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Exploring Graham Fletcher’s Three-Act Lessons

Exploring Graham Fletcher’s Three-Act Lessons

Kid learning math

Last week I traveled to an elementary school to meet with my third-grade friends and their teacher. Students were just developing their ideas about fractions and area. The classroom environment was one in which students felt comfortable taking risks. These third-graders were comfortable engaging in tasks without relying on teacher direction. Students had previous experiences with Graham Fletcher’s Three-Act Lessons GFletchy.com and loved the exploration that accompanied Act 2! (If you are not familiar with Graham Fletcher’s site, summer is a good time to peruse his work.)

The lesson we chose for students to explore was The Big Pad. Act 1 presents students with a visual situation that begs students to ask a mathematical question. Teachers engage students’ curiosity with the less-than-60-second Fletcher’sAct 1 video .

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After showing my third-grade friends the video once, and a second time, students were asked what they noticed and what they wondered. Students noticed the color of sticky notes. They noticed the watch on Graham’s hand. One student thought it would take 16 smaller sticky notes to cover the big pad. The teacher suggested each student make a prediction about how many purple sticky notes it would take to cover the large yellow sticky note pad. All students wrote their prediction on a sticky note of course. These sticky notes were displayed in a line plot (2.MD.9) showing a range of 13-20 sticky notes needed to cover the area.

The teacher entertained all questions. The mathematical question that surfaced was: “How many purple sticky notes would it take to cover the yellow sticky pad?” Act Two asks students to think about solving their problem with two prompts: "What do you already know that will help you solve the problem?” and Is there anything else you need to know to solve the problem?"

Students reported that they knew how to cover the yellow sticky pad with the smaller purple sticky notes and a few noted it would take 16 purple sticky notes exactly. The information students wanted to know was the size of both the small purple sticky notes and the big yellow sticky notes. One student did volunteer she knew the purple sticky notes were 3-by-3 because she had seen it in Act 1. This led to a conversation about units, so we did project the two pictures below which state the dimensions of each sticky note. The class had sets of the 3-by-3 sticky notes, but students were not sure what to do about the larger sticky note. We handed them 11-by-11 squares and asked them to measure them to verify the measurements. (This was an opportunity for a formative assessment of students’ skills with using a ruler to measure side lengths 2.MD.1.)

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11x11 post its

Next, students spent 20-25 minutes working in pairs to answer the question of how many smaller sticky notes it would take to cover the area of the larger sticky note. All students were working to cover the area with lots of discussion and cooperation. “Oh, 16 sticky notes are too many," and “I think we will need to use fractions!” were some of the comments.

The moment arrived, however, when students realized there was not quite enough room on the 11 by 11 sticky note to fit four 3 by 3 sticky notes across the top or down the sides. I watched the perplexed look on the faces of my third-grade friends. They were involved with a productive struggle and had a myriad of approaches to the problem. Teacher questions such as: “How do you cover a given area with sticky notes?” or “Explain how it is possible for us to get more than one answer to this problem,” and “If the area remaining does not require one whole sticky note, how will you cover that area?” supported the students' efforts.

The teacher continued allowing students to struggle for a while, which is difficult to do. Students had creative ways to deal with the partial sticky notes. I overheard a pair of students ask, “Was a sticky note the correct amount for the leftover edges around the sticky note?” This question came up in several working pairs of students causing the teacher to call students to the front of the class for a mini lesson on unit fractions of using the small sticky note as the whole. Students then went back to work . While walking around I observed students at different stages of understanding about area, unit fractions and addition with fractions. One student had arranged his first two rows to read:

1

2

3

3-2/3

4-2/3

5-2/3

6-2/3

?

He and his partner were trying to give a name to the fractional area on the end of the second row. I asked him what he thought the amount might be. “Eight?” was his reply. When prompted for an explanation, he said, “It is more than 7 because 6 is only 1 away from 7.” When I asked him how he and his partner knew that fact, they both showed me how they had folded the sticky notes and could denote both as well as the remaining. Wow! This was significant conceptual understanding the two of them were discussing while answering the question of how many purple sticky notes it would take to cover the area. Many of the students had similar conversations. They knew the parts were fractional and understood they could be added to whole numbers to give a value for the area but they were not always sure how to group the fractions and what to name them.

Students folded sticky notes and labeled each sticky note withe the amount of area the note covered. Students used whole numbers and fractions including mixed numbers. (3.MD.7 and 3.G.2). Now students had a new question: What was the total big pad area that the sticky notes covered?

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Several pairs of students were asked to share their thinking to the entire class. The teacher asked students to point out the similarities and differences they saw in the work of their peers.

Students were 95% convinced that there was only one amount of area that the purple sticky notes were covering but they were still having trouble making connections amongst the different amounts their peers had decided was the answer. The teacher closed the lesson withAct 3 asking students to compare Graham’s work with their own work.

This task provided students with a challenging question and gave students exposure to new mathematical ideas while reinforcing the concept of area and unit fractions that represent values less than the specified unit. An important attribute of this Three Act Lesson is that students made choices when creating their model and had plenty of time to revise their original thinking. The students accessed the Standards for Mathematical Practices in their work individually, through their work with a partner, and as they viewed the work of their classmates.

Finally, when planning for the next lesson, this formative assessment will be useful.

-Ed