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* *Reflection: Developing a Conceptual Understanding
Math Maps (Part 3) - Section 1: Mathematical Evidence

To help students develop a conceptual understanding about percent, I choose to initially focus on working with finding percentages when the whole was already 100. Then, once students became comfortable with this concept, I pushed their thinking to find percents when a fraction could easily be converted into 100.

However, in many situations, trying to use equivalent fractions to find a percentage is not the most effective or efficient way. Therefore, it was important for me to also teach students to use division to find a decimal quotient, then use the decimal to determine the percentage. This strategy also serves as a great review.

All students found percentages (for fractional parts when the denominator was 20, 50, or 100) using both strategies.

To provide students with a more rigorous challenge, after they completed the group 3 paper, they were provided with an opportunity to find percentages when the total distances included many different numbers (ex: 13, 30, 45, 10, 283 etc).

This challenge handout provides students with a rigorous challenge because for each example, students should choose the best approach for solving (either division or equivalent fractions).

Throughout the independent practice, I check in with students as they complete this challenge portion to conference on their approach. Through this conferences, I can determine various levels of math proficiency based on the students approach.

Ex 1: One student who I conferenced with told me that she used the division strategy to solve all of the problems on the sheet. When I asked her why she choose to use the division strategy for 6/10 she said because that is the best way. Through this experience I learned that this student is memorizing a strategy. She needs more support in using the strategies interchangeably.

Ex 2: When I met with a second student that was working on challenge sheet told me that she used the same approach. "I used division to make each of these a decimal". When I asked her to also look at 6/10 again, she recognized, "It would be much easier to use equivalent fractions for this one, because 10 goes into 100. I should not have used division for 9/100 either. That is pretty much already done for me." This student is demonstrating more proficiency than the other student because with prompting, she was able to realize that different strategies are more appropriate for different examples.

Ex 3: A third student explained, "I used different strategies for different problems, some where easier to divide because I couldn't make the denominator into 100, for others I used equivalent fractions. When I got to 30/45 I actually used a few strategies. First, I knew that 15/45 was 33.3% so I thought, I could just double that and get 66.6%. I wanted to check my work to see if this was true, so I used the division strategy too. I got .666 so I knew that I could use my first approach." This student is demonstrating mathematical proficiency. She is thinking flexibly about each problem and using repeated reasoning.

I make conference notes throughout the class. At the group share, I use each of these students' approaches to demonstrate the continuum of progress toward proficiency.

*Provide additional challenges*

*Developing a Conceptual Understanding: Provide Additional Challenges*

# Math Maps (Part 3)

Lesson 8 of 10

## Objective: SWBAT make mathematical statements about a given location on a route.

#### Mathematical Evidence

*10 min*

Students complete a chart to determine the fraction, decimal, and percent of the 100 mile race at each of the 10 mile intervals.

Fraction and decimal representations are a review for the students. Percentages are relatively new, though some of my students have asked about finding percentages throughout the year. Student assessments are scored using standards based progress reporting so percentages are not a common part of their daily lives.

Students have varying prior knowledge about percentages. This lesson is designed to expose some students to percents, teach some students how to find percentages using fractions and decimals, and to challenge other students to find percentages using division. The lesson is contextualized within the context of the math maps project.

Before beginning the lesson, students will be prompted to think about their knowledge of finding percentage. They will then personally place themselves in a group based on their familiarity with the concept.

This lesson targets: Critical Area 2 - Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.

Group 1: Students will use decimals (in the hundredths place) to form percentages.

Group 2: Students will use decimals as well as division to find the percentage of any 10 points along the route.

Group 3: Students will find percentages for points on bike routes that are 20 miles and 50 miles long

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#### Communicating with Math

*30 min*

To wrap up the math portion of the service learning project, students use their mathematical findings to generate statements. These statements are used to make encouraging posters to support the bikers as they complete the ride.

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##### Similar Lessons

Environment: Urban

###### Show what you know + Equivalency

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Environment: Urban

Environment: Urban

- LESSON 1: Interpreting Data
- LESSON 2: Data Collection (Owl Pellets Day 1)
- LESSON 3: Organizing Data (Owl Pellets Day 2)
- LESSON 4: Conducting a Survey (Owl Pellets Day 3)
- LESSON 5: Interpreting Line Plots (Owl Pellets Day 4)
- LESSON 6: Maps Math (Part 1)
- LESSON 7: Math Maps (Part 2)
- LESSON 8: Math Maps (Part 3)
- LESSON 9: Ancient Board Game "Go"
- LESSON 10: Celebration of Learning Reflection