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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 (4x^{2} – 6x + 5) – (5x^{2} – 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 The method of solution that is used to solve an
equation |
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) |