Lesson plan - Study Island
|Math Lesson: Fractions, Decimals, and Percents |Grade Level: 7 |
|Lesson Summary: Students will convert between fractions, decimals, and percentages. Students will focus on converting fractions to decimals using division. |
|Advanced students work on converting repeating decimals to fractions. Struggling students work with fractions that have denominators that are factors of 100. |
|Lesson Objectives: |
| |
|The students will know… |
|that fractions, decimals, and percents can all represent the same ratio. |
| |
|The students will be able to… |
|convert between fraction, decimals, and percents. |
|Learning Styles Targeted: |
| |
|x |
|Visual |
|x |
|Auditory |
| |
|Kinesthetic/Tactile |
| |
|Pre-Assessment: |
|Use this quick assessment to see if students understand that fractions represent a ratio. |
|Write [pic] and [pic] as a decimal and a percentage. |
|Whole-Class Instruction |
|Materials Needed: Paper and pencil, PowerPoint Presentation* |
|Procedure: |
|Presentation |
|Use the pre-assessment problem to demonstrate converting between fractions, decimals, and percents. |
|Fraction to a decimal: divide numerator by denominator. [pic]= 0.444…, [pic]= 0.375. |
|Discuss repeating decimals when dividing. |
|Fraction to percent: take the decimal form and move the decimal two places to the right. |
|Decimal to fraction: a decimal is a fraction; 0.45 is 45 hundredths, [pic]. |
|Decimal to percent: move the decimal two places to the right. |
|Percent to decimal: move the decimal point two places to the left. |
|Percent to fraction: percent is a fraction out of 100; 34% = [pic] |
| |
|Explain why the above methods work. |
|Fractions represent division; [pic]means 4 divided by 9 and can be rewritten as 4 ÷ 9. |
|Decimals are fractions and percent is a fraction out of 100. |
| |
|Guided Practice |
|Have students work in groups to complete the guided practice slides on the PowerPoint Presentation. |
| |
|Review and discuss the steps for each conversion. |
| |
|Independent Practice |
|Have students work to complete the independent practice slides on the PowerPoint Presentation. |
| |
|Closing Activity |
|6) Open a discussion by asking students why we would use percentages instead of fractions or decimals. One reason is so that sets of data of different size can be|
|compared more easily. Also, people better understand a ratio out of 100, which is what a percent is. |
| Advanced Learner |
|Materials Needed: paper and pencil |
|Procedure: |
|Ask students how 0.555… could be written as a fraction. |
| |
|Explain that we can’t use [pic] or [pic] etc., as these are approximations. Show students the following steps. |
| |
|Let x equal the decimal: x = 0.5555… |
|Multiply each side of the equation by a power of 10 so that the repeating portion will subtract to 0: |
|10x = 5.55555.. |
|– x = 0.55555… |
|9x = 5 |
|x = 5/9 |
| |
|Have students convert 0.111…, 0.222…, 0.333…, up to 0.999… to fractions. |
| |
|Discuss what students found (they will see that each converts to ninths). This leads to a discussion that 0.999… is approximately equal to 1. |
| |
|Have students convert 0.0909…, 0.181818…, 0.2727…, up to 0.9090… to fractions and look for a pattern (here they will need to multiply by 100 to have the repeating |
|portion subtract away). |
| |
|Discuss what students find (the fractions are elevenths). |
|Struggling Learner |
|Materials Needed: paper and pencil |
|Procedure: |
|Ask students what numbers divide into 100 evenly. |
|Students will respond with 2, 4, 5, 10, 20, 25, and 50. |
|We also know that 2 x 50 = 100, 4 x 25 = 100, 5 x 20 = 100, and 10 x 10 = 100. |
| |
|Explain that any fraction with one of these denominators will convert to hundredths (or perhaps even 10ths) since they all divide 100 evenly. In the same way they |
|can be converted to percentages. We know how many times one of these numbers divides into 100, so we can multiply that number by the number of 100’s: |
|[pic]: 7.00 ÷ 25, 25 goes into 100 4 times, so it will go into 700 4 x 7 times, or 28: [pic] = 0.28. |
| |
|Have students work in pairs to write fractions for their partner to convert to decimals and percents. |
| |
|Discuss what students found and strategies that they used. |
*see supplemental resources
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