The Differentiated Math Classroom - Chapter 7 (part 2)

Chapter 7: Lessons as Lenses
The second lesson that the authors describe in chapter 7 addresses two- and three-dimensional shapes and is differentiated for readiness and accessibility (rather than for efficiency, as the first lesson was.)
During the course of studying these geometry terms, the teacher observed that some students were needing more time with concepts while others were needing a challenge. The lesson was designed to address these needs and was a tiered lesson with three different activities, two of which addressed the needs of those who required more time while the third addressed the need for challenge.

The launch part of the lesson was a whole group discussion of the traits of a hexahedron, which connected previous learning and modeled one of the lesson activities. The launch also included an explanation of the lesson activities.

The exploration was the working time in the activities, which were different, but related.  All groups began by describing a given three-dimensional object as completely as possible (as was done during the launch).
    Group 1’s activity provided an additional chance to work with shapes and their properties. They were required to create a poster that would classify two- and three-dimensional shapes into groups of their making. They then needed to write a mathematical description of these groups.  
    The second group worked on identifying the faces of three-dimensional shapes- tracing them, naming them, and then drawing a net. These students also had to create a poster, with descriptions.
    The third group’s task was to create a geometry concentration game.

Students did not finish the activities during the class period, so the class summary was a sharing of what the groups had completed, as well as what work they still had to complete. The next class period included a sharing of the products. Group members that finished their tasks early worked on anchor activities.

The authors take time to explain more about tiering, which is designed for predetermined groups based on readiness, multiple intelligences, or interests. The first tier should be a basic level, the second should be an extension for students that like challenge, and the third provides scaffolds for students that need more background or support. When thinking about tiering, the authors suggest to think about what comes before and after the basic concept.

The authors offer these steps for tiering a lesson, which were adapted from Pierce and Adams (2005.)     (I’m parapharasing.)
1) Identify the math standards/objectives
2) Identify the big idea/key concepts
3) Determine necessary prior knowledge
4) Determine what to tier – the content, process or product
5) Determine what to tier for – readiness, learning style, interest, etc
6) Determine number of tiers
7) Develop plan for formative and summative assessments.

The authors share another quick example of tiering for third and fourth grades, using an Array game.
Tier one is for students working on learning multiplication facts. Working with a partner, students deal the array cards with the array side (doesn't show product) faceing up. The students compare the arrays on their top card and whoever has the greatest product keeps the cards.
The second tier is for students who are ready to see relationships between multiplication facts. These students work in pairs, using the array cards as well, keeping the product side up. They start with one array and then find 2 others that will cover the original array
The third tier is for students who are ready for extension. Using the arrays with the product facing up, they write equations (with a partner) to show how the distributive property is modeled by decomposing the product in the sum of two products. Example given: 18 =  (1 x 6) + (2 x 6).

These examples have gotten my brain thinking about how I can add to what I already have in place. I’ve added the creation of tiered activities to my “To Do” list, which seems to be getting longer every day!

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