Designing a Unit (Sample)
Step 1: Comb through the core and find all the standards related to the unit you
will write. Identify topics and the mathematics that students will have to work
through. Some of these bullets come straight from the core and some are just
from brainstorming.
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Arithmetic and geometric sequences
Average rate of change vs instantaneous (which they won’t be using yet)
Linear and exponential relationships recursively
Growth can occur as a pattern, but not be linear
Interpet parameters in a linear or exponential functions in terms of their context
Building new functions from existing functions
Translating explicit and recursive equations for linear and exponential functions
Equal differences and equal factors
Build on and informally extend their understanding of integer exponents to consider exponential
functions.
Construct and compare linear, and exponential models and solve problems.
Interpret expressions for functions in terms of the situation they model. Including linear and
exponential of form: f(x) = bx + k
Build a function that models a linear or exponential relationship between two quantities.
Build new functions from existing functions. (Linear and exponential; focus on vertical
translations for exponential
Understand the concept of a function and use function notation. Learn as general principle.
Focus on linear and exponential (integer domains) and on arithmetic and
geometric sequences
Interpret functions that arise in applications in terms of a context. Linear and exponential,
(linear domain)
Analyze Linear and exponential functions using different representations.
Solve equations and inequalities in one variable, such as 2x = 1/16
Interpret the structure of Linear expressions and exponential expressions with integer exponents
Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a single entity. For
example, interpret P(1+r)n as the product of P and a factor not depending on P.
Distinguish between situations that can be modeled with linear functions and with exponential
functions.
Prove that linear functions grow by equal differences over equal intervals; exponential
functions grow by equal factors over equal intervals.
Recognize situations in which one quantity changes at a constant rate per unit interval relative
to another.
Recognize situations in which a quantity grows or decays by a constant percent rate per unit
interval relative to another.
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Construct linear and exponential functions, including arithmetic and geometric sequences, given
a graph, a description of a relationship, or two input-output pairs (include reading these from a
table).
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Interpret the parameters in a linear or exponential function in terms of a context.
Step 2: Sort and sequence the ideas from the core in a logical order for your
learning cycle.
Arithmetic and Geometric Sequences: Discrete Linear and Exponential Functions
Learning Cycles
Develop Understanding
Develop representations for discrete linear contexts such as: numeric sequences, tables, graphs, and
recursive and explicit equations.
Develop Understanding
Develop representations for discrete exponential contexts such as: numeric sequences, tables,
graphs, and recursive and explicit equations.)
Solidify Understanding
Solidify the ideas that arithmetic sequences have a constant difference between terms. Identify how
the constant difference (constant rate of change) appears in table, graph, and explicit and recursive
equations.) Practice writing explicit and recursive equations
Solidify Understanding
Solidify the ideas that geometric sequences have a constant ratio between terms. Identify how the
constant ratio (exponential rate of change) appears in table, graph, and explicit and recursive
equations. Practice writing explicit and recursive equations.
Solidify Understanding
Solidify arithmetic sequences can be increasing or decreasing at a constant rate using various
representations, with a focus on writing both explicit and recursive equations.
Solidify Understanding
Solidify geometric sequences can be increasing or decreasing at a constant rate using various
representations, with a focus on writing both explicit and recursive equations. Develops comparison
between linear and exponential rates of growth.
Practice Understanding
Practice writing explicit and recursive formulas for geometric and arithmetic sequences given a table.
Solidify Understanding
Solidify using the characteristics of arithmetic sequences to find arithmetic means.
Solidify Understanding
Solidify using the characteristics of geometric sequences to find geometric means. Develop/solidify
solving equations with exponents.
Practice Understanding
Practice writing arithmetic and geometric sequences given various information such as the difference
between terms, two terms, explicit or recursive equations, etc.