (one completely filled in to represent 1, and the other filled in to represent 0.6).
Skill Check
I can write decimals to represent the shaded part of a 10-by-10 square grid.
4. Review and Practice
Wrap up the lesson with a discussion followed by time for independent practice.
Display the number 0.78. Guide your learner in identifying what each digit represents: 0 represents zero ones, 7 represents seven tenths, 8 represents eight hundredths.
Ask: “Why might it make sense to name this decimal seventy-eight hundredths?” (Seven tenths and 8 hundredths is equivalent to 78 hundredths.)
Next, ask several questions to reinforce the idea that decimals can be equivalent, even if they are written differently.
Display the numbers 0.6 and 0.60. Ask your learner: “How do we say these numbers in words?” (Six tenths for 0.6, and sixty hundredths for 0.60).
“In both numbers, what does the 0 to the left of the decimal point represent?” (Zero ones). “In 0.6, what does the 6 represent?” (Six tenths). “In 0.60, what does the 60 represent?” (Sixty hundredths).
“Why can we use the same diagram to represent 0.6 and 0.60?” (They represent the same amount. Six tenths is equivalent to sixty hundredths, so 0.6 and 0.60 are equivalent.)
Skill Check
I can explain what each digit in a decimal number represents.
Summary
By exploring tenths and hundredths through fractions, decimals, and visual grids, your learner will gain a strong understanding of decimal notation and place value. This foundational knowledge will help them with reading, writing, and representing decimals, setting the stage for more advanced math concepts in future lessons.
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Skill Check