Curriculum Unit: Proportional Reasoning and Mathematical Communication

By Steve Rioux

Theme: Students will be able to generate, collect and organize data. They will be able to analyze and evaluate the data and explain is proportional significance.

Grade Level: Seventh Grade

Objectives (Based the CT Mathematics Framework and is aligned with the CMT 3^rd Generation Blueprint noted by strand identification number):

1. 9c. Solve multi-step problems involving whole number, decimals, fractions, and mixed numbers, including averages.

2. 9d. Solve problems involving whole number, decimals, fractions, and mixed numbers with extraneous information.

3. 10c. Determine the reasonableness or unreasonableness of an answer or estimate.

4. 11b. Use estimation to make and defend a decision.

5. 12a. Solve problems involving ratios.

6. 12b. Solve problems involving proportions.

7. 13a. Find percents of whole numbers or the percent a given number is of another number.

8. 20a. Draw and justify reasonable conclusions from graphs, tables and charts.

9. 23c. Evaluate expressions and use formulas.

10. 24. Solve problems involving the organization of data.

11. 25. Solve extended numerical and statistical problems.

Lesson One:

Topic: Introduction to Ratios

Objective: The students will write ratios in lowest terms.

Purpose: To develop proportional reasoning skills.

Student Arrangement: Students will be grouped in pairs.

Time Allocation: 40 minutes

Procedure:

Student will begin the period with a review of simplifying fractions.
Students will review book examples and discuss as a class the methods to write ratios.
Student will be given ten minutes of direct instruction and will take appropriate note.
Students will spend ten practicing writing rations and simplifying each ration.
Students will conclude the lesson by solving five real-world application problems involving ratios.
Homework: Students will write one paragraph in their journals describing the uses of ratios.

Assessment:

Journals will be reviewed on a weekly basis and comments provided.
Classroom examples will be review and solutions will be presented to the class.

Lesson Two:

Topic: Introducing Proportions

Objective: Students will solve proportions.

Purpose: Provide strategies to find unknown amounts of proportions. They will then use these skills to make predictions in patterns involving proportions.

Student Arrangement: Students will be grouped in pairs.

Time Allocation: 40 minutes

Procedure:

Students will review solving one-step equations.
Students will share journal responses.
Students will write solutions to five real-world problems on the white board.
Students will work in pairs to solve a proportional problem without instruction.
Students will discuss struggles and strategies.
Students will be given ten minutes of direct instruction.
Students will complete book assignment.
Students will write in their journals describing the learn experiences of the day.

Assessment:

Journal responses and classroom observations.

Lesson Three:

Topic: Converting fractions and decimals to percents.

Objective: To write fractions and decimals as percents and to write percents as fractions and decimals.

Purpose: Students need to understand percents to justify their estimations in later activities.

Student Arrangement: Students will be grouped in pairs

Time Allocation: 40 minutes

Procedure:

Students will share journal responses.
Discuss how percents, factions, and decimals are related.
Ten Minutes of direct instruction about conversions.
Students will work in pairs to solve assigned example from their text.
Students will use a calculator to check their answers.
Homework: Students will write in their journals describing how fractions, decimals, and percents are related. They will then provide three examples.

Assessment:

Informal classroom observations

Lesson Four:

Topic: Microsoft Excel

Objective: Students will use Microsoft Excel to organize three sets of data and find the mean, median, and mode of each set.

Purpose: Provide an introduction to Excel and organizing data.

Student Arrangement: Students will work individually in a computer lab.

Time Allocation: 40 minutes

Procedure:

Students will log onto the computers and download three sets of data from www.geocities.com/steve06241/rioux.html .
Students will then multitask and copy the information into an Excel document.
Students will label each category and design borders to separate the information.
Steve will sort the data in order to find the median and mode of each set of data.
Students will create formulas to find the mean of each set data.
Students will save their work into their work folders on the network.

Assessment:

Students will provide their answers on a sheet of paper and hand in at the end of the period.

Lesson Five:

Topic: Election by the Numbers

Objective: Students will analyze how percents are used in election and describe their meaning.

Purpose: Review concepts of elections and the Electoral College and interpret numerical data into literal meanings.

Student Arrangement: Students will work individually in the computer lab.

Time Allocation: 40 minutes

Procedure:

Students will view Mr. Ramthun’s PowerPoint presentation on the Electoral College from www.geocities.com/steve06241/rioux.html
Students will then view Mr. Rioux’s PowerPoint that will describe an Online Assignment and how it will be assessed.
Students will complete a PowerPoint critique checklist form and discuss their opinion in small groups.

Assessment:

Critiques will provide evidence of students viewing each PowerPoint.

Lesson Six:

Topic: Data Collection

Objective: Retrieve and store data in Excel

Purpose: Integrate subjects and develop a master of specific topics

Student Arrangement: Students will individual in the computer lab, but will be a part of a four person team.

Time Allocation: 40 minutes

Procedure:

Students will log onto the computers and retrieve directions form www.geocities.com/steve06241/rioux.html
Students will visit http://fisher.lib.virginia.edu/collections/stats/histcensus/ and collect data from the election of 1800 and 2000 then enter it into an Excel document
Students will then use the summation function in Excel to find the total population in 1800 and 2000
Students will find the proportion of Electoral votes assign to the New England states.

Assessment:

1. Students will provide a printout of their Excel document.

Lesson Seven:

Topic: Presentation

Objective: Students will communicate their results in tables and graphs and present the information in a PowerPoint Presentation.

Purpose: To increase mathematical Communication skills

Student Arrangement: Students will individual in the computer lab, but will be a part of a four person team.

Time Allocation: 40 minutes

Procedure:

Students will use data collected from previous two lessons.
Students will create a PowerPoint presentation and upload onto Mr. Rioux’s homepage for Students Work

Assessment:

1. PowerPoint Presentation