Solving Number Stories Lesson Study chico south - Michelle bunch, chris stedman, linda wren, sheyanne shanks

Math Message - Students were instructed to solve the problems using diagrams or tools to help. 1. Rushing Waters now has 26 water slides. That is 9 more than last year. How many water slides were there last year?
Students were provided the diagrams above as well as a 100's grid.

Potential answers were collected from the class and two were provided. 17 and 35

The first student explained she started at 26 on the hundreds grid, hopped up 10 to 36 then subtracted 1 to get 26 + 9 = 35.
This was the student's page showing her work. She started at 26 on the number grid and hopped back 9 places to 17. She commented that this was not the most efficient way to solve the problem, but it worked for her.

Two students used addition to solve the problem resulting in the correct answer.

This student wrote the problem as an addition problem with an unknown quantity.

A second problem was provided to students to problem solve.

2. The Loop Slide is 65 feet high. The Tower Slide is 45 feet high. How much shorter is the Tower Slide?

Potential answers were collected and everyone had 20 feetĀ as the answer. We had several students share to show their thinking and different problem-solving strategies.

This student shared that he simplified the problem to be 60 - 20 = 40. He accurately computed the answer but was having difficulty explaining that he took away 5 from 65 and 45 to solve the problem. Another student quickly clarified.
Here is her response to the problem.
This recorded their thinking by counting up by 10's from 45 to 65. They recorded a partial number grid puzzle to show their thinking.
Students then explored a chart of fish. We discussed how to read the chart to use information to solve word problems.
Students explored this first problem with partners.

Potential answers were collected. Students provided only two responses 4 and 32.

This student utilized partial sums to solve the problem. She added the tens and ones and came up with 32 inches.
This student respectfully disagreed and said you can count back from 18 to 14 on a number grid to show 4 inches was the answer.
The next student clarified that you could eliminate the 10's place completely to simplify the problem to 8 - 4 = 4 inches
We found several issues in running this lesson: 1. Students were moving ahead through the packet; 2. They weren't showing their thinking; 3. The diagrams provided on each problem actually hindered their ability to show work and lowered the cognitive demand from procedures with connections (3) to simple procedures (2); and 4. Some students were plugging numbers into the wrong spots;
What we learned: 1. Remove the diagrams from each problem; 2. Use fewer problems; 3. Spend more time on a problem; 4. Provide the fish diagram on a 1/2 sheet so they don't have to flip back and forth; 5. Hand out one problem and discuss; and 6. Students who are early finishers can solve it a second way.
Day 2 - Second Round of Teaching

Two problems were utilized for today's lesson. One problem from the math message and one problem from the lesson. More time was spent with students discussing their problem solving strategies.

Math Message - Students were instructed to solve the problems using diagrams or tools to help. 1. Rushing Waters now has 26 water slides. That is 9 more than last year. How many water slides were there last year?
The student decomposed 9 to use the "make a 10 strategy." Then the student could subtract from friendly numbers. 26-6=20 and 20-3=17.
The students were provided with the fish diagram on a 1/2 sheet of paper.
Student showing the problem can be solved with addition or subtraction, demonstrating inverse operations. Students did not understand switching the addends and ensuing discussion explored and clarified.

Conclusion - We learned to provide less support in the form of diagrams and less teacher dialogue. Student driven conversation was more powerful and increased the cognitive demand to a (4) doing math.

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