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The completion date is June 30, 2000.
STATE GOAL 8: Use algebraic and analytical
methods to identify and describe patterns and
relationships in data, solve problems and predict
results. (Illinois Learning Standards)

Statement
of Purpose about the Project and the Group
As the NCTM Principals and Standards document
states, “students in the middle grades should
learn algebra both as a set of competencies tied to
the representation of quantitative relationships
and as a style of mathematical thinking for
formalizing patterns, functions, and
generalizations.” (NCTM, p. 223). In this
section we have tried to build on the notions of
patterns and their expression both graphically and
algebraically. We try to show the connections
between algebra and geometry. We explore discrete
data and graphing in the context of linear
relationships.
The introduction of approriate tools at
appropriate times (from computers to angle rulers)
is an important part of exploring and developing
mathematical understanding.


In this unit, we begin with polygons and
interior angles. We explore the notion of patterns
and relations and the use of variables to make
these relationships clearer and to help us
interpret information. Beginning with geometry is a
deliberate effort to show that algebra and geometry
are related.


Part
1
pp. 23

Part
2
pp. 49

Part
3
pp.1021

Part
4
pp.2223

Content/Topic

Drawing a regular polygon

Tables, graphs, patterns and variables

Turning the problem around

Expanding and assessing

Activity

Try to draw a regular polygon

Make a table of angles and sides, draw a graph
of discrete points, use variables

Predict the results with nonregular polygons,
concave polygons, find the sides given the
angle

Find the number of diagonals in a polygon.
The swimming pool.

Assessment

Create the figures and make attempts at the more
difficult polygons

Create the graphs, tables, and formulae

Analyze the predictions, produce figures

Produce a problem that illustrates the need for
analyzing patterns and using variables

Standard

8.A

8.B

8.D

8.D

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