Working with Equivalent Fractions, Decimals & Percentages

Transcription

1 Virtual Math Girl: Module 3 (Student) and 4 (Teacher) Working with Equivalent s, Decimals & Percentages Activities and Supplemental Materials The purpose of Virtual Math Girl Module 3 (Student) and 4 (Teacher) is to familiarize students with fraction equivalents, fraction decimal equivalents and percentages. The activities are in order in which they are discussed in the VMG Module 4 (Teacher). Each page with graphics can be printed separately from this file by selecting Print from the File Menu and selecting the pages number(s) to be printed. Essential Vocabulary: fraction, decimal, equivalent fractions, converts, conversion, simplification, and percentages. Grade 5 Ohio State Mathematics Standards addressed in this Module of Virtual Math Girl Modules 3: Number, Number Sense and Operations Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods Compare, order and convert among fractions, decimals and percents Y2003.CMA.S01.G05-07.BB.L05.I01 Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole. Y2003.CMA.S01.G05-07.BB.L05.I02 Use various forms of "one" to demonstrate the equivalence of fractions. Y2003.CMA.S01.G05-07.BB.L05.I03 Identify and generate equivalent forms of fractions, decimals, and percents. Use models and pictures to relate concepts of ratio, proportion and percent. Y2003.CMA.S01.G05-07.BD.L05.I01 Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole. 1

2 Virtual Math Girl - Activity 1 Equivalents Name Review Equivalent s numbers are different, but fraction values are the same 1/4 2/8 4/16 8/32 Josh had Virtual Math Girl to help him figure out equivalent fractions, now it is your turn to try your hand at writing equivalent fractions. In the table below, draw a line between the equivalent fractions and tell the largest whole number you used to simplify the fraction First fraction expression 4/16 6/12 10/100 3/9 15/25 2/16 12/18 Largest whole number Alternate fraction expression 1/3 3/5 1/4 1/8 1/2 2/3 1/10 This is the cake that Josh made for his friend s party. Each layer is one- eighth of the cake. Express as a fraction the amount of the cake colored blue and green. How many layers of the cake would be ½ of the cake? Virtual Math Girl: Modules 3 & 4 Supplemental Materials 2010 WBGU- PBS. Permission is granted for non- profit educational use. 2

3 Virtual Math Girl - Activity 2 Reviewing Equivalents In each of the examples of Josh s cake layers, express the fractions with a denominator of 8 and then as the equivalent fractions where you can. What fraction of the cake is represented by the striped top layer? Can you express this as a fraction equivalent? What is that fraction equivalent? Equivalent What fraction of the cake is represented by the three striped layers? Can you express this as a fraction equivalent? If you can, what is that fraction equivalent? Equivalent What fraction of the cake is represented by the six striped layers? Can you express this as a fraction equivalent? If you can, what is that fraction equivalent? Equivalent 3

4 Virtual Math Girl - Activity 3 Applying Equivalents Josh was so successful in baking the 8 layer cake for his friend s party, that his Mom asked him to bake cookies for the school bake sale. Josh wants to bake 4 dozen cookies but the recipe Mom gave him makes only 2 dozen. For each ingredient listed, tell how much Josh will need to make the 4 dozen cookies he needs. Butterscotch Cookies (makes 2 dozen cookies) 1 package chocolate cake mix ½ cup vegetable oil 2 eggs 2/3 cup butterscotch chips ½ cup chopped nuts Fill in the chart with the amount of each ingredient that Josh will need to make 4 dozen. Use the space below the chart if you need to make some notes or do some calculations. Ingredient Amount needed for 4 dozen cookies box of cake mix vegetable oil eggs butterscotch chips chopped nuts 4

5 Virtual Math Girl - Activity 4 Decimal Equivalents (page 1) s can also be expressed as decimals. s are based on the number of divisions of the whole (denominator) Decimal equivalents to fractions can be found by dividing the denominator of the fraction into the numerator of the fraction. In each of the examples of Josh s cake layers, express the fractions with a denominator of 8 and then as the decimal equivalent. What fraction of the cake is represented by the striped layer? The striped layers represent the yellow layers in Josh s cake. Can you express this as a fraction equivalent? What is that decimal equivalent? Decimal equivalent What fraction of the cake is represented by the striped layers? The striped layers represent the yellow layers in Josh s cake. Can you express this as a fraction equivalent? What is that decimal equivalent? Decimal equivalent What fraction of the cake is represented by the striped layers? The striped layers represent the yellow layers in Josh s cake. Can you express this as a fraction equivalent? What is that decimal equivalent? Decimal equivalent 5

6 Virtual Math Girl - Activity 4 More Decimal Equivalents (Extended Activity) Josh has a family friend, Nik, visiting from Germany for a few weeks. Josh was bragging about his baking abilities. Nik asked Josh if they could bake cookies. Nik was not used to the English measuring system and needed help understanding the amounts of each ingredient in the recipe. Even though Josh did not know the metric measures, he could help Nik understand the recipe by giving him the decimal equivalents for each ingredient. What were those decimal equivalents? Fill in the chart with the amount of each fractional ingredient. Use the space below the chart if you need to make some notes or do some calculations. Ingredient Decimal equivalents for each ingredient 1/2 cup vegetable oil 2/3 cup butterscotch chips 1/3 cup chopped nuts Here is even more practice, with some harder problems. See how many you can calculate correctly. Decimal equivalent for each fraction 3/9 (Hint reduce first) 3/4 12/18 4/6 7/14 1/3 6

7 Virtual Math Girl - Activity 5 Percentages Converted to Decimal Equivalents, Then to s (Extended Activity) Decimals can also be expressed as percentage of the whole. Relationship of fractions to decimals and percentages 1/10 = 0.10 = 10% Try your hand at changing the following fractions to a decimal and then to a percentage. Remember to change a decimal to a percentage, multiply by 100 and include the % sign. 3/10 = 0.30 = 30% 1/2 = 0.50 = 50% 7/10 = 0.70 = 70% Decimal Percentage 2/3 2/8 3/9 25/100 5/5 4/8 7

8 Virtual Math Girl - Activity 6 Decimal Equivalents Converted into Percentages (Extended Activity) Relationship of fractions to decimals and percentages See if you can change the following percentages to a decimal and then to a fraction. 1/10 = 0.10 = 10% 3/10 = 0.30 = 30% 1/2 = 0.50 = 50% 7/10 = 0.70 = 70% Percentage Decimal 30% 66% 5% 50% 33% 40% 8