Q2W11 Algebra

Teacher Carol Barnes Algebra 7th/8th 11 Oct.25-29 Unit 4: Linear Equations, Functions, 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
• 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

Monday:

Whole Group:  Standard form for slope.  Take notes on ATA page.  Do problems 1-15 on board. Standard Form of Linear Equations

Small Group:  ATA   HW 2  Slope Intercept Standard Form  1-6

Independent:  Khan Academy -Convert Linear Equations to Standard Form  AND  Graph from Linear Standard Form

Tuesday (Periods 6,7,8)/Wednesday(Period 1):

Whole Group:  Slope Formula problem  y2-y1/x2-x1  (-4,2) and (-6,-1)

Small Group:  Test Review HW #5  Slope & Graphing Lines Review  HW 5 Linear Equations

Independent:  Khan Academy – Convert Linear Equations to Standard Form  AND  Graph from Linear Standard Form

Wednesday (Period 1):

Bell Ringer:  Word problem: A hot tub holds 300 gallons of water, and water is being added at a rate of 10 gallons per minute.  What is functions to represent the amount of water in the tab after x minutes   A. f(x) = -10x + 300   B. f(x) = 10x + 300    C. f(x) = 300x + 10    D. f(x) = 300x – 10

Whole Group:  Slope Formula problem  y2-y1/x2-x1  (-4,2) and (-6,-1)

Small Group:ATA Review Packet #2  Linear Equations and Slope, Functions

Independent:  Khan Academy – Convert Linear Equations to Standard Form  AND  Graph from Linear Standard Form

Wednesday (Periods 3,6,7,8):

Whole Group:  Test Review – HW # 5during 3rd period.  Go over Homework #5 worksheet (a review for test tomorrow) in 6th, 7th, and 8th period.   Students may come to board to work problems from study guide.

Thursday/Friday:

TEST on Linear Equations and Functions including Slope Formula, Slope-Intercept Formula (y=mx+b), Standard Form, Point Slope Form, and graphing.

Whole Group:  ATA Notes on Arithmetic Sequences.

Small Group:  Problems #10-17 on examples portion of ATA Arithmetic Sequences page.

Assignments Due

1. Slope from Graph
2. Slope from two points
3. Using slope and intercepts in context
4. Relating linear contexts to graph features
5. Writing linear word problems
6. Arithmetic Sequences