Notes & FAQs

In Algebra 1, students demonstrate fluency by creating, comparing, analyzing, solving, providing multiple representations, and identifying the structures of exponential & quadratic functions building on the understanding of linear functions from grade 8 to apply linear, quadratic and exponential models to data and unfamiliar problems.

Developmental Notes

Notes for A-CED.A

Tasks for this target will require students to create equations and inequalities in one variable to solve problems. Other tasks will require students to create and graph equations in two variables to represent relationships between quantities.

A-CED.A Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for F-IF.C

Tasks for this target will ask students to graph functions (linear... exponential... ) by hand or using technology and compare properties of two functions represented in different ways. Some tasks will focus on understanding equivalent forms that can be used to explain properties of functions and may be associated with Algebra Target H.

F-IF.C Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for A-REI.D

Tasks for this target will require students to interpret a line or curve as a solution set of an equation in two variables, including tasks that tap student understanding of points beyond the displayed portion of a graph as part of the solution set. Some of these tasks should explicitly focus on non-integer solutions (e.g., give three points on the graph of y = 7x + 2 that have x-values between 1 and 2).

Other tasks for this target will require students to approximate solutions to systems of equations represented graphically, including linear... exponential... (often paired with Target L - Interpret functions that arise in applications in terms of the context).

A-REI.D Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for F-BF.A

Tasks for this target will require students to write a function (recursive or explicit, as well as translate between the two forms) to describe a relationship between two quantities.

F-BF.A Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for A-SSE.B

Tasks for this target will require students to interpret a line or curve as a solution set of an equation in two variables, including tasks that tap student understanding of points beyond the displayed portion of a graph as part of the solution set. Some of these tasks should explicitly focus on non-integer solutions (e.g., give three points on the graph of y = 7x + 2 that have x-values between 1 and 2).

Other tasks for this target will require students to approximate solutions to systems of equations represented graphically, including linear... exponential... (often paired with Target L - Interpret functions that arise in applications in terms of the context).

A-SSE.B Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for N-RN.A

Tasks for this target will require students to use the definition of radicals and rational exponents and identify equivalent numeric and algebraic expressions involving rational exponents and radicals. Tasks for this target will require students to find the exact value of numbers expressed in terms of rational exponents or estimate their magnitude, where appropriate. Claim 3 tasks will tap student understanding of the properties of exponents and their ability to identify flawed reasoning applied to this target.

N-RN.A Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Notes for F-LE.1

Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

F-LE.1 Response Types, Stimulus Materials, Vocabulary & Calculator Use (DESMOS)

Frequently Asked Questions

Why is this unit placed here rather than after quadratics?

"Additive growth" of a linear function can be compared & contrasted with "multiplicative growth" of an exponential function. Having students keep track of folding a paper in half is a good illustration. Students create a T-chart with the # of folds plotted against the maximum # of layers (on a side view). 1 fold begets 2 layers, and 2 folds begets 4 layers. Stopping to ask students how many layers they expect on the next fold will usually illuminate both types of thinking. Those thinking "additively" will respond with 6, and those thinking "multiplicatively" will respond with 8. Checking their answers after folding, discussing the difference, and why it is so can provide helpful insight. Exploring the rate of change for both types of functions in various formats can further prepare students for comparing between functions (F-IF.9) and distinguishing between them (F-LE.1). So why is it here? The short answer is going from adding 2 to multiplying by 2 should be an easier leap if connected to the previous learning of linear functions.

What about sequences?

If sequences were not used as a transition into this unit, then you may wish to start with them to transition from the last unit, Unit 3.

What about the issue of discrete versus continuous functions?

This would be a good unit to begin the discussion of whether a function is discrete so students can interpret a function as a sequence as well, when discrete.

How do linear and sequences fit into this unit on exponential functions?

Interleaving and reengaging linear and sequence information by continuing to have students compare data and represent it in multiple ways to know what is linear, what is exponential, and if the data is a sequence within one of those functions is included in this unit, particularly as they pertain to F-LE.1 & F-IF.9.

For information on what is required in this unit, check out the assessment tab!