# Conversions among Fractions, Decimals, and Percents

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1 Conversions among Fractions, Decimals, and Percents Objectives To reinforce the use of a data table; and to reinforce renaming fractions as percents using a calculator and renaming decimals as percents. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Read and use large numbers. [Number and Numeration Goal 1] Explore repeating and terminating decimals. [Number and Numeration Goal ] Use a calculator to rename fractions as percents; rename decimals as percents by multiplying by 100. [Number and Numeration Goal ] Compare two quantities with like units using division. [Operations and Computation Goal 4] Round to the nearest whole-number percent. [Operations and Computation Goal 6] Use a data table. [Data and Chance Goal 2] Key Activities Students look up country population and land area data and convert these to percents of the world population and land area. Students complete the percent column of the Equivalent Names for Fractions table on journal pages 342 and 343. Ongoing Assessment: Informing Instruction See page 746. Materials Math Journal 2, pp. 342 and 343 Student Reference Book, pp. 271 and 281 Study Link 9 4 calculator classroom world map slate Advance Preparation Updating the World Tour Math Journal 2, pp , 336, and 337 Student Reference Book, pp. 276, 277, 281, 288, 289, 297, and Math Masters, pp. 419 and 420 (optional) Students continue the World Tour. Angle Addition and Subtraction Math Journal 2, pp. 260A and 260B Students practice finding unknown angle measures. Math Boxes 9 Math Journal 2, p. 260 Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 4. [Operations and Computation Goal 4] Study Link 9 Math Masters, p. 288 Students practice and maintain skills through Study Link activities. READINESS Rounding Percents Math Masters, p. 289 Students use a curved number-line model to round percents. EXTRA PRACTICE -Minute Math -Minute Math, pp. 93 and 181 calculator Students practice conversions among fractions, decimals, and percents. Teacher s Reference Manual, Grades 4 6 pp. 62, 63, 13, Unit 9 Fractions, Decimals, and Percents

2 Getting Started Mental Math and Reflexes Write fractions on the board. For each fraction, students write the equivalent decimal and percent on their slates. Have students explain their strategies for the problems. Suggestions: _ , % _ , 10% 20 71_ , 71% 12_ 0.48, 48% 2 67_ , 67% 1_, 00% 3 _ 0.0, % 100 _ 0., 0% 10 1_ 0.2, 2% 4 Math Message Use your calculator to rename these fractions as percents: 1_ 8, 3_ 8, _ 8, 7_ 8. Study Link 9 4 Follow-Up Review answers. Have students share the strategies they used to solve Problems 3 6. For example: Problem 3: 42_ 84_ 84_ 0 = (multiply numerator and denominator by 2); = 84% 2_ Problem 6: 12 = 1_ (divide numerator and denominator by 2); 1_ = 20% Ask if any student can describe a solution strategy to solve Problems 7 and 8 without a calculator. For example: 23_ Problem 7: 92 = 1_ 4 Problem 8: 12_ 3_ 40 = 10 (divide numerator and denominator by 23); 1_ 4 = 2% (divide numerator and denominator by 4); 3_ 10 = 30% 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS Go over the answers: 1_ 8 = 12.%; 3_ 8 = 37.%; _ 8 = 62.%; 7_ = 87.%. Students may have renamed the fractions as percents 8 in one of two ways. Use the percent key. For example, to rename 3_ as a percent, 8 TI-1: 3 8 Display: 37. Casio fx-: 3 8 Display: 37. Divide numerator by denominator, and multiply by 100. For example, divide 3 by 8 (= 0.37) and multiply by 100 (= 37.). Remind students that multiplying a decimal by 100 can be done by moving the decimal point two digits to the right. Students may use either method, but they should be able to use both. Adjusting the Activity ELL Ask students to explain how 1_ 8, 3_ 8, _ 8, and 7_ 8 could be renamed as percents without using a calculator. Record the steps on the board. _ 8 is half of 1_ 4. Because 1_ 4 = 2% and half of 2% is 12.%, 1_ 8 = 12.%. 3_ 8 equals 1_ 4 + 1_ 8, which is 2% + 12.%, or 37.%. _ 8 and 7_ 8 are renamed in the same way. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Lesson 9 74

4 Repeat this last routine to calculate the percent of the world s land area that is in Russia. Russia s area is about 6,92,800 square miles. The world s land area is about 7,900,000 square miles. The fraction of the world s area that belongs to Russia is about 6,93,000 7,900,000 = Multiply = 11%. So about 11% of the world s area belongs to Russia. Equivalent Names for Fractions Fraction Equivalent Fractions Decimal Percent 2 0 0% 2 2 4, % 3 Completing the Equivalent Names for Fraction Table (Math Journal 2, pp. 342 and 343) Students should already have filled in the equivalent fractions and decimals columns of the table on journal pages 342 and 343. Now they will fill in the percents column. On the first page of the table, students find the percents by using the percent key. If the calculator display shows an answer with more than 3 digits, they record only the first 3 digits. For example, for the fraction _, the percent answer will 6 be displayed on the calculator as , but only 83.3 should be recorded in the table. On the second page of the table, students can find the percents without using a calculator and without making any actual computations. The decimal names are already recorded in the table. Students need only multiply the decimal by 100 (move the decimal point two digits to the right) to rename the decimal as a percent. As before, ask students to record only the first 3 digits for any percent name Math Journal 2, p Equivalent Names for Fractions continued Fraction Equivalent Fractions Decimal Percent Math Journal 2, p. 343 Lesson 9 747

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