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|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: |

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|The students will know… |

|that fractions, decimals, and percents can all represent the same ratio. |

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|The students will be able to… |

|convert between fraction, decimals, and percents. |

|Learning Styles Targeted: |

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|x |

|Visual |

|x |

|Auditory |

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|Kinesthetic/Tactile |

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|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. |

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|Guided Practice |

|Have students work in groups to complete the guided practice slides on the PowerPoint Presentation. |

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|Review and discuss the steps for each conversion. |

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|Independent Practice |

|Have students work to complete the independent practice slides on the PowerPoint Presentation. |

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|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. |

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|Explain that we can’t use [pic] or [pic] etc., as these are approximations. Show students the following steps. |

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|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 |

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|Have students convert 0.111…, 0.222…, 0.333…, up to 0.999… to fractions. |

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|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. |

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|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). |

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|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. |

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|Have students work in pairs to write fractions for their partner to convert to decimals and percents. |

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|Discuss what students found and strategies that they used. |

*see supplemental resources

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