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ALGEBRA 1A TASKS

  UNIT 3: RAINING CATS AND DOGS    
Action Item 3.1: Exploring Functions and Equations TEKS TAKS
Activity 1:
Exploring Functions
and Equations
In this activity, you will be creating function rules to
investigate problems. From these functions you will write
equations that can be used to solve problems. You will
learn how to solve for the independent variable in an
equation.
111.32(c)(1)(B)
111.32(c)(3)(A)
111.32(c)(3)(B)
A(c)(1)(B)
A(c)(3)(A)
A(c)(3)(B)
Activity 2:
Looking Closer
at Equations
There are many ways to solve equations. Use this activity
to learn the Guess and Check method, which will
help you solve problems related to your animal shelter
investigation.
111.32(c)(3)(B) A(c)(3)(B)
Activity 3:
First Look at
Inequalities
In this activity, you will see that in some situations you
are not looking for a single answer to a problem, but
rather many values that will answer the question. When
you see phrases like “at least” or “at most”, you know that
there is more than one possible answer to the problem.
You will write functions from which you can write
inequalities. Tables, graphs, and guess and check are still
appropriate methods to answer the question.
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)
Activity 4:
Solving Equations
and Inequalities
Using Tables
and Graphs
You have been solving equations and inequalities using
tables, graphs, and Guess and Check. In this activity you
will have a chance to practice solving various problems
using these methods. You will also be introduced to a
second way that a graph may be used to solve a problem.
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)
Action Item 3.2: Using Commutative, Associative, and Distributive Properties
to Simplify Expressions
TEKS TAKS
Activity 5:
The Distributive
Property
The distributive property helps simplify algebraic
expressions. In this section you will learn why this
property works by looking at a problem involving area.
You can also follow the links to use algebra tiles to
explore this property. You can choose to manipulate the
online tiles or create your own paper tiles.
111.32(b)(1)(D)
111.32(b)(4)(B)
A(b)(1)(D)
A(b)(4)(B)
Activity 6:
Combining Like
Terms
Sometimes algebraic expressions can be simplified in
order to make a problem easier to solve. You will be
able to link to an algebra tile demonstration for practice
simplifying expressions and understanding algebraic
terms like coefficient and variable. You will also have
a chance to practice combining like terms in algebraic
expressions.
111.32(b)(4)(A) A(b)(4)(A
Activity 7:
Adding and
Subtracting
Expressions
In this activity you will have a chance to link to an algebra
tile demonstration that shows you how to add or subtract
algebraic expressions. You will have a chance to practice
problems such as (4x2 – 6x + 5) – (5x2 – 3x + 10).
111.32(b)(1)(D)
111.32(b)(4)(A)
A(b)(1)(D)
A(b)(4)(A)
Action Item 3.3: Solving Simple Equations With Manipulatives and Symbols TEKS TAKS
Activity 8:
Equations of the
form x + c = k
In this activity, you will begin to look at problems that
require the use of equations. You have learned how to
solve equations and inequalities using tables, graphs, and
guess and check. You will continue to practice using
these methods. There are some problems that may be
easier to solve using the algebraic rule and operations
on the equation. Also in this activity, you will solve
equations that look like x + c = k.
111.32(c)(3)(A)
111.32(c)(3)(B)
A(c)(3)(A)
A(c)(3)(B)
Activity 9:
Equations of the
form kx = w
In some of the situations you have investigated, there
were equations involving a number multiplied by a
variable. For example, in the last investigation you had
the equation 50,000 + 1500x = 92,000. You learned
what to do symbolically when something is added to or
subtracted from a variable. In this set of problems you
will learn what to do when a number is multiplied by a
variable. You will be able to link to a demonstration and
practice using cups and counters to solve this type of
equation.
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)
Action Item 3.4: Solving Equations of the Form kx + c = b and kx + c = mx + b TEKS TAKS
Activity 10:
Equations of the
form kx + c = b
In most of the situations that you have investigated in
this unit, the equations have combined two operations,
multiplication and either addition or subtraction. For
example in a previous investigation you had the equation
50,000 + 1500x = 92,000. In this activity you will learn
how to solve equations like this symbolically.
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)
Activity 11:
Equations of the
form kx + c = mx + b
Use this activity to learn how to write an equation that
has variables on both sides. You can solve this equation
using tables, graphs, or guess and check. You will learn to
solve this type of equation using the symbolic method.
You will also have a chance to practice using what you
have learned about combining like terms, simplifying
expressions, and solving equations symbolically.
111.32(c)(3)(A)
111.32(c)(3)(B)
A(c)(3)(A)
A(c)(3)(B)
Action Item 3.5: Introduction to Inequalities TEKS TAKS
Activity 12:
Inequality Properties
and Notation
You’ve learned how to solve equations using symbolic
methods. Use this activity to learn how to solve
inequalities using symbolic methods.
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)
Activity 13:
Solving Inequalities
In this activity you will have an opportunity to use what
you have learned about inequalities. You will set up a
function, create an inequality related to the function, use
the properties of inequalities to solve symbolically and
use your graphing calculator to check your solutions.
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)
Action Item 3.6: Comparing Notations and Methods TEKS TAKS
Activity 14:
Difference Among
Functions,
Equations, and
Inequalities
In this activity, you will be able to practice what you
have learned about functions, equations and inequalities.
You will be asked questions about the differences among
these three mathematical ideas.
111.32(a)(4)
111.32(c)(3)(A)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(C)
Activity 15:
Which Method
Should I Choose?
In the last activity of unit 3 you will use all the methods
you have learned so far. It is your chance to review all
of the ideas in this unit before completing your graded
assignment and your project report.

We have studied four different ways to solve equations
and inequalities.
Symbolically
Graphs
Tables
Guess and Check.

The method of solution that is used to solve an equation
or an inequality may depend on the problem.

111.32(a)(6)
111.32(c)(3)(A)
111.32(c)(3)(B)
111.32(c)(3)(C)
A(c)(3)(A)
A(c)(3)(B)
A(c)(3)(C)