6/9/2015Bell, Erhard, Perrow, & Smith 1 Lesson Study on Proportional Reasoning by OSO George Mason University

6/9/2015Bell, Erhard, Perrow, & Smith 2 Main Mathematical Task Students with special needs and language barriers will explore proportional reasoning while solving two main math dilemmas. Students are patiently encouraged to construct their own individual or group strategies for problem solving.

6/9/2015Bell, Erhard, Perrow, & Smith 3 Virginia Standards of Learning Virginia SOL 6.6 The student will a) multiply and divide fractions and mixed numbers; and b) estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions. Virginia SOL 6.7 The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals. Virginia SOL 6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions

Warm-Up 1: Find the Lowest Price The table shows the prices for CDs at 3 different stores. Which store has the lowest price per CD? How do you know? Use pictures, words, & numbers to show how you got your answer. Store# of CDs Total Price A4$30.00 B2$15.00 C1$8.99

6/9/2015Bell, Erhard, Perrow, & Smith 5 Warm-Up 2: Quinn’s Lollipops Quinn needed 15 bags of candy to give to her friends. Quinn wanted to put 3 lollipops in each bag. How many lollipops did Quinn need to buy? Use pictures, words, & numbers to show how you got your answer.

Main Problem: Caterpillars and Leaves A sixth grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars? Show your answer in words, pictures, and numbers.

6/9/2015Bell, Erhard, Perrow, & Smith 7 Relationship to the 6 th grade Math SOLs Problems were selected to encourage student’s abilities to develop their own rational problem solving strategies. Problems required the students to use estimation and multiple steps with addition, subtraction, multiplication, and division.

6/9/2015Bell, Erhard, Perrow, & Smith 8 Why We Chose these Activities Our team discussed the abilities of the sixth grade inclusion math class. We considered the high percentage of students who failed the 5th grade math SOL test. To maintain consistency, we used the same type of warm up activity the students have been doing all year.

6/9/2015Bell, Erhard, Perrow, & Smith 9 Student Strategies Students worked in groups of four to solve the main dilemma. They were encouraged to try a variety of ways to solve the problem. All ideas were considered. Students described and illustrated their strategies using posters.

6/9/2015Bell, Erhard, Perrow, & Smith 10 Three Strategies Observed Wesley’s group used the unit rate to solve the problem. 1 Caterpillar eats 2.5 leaves. Kylie’s group used equivalent the ratio. 2 caterpillars eat 5 leaves, 12 caterpillars must eat 6 times that many leaves. Jacob’s group used the co-variant method. The first two caterpillars ate 5 leaves, and the next two ate five leaves and the next two ate five leaves, adding 2 more caterpillars and 5 more leaves until 12 caterpillars are present.

Revisions pg. 1 For the original presentation, four different problems were prepared. Only two problems were used after the warm-up: 1. Caterpillar & Leaves, 2. Trick or Treating Dilemma. One team member used Quinn’s Lollipop warm-up that correlated with the caterpillar question. One team member eliminated the warm up due to time constraints. 6/9/2015Bell, Erhard, Perrow, & Smith 11

Revisions, pg. 2 Another member changed the number of leaves to even numbers and used paper leaves instead of counters. Paper leaves could be torn in half. Two of the members eliminated the Halloween question as their closure activity. One member created a new closure question that students had to work on independently. 6/9/2015Bell, Erhard, Perrow, & Smith 12

Manipulatives we used

6/9/2015Bell, Erhard, Perrow, & Smith 14 Reflection This PowerPoint is a composite of the most effective strategies we discovered for presenting this lesson. We all felt that we grew in our understanding and ability to encourage proportional reasoning among our students. We also develop a greater respect for allowing students to construct their own strategies for problems solving. This occurred most readily in a atmosphere of inquiry without judgment.