Unit Description
This
is the first unit of the algebraic strand in middle school mathematics. This unit develops the students’ ability to
explore a variety of situations involving change. These changes occur in the context of the
planning and implementation of a bicycle tour. Students explore three different ways to
represent change - narrative, table, and graph. They will then move into symbolic
representation using simple equations.
Throughout the unit, they compare advantages and disadvantages of
representing the data in the various ways.
After becoming proficient in writing symbolic rules, students will
learn how to use graphing calculators to make tables and graphs for any rule.
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Enduring Understandings
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The choice of data representation depends on the purpose of
communication and the data collected.
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A change in one variable can cause a change in a second
variable.
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Data analysis often reveals patterns and enables
prediction.
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Essential Questions
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When and why use a graph?
When does graphing help the audience and when does graphing help the
researcher?
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What advantages and disadvantages should be considered to
select an appropriate representation of data? How do I best represent this
data and how do I know? (i.e. tables,
graphs, verbal descriptions, and equations)
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In a coordinate graph of two related variables when is it
appropriate to connect the points?
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How can mathematical modeling be used to clarify
mathematical relationships? How can graphs be used to bend the truth?
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What are the advantages and disadvantages of using a
graphing calculator for interpreting data?
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GLEs: 1, 5, 10, 11, 14, 17,
18, 19, 24, 25, 26, 27, 28, 29, 31, 32, 33, 40
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Students will know…
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Table (organizing data)
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Graph (representing data so that relationships can be
identified)
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Pattern (provides and explanation for an identified
relationship)
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Variation (changes in data that may be caused by a pattern
or some other factor)
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Variable (represents a quantity that may change)
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Axes (labeling a graph so that a pattern between two
variables can be represented)
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Scale (choosing increments for each axes so that variables
are accurately displayed)
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Maximum/minimum (identifying largest/smallest values of a variable
from a table or graph and the largest/smallest changes in the variable)
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Rules (explaining a pattern between variables with tables,
graphs, words)
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Rate, Time, Distance (understanding linear relationship D =
R x T)
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Symbols (representing a variable with a letter)
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Symbolic Rules (using symbols to represent relationships
between variables)
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Generating representations (using symbolic rules to
generate tables/graphs with a graphing calculator)
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Students will be able
to…
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Write and graph inequalities in real life situations
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Collect data (conduct trials of an experiment)
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Interpret quantitative information (make inferences from a
table or graph)
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Generate a graph from a table (use information from a table
to make a graph and choosing most appropriate representation) i.e. box and
whiskers, circle, line, bar
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Generate a table from a graph (use information from a graph
to make a table)
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Translate graphs and tables (describe a written situation
with a graph or a table)
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Transfer words ß à symbols (express relationships between
variables given in words with a symbolic rule and vice versa)
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Compare rates (use information from tables, graphs, words,
or symbolic rules)
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Generate representation with a graphing calculator (use a
graphing calculator to generate table and graph representations of rules to
decide whether or not the rule, expressed in words or symbols, defines a
straight- i.e. Linear – line function)
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Interpret data
(describe in terms of patterns, clustered data, gaps, and outliers)
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Assessments
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Performance Task
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Performance Task Rubric
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Performance Task Key
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Variables/Patterns Review 1
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Variables/Patterns Unit Test 1
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Variables/Patterns Unit Test 1A
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Variables/Patterns Unit Test Modified
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Variables/Patterns Review 2
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Variables/Patterns Unit Test 2
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Variables/Patterns Unit Test 3
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Variables/Patterns Review PPT
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Variables/Patterns Review Key
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Translating Equations
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Expressions and Equations
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Rules and Formulas
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Order of Operations PPT
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Order of Operations Worksheet
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Order of Operations Quiz
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