Sides of Squares and the symbol ‘√’
From APEC HRDWG Wiki
The lesson “Sides of Squares and the symbol ‘√’” was captured on video for the APEC Education Network (EDNET) project called Classroom Innovations through Lesson Study. The lesson is an example of using the Lesson Study process of professional development in the teaching of Mathematics.
Lesson Overview
This 7th-grade lesson was conducted in May, 2009 at the Chicago Lesson Study Conference. The goal of this lesson is to introduce the square root symbol (√) as a way to represent the length of a side of a square with a given area. In the lesson, students look at squares on a pegboard with area 4 sq. inches, 9 sq. inches, 25 sq. inches, and then a "tilted" square with area 8 sq. inches. As the main problem of the lesson, students are asked to think about the length of the side of the square with area 8 sq. inches. This lesson runs into trouble when students have difficulty with the definition of a square and with the calculation of area.
[[Demonstration Practice  ] (see Resource Types)
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| Lesson Plan | Lesson Video in MPEG 4
(Video Clips and Highlights Available below. Right-click and select "Save Target As" to download the file.) |
Video Clips and Highlights from the Lesson
The video clips are selected from the full List of Episodes (above). The Full Lesson Video may be downloaded for further study.
| Description of Video Clip | Video Links |
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| During the previous day's lesson, students made quadrilaterals with area 8 sq. inches. To begin this lesson, students read a selection of what they wrote at the end of the previous day's lesson, "What I learned today..." | 0. Connecting to the previous day's work (1:45)
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| Working on the geoboard, students make squares with area 4, 9, and 25 square inches, and the teachers writes down the length of the side of each square. There is a brief discussion of the difference between inches and square inches. |
1. Warm-up (3:47) Watch the video (streaming version) |
| Students try to make a square with area 8 sq. in. Students hold up their results, and there is a discussion about whether their results are squares or not, and whether a rectangle is acceptable. After the teacher reminds students of their work the previous day, student remember how to make a square with area 8. There is some argument over whether the "tilted" square is actually a square. |
2. Making a square with area 8 sq. inches (6:00) Watch the video (streaming version) |
| The teacher asks students what the length of the side is. Students' first response is: 2 inches. The teacher arranges the squares in order by area and introduces this question (length of the side) as the main problem of the lesson. |
3. What is the length of the side? (3:24)
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| Students explain their thinking. One group argues 2 inches; one group 4 inches; one group 2.5 inches. The teacher challenges students to come up with a way to prove or disprove any of these. He helps them remember how to calculate the area of a square and suggests that this idea might apply to the square in question. Two girls articulate their dissonance between the idea that the side of the square is 2 inches and the idea that its area is 8. |
4. Discussion (5:53)
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| The teacher asks students to compute the area of a square with side 13, which several students do incorrectly. It becomes clear that several students do not have a solid understanding of the relationship between the side and the area. |
5. Square with side length 13
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| The teacher lists the areas and side lengths and the calculation that connects them. The teacher asks students to calculate the area using a side length of 2.5, and the class concludes that this side length is too small. The teacher classifies 2.5 and other lengths as either too big or too small, and asks students if they can think of another number to try. One student claims that there is no "just-right" number, but offers 2.83 as "close enough." |
6. Summarizing the discussion (4:58)
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| The teacher introduces the symbol for square root and shows how it can be used to represent the side lengths of all the squares looked at so far. |
7. Wrap-up
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