E Math: A. Numbers and Number Relationships Activity: Figure That!

Transcription

1 E Math: A. Numbers and Number Relationships Activity: Figure That! Science as Inquiry: As a result of their activities in grades 5 8, all students should develop Understanding about scientific inquiry. Abilities necessary to do scientific inquiry: identify questions, design and investigation, collect and interpret data, use evidence, think critically, analyze and predict, communicate, and use mathematics. National Council of Teachers of Mathematics (NCTM) Expectations Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Source: National Science Education Standards 1

2 E Math: A. Numbers and Number Relationships Activity: Figure That! Math Process Skills: Problem solving Converting Objective: The learner will solve problems using fractions, decimals, and percents. Time: 0 Minutes Note: This lesson is a 0 minute math activity for students to apply and practice solving problems using fractions, decimals, and percents. You can also use it to enrich the engineering design process, steps -, of the lesson Operation Bridge Quest. Instructor Materials: Computer loaded with PowerPoint presentation, Bridge Type Research Projection system Student Materials: Per student: Calculator (optional)

3 E Math: A. Numbers and Number Relationships Activity: Figure That! Instructor Background Information: Key Vocabulary Criteria A standard, rule, or test on which a judgment or decision can be based. It is the plural of criterion. Decimal A linear array of digits that represent a real number, every decimal place indicating a multiple of a negative power of ten. For example, the decimal.1 equals 1/10, 0.1 equals 1/100, equals 3/1000; also called decimal fraction. Denominator The expression written below the line in a common fraction that indicates the number of parts into which one whole is divided. Equivalent Fraction Fractions which have the same value, even though they may look different. Example, 1/ and / are equivalent. Numerical Data Data measured or identified on a numerical scale. Numerical data can be analyzed using statistical methods, and results can be displayed using tables, charts, histograms, and graphs. For example, a researcher will ask questions to a participant that include words how often, how many, or percentage. The answers from the questions will be numerical. Percent One part in a hundred. For example, 6 percent (also written 6%) means 6 parts out of 100. Quantify To determine or express the quantity of. Fraction An expression that indicates the quotient of two quantities, such as 1/3. Numerator The expression written above the line in a common fraction to indicate the number of parts of the whole. 3

4 E Math: A. Numbers and Number Relationships Activity: Figure That! Instructor Background Information: Numerical data is used to make decisions that need a factual basis and not just mere opinion. Using actual numbers collected from data gives more credibility to decisions that are made based on the data. It is important for students to understand how to use numerical data and how various forms of numerical data are used in different reporting situations. Numerical data can be reported in several ways, including fractions, decimals, and percents. Fractions represent numbers that are part of a whole or part of a group. The bottom number of a fraction is the denominator, used to show how many equal parts are in the whole. The top number is the numerator, used to show how many equal parts of the whole are being considered. Equivalent fractions are fractions that name the same amount. For example, / is the same as 1/. Decimals are numbers with one or more digits to the right of the decimal point. The word percent literally means for every 100 (prefix per meaning for every and the suffix cent meaning centi, or 100). Although fractions, decimals, and percents can be equivalent and interchangeable, sometimes one numerical representation is preferred to another based on the type of data being reported. Students should understand not only how to calculate equivalent numerical data but also how to select the numerical data appropriate for the problem.

5 E Math: A. Numbers and Number Relationships Activity: Figure That! Lesson: Note: You may change the scenario, making it unique to your site; however, ensure it is equal in scope to the one presented here. Strategic Question: Why do you think it s important to use numerical data instead of just offering your opinion? (Numerical data can be counted or measured and is based on facts.) 1. Present or have students read the scenario: The levee north of town has broken and altered the course of the river. As a result, the entire town of Water s Edge is stranded with only a ten day supply of food and water. As a member of the city s engineering department, you must select a company to build a new bridge and also determine the best type of bridge to build. You have been presented with proposals from four companies and data describing various types of bridges. You have two problems to solve: Problem 1: Analyze the proposal data and determine which company s proposal meets the most criteria (requirements). Problem : Analyze bridge data and determine which type of bridge would be best to build.. Explain to students that there are many ways to represent numerical data collected from research, such as fractions, decimals, and percents. Quantifying data (representing data with numerical values) allows one to make a decision based on facts instead of mere opinion. 3. Ask: If you were making a decision based on five criteria (requirements), which would be a better choice: a solution that meets two of the criteria or a solution that meets four or five of the criteria? Ask students to justify their answer. (Students should understand that meeting most or all of the criteria would be a better choice than meeting only a few of the criteria. ). Guide students through solving Problem 1: Have students examine each company s proposal information on their activity log page. Years of Experience Cost Estimate Company A Company B Company C Company D Bridge Design Construction Time Estimate 5

6 E Math: A. Numbers and Number Relationships Activity: Figure That! Strategic Question: Two types of bridges meet all criteria. What factors do you think would make one bridge a better choice than the other? (Possible Answers: Students should consider the purpose of the bridge, the location of the bridge, and whether it is permanent or temporary.) What other information would you need to know to choose the better bridge? (Possible Answers: Information necessary to know would include cost of the bridge design, the purpose of the bridge, the location of the bridge, the geology of the location, and whether it is permanent or temporary.) 5. Explain to students how to quantify data by placing numerical values on the data. Using the proposal data, guide students through calculating the fraction of proposal criteria met by each company and record this information on their activity log page. If needed, review the definitions of numerator and denominator. 6. Explain that there are other ways to numerically represent data. Two such numerical representations are percents and decimals. Review how to convert fractions to decimals and percent using the proposal criteria. Guide students to calculate the percent and decimal equivalent for each company s proposal. Then guide students through answering the questions that follow. 7. Once students have determined which company s proposal meets the most criteria, explain that their next task is to solve Problem by determining which bridge type would be best to build. 8. As a team or in pairs, have students read the information on bridge types (see PowerPoint presentation, Bridge Type Research ) and complete the fraction, percent, and decimal equivalent chart for Problem (Bridge Type Criteria). (Optional: you may want to incorporate calculators as a tool for students to use). 9. Check chart answers as a total group. 10. Have students use their numerical data to answer the problems that follow the bridge criteria chart. Circulate and assist while students are working to ensure accurate responses and check for understanding. Check for Understanding: Which two bridge types satisfy the most criteria? (Students should determine that the beam and floating bridges meet the most criteria.) Which company s proposal should be selected based on the criteria? (Students should select Company D because their proposal meets all of the criteria.) 6

7 Figure That! PROBLEM 1: WHICH COMPANY S PROPOSAL BEST MEETS THE CRITERIA? Activity Log Each company s proposal must include these four criteria (requirements). Listed below are the criteria (requirements) each company s proposal actually included: Company A Company B Company C Company D Years of Experience Cost Estimate Bridge Design Construction Time Estimate 1. Quantify the data by showing each company s proposal information as a fraction, decimal, and percent.. In a fraction, is the total number of criteria represented by the numerator or denominator? Company Fraction Percent Decimal Equivalent A B C D 3. Company B s proposal includes only out of criteria, or. Write this as a reduced fraction.. What fraction of the companies submitted proposals include at least 75% of the required proposal criteria? Write this fraction as a decimal. 5. What percentage of companies that submitted proposals meet all the criteria? 6. Which company s proposal would you choose based on the data? Why?

8 Figure That! Activity Log PROBLEM : WHICH TYPE OF BRIDGE IS BEST? Bridge Type Span (00 meters) Criteria for Bridge (Requirements that must be met) Load (Light Loads) Construction Time (Quick) Beam (Can be, but not always.) Can it be temporary? (Can be, but not always.) Suspension Arch Floating Quantify the Data What fraction, percent, and decimal equivalent of the criteria are met by each type of bridge? Bridge Type Fraction Percent Decimal Equivalent Beam Suspension Arch Floating

9 Figure That! Activity Log 1. If one bridge meets of the criteria and another bridge meets 1 of the criteria, can you make a decision on which bridge is best based on this information? Why? Yes or NO. If you were eliminating the bridge types that meet only 50% or less of the criteria, what fraction of the bridge types would you eliminate? 3. If you wanted a temporary bridge with quick construction time, which bridge would you choose based on the data provided? Why?. Describe how using fractions, decimals, and percent help in solving problems.

10 Figure That! PROBLEM 1: WHICH COMPANY S PROPOSAL BEST MEETS THE CRITERIA? Activity Log Each company s proposal must include these four criteria (requirements). Listed below are the criteria (requirements) each company s proposal actually included: Company A Company B Company C Company D Years of Experience Cost Estimate Bridge Design Construction Time Estimate 1. Quantify the data by showing each company s proposal information as a fraction, decimal, and percent. Company Fraction Percent Decimal Equivalent A 3/ 75% 0.75 B / 50% In a fraction, is the total number of criteria represented by the numerator or denominator? Denominator C 3/ 75% 0.75 D / 100% Company B s proposal includes only out of criteria, or. Write this as a reduced fraction. 1. What fraction of the companies submitted proposals include at least 75% of the required 3 proposal criteria? Write this fraction as a decimal What percentage of companies that submitted proposals meet all the criteria? 5% 6. Which company s proposal would you choose based on the data? Company D Why? Their proposal includes all the criteria.

11 Figure That! Activity Log PROBLEM : WHICH TYPE OF BRIDGE IS BEST? Bridge Type Span (00 meters) Criteria for Bridge (Requirements that must be met) Load (Light Loads) Construction Time (Quick) Beam (Can be, but not always.) Can it be temporary? (Can be, but not always.) Suspension Arch Floating Quantify the Data What fraction, percent, and decimal equivalent of the criteria are met by each type of bridge? Bridge Type Fraction Percent Decimal Equivalent Beam 100% 1.0 Suspension 50% 0.5 Arch 50% 0.5 Floating 100% 1.0

12 Figure That! Activity Log 1. If one bridge meets of the criteria and another bridge meets 1 of the criteria, can you make a decision on which bridge is best based on this information? Yes or No Why? Because these are equivalent fractions; they represent the same amount.. If you were eliminating the bridge types that meet only 50% or less of the criteria, what 1 fraction of the bridge types would you eliminate? 3. If you wanted a temporary bridge with quick construction time, which bridge would you choose based on the data provided? Beam or Floating Why? Beam and floating bridges meet all construction criteria. Both can be built as a temporary structure, constructed quickly, provide the required span, and support the required load.. Describe how using fractions, decimals, and percent help in solving problems. Representing data using numerical values (fractions, decimals, or percents), prevents making decisions based on opinion. Quantifying data allows one to make a decision based on factual data.

13 Figure That! Assessment Suggested Final Assessment Questions 1. Why is numerical data helpful to make decisions?. Show 50 out of 100 three numerical ways? 3. Show how you can visually represent the numerical data in the chart to compare the bridge types. 16

14 Figure That! Assessment Suggested Final Assessment Questions Analysis 1. Why is numerical data helpful to make decisions? It is based on measurable facts. Application. Show 50 out of 100 three numerical ways? a. 50/100 or 1/ b. 50% c Synthesis 3. Show how you can visually represent the numerical data in the chart to compare the bridge types. Create a graphical representation such as a bar graph. 17

15 E Math: A. Numbers and Number Relationships Activity: Figure That! References: Criteria. (n.d.). In Glossary. Retrieved from Decimal. (n.d.). In The Free Dictionary by Farlex. Retrieved from Denominator. (n.d.). In The Free Dictionary by Farlex. Retrieved from Equivalent Fraction. (n.d.). In Math is Fun. Retrieved from Fraction. (n.d.). In The Free Dictionary by Farlex. Retrieved from Numerator. (n.d.). In The Free Dictionary by Farlex. Retrieved from Numerical Data. (n.d.). In The Free Dictionary by Farlex. Retrieved from Percent. (n.d.). In The Free Dictionary by Farlex. Retrieved from Quantify. (n.d.). In The Free Dictionary by Farlex. Retrieved from 18