In this module, you will see how an experienced TTP practitioner plans and teaches a series of TTP lessons. Specifically, you will discover how the different instructional supports for a TTP lesson come together to build students’ understanding of a particular mathematical topic: area of polygons.
3.1 Examine the Content
To help students build the concepts in the mathematics curriculum– rather than be told those concepts –teachers need to know what their students currently know. Teachers also need to imagine how students might use their current knowledge to build the next mathematics in the curriculum. For these reasons, the first part of TTP lesson planning is investigating the curriculum content and students’ current understanding of it. When you do this in your own setting, you can draw on your own curriculum and standards.
Investigate Standards & Curriculum
Imagine that you want to plan a TTP lesson around the L-shape task below:
You first need to understand the unit context and larger mathematical trajectory into which this task fits. What role does this task play in building bigger mathematical ideas? What do students need to know to solve it? What are the important insights students might gain from solving this task?
Your Teacher’s Edition may explain the rationale for each task and how it relates to the unit and content trajectory. Or you may need to consult additional resources. In the case of this task, the Common Core State Standards and related Progressions for Geometry (especially pages 2-5 and p.16) and Geometric Measurement (especially pages 16-18) identify two important understandings that elementary students need to develop.
Composing and decomposing. Composing and decomposing figures provides an opportunity for students to learn about area as the “amount of two-dimensional surface that is contained within a plane figure” and to learn that “area is additive, i.e, the area of the union of two regions that overlap only at their boundaries is the sum of their areas” (CCSS progression geometry measurement K-5, 2012, p.4).
Spatial structuring. To measure area, students must mentally structure the space within a figure–for example, mentally structure a rectangle into rows and columns of square iterated units. The CCSS Progression for Geometry (p.4) notes that “Such spatial structuring precedes meaningful mathematical use of the structures, including multiplication and, later area….” and that “Early composition and decomposition of shape is a foundation for spatial structuring.” Students who are still developing an understanding of area may overlap or gap square units as they attempt to measure.
Below is a lesson plan developed by Dr.Takahashi that includes an explanation of the unit context and larger mathematical trajectory into which this task fits. Optional: Also included below is the video 'Can You Find the Area? (48 minutes). This video provides highlights from Dr. Takahashi's teaching of the three lessons described in the lesson plan. Segments of this video are used throughout the rest of this module.