Algebra+1

**A l g e b r a 1 **

**Assignments** **January 11, 2012 due January 12, 2012** 6.1.1 (6-7 to 6-12) Mathematical Sentences Spoken and written languages use //sentences// to convey information. A sentence has a subject and verb, follows the rules of grammar, and is structured with punctuation. Likewise, algebra uses **mathematical sentences**, such as //b// + //g// = 23, which also convey information and follow structural rules. During this lesson, you will explore various mathematical sentences and learn how to interpret their meanings. Then you will write mathematical sentences of your own. **January 12, 2012 due January 16, 2012** 6.1.2 (6-16 to 6-21) Solving Word Problems by Writing Equations In Lesson 6.1.1, you examined mathematical sentences (equations that convey related information). Today you will learn more ways to translate written information into algebraic symbols and will then solve the equations that represent the relationships. **January 16, 2012 due January 17, 2012** 6.1.3 (6-26 to 6-31) Solving Problems by Writing Equations In Lessons 6.1.1 and 6.1.2, you created mathematical sentences that represented word problems. But how can you tell if you can use one variable or two? And is one method more convenient than another? Today you will compare the different ways to represent a word problem with mathematical symbols. You will also explore how to use the Equal Values Method to solve systems containing equations that are not in //y// = //mx// + //b// form. **January 17, 2012 due January 18, 2012** 6.2.1 (6-37 to 6-42) Solving Systems of Equations Using Substitution In Chapter 4, you learned that a set of two or more equations that go together is called a **system of equations**. In Lesson 6.1.3, you helped Renard develop a method for solving a system of equations when one of the equations was not solved for a variable. Today you will develop a more efficient method of solving systems that are too messy to solve with the Equal Values Method. **January 18, 2012 due January 19, 2012** 6.2.2 (6-50 to 6-55) Making Connections: Systems, Solutions, and Graphs In this chapter you have practiced writing mathematical sentences to represent situations. Often, these sentences give you a system of equations, which you can solve using substitution. Today you will start to represent these situations in an additional way: on a graph. You will also examine more closely what makes a solution to a two-variable equation. **January 19, 2012 due January 23, 2012** 6.2.3 (6-61 to 6-66) Solving Systems Using Elimination In this chapter, you have learned the Substitution Method for solving systems of equations. In Chapter 4, you learned the Equal Values Method. But are these methods the best to use for all types of systems? Today you will develop a new solution method that can save time for systems of equations in standard form. **January 23, 2012 due January 24, 2012** 6.2.4 (6-7 to 6-12) More Elimination In Lesson 6.2.3, you learned how to use the Elimination Method to solve systems of equations. In this method, you combined two equations in a way that made one variable disappear. This method is particularly useful for solving systems of equations where neither equation is in //y// = //mx// + //b// form. Today you will practice using the Elimination Method while learning to deal with various complications that systems of equations sometimes present. As you solve these systems, ask your teammates these questions: How can you create one equation with only one variable? How can you eliminate one variable? How do you know your solution is correct? **January 24, 2012 due January 25, 2012** 6.2.5 (6-7 to 6-12) Choosing a Strategy for Solving Systems When you have a system of equations to solve, how do you know which method to use? Focus today on how to choose a strategy that is the most convenient, efficient, and accurate for a system of equations. **January 25, 2012 due January 26, 2012** 6.3.1 (6-7 to 6-12) Pulling It All Together This lesson contains many problems that will require you to use the algebra content you have learned so far in new ways. It will require you to use all five Ways of Thinking (justifying, making connections, applying and extending, reversing thinking, and generalizing) and will help you solidify your understanding. Your teacher will describe today’s activity. As you solve the problems below, remember to make **connections** between all of the different subjects you have studied in Chapters 1 through 6. If you get stuck, think of what the problem reminds you of. Decide if there is a different way to approach the problem. Most importantly, discuss your ideas with your teammates. **January 26, 2012 no due date** Chapter 6 Closure Reflection and Synthesis The activities below offer you a chance to reflect on what you have learned during this chapter. As you work, look for concepts that you feel very comfortable with, ideas that you would like to learn more about, and topics you need more help with. Look for connections between ideas as well as connections with material you learned previously. ** Test ** ** Chapter 6 Test - January 30, 2012 ** 5.1.1 (5-4 to 5-9) Exploring an Area Model In Chapter 2, you used tiles to rewrite algebraic expressions involving addition and subtraction. In this chapter, you will use algebra tiles again, but this time you will rewrite expressions using multiplication. 5.1.2 (5-15 to 5-20) Multiplying Binomials and the Distributive Property In Lesson 5.1.1, you made rectangles with algebra tiles and found the dimensions of the rectangles. You wrote the area both as a sum and as a product. Today you will **reverse** the process, starting with the product of the dimensions of a rectangle and finding its area as a sum.
 * November 22, 2011 due November 23, 2011 **
 * November 23, 2011 due November 28, 2011 **

5.1.3 (5-27 to 5-32) Using Generic Rectangles to Multiply You have been using algebra tiles and the concept of area to multiply algebraic expressions. Today you will be introduced to a tool that will help you find the product of the dimensions of a rectangle. This will allow you to multiply expressions without tiles.
 * November 28, 2011 due November 29, 2011 **

5.1.4 (5-39 to 5-44) Solving Equations With Multiplication Now that you know how to multiply algebraic expressions, you can solve equations that involve multiplication.
 * November 29, 2011 due November 30, 2011 **

5.1.5 (5-49 to 5-54) Working With Multi-Variable Equations So far in this course, you have used your equation mat to find solutions for all types of linear equations with one variable. Today you will learn how to **apply** these skills to solving linear equations with two variables. As you work today, keep the following questions in mind: What is a solution to an equation? What does it look like? What is the growth factor? What is the //y//-intercept?
 * November 30, 2011 due December 1, 2011 **

5.1.6 (5-57 to 5-62) Solving Equations Without Manipulatives So far, you have developed your equation-solving skills in three major sections of this course (Sections 2.1, 3.2, and 5.1). Today you will practice solving equations while moving away from using algebra tiles. At the end of the lesson, you will summarize everything you know about solving equations.
 * December 1, 2011 due December 5, 2011 **

5.2.1 (5-67 to 5-71) Setting Up and Solving Proportions In Chapter 2, you studied proportional situations and used several strategies to solve problems involving such situations. Since then, you have learned to set up and solve equations to solve many types of problems. Today you will investigate methods for using equations to solve proportion problems.
 * December 5, 2011 due December 6, 2011 **

5.2.2 (5-77 to 5-82) Practice With Proportions In the last lesson, you used equations to solve problems involving proportional situations. Today you will practice writing and solving these special equations, called **proportions**, while you help a student set up a recycling program for her school. As you work, focus on these questions: What information can you use to answer this question? How can you use that information to write an equation?
 * December 6, 2011 due December 7, 2011 **

5.2.3 (5-85 to 5-89) Applying Proportions
 * December 8, 2011 due December 12, 2011 **

Chapter 5 Closure Reflection and Synthesis The activities below offer you a chance to reflect on what you have learned during this chapter. As you work, look for concepts that you feel very comfortable with, ideas that you would like to learn more about, and topics you need more help with. Look for connections between ideas as well as connections with material you learned previously.
 * December 12, 2011 **

4.1.1 (4-2 to 4-7) and 4.1.2 (4-13 to 4-17)
 * November 1, 2011 due November 2, 2011 **

Finding Connections Between Representations In Chapter 3 you studied different ways to represent patterns. You organized information into tables, graphed information about patterns, and learned how to find the rules that govern specific patterns. Starting today and continuing throughout this chapter, you will find connections between different representations of the same pattern, explore each representation more deeply, and learn shorter ways to go from one representation to another. By the end of this chapter, you will have a deeper understanding of many of the most powerful tools of algebra.

Seeing Growth in Different Representations In Lesson 4.1.1, you looked at four different ways of representing patterns and began to find connections between them. Throughout this chapter you will explore connections and find shortcuts between the representations. Today, you will look for specific connections between geometric patterns and equations. As you work today, keep these questions in mind: How can you see growth in the rule? How do you know your rule is correct? What does the representation tell you? What are the connections between the representations?

4.1.3 (4-21 to 4-25) Connecting Linear Rules and Graphs You have been looking at geometric patterns and ways that those patterns can be represented with equations, graphs, and x → y tables. In Lesson 4.1.2 you worked with four different tile patterns and looked for connections between the geometric shapes and the numbers in the equations. Today you will go back to those four equations and look for connections to other representations. By the end of this lesson, you should be able to answer the following target questions: How is growth shown in a rule? How is growth shown in a graph? How can you determine the number of tiles in Figure 0 from a graph? How can you determine which tile pattern grows faster from a graph?
 * November 2, 2011 due November 3, 2011 **

4.1.4 (4-32 to 4-36) y = mx + b In Lessons 4.1.2 and 4.1.3, you investigated connections between tile patterns, x → y tables, graphs, and rules (equations). Today you will use your observations about growth and Figure 0 to write rules for linear patterns and to create new tile patterns for given rules.
 * November 3, 2011 due November 7, 2011 **

4.1.5 (4-39 to 4-48) Checking the Connections In the last several lessons you have been finding connections and relationships between different representations of patterns. You have worked backward and forward and have used information about Figure 0 (or the starting point) and the growth factor in order to write rules. In today’s activity, you will check your connections by using pieces of information from different parts of the web to generate a complete pattern.
 * November 7, 2011 due November 8, 2011 **

4.1.6 (4-54 to 4-58) Graphing a Line Without an x → y Table You have now used your knowledge of growth factors and Figure 0 to create tile patterns and x → y tables directly from rules. You have also looked at graphs to determine the equation or rule for the pattern. Today you will reverse that process and use an equation to create a graph without the intermediate step of creating an x → y table.
 * November 8, 2011 due November 9, 2011 **

4.1.7 (4-62 to 4-66) Completing the Web After all of the work you have done with equations in y = mx + b form, you know a lot about starting with one representation of a pattern and moving to different representations. Today you will work with your team to make sure you are confident moving around the representations web.
 * November 9, 2011 due November 10, 2011 **

4.2.1 (4-71 to 4-75) Introduction to Systems of Equations In Section 4.1, you graphed lines and curves that represented tile patterns. But what happens when you graph two lines at the same time? What can you learn? Today you will use data, graphs, and rules to examine what happens when two lines (or curves) intersect.
 * November 10, 2011 due November 14, 2011 **

4.2.2 (4-80 to 4-84) Writing Rules from Word Problems In Lesson 4.2.1, you discovered that the point of intersection of two lines or curves can have an important meaning. Finding points of intersection is another strategy you can use to solve problems, especially those with two quantities being compared.
 * November 14, 2011 due November 15, 2011 **

4.2.3 (4-90 to 4-94) Solving Systems Algebraically So far in Section 4.2, you have solved systems of equations by graphing two lines and finding where they intersect. However, it is not always convenient (nor accurate) to solve by graphing. Today you will explore a new way to approach solving a system of equations. Questions to ask your teammates today include: How can you find a rule? How can you compare two rules? How can you use what you know about solving?
 * November 15, 2011 due November 16, 2011 **

4.2.4 (4-96 to 4-106) Extending the Web to Other Linear Situations Today you will take what you have learned in this chapter and apply it to linear situations that are not tile patterns.
 * November 16, 2011 due November 17, 2011 **

Chapter 4 Closure Reflection and Synthesis The activities below offer you a chance to reflect on what you have learned during this chapter. As you work, look for concepts that you feel very comfortable with, ideas that you would like to learn more about, and topics you need more help with. Look for connections between ideas as well as connections with material you learned previously.
 * November 17, 2011 **

In case you forget your book at school you can access the information here ** October 3, 2011 due October 5, 2011 ** 3.1.1 (3-4 to 3-8)  Extending Patterns and Finding Rules You have been learning how to work with variables and how to find values for variables in equations. In this section, you will learn how to **extend** patterns and how to **generalize** your pattern with a rule. As you work with your team, use these questions to focus your ideas: How is the pattern growing? What is the rule? Is there another way to see it? How can you tell if your rule is correct? 3.1.2 (3-13 to 3-17) & 3.1.3 (3-23 to 3-31) Using Tables, Graphs, and Rules to Make Predictions In Lesson 3.1.1, you wrote rules for patterns found in //x//→//y// tables. In this lesson, you will focus on using variables to write algebraic rules for patterns and contextual situations. You will use a graph to help predict the output for fractional //x//-values and will then use a rule to predict the output when the input is too large and does not appear on the graph. While working today, focus on these questions: How can you write the rule without words? What does //x// represent? How can you make a prediction?
 * October 5, 2011 due October 6, 2011**

Using the Graphing Calculator and Identifying Solutions In the last two lessons, you examined several patterns and learned how to represent the patterns in a table and with a rule. For the next few days, you will learn a powerful new way to represent a pattern and make predictions. As you work with your team today, use these focus questions to help direct your discussion: What is the rule? How can you represent the pattern?

3.1.4 (3-36 to 3-40) Completing Tables and Drawing Graphs In Lesson 3.1.3, you used a graphing tool to represent all of the //x//→//y// pairs that follow a particular rule. Today you will learn how to make your own graphs for rules and how to recognize patterns that occur in graphs.
 * October 17, 2011 due October 18, 2011**

3.1.5 (3-45 to 3-49) Graphs, Tables, and Rules In Lesson 3.1.4, you practiced setting up the correct axes to graph data from a table. Today you will graph a rule by first making a table, and then by plotting the points from your table on a graph. You will also continue to find patterns in tables and graphs.
 * October 18, 2011 due October 19, 2011**

3.1.6 (3-55 to 3-59) Complete Graphs Over the past several days you have learned to make graphs from tables, then graphs from rules. Today you will continue to study graphs by deciding what needs to go into a graph to make it complete.
 * October 19, 2011 due October 20, 2011**

3.1.7 (3-64 to 3-68) Identifying Common Graphing Errors In this chapter you have used rules to find //y//-values to go with //x-//values in tables. Then you graphed the //x//→//y// pairs you found. Today you will be examining how rules, tables, and graphs can be used to represent new situations. You will also learn how to avoid common graphing errors. As you work, revisit the following questions: What //x//-values should go in my table? How can I correct this error? How should I scale my graph?
 * October 20, 2011 due October 24, 2011**

3.2.1 (3-73 to 3-77) Solving Equations and Testing the Solution In Section 2.2, you learned to solve equations on an equation mat. In this section, you will practice your equation-solving skills while adding a new element: You will check your answer to make sure it is correct. While solving equations in this lesson, keep these focus questions in mind: What is your goal? How can you start? How can you simplify? Can you get //x// alone?
 * October 24, 2011 due October 25, 2011**

3.2.2 (3-82 to 3-86) Determining the Number of Solutions In Lesson 3.2.1, you reviewed your equation-solving skills to remember how to find a solution to an equation. But do all equations have a solution? And how can you tell if an equation does not have a solution? Today you will continue to practice solving equations and will continue to investigate the meaning of a solution.
 * October 25, 2011 due October 26, 2011**

3.2.3 (3-92 to 3-96) & 3.2.4 (3-100 to 3-104) Solving Equations to Solve Problems In the last two lessons you have practiced solving equations. In this lesson you will **apply** your equation-solving skills to the patterns you found at the beginning of this chapter. As you solve these problems, keep these questions in mind: How can you simplify? Is there more than one way to solve? Can you get //x// alone? How can you check your solution?
 * October 26, 2011 due October 27, 2011**

More Solving Equations to Solve Problems

Chapter 3 Closure - all questions answers at end of chapter
 * October 27, 2011 (no due date)**

**Test** **Chapter 3 Test - October 31, 2011** **Chapter 4 Test - November 21, 2011** **Chapter 5 Test - December 13, 2011** **Midterm Test - December 14, 2011**