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

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.

**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).

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