# Equivalent Fractions

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## Objective

SWBAT use the strategy learned to convert fractions to decimals using equivalent fractions with a denominator that is a power of 10.

#### Big Idea

Students will reflect on the definition of decimals as fractions.

## Launch

5 minutes

The Problem of the Day (POD) will require students to convert a fraction into a decimal. At this point in the unit I am looking for fluency and comfort with the algorithm. Are my students able to use the algorithm without additional support from me? The lesson today will involve students converting fractions with denominators made up of powers of ten, so the POD will do the same to get them thinking along those lines.

POD: How do you convert the fraction 4/5 into its decimal equivalent? Don't just make the conversion, also describe how to make the conversion.

## Explore

30 minutes

To explore the idea further, students will work with a partner to answer the questions on the Equivalent Fractions worksheet.  As they work through the problems they will have more exposure to using the long division algorithm and thinking about the relationship between fractions and decimals. As they apply the thinking outlines in the first problem they should make connections between equivalent fractions. Using ratio concepts, students will have the opportunity to discuss and discover the strategy presented in the problem. After they finish the first problem, I will have students switch partners to give them the opportunity to discuss the strategy with another student.  They can work through the second problem with a fresh set of eyes and ears to hear and share another perspective. Once both problems are finished, we will discuss as a class the connections and patterns they identified. I want to help them recognize the decimals created when the fraction denominator is a factor of a power of ten. My students seem to have trouble with the meaning of "powers of ten" and "multiples of ten". While a multiple may be a power of ten, each place in a decimal cannot always be simply copied as a multiple. I also want them to learn a useful strategy for changing the fractions into decimals. When they finish, I will have volunteers use the SMARTboard to share the work they did to find each solution. As they demonstrate solving the problem on the board, other students will have a chance to ask questions if they don't understand or verify the work they have done if they do understand. I will also take the opportunity to check the work being done and provide support if needed.

## Summary

5 minutes

To wrap up the lesson, I want students to reflect on what they learned in class today, The Exit Ticket question will be: Describe what you learned about fractions that have a denominator that can be converted into a power of 10. Why is that important to know? Asking my kids to describe what they know will give me an indication as to whether they know how to make the conversion and if they recognize and understand why being able to make the conversion can be useful. I want them to recognize that if the denominator is expressed as a power of 10 that will be the place where the decimal terminates. If that relationship is not recognized I can integrate the concept into a future lesson.