In this lesson plan, your learner will make sense of tenths, hundredths and thousandths using hundredths grid diagrams, fractions, and decimals. They will also see relationships between these values, such as a tenth of a tenth is a hundredth, and a tenth of a hundredth is a thousandth.
Here are a few ways that tenths, hundredths and thousandths will be represented throughout the lesson plan.
Tenths: Fractions with a denominator of 10. They can be written as fractions (1/10), decimals (0.1), and represented on grids. Each row or column in a 10-by-10 grid can represent 1/10 if ten squares are shaded.
Hundredths: Fractions with a denominator of 100. They can be written as fractions (1/100), decimals (0.01), and represented on grids. Each square in a 10-by-10 grid represents 1/100.
Thousandths: Fractions with a denominator of 1000. They can be written as fractions (1/1000), decimals (0.001), and represented on grids with further subdivisions.
Relationships Between Tenths, Hundredths and Thousandths
As your learner works with decimal numbers that extend to different place values, it is important that they understand the relationships between numbers.
Part-Whole Relationships: There are 10 tenths in a whole. There are 10 hundredths in a tenth and 100 hundredths in a whole. There are 10 thousandths in a hundredth and 1,000 thousandths in a whole.
Multiplicative Relationships: A tenth is ten times a hundredth (0.1 = 10 × 0.01). A hundredth is ten times a thousandth (0.01 = 10 × 0.001). A tenth is one hundred times a thousandth (0.1 = 100 × 0.001).
Teaching Plan
The following activities will help your learner become confident working with fractions and decimals up to the thousandths. Remember to go at a pace that is comfortable for your learner.
Examples and visuals to support the lesson:
1. Small Fractions in Real-World Contexts
This activity will encourage your learner to think about small fractions of a quantity in a real-world context.
Show a picture made of many small items, such as a tiled mosaic. Ask your learner “What fraction of the whole picture is a single square tile?”
Have them give estimates that are too low, too high, and about right. Encourage them to describe their reasoning. For example, they might say “I tried to estimate about how many tiles made the whole picture and then used that as my denominator.”
Discuss how the size of the denominator in a fraction affects the value of the number. For example, 1/1,000 is smaller than 1/10 because dividing an object into 1,000 parts means each part is smaller than if the object was divided into ten parts.
Skill Check
I can use fractions to estimate very small numbers.
2. Representing Tenths, Hundredths and Thousandths
The purpose of this activity is for your learner to share what they know about one tenth and one hundredth, and consider what they might know about one thousandth.
Encourage your learner to think about how these numbers used in real-life. You can even go for a “number hunt” to find examples in stores, on road signs, etc.
Have your learner make a poster showing what they know about these numbers, representing them as fractions, decimals, or using visual models like grids, bar models, or number lines.
Wrap up the activity with a discussion about the different ways they chose to represent the numbers on their poster. Also, discuss any challenges they may have had and why.
Skill Check
I can find real-life examples of decimals and represent them different ways.
3. Tenths, Hundredths and Thousandths on Diagrams
In this activity, your learner will represent tenths, hundredths and thousandths with diagrams and decimals. The diagrams can be used to highlight the relationships between these quantities.
Start with a diagram that has one-tenth shaded. Ask your learner what the shaded region represents and have them explain their reasoning.
Next, show diagrams with one-hundredth shaded and then one-thousandth shaded. Ensure your learner can write each number as a fraction and as a decimal value.
Spend time discussing and exploring the relationships between the diagrams and the written numbers. Build towards the understanding that there are 10 tenths in a whole, 10 hundredths in a tenth, and 10 hundredths in a thousandth.
Skill Check
I can use diagrams to show that there are 10 tenths in a whole, 10 hundredths in a tenth, and 10 hundredths in a thousandth.
Summary
By exploring tenths, hundredths and thousandths 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 become confident with reading, writing, and representing decimals, setting the stage for more advanced math concepts in future lessons.
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Skill Check