Lesson Notes. Lesson 17. Objective. Materials. For use before Module 9 Ratio, Proportion, and Percent Lesson 7 Understanding Percents

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1 Lesson 17 For use before Module 9 Ratio, Proportion, and Percent Lesson 7 Understanding Percents Texas Edition: For use before Module 7 Ratio, Proportion, and Percent Fractions, Decimals, and Percents Objective To use decimal grid paper to model fractions, decimals, and percents Materials Copy Master: Decimal Grid Paper colored pencils or crayons Lesson Notes Before beginning the lesson, be sure each student has a Student Book, a copy of the Copy Master: Decimal Grid Paper, and colored pencils or crayons. By coloring decimal grids as models, students will see the relationship between fractions and decimals. Because percent means hundredths, any fraction in hundredths is expressed easily as a decimal and as a percent. Problem 1 How many congruent parts is the rectangle divided into in problem 1? (5) Because there are 5 congruent parts, each part is called a fifth. How many fifths are shaded? (3) What fraction of the rectangle is shaded? ( 3 5 ) Problem 2 In problem 2, how many congruent parts is the rectangle divided into? (10) Because there are 10 congruent parts, what is each part called? (tenth) How many tenths are shaded? (6) What fraction of the rectangle is shaded? ( 6 10 ) What is 6 10 written in simplest form? ( 3 5 ) What is noticeable about the shaded parts in problems 1 and 2? (They are both the same size. The fractions 6 10 and 3 5 are equivalent.) Problem 3 How many congruent parts is the grid divided into in problem 3? (100) Because there are 100 congruent parts, what is each part called? (hundredth) How many hundredths are shaded? (70) What fraction of the grid is shaded? ( ) What is the numerator of the fraction? (70) What is the denominator of the fraction? (100) Because the denominator is 100, the fraction can be written as a decimal in hundredths. What is the decimal? (0.70) The word percent means hundredths. This is the symbol for percent. Write % on the board. Because 70 out of 100, or , or 0.70 of the grid is shaded, we can say that 70% of the grid is shaded. Problem 4 How many congruent parts is the square divided into in problem 4? (10) Because there are 10 congruent parts, what is each part called? (tenth) How many tenths are shaded? (7) What fraction of the grid is shaded? ( 7 10 ) What is the numerator of the fraction? (7) What is the denominator of the fraction? (10) Because the denominator is 10, you can write the fraction as a decimal in tenths. What is the decimal? (0.7) To write a percent, the denominator of a fraction must be 100 or a decimal must be in hundredths. What decimal in hundredths is equivalent to 0.7? (0.70) Why? (The model of 0.7 is the same size as the model for Writing 0 to the right of the tenths place does not change the value.) What percent of the grid is shaded? (70%) Now look back at problem 3. How are these problems similar? (Both represent 70%.) What does one column on a decimal grid represent? (1 tenth) Hands-On Lesson 17 Modeling Fractions, Decimals, and Percents Using Decimal Grid Paper 37

2 Lesson 17 Model 50% on the decimal grid. How many parts did you shade? (50) How can you write as a decimal? (0.50) How many tenths are shaded? (5 tenths) How can you write 5 tenths as a decimal? (0.5) What fractional part of the grid is shaded? ( 1 2 ) So, 50%, 1 2, and 0.5 all represent the same amount. Problems 7 10 Now that students have used decimal grid paper to understand the relationship between fractions, decimals, and percents, have them complete problems For problem 9, remind students to use 0 as a placeholder when writing 4 hundredths as a decimal. For problem 10, point out that the denominator of the fraction is 10 and that each column on a decimal grid represents 1 tenth. Lesson Adaptations for Module 9 Problem 5 Look at problem 5. Take out your copy of Decimal Grid Paper and your crayons or colored pencils. How many parts is the decimal grid divided into? (100) Shade 9 out of 100 parts. Does it matter which 9 parts you shade? (no) What fraction of the grid is shaded? ( ) How is the fraction written as a decimal? (0.09) What percent of the grid is shaded? (9%) Problem 6 Look at problem 6. Shade 45 out of 100 parts on a decimal grid. Does it matter which 45 parts you shade? (no) What fraction of the grid is shaded? ( ) How is the fraction 100 written as a decimal? (0.45) What percent of the grid is shaded? (45%) Lesson 9.7 In Lesson 9.7 students explore the meaning of percent. You may want to have students model some of the problems on a decimal grid. 38 Level H Module 9 Ratio, Proportion, and Percent

3 Objective To write percents as decimals and decimals as percents Preskills Understanding Percents Transparency H.7.7 Decimals and Percents Name Class Date 1 16 out of 100 a b. % % Materials transparency H % a % b % REVIEW PRESKILLS Problem 1 Student Book pxx What is the ratio in problem 1? (16 out of 100) What is 16 out of 100 written as a decimal? (0.16) What is 16 out of 100 written as a percent? (16%) Voyager Expanded Learning, Inc. Order the numbers from least to greatest: 0.09, 75%, 0.57, 20% 0% 20% 75% 100% % % The numbers from least to greatest are, 0.09, 20%, 0.57 and. 75% BUILD THE CONCEPT Level H Module 7 Ratio, Proportion, and Percent 5 MODEL NEW SKILLS Problem 2 The percent in problem 2 is greater than 100%. How many total small squares are shaded in the model shown in problem 2? (105) The model represents 105%. How many whole grids are shaded? (1) In the grid on the right, 5 out of 100 squares are shaded. What is 5 out of 100 written as a decimal? (0.05) To write a percent as a decimal, move the decimal point two places to the left and drop the percent symbol. Where is the decimal point in 105%? (to the right of 5) Move the decimal point two places to the left and drop the percent symbol. What is 105% written as a decimal? (1.05) Problem 3 The percent in problem 3 is less than 100% because less than one whole grid is shaded. Where is the decimal point in 8%? (to the right of the 8) To write the percent as a decimal, move the decimal point two places to the left and drop the percent symbol. Since there is only one digit, 8, write a 0 to the left of 8 as a placeholder when moving the decimal point. What is 8% written as a decimal? (0.08) Problem 4 In problem 4a, the model represents How many small squares are shaded in the model shown in problem 4? (68) What is 68 out of 100 written as a percent? (68%) To write a decimal as a percent, which way does the decimal point move? (to the right) How many places does the decimal point move? (two) So, to write a decimal as a percent, move the decimal point two places to the right and write the percent symbol. In problem 4b, the decimal is To write the decimal as a percent, move the decimal point two places to the right and write the percent symbol. Where is the decimal point in 0.075? (to the right of the first 0 from left to right) What is written as a percent? (7.5%) 32 Level H Module 7 Ratio, Proportion, and Percent

4 Student Book pxx 6 Voyager Expanded Learning, Inc. Write each percent as a decimal. 5 22% 6 3% 7 118% Write each decimal as a percent % % 49 Write a Percent as a Decimal Using Symbols 58% % 0.58 Write a Decimal as a Percent Using Symbols % % Decimals and Percents Using Words Move the decimal point two places to the left and drop the percent symbol. Using Words % 7 Move the decimal point two places to the right and write the percent symbol. HOW TO SCAFFOLD INSTRUCTION Problem 5 How is a percent written as a decimal? (by moving the decimal point in the percent two places to the left and dropping the percent symbol) What is 22% written as a decimal? (0.22) Problem 6 How is a percent written as a decimal? (by moving the decimal point in the percent two places to the left and dropping the percent symbol) To write 3% as a decimal, what needs to be added? (a 0 as a placeholder) What is 3% written as a decimal? (0.03) Problem 7 How is a percent written as a decimal? (by moving the decimal point in the percent two places to the left and dropping the percent symbol) What is 118% written as a decimal? (1.18) To order the numbers 0.09, 75%, 0.57, and 20%, they should either all be written as decimals or all be written as percents. For this problem, change the percents to decimals. To write 75% as a decimal, move the decimal point two places to the left and drop the percent symbol. Where is the decimal point in 75%? (to the right of 5) Move the decimal point two places to the left and drop the percent symbol. What is 75% written as a decimal? (0.75) Where is the decimal point in 20%? (to the right of 0) Move the decimal point two places to the left and drop the percent symbol. What is 20% written as a decimal? (0.20) The decimal 0.20 is the same as 0.2. Graph the decimals on the number line and label the original numbers. Read the numbers off the number line from left to right. What are the numbers written in order from least to greatest? (0.09, 20%, 0.57, 75%) Problem 8 How is a decimal written as a percent? (by moving the decimal point in the decimal two places to the right and writing the percent symbol) What is 1.08 written as a percent? (108%) Problem 9 How is a decimal written as a percent? (by moving the decimal point in the decimal two places to the right and writing the percent symbol) What is 0.49 written as a percent? (49%) Problem 10 How is a decimal written as a percent? (by moving the decimal point in the decimal two places to the right and writing the percent symbol) What is 0.07 written as a percent? (7%) Decimals and Percents 33

5 USE CORRECTION PROCEDURES Preskills Correct errors by reviewing or reteaching how to understand decimals. Use the HOW TO process from the lesson transparency listed in the preskills box on page XX. New Skills For reteaching: Review the Support examples shown in VmathLive in the Percents and Decimals activity in the Ratio, Proportion, and Percent module. Use Reteach Copy Master H.7.8 and the modeled teacher text to show students an alternative method for writing percents as decimals and decimals as percents. Have students complete the Copy Master. For additional practice: Assign the VmathLive Percents and Decimals activity in the Ratio, Proportion, and Percent module. Have students complete the Extra Practice problems on Student Book page XX. Voyager Expanded Learning, Inc. Go to VmathLive.com SKILL BUILDING: NEW AND REVIEW Write each percent as a decimal. 1117% % 13125% Write each decimal as a percent % 98% 27.4% Write each ratio as a decimal and as a percent out of out of out of ; 14% 0.77; 77% 0.03; 3% PROBLEM-SOLVING: NEW AND REVIEW Solve each problem. Module Ratio, Proportion, and Percent Activity Percents and Decimals 20 Alicia spent 3% of her money at the bookstore. How is this percent written as a decimal? Seven tenths of Martin s marbles are red. How is this decimal written as a percent? 70% 22 A bakery sells 87 out of 100 sticky buns that they made for the day. What percent of the sticky buns did not get sold? 87% were sold; 100% 87% 13%; 13% did not get sold 23 Of the books on a store shelf, 67 out of 100 are paperbacks. Write the ratio of paperbacks to total books as a ratio three different ways. 67 to 100; 67:100; Level H Module 7 Ratio, Proportion, and Percent 7 Student Book pxx Student Book pxx MONITOR INDEPENDENT WORK Before students begin independent work, review the HOW TO process example. As you review, HOW TO emphasize the words of mathematics by having students read aloud the words shown at the right for each process step. Problems Have students work independently. Check work and have students total the number correct and record results. Instruct students to record a 6 if they got 12 or 13 correct, a 5 for 11 correct, a 4 for 10 correct, a 3 for 8 or 9 correct, a 2 for 7 correct, and a 1 for 1 6 correct. Use Correction Procedures as needed. ASSESS INFORMALLY Error Analysis Check work and record results. Use the error analysis below to determine which skills need review, reteaching, or extra practice. MATH WRITE If student answered problem 3 incorrectly: Remind the student to write each answer choice as a decimal, then compare it to As you review the Explain It problem together, understand that the correct answer is only part of the solution. Appropriate math vocabulary, a logical method for solving the problem, and the justification of a reasonable answer complete the student response. Explain It problem answers can be used as part of a daily math journal. 34 Level H Module 7 Ratio, Proportion, and Percent

6 Answer each question. 1 Which of the following is equal to 0.042? a. 42% b. 4.2% c. 420% d % 2 Jay wrote 75% of a paper for school. Which decimal represents this amount? a. 75 b. 7.5 c d How can the answer choices to problem 1 be checked? Change each answer choice to a decimal and see which one is equal to MATH WRITE A percent is written as a decimal. If the percent is greater than 100%, what is known about the number in the decimal that is to the left of the decimal point? Explain. One hundred percent written as a decimal is 1. The number to the left of the decimal point will be 1 or greater. DIFFERENTIATION Additional Resources VmathLive Module: Ratio, Proportion, and Percent Activity: Percents and Decimals Vmath Reteach Copy Master H.7.8 page XX Instructional Support page XX Extra Practice Student Book page XX 8 Voyager Expanded Learning, Inc. 4 Without converting the decimals to percents, which percent will be the greatest? Explain , 0.88, ; When a decimal is converted to a percent, the decimal point is moved to the right. So, the decimal with the greatest first digit to the right of the decimal point will be the decimal that is the greatest percent. Eight is the greatest digit in the tenths place. Decimals and Percents CRITICAL THINKING English Language Learners To familiarize students with percent, have them shade different figures according to a given percent. For example, have them shade a heart to show about 38% shaded. Have students compare their drawings with those of other students. Then, have students vote for the most accurate representation. Students with Special Needs Write several percents on an index card or sticky note. Allow students to use a counter or a coin to represent the decimal point. Remind students to move the decimal point two places to the left to show the number as a decimal. Now, ask students to move the decimal point (counter or coin) in order to show the number as a decimal. Students will become more proficient with renaming decimals and percents if they practice physically manipulating the decimal point. Repeat this activity, using different numbers or using decimal numbers that students make into percents by moving the decimal two places to the right. Decimals and Percents 35

7 Lesson 18 For use before Module 9 Ratio, Proportion, and Percent Lesson 13 Applications of Percent Texas Edition: For use before Module 7 Ratio, Proportion, and Percent Lesson 12 Applications of Percents Objective To use a model to explore markup and discount as percents of change Materials Gizmo: Percent of Change Gizmos Log In Instructions Log in to VmathLive using the Username and Password provided in VPORT. Select the Gizmos tab. Click on the Percent of Change Gizmo link. Lesson Notes Before beginning the lesson, be sure students have their Student Books and are ready to work at the computers. Complete problem 1 before students log in to the Percent of Change Gizmo. If students have additional time, have them answer Assessment Questions 1 3 in the Gizmo. They can click on the Check Your Answers button to see how well they did on the assessment. Problem 1 In problem 1, 40 is changing to 48. Is the change an increase or a decrease? (increase) The first step in finding a percent increase is to find the amount of increase. How is the amount of increase found? (Subtract the original amount from the amount after the increase.) What is the original amount? (40) What is the amount after the increase? (48) What is 48 minus 40? (8) So, the amount of increase is 8. The next step is to divide the amount of increase by the original amount. What is the division problem? (8 40) What is 8 divided by 40? (0.2) What is 0.2 written as a percent? (20%) So, the percent change from 40 to 48 is 20%. Problem 2 Have students log in to the Percent of Change Gizmo using the instructions in the box. Look at problem 2. A store charges more for an item than the store paid for it. This is how a store makes money. A store sells a sweater for $45. The sweater cost the store $30. To model this situation, drag the Selling price handle to $45 in the Markup portion of the Gizmo. Then drag the Original cost handle to $30. Look at the model. The selling price is the sum of what two amounts? (the original cost and the markup) The amount of increase from the original cost to the selling price is the markup. The increments on the ruler are labeled every $5. According to the model, what is the amount of the markup? ($15) Compare the length of the Markup bar to the length of the Original cost bar. The length of the Markup bar is 1 2 the length of the Original cost bar. One-half can be written as what percent? (50%) So, the length of the Markup bar is 50% of the length of the Original cost bar. So, the markup is 50% of the original cost. The selling price can be written as a percent of the original cost. Look at the Selling price bar and the Original cost bar. The Selling price bar is times the length of the Original cost bar. One and onehalf can be written as what percent? (150%) So, the selling price is 150% of the original cost. Gizmo Lesson 18 Percent of Change 39

8 Lesson 18 Problem 3 Look at problem 3. A shirt costs a store $20. The store wants to mark up the price by 25%. To model this situation, drag the Original cost handle to $20 in the Markup portion of the Gizmo. What is the percent increase? (25%) So, the length of the Markup bar should be 25% of the length of the Original cost bar. What is 25% written as a fraction? ( 1 4 ) So, the length of the Markup bar should be 1 4 of the length of the Original cost bar. Look at the length of the Original cost bar. What length is 1 4 the length of the Original cost bar? ($5) Drag the Markup bar handle so that the selling price is $5 more than the original cost. The percent below the model is 25%. According to the model, what is the selling price? ($25) Problem 4 Look at problem 4. Stores often have sales in which they reduce their prices. The difference between the original price and the sale price is the discount. A book that originally sold for $40 is put on sale for $30. To model this situation, drag the Original price handle to $40 in the Discount portion of the Gizmo. Then drag the Sale price handle to $30. Look at the model. The sale price is the difference of what two amounts? (the original price and the discount) The amount of decrease from the original price to the sale price is the discount. According to the model, what is the amount of the discount? ($10) Compare the length of the Discount bar to the length of the Original price bar. The length of the Discount bar is 1 4 the length of the Original price bar. One-fourth can be written as what percent? (25%) So, the length of the Discount bar is 25% of the length of the Original price bar. The discount is 25% of the original price. The sale price can be written as a percent of the original price. Look at the Sale price bar and the Original price bar. The Sale price bar is 3 4 the length of the Original price bar. Three-quarters can be written as what percent? (75%) The sale price is 75% of the original price. Problem 5 Look at problem 5. A store is currently selling a DVD for $30. The store wants to discount the price by 50%. To model this situation, drag the Original price handle to $30 in the Discount portion of the Gizmo. What is the percent decrease? (50%) The length of the Discount bar should be 50% of the length of the Original price bar. What is 50% written as a fraction? ( 1 2 ) So, the length of the Discount bar should be 1 2 of the length of the Original price bar. Look at the length of the Original price bar. What length is 1 2 the length of the Original price bar? ($15) Drag the Discount bar handle so that the sale price is $15 less than the original price. The percent below the model is 50%. According to the model, what is the sale price? ($15) 40 Level H Module 9 Ratio, Proportion, and Percent

9 Lesson 18 Look at the percents in the Markup portion of the screen. Which bar lines up with 100%? (Original cost) If the selling price were equal to the original cost, the selling price would be what percent of the original cost? (100%) Is the selling price usually greater or less than the original cost? (greater) If the selling price were written as a percent of the original cost, the percent should be greater than 100% because the selling price is greater than the original cost. Look at the percents in the Discount portion of the screen. The sale price and discount can be written as percents of the original price. If the sale price were equal to the original price, the sale price would be what percent of the original price? (100%) Is the sale price usually greater or less than the original cost? (less) If the sale price or discount were written as a percent of the original price, the percent should be less than 100% because the sale price or discount is less than the original price. Problems 6 8 Have students work individually. Students will use the Gizmo to find percents of change. Gizmo Lesson 18 Percent of Change 41