# Q2W10 Algebra Teacher Carol Barnes Algebra 7th/8th Q2W10 Oct.19-22 Unit 4-Linear Equations, Functions, and Inequalities
Standard(s) Taught

MAFS.912.F-LE.1.3  Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.  For example, the Fibonacci sequence is defined recursively by f(0) = f(1) =1, f(n + 1) = f(n) + f(n-1) for n>=1.

MAFS.912.F-LE.1.2  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).

MAFS.912.F-BF.1.1a  Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.

MAFS.912.A-CED.1.3  Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context.For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

MAFS.912.S-ID.3.7  Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Learning Targets and Learning Criteria
• create a table from a list of numbers (sequence) by making the term number (position) the inputs and the elements the outputs.

• define an arithmetic sequence as a sequence of numbers that is formed so that the difference between consecutive terms is always the same known as a common difference.

• recognize arithmetic sequences as linear functions.

• explain that a recursive formula tells me how a sequence starts and tells me how to use the previous value(s) to generate the next element of the sequence.

• explain that an explicit formula tells me how a sequence starts and tells me how to find any term of the sequence by knowing the difference by which the sequence increases or decreases.

• find an explicit or recursive rule for a sequence.

• write specified terms for a sequence, defined explicitly or defined recursively.

• describe the algebraic process used to construct the linear function that passes through two points.

• decide if a graph, verbal description, data, or sets of ordered pairs models an arithmetic sequence (linear) and write the equation.

• distinguish between explicit and recursive formulas for sequences.

• identify the quantities being compared in a real-world problem.

• write an explicit function, define a recursive process, or complete a table of calculations that can be used to mathematically define a real-world context.

• write a recursive definition for a sequence that is presented as a sequence, a graph, or a table.

• create equations and inequalities that best models the constraints of a real- world problem.

• interpret the solution of a real-world context as viable or not viable.

• interpret the meaning of the slope in terms of the units stated in the data.
• interpret the meaning of the y-intercept in terms of the units stated in the data.
• express linear functions in slope intercept form, standard form, and point slope form.
Classroom Activities

Tuesday:

Bellringer:  What type of shifts does the function f(x)=(x-6)squared + 4 have?  What are the end behaviors of this function?

Whole Group:  ISN page 20 – Linear Functions page for reference.  Define terms for linear functions including linear function parent function, slope-intercept form, standard form, point-slope form, slope, and review formulas for each.  Linear Functions Rate of Change Note-taking Sheet.

Small Group:  Worksheet on Linear Functions – Finding slope and graphing linear equations.

Independent:  Khan Academy – Slope-Intercept equation from graph (4 questions)

Wednesday:

Bellringer:  What is the slope of a line that passes through points (2,4) and (6,8)

Whole Group:  ISN page 21 Arithmetic Sequence

Small Group: Arithmetic Sequence Task Cards

Independent:  Khan Academy – Arithmetic Explicit Sequences (4 questions),  and  Arithmetic Recursive Sequences (4 Questions)

Thursday/Friday:

Bellringer:  Find the slope of the line on the graph on entrance ticket

Whole Group:  Slope-Intercept Formula and Standard Form of Linear Equations – Note taking pages ISN page 22.

Small Group:  Slope Formula Tic-Tac-Toe

Independent:  Khan Academy Slope Intercept form linear equations.

Assignments Due

All Khan Academy assignments- two-three on linear functions and two on arithmetic sequences.

Printed worksheet with graphs and slopes from All Things Algebra.

Homework Sheet on y=mx+b slope-intercept form practice problems from All Things Algebra.