Host teacher : Beth Moore

1. Using Multiple Strategies to Complete Multi-step Addition and Subtraction ProblemsDale City Elementary Host teacher: Beth Moore Team Members: Beth Alvarez, Cheryl Ayres, Alise Brooks, Kathe Carney

2. Lesson Goals • Professional Learning Goal: • We will develop math lessons that address students at all levels and allow them to participate in inquiry-based activities. • Student Learning Goal: • The students will participate appropriately and learn from their peers. • The students will learn new strategies to solve word problems.

3. Math Task There are 23 students in our class. We want to walk 230 laps on the track. If each student walks the same amount, how many laps will each student walk? What if the students do not have to walk the same amount, how could the class get to 230 laps?

4. Describe the Math Task • We focused on part a of the problem in the initial explanation and in the concluding discussion. The second page (part b of the problem) was to provide extension for students who were able to complete part a successfully. • SOL Objectives: • 2.6B Find the sum of two whole numbers whose sum is 99 or less, using various methods of calculation.   • 2.7B Find the difference of two whole numbers, each of which is 99 or less, using various methods of calculation. • 3.4 Estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping. • 4.4D Solve single-step and multistep addition, subtraction, and multiplication problems with whole numbers.

5. Student Work Desirae overheard the answer of 10, but her work showed no understanding of how to get there.

6. Student Work Jaedyn counted out 23 tens rods. She showed a proof of an intuitive understanding that the answer was 10, not a strategy to find the answer of 10.

7. Student Work Kevin counted 23 tens using hundred flats and tens rods. Kevin also showed a proof of an intuitive understanding that the answer was 10, not a strategy to find the answer of 10.

8. Revisions to Original Lesson (3rd grade) We reworded the story to decrease misconceptions such as doing 230 times 10. We made the numbers smaller to bring them into a range where the students are more comfortable working. We changed the numbers to decrease the likelihood that the students would be able to answer intuitively without working through the problem. We decided to limit the number of manipulatives available to help the students choose tools that would be really helpful for this problem.

9. Beth Alvarez • 1st Grade Study Lesson

10. Revisions to Original Lesson (1st grade) I changed the numbers to 3 students and 12 laps. I also gave the students names instead of just saying 3 students. When I presented the lesson, I started with a story problem aloud with 2 students and 6 laps. I used 2 students in the class to help demonstrate the problem and we solved it as a whole group. Then I read the story that the students were going to solve in pairs. The only manipulatives provided to the students were cubes and the option to draw a picture. They were told that they could ask for something additional if they needed something specific, though no one did during the lesson.

11. Revisions to Original Lesson (1st grade) Maya drew 12 lines and made three groups out of them. Angie used 3 cubes and moved them around the track 12 times total. Some students misinterpreted the question and assumed the each student would walk 12 laps. These students needed to have the task explained in their small group.

12. Alise Brooks • 2nd Grade Lesson Study

13. Math Task – Modified 2nd Math Question Modified Question for 2rd Grade: There are 6 student who want to walk a total 42 laps. If each person wants to walk the same number of laps, how many laps will each student walk? Objective that we worked on was 2.6B Find the sum of two whole numbers whose sum is 99 or less. Using various methods of calculation. Find solutions to and solve single-step and multistep problems involving the sum.

14. Alise Brooks - Misconceptions • Several children added 42 six times. (42+42+42+42+42+42= ____). • Some children tried to count by tens and ones (4 tens and 2 ones). • Some children knew to make 6 groups, but did not know what to do next. • Add 6+6+6+6+6+6+6=42

15. Alise Brooks - Success Used cubes to make 6 stacks of 7 to get to the amount of laps. Some children put 42 tally marks in 6 groups until they reached 7 laps. Some of children were able to figure out in their head and multiply 6 X 7 = 42.

16. Cheryl Ayres Fourth Grade The Fourth Grade problem was modified to read: There are 28 students in our class. We want to walk 308 laps on the track. If each student walks the same amount, how many laps will each student walk?

17. Revisions to Original Lesson (4th grade) • The numbers the students worked with were more challenging. • Students divided a 3 digit number by a 2 digit number. • A wider range of solutions to the problem were encouraged and accepted. • Some students drew pictures while some students used multiplication to solve a division problem.

18. Analysis of Lesson (4th grade) • Students found dividing a 3 digit number by a 2 digit number to be challenging. • Some students had difficulty deciding where to start. • Some students relied on creating visual representations while others wanted to make an open array. • We had productive discussions about “friendly numbers.”

19. Fourth Grade Successes • Some students were able to skip count by 28 until they reached 308. They understood that they skipped 11 times. • Some students used multiplication to help them solve the problem. • Multiplication was seen as the inverse of division.

20. Kathe’s Special Education Students- Grade 4 • This class used the revised question from Beth’s lesson on the first day; the second revised question was presented on the second day to assess generalization of these math concepts and the ability to develop more than one strategy for this type of problem.

21. Kathe’s Special Education Students – Grade 4 • This class is comprised of 6 students with significant emotional and learning disabilities; in addition, there are severe weaknesses in communication and ESOL. The math discussion was limited to responses to the teacher’s probing questions. Students demonstrated their strongest intelligence when problem solving.

22. Kathe’ s Special Education Students – grade 4 Fatu set up her students as six groups; then she dealt laps to each student until she reached the total of 96 laps. Then she proceeded to use the “box model” for multiplication to check her results. Nayeli is an ESOL student who is a selective mute; she visualized the students as a column of snap blocks and then used cm cubes to represent the laps. She used the traditional algorithm to check her work.

23. Kathe’s Special Education Students-Grade 4 Kendric attempted to use the manipulatives to solve the problem; he was not able to picture how to do this, so he used the game Circles and Stars to model his problem-solving. Lierin’s basic problem solving revolved around her artistic intelligence. She drew team captains and counted the laps. However, when she got to ten, the solution became obvious.

24. How Lesson Study Supported Our Professional Learning • the wording and numbers in a problem • affect the students’ ability to solve • the problem • manipulatives need to be made • available in a thoughtful way • it is best to group students in pairs

25. Further Questions to Explore • fractions • division • arrays • grouping