Algebra 1Algebra 1

Doug Smeltz

Fort Hayes

Arts/Academic H.S.

dsmeltz@columbus.rr.com

Big Ideas

All students at Fort Hayes take 4 years of mathematics instruction

Algebra 1 and Geometry can not be repeated at Fort Hayes

Algebra 1 is double blocked (80 minutes per day, every day)

Mastery Testing

• Mastery tests are predetermined for each nine weeks

• Mastery tests will be retested until a 75% or above level is reached

• If all mastery tests are passed, the student receives a 60% passing score no matter what happens with the other grades.

Mastery Tests (Continued)

• No student can pass for the nine weeks without passing all mastery tests with at least a 75% score

• No student will receive credit without passing all masteries.

• Mastery tests will be given in class until more that 50% of the students are successful.

Calculator Philosophy

• Students will learn how to incorporate the calculator to support their algebraic paperwork.

• Students will not become dependent on the calculator but rather comfortable with technology and it’s value to empower a student to know when they are correct.

Testing

Weekly tests Spiral Testing – Material from previous

tests not mastered will be repeated. Unit test on week 9 replaces lowest score. If more than 5 weekly tests occur, low

score is dropped.

Research

http://www.math.ohio-state.edu/~elaughba/

IMPLEMENTATION TO A FUNCTION APPROACH

Function Implementation Document

Approach

Arithmetic Expressions (2*8 –9*3) Algebraic Expressions (2x –7) Real Life linear relationships Linear Functions y = -3x -4 Linear Equations 3x + 4 = 2x + 7 Linear inequalities x –2 < 3x +2 Linear function inequalities y < 2x -7

Arithmetic Expressions

Simplify any expression involving adding, subtracting, multiplying, and dividing.

ALGTEST 0 AND ALGTEST1 using the TI-82/83/83+/92

45 correct of 50 questions in 5 minutes Record progress and praise improvement

Algebraic Expressions

Add, Subtract, Multiply, and Divide any two monomials. (Linear Monomials)

ALGTEST2 is required 45/50 in 5 minutes Understand the concept of variable and get

comfortable with the abstraction Start talk about input and output

Distributive Property

ALGTESTD– Level 0,1,2– 3(x-1)– 3x(2x+1)– 3x^2(4x^2 + 3x)

Function Machine

A list of all input would be the Domain!

A list of all output would be the Range!

Input

Output

Function Engine

Independent

Dependent

Function Machines

Concept of Input vs. Output Words vs. Expressions Concept of Domain vs. Range Concept of independent vs. dependent Function Notation

Word Description Example

Input | Output -3 | -3 -1 | 3 0 | 6 2 | 12

Input

Output

Add Two then multiply by 3

Using the TI-83 to Illustrated Input/Output

Linear Functions

Given expressions in the form of ax+b where a and b are constants and x is a variable

Tables (x, ax+b) talk about change in x and the resulting change in ax+b. Introduce independent(x) /dependent(ax+b)

Scatter Plots (x, ax+b) Y= use graphing y = ax+b

Function Notation on TI-83

Linear Equations

Form : a x + b = c x + b Simplify to that form Talk about each side and its representation

graphically. Help them see relationship of linear functions and linear equations.

Find solution graphically (y = a x+b and y = c x + d) Solve algebraically

Linear Inequalities

Form : a x + b < c x + d Look at tables, graphs of expressions Learn process to solve algebraically but

check graphically Test menu on TI-83 to graph boolean

expressions : y = a x + b < c x + d TI-83 Program INEQUAL

Inequalities in two variables

Linear Function inequalities Shading Solving for y to get into the form

y < a x + b

Info – Papers - Programs

Get T.I. Interactive –either buy or download demo and buy later at education.ti.com

Using T.I. Interactive, go to my website at www.dsmeltz.eboard.com

Click on Algebra Tab Download tests, mastery tests, this

PowerPoint presentation