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.
1) Write and as a decimal and a percentage.
Whole-Class Instruction
Materials Needed: Paper and pencil, PowerPoint Presentation*
Procedure:
Presentation
1) Use the pre-assessment problem to demonstrate converting between fractions, decimals, and percents.
· Fraction to a decimal: divide numerator by denominator. = 0.444…, = 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, .
· 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% =
2) Explain why the above methods work.
· Fractions represent division; 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
3) Have students work in groups to complete the guided practice slides on the PowerPoint Presentation.
4) Review and discuss the steps for each conversion.
Independent Practice
5) 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:
1) Ask students how 0.555… could be written as a fraction.
2) Explain that we can’t use or 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
3) Have students convert 0.111…, 0.222…, 0.333…, up to 0.999… to fractions.
4) 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.
5) 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).
6) Discuss what students find (the fractions are elevenths).
Struggling Learner
Materials Needed: paper and pencil
Procedure:
1) 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.
2) 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:
: 7.00 ÷ 25, 25 goes into 100 4 times, so it will go into 700 4 x 7 times, or 28: = 0.28.
3) Have students work in pairs to write fractions for their partner to convert to decimals and percents.
4) Discuss what students found and strategies that they used.
*see supplemental resources
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