The Percent Circle: Making Circle Graphs

Transcription

1 The Percent Circle: Making Circle Graphs Objective To introduce constructing circle graphs using the Percent Circle. 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 Find fraction and percent equivalents. [Number and Numeration Goal 5] Measure sectors of a circle graph using the Percent Circle. [Measurement and Reference Frames Goal ] Construct circle graphs from table data. [Data and Chance Goal ] Interpret data presented in various forms. [Data and Chance Goal 2] Key Activities Students use the Percent Circle to construct circle graphs. They use journal page data and the snack-survey data collected in Lesson 5 9. They practice finding fractional parts of sets by playing Fraction Of. Ongoing Assessment: Informing Instruction See page 35. Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, page 44). [Data and Chance Goal ] Materials Math Journal, pp. 5, 57, and 58 Student Reference Book, p. 33 Study Link 5 0 Math Masters, pp. 44, 426, and 427 (optional); pp and 469 Geometry Template Class Data Pad (optional) chalkboard compass, for demonstration purposes counters Finding Decimal Equivalents for Sevenths and Eighths Math Journal, inside back cover Students fill in the decimals for sevenths and eighths in the Table of Decimal Equivalents. Math Boxes 5 Math Journal, p. 59 Students practice and maintain skills through Math Box problems. Study Link 5 Math Masters, p. 50 Students practice and maintain skills through Study Link activities. READINESS Measuring Circle Graphs Math Masters, p. 428 Geometry Template Students use a Percent Circle to measure sectors in a circle graph. ENRICHMENT Calculating Percents: On the Square index card sheet of scrap paper per group: masking tape, 2" by 2" paper square Students collect, calculate, and compare fractions and percents in statistical data. Advance Preparation For Part, convert snack-survey data from Lesson 5 9 to percents, rounded to the nearest whole percent. List the snacks and percents in a table on the board or the Class Data Pad. Students will need Percent Circles from the Geometry Template or Math Masters, page 426 or 427. For the optional Readiness activity in Part 3, divide each circle on Math Masters, page 428 into three or four sections and label them A, B, C, and D. Write the same labels in the boxes to the left of the answer blanks before copying the master. Teacher s Reference Manual, Grades 4 6 pp , 6 67, Lesson 5 349

2 Getting Started Mental Math and Reflexes Have students rename percents as fractions. Encourage them to find fractions with denominators that are less than 00. Suggestions: Math Message Turn to Problem 2 on journal page 5. Copy the number of votes for each snack into the second column of the table on journal page 58. Leave the rest of the table blank. 50% _ 2 33 _ 3 % _ 3 25% _ 4 40% 2_ 5 20% _ 5 80% 4_ % 3_ % 7_ 8 68% 7_ 25 Study Link 5 0 Follow-Up Briefly review answers for Problems and 2. Ask volunteers to share their data sets for Problem 3. Teaching the Lesson Math Message Follow-Up (Math Journal, pp. 5 and 58) Survey the class to verify that students have copied the data from Lesson 5-9 correctly. Ask students to write the number of votes for each snack as a fraction of the total number of votes. Students should write this fraction in the third column of the table on journal page 58. Date LESSON 5 Time Making Circle Graphs: Concrete Recipe Concrete is an artificial stone. It is made by first mixing cement and sand with gravel or other broken stone. Then enough water is mixed in to cause the cement to set. After drying (or curing), the result is a hard piece of concrete. The cement, sand, and gravel are commonly mixed using this recipe. Recipe for Dry Mix for Concrete Material Fractional Part of Mix Percent Part of Mix Cement % Sand % Gravel 50% 2 Use your Percent Circle to make a circle graph for the above recipe in the circle below. Label each sector of the graph and give it a title. Recipe for Dry Mix for Concrete gravel cement Math Journal, p. 57 sand Constructing a Circle Graph Using the Percent Circle (Math Journal, p. 57) WHOLE-CLASS As a class, read the information about mixing concrete on journal page 57. Ask volunteers how they would go about constructing a circle graph for this data. Ask students questions such as the following: How many pieces (sectors) must the graph have? Three one for each dry ingredient (concrete, sand, and gravel) How should the pieces be labeled or colored? If the graph is labeled correctly, colors might help, but they are not necessary. Some students may suggest using symbols to mark the pieces. How can the Percent Circle be used to make each piece the correct size? Use the tick marks on the Percent Circle to draw sectors with measures matching the percents given on the table. Have students demonstrate their circle-graph construction methods, using a chalkboard compass and a large paper Percent Circle on the board (or a compass and transparency of the Percent Circle on the overhead). Have students take turns sketching sections of the circle. Then have them complete the circle graph on journal page Unit 5 Fractions, Decimals, and Percents

3 NOTE Water is a necessary fourth ingredient in concrete. It is usually added to a dry mix of the other ingredients. About 5 to 7 gallons of water are used for a 94-pound bag of cement. When the concrete has dried (cured), the water is gone and the proportions of cement:sand:gravel are still :2:3. Ongoing Assessment: Informing Instruction Watch for students who have difficulty devising a method for constructing the circle graph. Demonstrate the following.. Use a board compass to draw a 2-inch diameter circle. Mark the center with a dot. 2. Place the center of the Percent Circle over the center of the circle on the board and make tick marks on the chalk circle at the 0 and _ 6 (6 2_ 3 %) points. 3. Remove the Percent Circle and draw a line segment from the center of the circle through the tick marks. This _ 6 section represents the proportion of cement in the mix. 4. Now place the Percent Circle 0% line along the line segment drawn at the _ 6 mark. Then mark the _ 3 (33%) measure. Draw a line segment from the center of the chalk circle to the tick mark to get the _ 3 section. This represents the proportion of sand in the mix. 5. Measure the remaining section to verify that it is _ 2 (50%) of the circle. This represents the amount of gravel in the mix. 6. Label the graph and add a title. Date LESSON 5 Time Making Circle Graphs: Snack Survey Your class recently made a survey of favorite snacks. As your teacher tells you the percent of votes each snack received, record the data in the table at the right. Make a circle graph of the snack-survey data in the circle below. Remember to label each piece of the graph and give it a title. Sample answers: Favorite-Snack Survey Results fruit other candy bar Math Journal, p. 58 Snack Number Fraction Percent Cookies Granola Bar Candy Bar Fruit Other Total % 6% 40% 8% 4% About 00% cookies granola bar Votes Constructing a Circle Graph for the Snack-Survey Data (Math Journal, p. 58) PARTNER PROBLEM SOLVING Display the snack-survey percents on the board or Class Data Pad. (See Advance Preparation.) Ask students to copy the percents into column 4 of the table. Ask: Why do you think the table has About 00% in the Percent column? The total should be 00%, but it may not be exact because of rounding. Have students check their totals, then construct a circle graph using the snack-survey data. Suggest that they draw the smallest sector of the circle graph first and work their way up to the largest. This way, slight errors in their sections will be absorbed into the largest piece at the end. Circulate and assist. Ongoing Assessment: Recognizing Student Achievement Exit Slip Use an Exit Slip (Math Masters, p. 44) to assess students understanding of how to use the data-set fractions to draw circle-graph sectors. Have students write a response to the following: How can finding the fraction of the whole for each category in the data set help you construct a circle graph? Students are making adequate progress if they relate the fractions to estimating the size of the sector before or after drawing it and/or refer to using the fraction to align the Percent Circle. [Data and Chance Goal ] Lesson 5 35

4 Game Master Name Date Time Fraction Of Set Cards Playing Fraction Of PARTNER (Math Masters, pp , and 469; Student Reference Book, p. 33) 3 counters 4 counters 5 counters 6 counters 20 counters 2 counters 2 counters 28 counters 5 counters 30 counters 20 counters 40 counters 8 counters 0 counters 2 counters 5 counters 27 counters 32 counters 30 counters 36 counters 20 counters 24 counters 25 counters 20 counters 8 counters 20 counters 2 counters 25 counters 36 counters 4 counters 30 counters 6 counters 0 counters 3 counters 24 counters 40 counters 28 counters 30 counters 36 counters 40 counters 35 counters 32 counters 20 counters 8 counters 30 counters 5 counters 24 counters 25 counters Math Masters, p. 469 Students practice finding fractional parts of sets by playing Fraction Of. Review the directions on Student Reference Book, page 33, and then play several sample turns with the class. 2 Ongoing Learning & Practice Finding Decimal Equivalents for Sevenths and Eighths (Math Journal, inside back cover) Students continue to find and record decimal equivalents for fractions in the table on the inside back cover of the journal. Assign the denominators in rows 7 (sevenths) and 8 (eighths). PARTNER Adjusting the Activity To make the activity a challenge to mental math skills, encourage students to use their calculators for the first 3 or 4 columns in a row and identify the pattern. Students then use the pattern and mental math to complete the row. Denominator Numerator Inside back cover of Math Journal. Completed rows 7 and 8. AUDITORY KINESTHETIC TACTILE VISUAL Games Fraction Of Materials deck of Fraction Of Fraction Cards (Math Masters, pp. 464 and 465) deck of Fraction Of Set Cards (Math Masters, p. 469) Fraction Of Gameboard and Record Sheet for each player (Math Masters, p. 466) Players 2 Skill Multiplication of fractions and whole numbers Object of the game To score more points by solving fraction of problems. Directions. Shuffle each deck separately. Place both decks number-side down on the table. 2. Players take turns. On your turn, draw card from each deck. Use the cards to create a fraction of problem on your gameboard. The Fraction Card indicates what fraction of the set you must find. The Set Card offers 3 possible choices. Choose a set that will result in a fraction of problem with a wholenumber solution. Solve the fraction of problem and set the 2 cards aside. The solution is your point score for the turn. 28 counters 35 counters 0 30 counters Player draws and. 0 of 28 will not result in a whole-number solution. 0 of 28 counters is 2.8 counters. 0 of 35 will not result in a whole-number solution. 0 of 35 counters is 3.5 counters. 0 of 30 will result in a whole-number solution. 0 of 30 counters is 3 counters. Player chooses 30 counters as the set for the fraction of problem. Student Reference Book, p Unit 5 Fractions, Decimals, and Percents

5 Math Boxes 5 (Math Journal, p. 59) Mixed Practice Math Boxes in this Lesson are paired with Math Boxes in Lesson 5-9. The skill in Problem 5 previews Unit 6 content. Writing/Reasoning Have students write a response to the following: Describe the strategy you used to solve Problem 4 and explain your reasoning. Answers vary. Study Link 5 (Math Masters, p. 50) Home Connection Students use the Percent Circle to make a circle graph. They do not have to calculate the percents because all percents are given. 3 Differentiation Options Date LESSON 5 Math Boxes. Write a 5-digit number with 5 in the tens place, 5 in the thousandths place, and 0 in all the other places Write this number in words. Fifty and five thousandths 5 3. Use your Percent Circle and the information in the bar graph to complete the circle graph. Favorite Warm Weather Sports 50 Title: 5th-Grade Students Marcus had $5 to spend on lunch. He bought a hot dog for $.75 and some French fries for $0.69. How much money did he have left to spend on dessert? $2.56 Soccer Swimming Basketball Bicycling Other Sports Math Journal, p Time 2. Use the division rule to find equivalent fractions in simplest form. 25 a b c d Favorite Sports basketball 40% other 5% soccer 25% swimming 5% bicycling 5% 5. Cheryl has a babysitting business. In five months, she made the following amounts: $28, $42, $59, $42, $64 a. Find the range. b. Find the mode. $36 $42 $42 c. Find the median. d. Find the mean. $ READINESS Measuring Circle Graphs (Math Masters, p. 428) 5 30 Min To explore measuring sectors of a circle graph with the Percent Circle, have students complete the Math Masters page. Individualize the problems to address specific student needs, such as using the fraction marks on the Percent Circle, or measuwring smaller sectors. (See Advance Preparation.) ENRICHMENT SMALL-GROUP Calculating Percents: On the Square 5 30 Min To apply students knowledge of percents, have them conduct an experiment and report the results. Number index cards from to the number of students in the class, and give one card to each student. Each student also needs a sheet of scrap paper wadded into a ball. Place groups in separate areas of the room to set up for this activity. Students tape a 2-inch square to the floor and mark a tape line 6 feet from the square. The object is to see how many times a student can toss a paper ball so it lands inside of the taped square. Give students the following instructions: Name Date Time STUDY LINK 5 What s in a Landfill? People who study landfills have estimated the percent of landfill space (volume) taken up by paper, food, plastic, and so on. Space in landfills taken up by: Think of it this way: Paper % For every 00 boxes of garbage Food and yard waste.... 3% hauled to the dump, expect that about 50 boxes could be filled with Plastic % paper, 6 with metal, with glass, Metal % and so on. Glass % Other waste %. Cut out the Percent Circle. Use it to make a circle graph for the data in the table. (Remember to label the graph and give it a title.) Landfill Contents Practice paper Study Link Master 7 other waste metal plastic food and yard waste glass 23 80% 75% 70% 85% 65% 90% 60% 95% 0% 5% 0% 55% 50% 45% /0 /8 /6 /3 /5 3/4 /4 2/3 /2 5% 35% 40% 26 20% 25% 30% Math Masters, p. 50 Lesson 5 353

6 Teaching Aid Master Name Date Time Measuring Circle-Graph Sections Use your Percent Circle to find the percent of each piece (sector) within the whole circle Math Masters, p Students take turns standing at the taped line. They are allowed to toss the ball as many times as the number indicated on their index cards. 2. Each student tosses the paper ball toward the taped square. 3. The group counts the number of times the ball lands inside the square. 4. At the end of a turn, the student writes how many times the ball landed inside the square as a fraction of the number of times he or she tossed the ball. 5. After every member of the group has had a turn, students convert their fractions to percents. When students have calculated their percentages, discuss questions such as the following: Who had the greatest percentage in each group? Who had the greatest percentage in the class? Was the activity fair, or did it favor some students more than others? The activity might favor those students who had more tosses. However, some students might be more accurate with their tosses regardless of the number of tosses. How could students improve their percents? The more tosses they make, the greater the opportunity becomes to land in the square. 354 Unit 5 Fractions, Decimals, and Percents