Implementing Lesson Study: The MCTM Project. Evans Elementary. Long and Short Term Goals. To develop a responsible and positive attitude we chose Respect for Self, Others and Learning for the long term goal.
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The MCTM Project
A work booklet was designed. The question, “How many pieces would I get?” was inside the booklet on the second page. After children worked independently for about 5 minutes, the teacher would ask them to share their ideas with their group. She would suggest that thinking about the number of pieces you would get in 1/3 or 1/4 may help you decide which is the bigger part.
Children first worked individually,
then in pairs.
We picked ¼ because the bottom number is 4 and the other bottom number is smaller so ¼ is bigger.
1/4 is more than 1/3.Students’ Ideas
Some students still didn’t understand.
Me and my partner think the 1/3 is bigger because the less pieces the bigger the pieces are.Students’ Ideas
Some children used multiple representations to show this concept and they could explain it.
At first, all students said 1/4 was larger than 1/3.
Their ideas began to change during small group work.
1/4 is bigger or larger because there is 4 pieces. pieces the bigger the pieces are.
1/3 is smaller because there is 3 pieces.
is smallerSecond Implementation
At the beginning of the class discussion, some students were still convinced that 1/4 was larger.
In this group, all the students agreed that 1/3 was larger, but one child said 1/3 was 9 pieces and another child said it was 4.
1 pieces the bigger the pieces are.
We think it is 1/3 is because you want as much as you can get. Just because the bottom number is biggest doesn’t mean you get more.
.The Turning Point
After this group argued that just because the bottom number is biggest it doesn’t mean you get more, students began to raise their hand to say they changed their mind.
At the end of class all except one student agreed that 1/3 was bigger than 1/4. This student said, “If you subtract 1 from 1/3 it would be two big pieces. If you subtract 1 from 4, it would be 3.” He was still thinking about whole numbers.