Instructional Design

Instructional Design Tools of Algebra

By: Michelle Corron Unit Outcomes

Unit 1: Tools of Algebra

 The students will be able to state the order of operations. (memory/ recall)  The students will be able to explain the reasoning behind the use of order of operations. (comprehension)  The students will be able to apply order of operations to simplifying numerical expression. (application)  Given numerous numerical expressions and a solution each student will be able to determine whether or not order of operations was used correctly. (analysis)  The students will be able to apply order of operations to evaluating algebraic expressions. (application)  Using their knowledge on order of operations, students should be able to simplify compound expressions including real world problems. (evaluation)

Unit 2: Solving Equations

 The students will be able to state the addition and subtraction properties of equality. (memory/recall)  The students will be able to state the multiplication and division properties of equality. (memory/recall)  The students will be able to apply the addition and subtraction property of equality to solve equations. (application)  The students will be able to apply the multiplication and division property of equality to solve equations. (application)  The students will be able to create an equation model for a real world problem. (synthesis)  The students will be able to explain the steps used in solving a two-step equation. (comprehension)  Given the task to buy enough fencing to fence in a specific area, students will be able to apply what they are learning to decide on a conclusion. (application)  Given numerous equations the student will be able to state whether it is an identity equation and has more than one answer. (analysis)  The student will be able to analysis a collection of data by using his or her knowledge of mean, median, and mode. (application)  Students will be able to develop formulas for the surface area of several different three-dimensional shapes. (application)

Unit 3: Proportions

 The students will be able to explain the use of ratio and rates. (comprehension)  The students will be able to define ratio. (memory/ recall)  The students will be able to solve proportions. (application)  Given two shapes, students will be able to determine whether they are similar. (analysis)  Students will be able to construct proportions that model real world situations. (synthesis)  The students will be able to use their knowledge of proportions to solve percent problems. (application)

Unit 4: Graphs and Functions

 Students should be able to explain a situation by analyzing the graph. (analysis)  Students will be able to define domain and range. (memory/recall)  Students will be able to explain the difference between a relation and a function. (comprehension)  Students will be able to explain what and how the vertical line test is used. (comprehension)  The students will be able to model their functions by use of graphing calculator (synthesis)

Unit 5: Linear Equations and Graphs

 The student will be able to state the formula for slope. (memory/recall)  The student will be able to explain what slope is and what the formula means. (comprehension)  Find the slope of several different linear equations. (application)  Show why two lines are parallel or perpendicular by using the formula for slope. (application)  When a student is asked to build a ramp given certain stipulations, they are able to apply their knowledge of slope and construct a ramp. (evaluation) Pre-Assessment of Tools of Algebra

Directions: Circle the number that best resembles your knowledge of the following. 1- expert 2- above average 3- average 4- below average 5- never seen

1. Using Variables 1 2 3 4 5

2. Writing Equations 1 2 3 4 5

3. Exponents 1 2 3 4 5

4. Order of Operations 1 2 3 4 5

5. Natural Numbers 1 2 3 4 5

6. Whole Numbers 1 2 3 4 5

7. Integers 1 2 3 4 5

8. Irrational Numbers 1 2 3 4 5

9. Identity Equations 1 2 3 4 5

10. Absolute Value 1 2 3 4 5

11. Adding and Subtracting Real Numbers 1 2 3 4 5

12. Multiplying and Dividing Real Numbers 1 2 3 4 5

13. Distributive Property 1 2 3 4 5

14. Commutative Property 1 2 3 4 5

15. Associative Property 1 2 3 4 5

16. Identity Property 1 2 3 4 5

17. Inverse Property 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Write 2 less than x in an algebraic expression.

2. Solve 32.

3. Solve 11(5  3)  (4  2).

4. Solve3(2  5)2  20.

7 5. Name the set the following numbers belong to: -3, 2.35, 11 6. Solve 12 .

7. Solve –3 + 9.

8. Solve –3(9).

9. Solve 6(x + 2).

1 10. Solve 8 . 8 Michelle Corron

I. Audience/General

 Algebra I  50 minute sessions

II. Concept

 Adding and Subtracting Real Numbers

III.Objectives

 SWBAT add real numbers  SWBAT subtract real numbers  SWBAT apply what they know about adding and subtracting real numbers to solve real world problems

IV. Lesson Procedure

 Introductory Activity o Lets pretend, pick a student, lives at house A. o Lets pretend, pick a second student, lives at house B. o Draw house A and house B on the board. o What if student A moves six miles farther away from student B then they were before. o Student A now lives fifteen miles away from student B. o How many miles did student A live from student B? o We can use a number line to help us determine the answer. o Draw a number line on the board above where the houses are drawn. o By counting out the spaces we are able to figure out the two students originally lived nine miles away from each other.

 Developmental Activity o Today we are going to be able to this without having to draw a number line and count off spaces every time. o Example . If a football team loses four yards on the first down, the loss is represented by (–4). If they lose another three yards (-3) on next down, they have lost seven yards (-7) in all. –4 + -3 = -7 o Use a number line to show how we received our answer. o Looking at just the (–4) and the (–3) can we take a guess if our answer is going to be positive or negative. o We only have negative numbers so we can be sure our answer is going to be negative. o So from there, since the signs are the same, we can add 4 and 3, which is 7 and put the negative on because we previously determined that. o Lets try another one. o Example . If a football team loses five yards on the first down, the loss is represented by –5. If they lose another six yards (-6) on next down, they have lost 11 yards (-11) in all. –5 + -6 = -11 o We can first determine that our answer is going to be negative because both of our numbers are negative. o Second, our signs match so we can add 5 and 6 and then apply the negative. o To find our answer is –11. o In football they do not always lose yardage, then also gain yardage. o Example . If a football team loses 8 yards on the first down, the loss is represented by –8. If they gain three yards (3) on next down, they have lost 5 yards (-5) in all. . –8 + 3 = -5 o Show the answer on the number line. o So here we have two different signs, so know what do we do? o Lets look at which sign we have more of. o We have 8 negative and 3 positive, so we have more negative. o This tells us that our answer is still going to be negative. o Now can we just add them like we did on the other one? o If we add the two we will have 11, which is not the correct answer. o If the signs are different then we need to subtract our numbers. o So if we subtract 3 from 8 we get 5. o Apply our negative, because we decided our answer was negative. o There we have our –5. o Lets try another one. o Example . If a football team loses four yards on the first down, the loss is represented by –4. If they gain 15 yards (15) on next down, they have gained 11 yards (11) in all. –4 + 15 = 11 o Lets look at which sign we have more of. o We have 4 negative and 15 positive, so we have more positive. o This tells us that our answer is going to be positive. o So if we subtract 4 from 15 we get 11. o We do not need to apply a negative, because we decided our answer was positive. o So we have our answer, 11. o Have students get into their groups. o Each group should get a spinner and each student should get a sheet with the scorecard on them. o The spinners will have numbers ranging from –5 to 5. o Each player should take a turn spinning the wheel and recording his or her score. o Students will need to use the information they have just learned to compute their score after each spin. o The game continues for ten spins, if a tie occurs the players that are tied will spin again. o There should be enough time for students to play more then once. o While students are playing walk around answering any question student my encounter. o Have students move back to their original seat.

 Concluding Activity o In you journals explain how to add and subtract real numbers. Explain it as if you were teaching another individual.

V. Evaluation

 Homework: come up with seven ideas where adding and subtracting of real numbers can be used out side of the classroom. It can be something you do now or something you might do in a future career.

VI. Extension

 Complete worksheet, Skill Practice 2-2

VII. Materials

 Number Spinners  Student’s journals  Worksheets o Score Sheet o Skill Practice 2-2

Players Name______

Turn Number Spin Number Scor e

Turn Number Spin Number Scor e Student Journal

Name______

Date______

Topic______

______

Response______

______

______Michelle Corron

I. Audience/General

II. Concept

 Multiplying and Dividing real numbers

III. Objectives

 SWBAT multiple real numbers  SWBAT divide real numbers  SWBAT apply what they know about multiplying and dividing real numbers to solve real world problems

 Introductory Activity o Last night for homework we made a list of ideas where adding and subtracting of real numbers was used in the real world. o Talk about some of the ideas students had. o Collect homework. o Place a chart on the board stating to purchase copies it will cost o 50 or less..……… 15 cents per copy o 51 – 100…………12 cents per copy o 101 – 150………..10 cents per copy o 151 – over ………. 8 cents per copy o You need to make two copies of a report that is two pages long, how many pages total will we need? o We would need four pages. o Could we add like we were doing yesterday to determine the cost? o 15 + 15 + 15 + 15 = 60 o What if I need to make six copies of a one-page worksheet? o We could still add and it would cost us 90 cents. o What if I said I want 53 copies of a one-page worksheet? o Would you want to add up all of those numbers?

 Developmental Activity o What other way could we figure out how much we would owe? o Let students figure out what we could do. o We could multiple. o So what would our answer be? 636 cents or $6.36 o Lets do a few more, pick a student and have them tell you what they need copied. o Have the other students figure out the cost. o Repeat a few times. o Does everything in the real world always deal with only positive numbers? o No, we found that out when we were looking at adding and subtracting. o What happens in a situation like this? o Example, on overhead o You can use the expression –5.5(a/1000) to calculate the change in temperature in degrees Fahrenheit for an increase in altitude a, measured in feet. A hot-air balloon starts on the ground and then rises 8000 ft. Find the change in temperature at the altitude of the balloon. o So we know that we are multiplying a positive and a negative number, but we are not sure what we are going to get. o So lets come back to this question. o Pass out Math Reasoning worksheet, one to each student. o Students should work individually. o When all students have completed the worksheet, discuss the pattern they found in the answers. o So an even number of negative numbers in a problem results in what type of answer? Positive solution. o And an odd number of negative numbers in a problem results in what type of answer? Negative solution. o Put the example back on the overhead. o Do we have an even or an odd number of negatives in the problem? o So our answer will be negative. o So lets figure out the solution. –44 o What about division, in the hot air-balloon problem we had division. o We know a positive number divided by a positive number is positive. o What about if one or both are negative? o Lets think back to multiplication. o 4 * -3 = -12 o Can we make this into a division problem? o -12 / 4 = -3 so a negative divided by a positive is negative. o -12 / -3 = 4 so a negative divided by a negative is positive o So we have looked at every combination accept what? o Let students answer. o Positive divided by a negative. o What about –2 * -5 = 10 o Turn it into a division problem. o 10 / -2 = -5 o So what is the answer when a positive is divided by a negative the answer is a negative number. o Example, on overhead o Three of the measurements nurses commonly use are cubic centimeters (cc), drops, and grains. A doctor orders 1/400 of grain of medicine to be given to a patient. The nurse has a vial labeled 1/200 grains per cc. How many cc of the medicine should the nurse give the patient? o Solution: (1/400) / (1/200) = 1/2

 Concluding Activity o Take out your journal; we have seen copies, hot air-balloons, and nursing come in to play. Create your own story problem using a real world scenario and either multiplication or division, or both, with at least on negative number.

V. Evaluation

 Homework: Worksheet, Multiplying and Dividing

VI. Extension

 Continue the example o The doctor also prescribes a 1000-cc intravenous (IV) bottle to be given to the patient over an 8-hour period. If there are 15 drops in 1 cc, for how many drops per minute should the nurse set the IV?

VI. Materials

 Overhead o Example  Student’s journal  Worksheet o Math Reasoning o Multiplying and Dividing You can use the expression –5.5(a/1000) to calculate the change in temperature in degrees Fahrenheit for an increase in altitude a, measured in feet. A hot-air balloon starts on the ground and then rises 8000 ft. Find the change in temperature at the altitude of the balloon.

Three of the measurements nurses commonly use are cubic centimeters (cc), drops, and grains. A doctor orders 1/400 of grain of medicine to be given to a patient. The nurse has a vial labeled 1/200 grains per cc. How many cc of the medicine should the nurse give the patient?

The doctor also prescribes a 1000-cc intravenous (IV) bottle to be given to the patient over an 8-hour period. If there are

15 drops in 1 cc, for how many drops per minute should the nurse set the IV? Student Journal

Name______

Date______

Topic______

______

Response______

______

______Multiplying and Dividing

Name ______Date ______

1. Suppose you multiply several negative numbers a, b, c, … together. Give a rule, based on how many numbers are being multiplied, for determining whether the product will be positive or negative.

2. In an ionized solution, such as you would find inside a car battery, there is the same number of negatively charged ions, so that the net charge is zero. a. Suppose six negatively charged ions, each with a charge or – 2, are added to the solution. What will the net charge of the solution be?

b. Suppose five negatively charged ions, with the same charge as before, are removed from the original solution. What will the net charge of the solution be?

3. To map the features of the ocean floor, scientists take several sonar readings. Find the mean of these readings: -14,235 ft, -14,246 ft, and –14,230 ft. Michelle Corron

I. Audience/General

 Algebra I  2- 50 minute sessions

II. Concept

 Distributive Property

III. Objective

 SWBAT use the distributive property  SWBAT solve equations that involve the distributive property

 Introductory Activity o A high school basketball court is 84 ft long by 50 ft wide. o Do you think that a college court is the same size? o No, it is actually bigger. o How much bigger do you think? o A college basketball court is 10 ft longer than a high school basketball court. o With a partner, figure out two different ways to find the area of the court. o Have a student remind the class what the formula for area of a rectangle is. o When students figure out the two different ways to figure out the answer write them on the board.

 Developmental Activity o Tell students what we are showing here is the distributive property. o Define Distributive Property: a(b + c) = ab + ac o Hand out a package of Algebra Tiles to each student o Show them how to use the tiles o 2( 3 + 4) o Pass out The Distributive Property worksheet, have students complete working with a partner. o If students feel better with out the tiles they can complete the worksheet without the tiles. o Go over answers when all students have completed worksheet. o In your journal write a few sentences explaining to another student how to use the distributive property. o Collect journal

 Concluding Activity o Take the rest of the class time to brainstorm with your group to come up with a store and some sale items.

V. Evaluation

 Homework: Make a final decision on the store and sale items. Also come up with four questions using the distributive property that go along with your store.  Day 2  Tomorrow we will spend the beginning of class creating a sign for our store with our four questions on it; we will then go shopping around the room, answering the questions that are placed on the signs.

VI. Extension

 Let students begin to work on their signs.

VI. Materials

 Algebra Tiles  Student’s journals  Large sheets of paper, one per student  Markers  Scissors  Glue  Worksheets o The Distributive Property Student Journal

Name______

Date______

Topic______

______

Response______

______

I. Audience/General

 Algebra I  2-50 minute sessions

II. Concept

 Graphing Coordinate Points

III. Objective

 SWBAT plot points given to them on a coordinate plane  SWBAT name points that are plotted on coordinate planes

 Introductory Activity o Show a picture of string artwork (see http://www.geocities.com/CollegePark/Lab/2276/4eves.gif). o Discuss how it is done.

 Developmental Activity o Show the coordinate plane on the overhead. o Define the quadrants. o Plot some coordinates on the overhead. o Have students write down what they are. o Place the order pairs on the overhead have students check their answers. o Answer any questions students might have. o Pass out graph paper to each student. o Students are going to create their own artwork on graph paper. o They can only use straight lines connecting two points to make their design. o They can use different colors or all one it is their own decision.

 Concluding Activity

o Students will continue working on their artwork for the rest of the class time.

V. Evaluation  Homework: Students will go through there artwork and write down the coordinates that are at the end of each line segment, be sure to label what color the line is.  Day 2  Tomorrow student’s directions for the artwork will be switched with each other and the other student will attempt to remake the piece of art.

VI. Extension

 Have students complete two pieces of art.

VI. Materials

 Picture  Overhead o Coordinate Plane o Quadrants o Points o Ordered Pairs  Large Graph Paper, one for each student  Markers

Post-Assessment of Tools of Algebra

1. Using Variables 1 2 3 4 5

2. Writing Equations 1 2 3 4 5

3. Exponents 1 2 3 4 5

5. Natural Numbers 1 2 3 4 5

6. Whole Numbers 1 2 3 4 5

7. Integers 1 2 3 4 5

8. Irrational Numbers 1 2 3 4 5

10. Absolute Value 1 2 3 4 5

11. Adding and Subtracting Real Numbers 1 2 3 4 5

12. Multiplying and Dividing Real Numbers 1 2 3 4 5

14. Commutative Property 1 2 3 4 5

15. Associative Property 1 2 3 4 5

16. Identity Property 1 2 3 4 5

17. Inverse Property 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Write 2 less than x in an algebraic expression.

2. Solve 32.

3. Solve 11(5  3)  (4  2).

4. Solve3(2  5)2  20.

7 5. Name the set the following numbers belong to: -3, 2.35, 11 6. Solve 12 .

7. Solve –3 + 9.

8. Solve –3(9).

9. Solve 6(x + 2).

1 10. Solve 8 . 8 Instructional Design Solving Equations

Unit 3: Proportions

 The student will be able to state the formula for slope. (memory/recall)  The student will be able to explain what slope is and what the formula means. (comprehension)  Find the slope of several different linear equations. (application)  Show why two lines are parallel or perpendicular by using the formula for slope. (application)  When a student is asked to build a ramp given certain stipulations, they are able to apply their knowledge of slope and construct a ramp. (evaluation) Pre-Assessment of Solving Equations

1. Solving One-Step Equations 1 2 3 4 5

2. Addition and Subtraction Properties 1 2 3 4 5

3. Multiplication and Division Properties 1 2 3 4 5

4. Solving Two-Step Equations 1 2 3 4 5

6. Solving Multi-Step Equations 1 2 3 4 5

8. Equations With Variables on Both Sides 1 2 3 4 5

10. 10. Using Equations to Solve Problems 1 2 3 4 5

11. Distance, Rate, and Time Problems 1 2 3 4 5

12. Using Formulas to Solve Equations 1 2 3 4 5

13. Geometric Formulas 1 2 3 4 5

14. Using Measures of Central Tendency 1 2 3 4 5

15. Mean, Median, Mode, and Outliers 1 2 3 4 5

16. Range 1 2 3 4 5

17. Stem-and –Leaf Plots 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

I. Solve x - 3 = - 8.

II. Solve 23 + t = 16.

r III. Solve  11. 4

IV. Solve 4 c = -96.

m V. Solve 10   2. 4 VI. Solve –2 (b – 4) = 12.

VII. Find the value of x, 6 x + 3 = 8 x – 21.

VIII. The sum of three consecutive integers is 147. Find the integers.

IX. Solve x y – z = w, for y.

X. Suppose your grades on three exams are 80, 93, and 91. What grade do you need on your next exam to have a 90 average on the four exams? Michelle Corron

I. Audience/General

II. Concept

 Solving One-Step Equations

III. Objectives

 SWBAT solve equations using addition and subtraction properties of equality.  SWBAT solve equations using multiplication and division properties of equality.

 Introductory Activity o Lets think about money, it is something everyone wants. o Discuss how many students received an allowance when they were younger. o Discuss if the student and their siblings received the same amount and if not what they would have to do to make the amounts equal. o If there are not many that had siblings that received different amounts, compare the student’s amounts to each other.

 Developmental Activity o Explain to the students that we are trying to make the two amounts “Equal.” o By using this same money idea, show the students the Addition Property of Equality and the Subtraction Property of Equality. o Explain to students that these properties are called inverse operations, which is an operation that will undo another operation. o Do a problem with the group using the Addition Property of Equality, show that you are able to check your answer by putting it back into your equation and seeing that the results will be equal. ( x – 4 = 3 ) o Hand out a bag of Algebra Tiles to each group of students. o Hand out a worksheet (practice) to each student. o Have students work together to resemble equations 1-3 using the Algebra Tiles and then checking their solutions on paper. o Looking back at the money idea, did anyone get paid depending on how many times they did a certain chore? For example if you dusted your living room twice in one week you would get paid one dollar for each time. o By using this example we can show the Multiplication Property of Equality and the Division Property of Equality, these are also inverse operations. o Have students within their groups work through problems 6-9. o If time permits have students work through problems 22-26. o Day 2 o Have students within their groups work through story problems that were created by students the night before. o Algebra Tiles can be used. o Pass out worksheet “A Square Deal” have students complete in groups using the Algebra Tiles to assist them in finding the answers. o Remind them to check their answers so the squares will fit together properly.

 Concluding Activity o Have students in their journals explain the steps involved in solving all types of One-Step Equations. o Students should know that the inverse operations are the operations that are used to solve the problem, have students also explain what the inverse operation is.

V. Evaluation

 For homework (day 1), have students create five of their own story problems using a One-Step Equation.  Tomorrow we will trade with other students in our group and have them solve the problems.  For homework (day 2), Students should write down what they believe an equation would look like if two of these properties were required to solve it. A written response is required.

VI. Materials

 Algebra Tiles  Worksheet o Solving Equations o A Square Deal  Scissors

Michelle Corron

I. Audience/General

II. Concept

1. Solving Multi-Step Equations

III. Objectives

 SWBAT use their knowledge of solving One and Two-Step Equations to solve Multi-Step Equations.  SWBAT apply what they learn about Multi-Step problems to solve story problems that resemble real world problems.

 Introductory Activity 1. Remind the class that we have been looking at the steps used to solve one, two, and multi-step linear equations. 2. Have students take a minute to think of when they would use an equation like this in their everyday lives. 3. Simple idea: If I were going to exercise today twice as long as I did yesterday and I know that I exercised for a half hour yesterday how long would I be exercising for? 4. We know that we are just going to double the time, so therefore we will be exercising for one hour. 5. What if we had a more in depth problem, such as this problem about an African Violet houseplant? 1. After reading through it we can see that we are unable to compute this in our heads. 2. By the end of today’s lesson we will have the knowledge to complete any problem similar to this.

 Developmental Activity o Lets first review solving linear equations with one and two- steps. o Ask the class if there are any major concerns dealing with this information before moving on to the activity. o If there are no major concern, then could I please have all of you move into groups of four. If there are still some questions that exist then answer all questions before moving onto today’s activity. o Once the students are in their groups, give each group a deck of 36 cards, each containing 12 books. A book consists of 3 cards containing equivalent equations. o Each team should shuffle the deck of 36 cards and distribute them evenly to each group member. o The first player will start by laying an initial equation card (this card will be in the form ax + b = c) in the center of the table. The second player (the player to the left) will lay either the second card in the original book or if he or she does not poses that card they will lay another initial card that will start a second book. (A card cannot be played unless it is the initial card in a book or the previous card of the book is already played.) o The entire group must agree on the card before play can move to the next player. (Players are able to use Algebra Tiles or calculators to help them conclude the answer if necessary) o The game ends when all the books are completed. o When the groups have finished their game have them switch decks with other groups around them and play again. o While groups are working on the activity, walk around the room being sure to stop at every group to check and see how they are doing. Look for any difficulties they may be experiencing while solving the problems, take note of this for further review. o Day 2 o Lets begin looking at writing these linear equations. o We talked at the beginning of yesterday’s class about the exercise problem and exercising twice as long as the day before. What if we wanted to make it a little more difficult to figure out in our heads, say we wanted to exercise 45 minutes more today than yesterday, how would we figure that out? o We exercised 30 minutes yesterday and we want 45 minutes more today, writing down these two numbers ask the students what we would want to do to the two numbers. o Work through more examples with the whole class, selecting random students to contribute: o I want to exercise 10 minutes more than I did yesterday. o If I exercise for a total of 45 minutes how much longer did I exercise today? o If I exercise for a total of 20 minutes how much shorter time did I exercise today? o If I want to exercise three times as long, how long will I exercise? o If I want to exercise 10 minutes more than three times as long, how long will I exercise? o If I want to exercise 20 minutes less than twice as long, how long will I exercise? o Is everyone starting to understand, does anyone have any major questions or concerns? o Pass out Constructing Numerical Equations, Practice Sheet 1. o Go over all problems together with the whole class, selecting random students to contribute. o Pass out Constructing Numerical Equations, Practice Sheet 2 and 4. o Have students work alone on the worksheet for about 10-15 minutes, and then have students work together with their neighbor making sure that both of them understand what they are doing. During this time walk around the classroom answering any questions that may arise. o Collect Practice Sheet 2 and 4 when completed.

 Concluding Activity o It is important for my students to be able to communicate mathematical concepts by writing. o Have each student pull out a piece of paper for their three sentence mini journal. . What I feel I know about writing multiple step equations. . What things I am still unsure about. . What parts I would like to go over more.

V. Evaluation

 As students are finishing their mini journal entries assign the (day 2) nights homework. o Pass out Puzzling Numbers worksheet to be completed as homework. o Pass out a copy of the Plant Problem that was shown at the beginning of class to be attempted for homework.

VI. Materials

 Deck of 36 cards for each group of 4 students  Algebra Tiles (a package for each student)  Calculators (one for each student)  Worksheets o A Tangle of Mathematical Yarns o Constructing Numerical Equations o Puzzle

Michelle Corron

I. Audience/General

II. Concept

 Using Formulas

Objectives

 SWBAT transform equations, using their knowledge of multi-step equations.  SWBAT develop geometric formulas, using their knowledge of geometric shapes.

3. Lesson Procedure

 Introductory Activity o Talk to the students about different sports they like, make a list of the responses you receive. o Ask the students where speed would matter in each of the sports. o Talk about how in each of these sports we could apply the formula d = rt, to find the rate of something if we knew the distance and the time or any other combination of these.

 Developmental Activity o Talk about some formulas that students know, make a list on the board. o Talk about the equations and how most of them are set equal to one variable. Ask students if they will ever want to use the formula to solve for one of the other variables. o Pick out a few of the formulas and play with moving it around to make it equal to the variable they want to find. o Talk about the advantage to plugging in your numbers at the end. o Have students in their groups explore other equations and solving them for different variables within the equations. o If time permits have students look at a few story problems relating to real world situations. o The second day of the lesson students will be looking at developing their own formulas from their knowledge of three- dimensional geometric shapes. o From the student’s responses, make a list of several different geometric shapes. o Students within their groups will construct three-dimensional shapes using construction paper. (cube, pyramid, cylinder) o Using these shapes students will discuss their ideas for the formulas for surface area and for volume. o After letting them explore, talk to them about drawing a net diagram of each shape. o Have them explore and see if this idea changes any of their thoughts.

 Concluding Activity o Have each student look at all of the geometric formulas they have developed within their groups. o Have each student solve two of the equations for all the variables in them showing and explaining each step that is used.

4. Evaluation

 For homework (day 1), have students think of different formulas they encounter around the house or on the way home from school and make a list of them.  For homework, (day 2) each student should write five different story problems involving the formulas they encounter around their house or on their way home from school.  Tomorrow we will trade with other students in our group and have them solve the problems.

5. Materials  Construction Paper  Scissors  Tape  Rulers Post-Assessment of Solving Equations

1. Solving One-Step Equations 1 2 3 4 5

2. Addition and Subtraction Properties 1 2 3 4 5

3. Multiplication and Division Properties 1 2 3 4 5

4. Solving Two-Step Equations 1 2 3 4 5

6. Solving Multi-Step Equations 1 2 3 4 5

8. Equations With Variables on Both Sides 1 2 3 4 5

10. Using Equations to Solve Problems 1 2 3 4 5

11. Distance, Rate, and Time Problems 1 2 3 4 5

12. Using Formulas to Solve Equations 1 2 3 4 5

13. Geometric Formulas 1 2 3 4 5

14. Using Measures of Central Tendency 1 2 3 4 5

15. Mean, Median, Mode, and Outliers 1 2 3 4 5

16. Range 1 2 3 4 5

17. Stem-and –Leaf Plots 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Solve x - 3 = - 8.

2. Solve 23 + t = 16.

r 3. Solve  11. 4

4. Solve 4 c = -96.

m 5. Solve 10   2. 4 6. Solve –2 (b – 4) = 12.

7. Find the value of x, 6 x + 3 = 8 x – 21.

8. The sum of three consecutive integers is 147. Find the integers.

9. Solve x y – z = w, for y.

10. Suppose your grades on three exams are 80, 93, and 91. What grade do you need on your next exam to have a 90 average on the four exams? Instructional Design Proportions

Unit 3: Proportions

 The student will be able to state the formula for slope. (memory/recall)  The student will be able to explain what slope is and what the formula means. (comprehension)  Find the slope of several different linear equations. (application)  Show why two lines are parallel or perpendicular by using the formula for slope. (application)  When a student is asked to build a ramp given certain stipulations, they are able to apply their knowledge of slope and construct a ramp. (evaluation) Pre-Assessment of Proportions

1. Ratio 1 2 3 4 5

2. Rate 1 2 3 4 5

3. Unit Rate 1 2 3 4 5

4. Proportions 1 2 3 4 5

5. Cross Products 1 2 3 4 5

6. Similar Figures 1 2 3 4 5

7. Scale Drawings 1 2 3 4 5

8. Percent Equations 1 2 3 4 5

9. Percent of Increase 1 2 3 4 5

10. 10. Percent of Decrease 1 2 3 4 5

11. Theoretical Probability 1 2 3 4 5

12. Experimental Probability 1 2 3 4 5

13. Sample Space 1 2 3 4 5

14. Outcomes 1 2 3 4 5

15. Compound Events 1 2 3 4 5

16. Dependent Events 1 2 3 4 5

17. Independent Events 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Complete the sentence, 2 hours = __ seconds.

$3 2. Solve . 8lbs

2 11 3. Solve  . 4 x

9 81 4. Solve  . x 10

5. What percent is 32 of 120? 6. What is 30% of 90?

7. What is the percent change in 34 to 28?

8. Using a die what is the sample space?

9. From a normal deck of cards, what is the P(Drawing a King)?

10. What is the probability of rolling a 6 on a die? Michelle Corron

I. Audience/General

II. Concept

 Ratio and Rate

III. Objective

 SWBAT find ratios and rates

 Introductory Activity o Buying fruit by weight how do they know what to charge you if you only buy .23 of a pound? o Buying baseball cards buy five packs for $8, how do you know the price if you only buy three? o Ask about what jobs would be concerned with these types of ideas.

 Developmental Activity o Define Ratio: a comparison of two numbers by division o Define Rate: if the ratio is comparing two things with different units o Example . Buying fruit again, if a 16oz apple cost 72 cents, how much does an apple cost per ounce? . 45 cents o Have students come up with some other examples, similar to this one. o Lets play around with some ratios. o Have students get into their groups. o Pass out worksheet, Working With Ratios. o Pass out project materials. o When every group has finished, go over all answers together. o Have students move back to their seats.

 Concluding Activity o Who can explain to the rest of us what a ratio is? o Who can explain to us the different between a ratio and a rate? o Take out your journals, I would like you to think a ten different times outside of class that you see or use ratios or rates.

V. Evaluation

 Worksheet, Ratio

VI. Extension

 Also in your journal write a small paragraph of a time that you might use ratios or rates when you get older in your career of choice.

VII. Materials

 Worksheet o Working With Ratios o Ratio  Ruler, one per group  Plain wooden pencil, one per group  Nickels, four per group  Pennies, eight per group  Student’s journal Student Journal

Name______

Date______

Topic______

______

Response______

______

I. Audience/General

II. Concept

 Similar figures

III. Objective

 SWBAT finding missing measurements on similar figures  SWBAT use similar figures to find new measurements

 Introductory Activity o Designing a house or room in a house do they draw a life size figure? o Designing clothes? o Using a recipe to cook for a large gathering? o Discuss.

 Developmental Activity o Look at two similar shapes on the overhead. o Find ratios of different sides. o Repeat with another shape. o Apply back to intro items. o Thinking of another place this is used MAPS. o Pass out maps and use the scale to measure distances between places that the students chose.

 Concluding Activity o Take out journal and write a few sentences about five jobs that proportions with similar figure would apply.

1. Evaluation

 Homework: draw a design of something with a scale; label what the actual measurements are supposed to be. VI. Extension

 Within your journal talk about what you want to be when you grow up and where this could be used in you career choice.

2. Materials

 Overhead shapes o Triangle o Square  State map  Ruler  Student’s journal

Student Journal

Name______

Date______

Topic______

______

Response______

______

I. Audience/General

II. Concept

 Percent

III. Objective

 SWBAT use proportions to solve percent problems  SWBAT write and solve percent equations

 Introductory Activity o Where do we see percentages used a lot of time? o Make a list of what students say on the board or overhead. o Pick out a few and discuss how percents are used. . Ex. Discounts: percent of total is taken away from the bill

 Developmental Activity o How do we accomplish what we are talking about though? o Revisit what a ratio is. o Comparison of two numbers by division. o Percent is a ratio where a number is being compared to 100 o Percent is n/100 = part/whole o Do 4 examples . What percent of 40 is 20? . What is 80% of 20? . 15% of what number is 24? . 42 is 30% of what number? o What if there is a change in the number and we want to find the percent of change. o Give an example: . Ask students for an item that is for sale. . Ask student for the original price. . Ask student for the new price. . We want to find the percent of difference in the two prices. o Can this be done? o What number will we be changing, our part or our whole? o The part will be changing. . The part is equal to the difference in the two prices o The whole is going to be what? o The whole is equal to the original price. o Finish the example to find the final percent. o Pass out the practice worksheet. o Students work individually on the worksheet taking about 10 minutes, 15 minutes at the most. o Have students get into their groups and check answers with each other’s, if any answers are different, the students are to work together to figure out the correct solution. o Students are only able to ask for help after they have tried to solve together in the group. o When students think they have all problems correct they are to turn in all of the sheets from the group together. o Students work will be corrected and returned the next day, any errors most be corrected for homework the following day.

 Concluding Activity o Look back at the original list of the student’s ideas; reiterate that the ideas are all real world applications of the usages of percents. o If population is on the list point it out otherwise add it to the list yourself. o Place transparency 3 on the overhead and pass out worksheet. o Read aloud the beginning paragraph. o Go through the answers together for problems 1-4.

V. Evaluation

 Homework: Worksheet, Percents. Included on the worksheet is three real world questions and one question asking students to come up with five of his or her own. Students should be creative it can be all his or her own ideas or you can find charts, graphs, or tables form any type of media source to use in the problem.  If you use a type of media it most be brought in with the problem.  If media is used you most only complete three problems.

VI. Extension

 Discuss the list of ideas on the board and where the students later in their lives could use the ideas.  Students should be giving all ideas, if they seem to get stuck give them one situation, to help get their brainstorming started.

VII. Materials

 Overhead o Population  Worksheet o Practice o Population o Percents Percents

Name ______Date ______

1. In Louisiana the state sales tax is 4%. If your buy a $2100 computer in Louisiana, how much tax will you pay?

2. Alaska is the largest state in the United States, with an area of 570,374 mi2. It accounts for about 15% of the country’s area. Estimate the area of the United States.

3. You received $41.60 in interest for a two-year investment at 6.5% simple interest. How much money did you invest?

4. Come up with five of your own story problems, be creative. It can be all your own idea or you can find charts, graphs, or tables from any type of media source to use in your problem. a. If you use a type of media it most be brought in with the problem. b. If you use a type of media, you only have to complete three story problems. Michelle Corron

I. Audience/General

II. Concept

 Probability

III. Objective

 SWBAT find theoretical probability  SWBAT find experimental probability

 Introductory Activity o Write the word probability on the board. o Ask students to make a list to place on the board where they have heard the word probability used. o Pick the list apart to talk about what the word probability means within the situations mentioned. o Pick apart what the students are saying and write words on the board: total outcome, wanted outcome, event, and sample space.

 Developmental Activity o Define probability: the ratio of the number of favorable outcomes for an event to the number of possible outcomes of the event. o Have students think about the percentages from the other day, it is part of a whole. o Two kinds of probability. o Theoretical probability: when all out comes are equally likely to happen o P(a)= number of favorable outcomes/total number of possible outcomes o Remind students that it can be expressed as a fraction, decimal, or a percent. o Example o Every evening after work, Carlos puts all of his change in a jar. One evening Carlos counts his coins and finds he has the following: 10 quarters 15 dimes 25 nickels o Look back at the words on the board go through each and define with this example. o Total outcome: How many coins can Carlos take from his jar? 50 o Wanted outcome: Depends on the questions being asked Quarters: 10 Dimes: 15 Nickels: 25 o Event: Taking the coin from the jar o Sample Space: All possible outcomes . Carlos could remove a Quarter, Dime, or a Nickel o P(Quarter)= 10/50 = 20% o P(Dime)= 15/50 = 30% o P(Nickel) = 25/50 = 50% o What does the probability have to be, for you know it will happen for sure? o Discuss; let students come up with the answer. o Think of the batting average. o What does the probability have to be for you to know that it will never happen? o Discuss. o Botanist example on overhead. o Experimental Probability: based on repeated trials o P(a) = number of times the event occurs/number of times the experiment is done o Defective Bulbs example on overhead. o Skateboards example on overhead.

 Concluding Activity o Now that we have worked through examples of both Theoretical and Experimental Probability are there other career choices that we can think of now where probability would be used? o Add to our original list.

V. Evaluation

 Homework: Complete Probability worksheet

VI. Extension

 Have students write about what they want to be when they grow up and how probability would be used.  If their career choice is listed on the board, the student most think of an aspect that was not mentioned during class. 3. Materials

 Overhead o Botanist o Defective Bulbs o Skateboard  Worksheet o Probability  Student’s journal Botanist

Sondra is a botanist. She is developing new plants for a local nursery. She is crossing plants that have red flowers with plants that have white flowers. A red-flowering plant has two red genes (RR). A white-flowering plant has two white genes (WW). Each parent contributes one gene to the seedlings.

Use a chart to model the possible color combinations for the seedlings. The top row shows the genes for the red-flowering plant. The left column contains the genes for the white-flowering plant. Each seedling has one gene from each parent and produces a pink flower (RW).

Red Flowering Plant R R e

t W RW RW i h W g n

i RW RW

r W e w o l F t n a l P

Sondra now crosses two of the pink-flowering plants. To see what the results might be, Sondra makes a new chart for the second generation.

Pink Parent Plant R W

k R RR RW n i P t n e r RW WW a W P t n a l P

What is the probability that a plant in the second generation is a. pink b. red c. white A quality control engineer at Everglow Bulbs tested 400 bulbs and found 6 of them to be defective.

a. What is the experimental probability that an Everglow bulb will be defective?

a. In a shipment of 75,000 bulbs, how many are likely to be defective?

After receiving complaints, a skateboard manufacturer inspected 1000 skateboards at random. The manufacturer found no defects in 992 skateboards. What is the probability that a skateboard selected at random has no defects? Write the probability as a percent. Student Journal

Name______

Date______

Topic______

______

Response______

______

______Post-Assessment of Proportions

1. Ratio 1 2 3 4 5

2. Rate 1 2 3 4 5

3. Unit Rate 1 2 3 4 5

4. Proportions 1 2 3 4 5

5. Cross Products 1 2 3 4 5

6. Similar Figures 1 2 3 4 5

7. Scale Drawings 1 2 3 4 5

8. Percent Equations 1 2 3 4 5

9. Percent of Increase 1 2 3 4 5

10. Percent of Decrease 1 2 3 4 5

11. Theoretical Probability 1 2 3 4 5

12. Experimental Probability 1 2 3 4 5

13. Sample Space 1 2 3 4 5

14. Outcomes 1 2 3 4 5

15. Compound Events 1 2 3 4 5

16. Dependent Events 1 2 3 4 5

17. Independent Events 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Complete the sentence, 2 hours = __ seconds.

$3 2. Solve . 8lbs

2 11 3. Solve  . 4 x

9 81 4. Solve  . x 10

5. What percent is 32 of 120? 6. What is 30% of 90?

7. What is the percent change in 34 to 28?

8. Using a die what is the sample space?

9. From a normal deck of cards, what is the P(Drawing a King)?

10. What is the probability of rolling a 6 on a die? Instructional Design Graphs and Functions

Unit 3: Proportions

 The student will be able to state the formula for slope. (memory/recall)  The student will be able to explain what slope is and what the formula means. (comprehension)  Find the slope of several different linear equations. (application)  Show why two lines are parallel or perpendicular by using the formula for slope. (application)  When a student is asked to build a ramp given certain stipulations, they are able to apply their knowledge of slope and construct a ramp. (evaluation) Pre-Assessment of Graphs and Functions

1. Interpreting Graphs 1 2 3 4 5

2. Analyzing Graphs 1 2 3 4 5

3. Sketching Graphs 1 2 3 4 5

4. Domain 1 2 3 4 5

5. Range 1 2 3 4 5

6. Vertical Line Test 1 2 3 4 5

7. Function Notation 1 2 3 4 5

8. Using Tables 1 2 3 4 5

9. Independent Variables 1 2 3 4 5

10. Dependent Variables 1 2 3 4 5

11. Direct Variation 1 2 3 4 5

12. Constant of Variation 1 2 3 4 5

13. Inductive Reasoning 1 2 3 4 5

14. Sequence 1 2 3 4 5

15. Common Difference 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Sketch a graph showing the path a baseball takes after being hit.

2. What is the domain of the following set (2, 4), (5, 3), (7, 1), (9, -2).

3. What is the range of the following set (2, 4), (5, 3), (7, 1), (9, -2).

4. Evaluate f(3) = 2x - 10.

5. Evaluate f(5) = -4x + 2. 6. When talking about the price of movies rising over time, what is the independent variable?

7. When talking about the price of movies rising over time, what is the dependent variable?

8. Model the following function with a table of values f x  2x  3.

 2 9. What is the constant of variation in the following y  x ? 5

10. Describe the following pattern, 9, 15, 21, 27, … Michelle Corron

I. Audience/General

II. Concept

 Situation Graphs

III. Objective

 SWBAT interpret graphs of a situation  SWBAT sketch a graph of a situation  SWBAT analyze a graph of a situation

 Introductory Activity o Lets think about a portion of a roller coaster that does not go upside done in a loop. o Pick a student to draw a segment of one on the board that is about two feet in width. o Draw an x and y-axis around the roller coaster track. o Talk about what is going on in the picture, label items that are being discussed. o Time is changing as the roller coaster moves therefore we can label the x-axis. o What would go on the y-axis? o Move your figure along the roller coaster path talking about what is happening at each point. o Student may mention speed or height label everything they say. o Go back through and talk about what they have label to see what is consistent, this will rule out speed and leave the students with the correct label, height.

 Developmental Activity o What did we just do to this picture? o Analyzed: discussed what was going on in the graph o Label the independent and dependent variable. o Independent variable: variable whose value is subject to choice o Dependent variable: value depends on the value of the independent variable o Independent variable: time o Dependent variable: height o Interpret what was happening at each step during the graph. o Example o Draw the following graph on the board

o The graph represents the height of a football after it is kicked downfield. Identify the independent and the dependent variable. Then describe what is happening in the graph. o Independent variable: time o Dependent variable: height o Interpret: starts on the ground, moves into the air until it reaches its maximum height, and then it loses altitude until landing back on the ground. o Example o Draw the following graph on the board

o The graph represents the height of a baseball after it is hit across the field. Identify the independent and the dependent variable. Then describe what is happening in the graph. o Independent variable: time o Dependent variable: height o Interpret: starts at a height above the ground where it left the bat, moves into the air until it reaches its maximum height, then it loses altitude until landing back on the ground. o What if we are given all the information and we are asked to draw a graph that represents the information that we were given, are we able to that? o Example o Think about driving a car. When you start you are at a complete stop, you begin to accelerate until you have reached your desired speed. You will stay at that speed for a little while and then you most slow to a complete stop because a stop sign is coming up. o What is the independent variable: time o What is the dependent variable: speed o Draw a sketch of the graph that would best represent the given description. o Example o Think about a bank account. The account has an initial value, which then increases to a certain amount, and stays constant for a while. The account then starts to decrease until the last withdraw that takes it to zero dollars. o What is the independent variable: time o What is the dependent variable: balance o Draw a sketch of the graph that would best represent the given description.

 Concluding Activity o In journals students should discuss why it is important to know how to analyze a graph. Describe if you have ever seen a graph before (not in school) that you had to figure out what it was telling you.

V. Evaluation

 Homework: Complete Graphs and Functions worksheet. Your answers should contain detail; they should not be one-word answers. Also make up one graph with labels that represents something you did today.

VI. Extension

 Example Draw the following graph on the board Parking Garage Costs

Answer the following questions 1. How much does it cost to park for 2 hours? $3 2. How much does it cost to park for 121 minutes? $6 3. Suppose your mother pays $6 for parking. About how long was her car parked in the garage? 2hours and 1min to 4hours

VII. Materials

 Student’s journal  Worksheet o Graphs and Functions Student Journal

Name______

Date______

Topic______

______

Response______

______

Michelle Corron

1. Audience/General

II. Concept

 Relations and Functions

III. Objective

 SWBAT identify relations  SWBAT identify functions  SWBAT identify domain and range  SWBAT use the vertical line test

 Introductory Activity o Talk about different summer jobs and how they pay you, hourly or for a week. o Suppose your summer job pays $4.25 an hour. Your pay depends on the number of hours you work. o Make a table from this information including 0, 1, 2, and 3 hours worked. o Label the independent and dependent variable.

 Developmental Activity o If we wanted to graph this information could we? o Graph. o What are the points that we are plotting called? Ordered pairs or coordinates o Lets write out the ordered pairs as a list. Which is also called a Set. o Define Relation: set of ordered pairs o So we have seen many relations before and have just not called them that. Artwork. o What about a function, we have all heard it but what is it? o Define Function: it is a special relation that assigns exactly one y-value to each x-value. o Put two charts on board and discuss which is a relation and which is a function. X Y_ X Y__ 1 -3 -4 -4 6 -2 -1 -4 9 -1 0 -4 1 3 3 -4

Relation: 2 of the same Function: none of the same x values x values

o Pass out Relation and Function worksheet o Students should work on problems 1-13 together with their group discussing whether each question is describing a relation or a function. o After students have worked through all of the questions, go over the answers. o Define Domain: Every relation and function has a domain; it is the set of x-values o Define Range: Every relation and function has a range; it is the set of y-values o Go back through the worksheet having students define the domain and ranges aloud. o One last thing to look at on the worksheets are the graphs, here is a quick and easy way to determine if it is a function. o Vertical Line Test: a vertical line moving horizontally across a graph should never touch the graph more than once at a time. o The last thing we will be covering in this section is evaluating functions. o Evaluating Functions. o For every input you will receive an output. o When written in function notation f(x) (read “f of x”) will always be the output, the number or letter in place of the x will be the input. o Example o The cost of a long-distance telephone call c is a function of the time spent talking t in minutes. The rule c(t) = 0.09t describes the function for one service provider. Find the cost of a 15- minute, 30-minute, 45-minute, 1-hour, and 2-hour phone conversation. o Go back to our worksheet and complete problems 14-24 even.

 Concluding Activity o Lets go back to the beginning of class when we were talking about the summer job. o If we were being paid $4.25 an hour, how would we represent this with an equation in function notation? o What numbers would make a reasonable range, based upon a week of work?

V. Evaluation

 Homework: Public Debt worksheet

VII. Extension

 Example  An appliance store pays its full-time employees a weekly base salary plus a commission, as shown by these functions where x is the dollar amount of sales per week. F(x) = 200 + 0.05x when x < $2,000 F(x) = 100 + 0.1x when x  $2,000

 Evaluate the appropriate function to find the earnings for salespeople who made the following dollar amounts in sales last week. a. $3,500 b. $2,000 c. $1,900

 What is the domain and range of each function?

VIII. Materials

 Overhead o Graph paper  Worksheet o Relation and Function o Public Debt Michelle Corron

I. Audience/General

II. Concept

 Functions

III. Objective

 SWBAT model functions using function notation  SWBAT model functions using tables  SWBAT model functions using graphs

 Introductory Activity o How many students have to do chores around their house? o How many students get paid to do their chores? o Someone give me an amount that they get paid per week. o What would we make in two weeks then and three? o Figure out about five weeks.

 Developmental Activity o Are we able to put this information into a table? o What is the Independent and Dependent variables? o Looking at our table we made is this a function that we are working with? o Can we write an equation for it in function notation? . P(w) = $(w) o Can we also graph the information? o So could anyone tell me three different ways to look at a function? o Graph, Table, and Equation. o Pass out example worksheet. o Example o Suppose your television broke at home and you were not going to be able to watch your favorite show. So your mother or father has to call and have a repairperson come out to fix it. After calling they are told that the charge for a house call is $12 and $7 per hour, so your function is c(t) = 12 + 7t. Your mother or father only has $40 on them so how long can the repairperson possibly stay. o Set up a table. o Start at 0 hours keep figuring until you go over $40. o Make a graph of the data. o Approximately how long could he or she stay if your mother or father had $55? o Example o Suppose your group recorded a CD. Now you want to copy and sell it. One company charges $250 for making a master CD and designing the art for the cover. There is also a cost for $3 to burn each CD. The total cost P(c) depends on the number of CDs c burned. Use the function rule P(c) = 250 + 3c to make a table of values and a graph. o Another company charges $300 for making a master and designing the art. It charges $2.50 for burning each CD. Use the function rule P(c) = 300 + 2.5c. Make a table of values and a graph. o Compare your graph from part (a) to the graph in part (b). For what number of CDs is the studio in the Example less expensive?

 Concluding Activity o Looking back at our allowance money. o If there was something we wanted to buy using this idea could help us to determine when we were going to be able to buy it, but which way would be the best to look at the function notation, a table, or a graph. o In your journal write a one paragraph about where you could use this now outside of school. o Collect journals

V. Evaluation

 Homework: worksheet Capers

VI. Extension

 Also write one paragraph about where you will encounter this idea later in the real world, whether it is in your career or your home life. VII. Materials

 Overhead o Graph paper  Student’s journals  Worksheet o Examples o Capers Student Journal

Name______

Date______

Topic______

______

Response______

______

______Function Examples

Suppose your television broke at home and you were not going to be able to watch your favorite show. So your mother or father has to call and have a repairperson come out to fix it. After calling they are told that the charge for a house call is $12 and $7 per hour, so your function is c(t) = 12 + 7t. Your mother or father only has

$40 on them so how long can the repairperson possibly stay.

Suppose your group recorded a CD. Now you want to copy and sell it. One company charges $250 for making a master CD and designing the art for the cover. There is also a cost for $3 to burn each CD. The total cost P(c) depends on the number of CDs c burned. Use the function rule P(c) = 250 + 3c to make a table of values and a graph. Another company charges $300 for making a master and designing the art. It charges $2.50 for burning each CD. Use the function rule P(c) = 300 + 2.5c. Make a table of values and a graph.

Compare your graph from part (a) to the graph in part (b). For what number of CDs is the studio in the Example less expensive? Michelle Corron

I. Audience/General

II. Concept

 Function Notation

III. Objective

 SWBAT write a function in function notation from a table.  SWBAT write a function in function notation from a real world situation.

 Introductory Activity o Now that we are all getting older we will start to get jobs and wanting to buy more expensive things. Brandon wants to buy a new computer, but does not want to wait for his minimum wage job to pay for it. So his parents bought it for him and he gives them all of his paychecks until it is paid off. If the computer was $689 and he is getting paid $4.50 per hour, how many hours will he have to work to pay them off. (Let students pick out the item to buy, the job to get, and the amount they will get paid) o Discuss the possible ways to figure this out.

 Developmental Activity o What about function notation? o Write it out in words: total profit is $4.50 times hours worked minus $689 o Define the variables: h = hours worked P(h) = total profit o Write the function: P(h) = 4.5h – 689 o What if instead of being given the whole story, what if you are only given the table, can we make the function notation from that point? o Example Year Height (inches) 1. 8 2. 16 3. 24 4. 32 5. 40 o From this information, define the variables and write the function. o Go through each year and write down what is happening from year to year. o Multiplying by 8. o Define the variable: x = number of years H(x) = total height o Write the function: H(x) = 8x o Answer any specific questions that any student has. o Pass out two note cards to all students. o Students are to only write on one side of the note cards. o On one note card they are to make up a story problem that has to do with their personal career goal. Place the career name at the top of the card. The problem should be asking one to create the function notation that corresponds to the story. o On the other card the student should write out the solution. You do not have to define your variables on either card. o The class will then divide into two sections with their cards the students will shuffle them all together and place face down in rows. o Students will be playing Memory trying to match the story card to the function card. o Sections can be divided more or less depending on the size of the class. o When students are done with their set of cards the cards should be switched with the other group.

 Concluding Activity o Today we have talked a little about how this section could be used now in your everyday life, and we have seen a lot of different places where it can be used later in several careers. o In your journal I would like a paragraph that you would be writing to a younger individual telling them where math is seen besides in the classroom. Give details get that individual excited about learning mathematics. o In your journal I would like you to note anything up to this point within this unit you do not understand and would like some review on. V. Evaluation

 Homework: Function Grafun worksheet.

VI. Extension

 Pass out graph paper, one for each student.  On the board write: Make a table and a graph for the following functions. Functions: y = x2 y = 4x – 2 y = 7x + 3 y = -4 – x

VII. Materials

 Note cards, two per student  Student’s journal  Graph paper  Worksheet o Function Grafun Student Journal

Name______

Date______

Topic______

______

Response______

______

______Post-Assessment of Graphs and Functions

1. Interpreting Graphs 1 2 3 4 5

2. Analyzing Graphs 1 2 3 4 5

3. Sketching Graphs 1 2 3 4 5

4. Domain 1 2 3 4 5

5. Range 1 2 3 4 5

6. Vertical Line Test 1 2 3 4 5

7. Function Notation 1 2 3 4 5

8. Using Tables 1 2 3 4 5

9. Independent Variables 1 2 3 4 5

10. Dependent Variables 1 2 3 4 5

11. Direct Variation 1 2 3 4 5

12. Constant of Variation 1 2 3 4 5

13. Inductive Reasoning 1 2 3 4 5

14. Sequence 1 2 3 4 5

15. Common Difference 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Sketch a graph showing the path a baseball takes after being hit.

2. What is the domain of the following set (2, 4), (5, 3), (7, 1), (9, -2).

3. What is the range of the following set (2, 4), (5, 3), (7, 1), (9, -2).

4. Evaluate f(3) = 2x - 10.

5. Evaluate f(5) = -4x + 2. 6. When talking about the price of movies rising over time, what is the independent variable?

7. When talking about the price of movies rising over time, what is the dependent variable?

8. Model the following function with a table of values f x  2x  3.

 2 9. What is the constant of variation in the following y  x ? 5

10. Describe the following pattern, 9, 15, 21, 27, … Instructional Design Linear Equations and Graphs

Unit 3: Proportions

 The student will be able to state the formula for slope. (memory/recall)  The student will be able to explain what slope is and what the formula means. (comprehension)  Find the slope of several different linear equations. (application)  Show why two lines are parallel or perpendicular by using the formula for slope. (application)  When a student is asked to build a ramp given certain stipulations, they are able to apply their knowledge of slope and construct a ramp. (evaluation) Pre-Assessment of Linear Equations and Graphs

1. Slope 1 2 3 4 5

2. Rate of Change 1 2 3 4 5

3. Slope-Intercept Form 1 2 3 4 5

4. Linear Equation 1 2 3 4 5

5. Y-Intercept 1 2 3 4 5

6. X-Intercept 1 2 3 4 5

7. Standard Form 1 2 3 4 5

8. Point-Slope Form 1 2 3 4 5

9. Parallel Lines 1 2 3 4 5

10. Perpendicular Lines 1 2 3 4 5

11. Reciprocal 1 2 3 4 5

12. Scatter Plots 1 2 3 4 5

13. Line of Best Fit 1 2 3 4 5

14. Correlation 1 2 3 4 5

15. Translations 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Find the slope between (2, 11) and ( 5, 7).

2. What is the slope of the line y = 4x + 1?

3. Can a horizontal line have a slope?

4. What is the y-intercept of the line y = -2x - 7.

5. Write the following line in slope-intercept form –5x – y = 13 6. Draw two perpendicular lines.

7. Draw two parallel lines.

8. What is the negative reciprocal of -2?

9. Draw a line representing a positive correlation.

10. Translate the graph y  x up 2. Michelle Corron

I. Audience/General

II. Concept

 Rate of Change and Slope

III. Objective

 SWBAT find the rate of change from tables  SWBAT find the rate of change from graphs  SWBAT find slope

 Introductory Activity o Has anyone been skiing? o What are some words that you hear when you talk about skiing? o Ask what the slopes are. o Do other things have a slope or is that only what you ski one? o Make a list of about ten different items that have slope. o Are all of the slopes the same?

 Developmental Activity o What we are actually looking at is the SLOPE or RATE OF CHANGE o Slope or Rate of change = vertical change / horizontal change (rise / run) o Pick one of the items that are listed and sketch it on the board. o Pick an item that has a positive slope. o Make up some close to realistic measurements for the object. o Figure out the slope of the object. o Repeat with a two more of the objects, having students give you the measurements. o Again pick objects with a positive slope. o So these are all physical objects that we have been given the measurements of the sides, could we find the slope of something that we are not given the exact measurement to? o Let students think for a minute or two. o What about the slope of a graph showing the amount of money in your bank account? o Draw it on the overhead with a steady deposit of $25 every month. o Draw a table and a graph of the information (using graph paper makes it easy to count the spaces). o How are we able to figure out the slope of that line? o What is our formula for slope? o So lets see what our vertical change is? o y – y` o Horizontal change? o x – x` o So what is the slope of the graph? o Go back to the original list and pick an item that has a negative slope? o Draw a sketch on the board with measurements and figure the slope. o What about a bank account, that has steady withdrawals of $15 per month. o What is the slope of the graph? o So now we know how to find positive slope of a line and also negative slope of a line. Draw an example of each on the board. o Looking at two different positively sloped lines, can we say just from looking at them, which will have a greater slope? o The steeper the line the higher the slope will be.

 Concluding Activity o Have we left out any direction that a line could go? o If students do not guess horizontal or vertical draw some lines to show the ones we have looked at skipping the horizontal and vertical lines. o So a horizontal line, is that a positive slope or a negative slope? o Think back to skiing, a horizontal line is kind of like cross- country skiing. o Cross-country skiing we are going straight on flat line, so what do we think the slope is. o Let students figure out zero. o So now have we covered all direction of lines? o Repeat process if they are unable to guess vertical. o Think about skiing again is it possible to ski up or down a vertical hill? o Vertical slope is undefined. o Show that rise over run would put zero on the bottom, which they know is undefined. V. Evaluation

 Homework: Complete Calculating Slope worksheet and make a list of at least ten items that you encounter from the time you leave school to the time you go to bed. The items can have a visible slope or can create slope over time.

VI. Extension

 In their journals explain how to find the slope of a line and also explain why a vertical line is unable to have a slope.

VII. Materials

 Overhead o Graph paper  Worksheet o Calculating Slope  Ruler  Student Binder  Student’s journal Student Journal

Name______

Date______

Topic______

______

Response______

______

I. Audience/General

II. Concept

 Slope-Intercept Form

III. Objective

 SWBAT write the equation of a line in slope-intercept form.  SWBAT graph linear equations.

 Introductory Activity o Roller coasters have a ton of different slopes in them right? o Draw an example path on the board. o They have a positive slope, which is when they are going up hill. o They have a negative slope, which is when they are going down hill. o Do they every have a slope of zero? o When they are loading. o Do they every have a slope that is undefined? o No the cars would not stay on the track. o How do you think the builders come up with these roller coaster ideas? o They have to have some kind of equation for these hills so they know it is a realistic slope. o Were going to find out how to write equations for these straight paths today, not the curves just the straight part.

 Developmental Activity o Define linear equation: an equation whose graph is a line o Also known as a linear function. o On the overhead graph paper, draw a short line crossing the positive portion of the y-axis. o What is one thing that everyone knows how figure our about this line? . Slope o Have students explain to you how to find the slope of the line. o Show students the slope-intercept form y = mx + b. o In this equation we are looking to fill in the m and b. . m = slope or rate of change . b = y intercept or where the line crosses the y-axis o So what is our equation for our line? o Fill in the two parts. o What if my line crossed in the negative portion of the y-axis? o Draw a line and repeat, figuring out the slope and the y-intercept. o Then write the equation of the line in slope-intercept form. o What if we were given the equation of the line and then asked to graph it? o Example . y = 2x –3 . What is the first thing that we can do? . Plot the y-intercept, which is? . Do we know another point off hand that we are able to plot? . We know that slope is rise over run, which tells us we are moving up 2 and over 1 space. . From our point count up 2 over one and plot our next point. . Draw a line connecting the two points.

 Concluding Activity o At the beginning of class we discussed how roller coasters have several different slopes that can be written as a linear equation that can also be called a what? o Pass out Slope-Intercept Form worksheet o The worksheet contains other real world situations where slope-intercept form is used. o Students can work with a partner, however be sure that both of you understand what you are doing. o When everyone has finished, go over the answers. o Have students explain what they did to achieve the answers.

V. Evaluation

 Homework: In your journal write a paragraph explaining how to go from a graph to a linear equation. Then write a paragraph explaining how to go from a linear equation to a graph. Then I would like you to think of an object that has a slope, it can be anything you would like, write a linear equation for the object. VI. Extension

 Draw a roller coaster with several hills in it on the overhead using graph paper  All together go through the roller coaster and figure out the linear equation for each part.

VII. Materials

 Overhead o Graph Paper o Large Graph Paper  Worksheet o Slope-Intercept Form  Student’s journal Slope-Intercept Form

The base pay of a water-delivery person is $210 per week. He also earns 20% commission on any sale he makes. The equation t = 210 + 0.2s relates total earnings t to sales s. Graph the equation.

When the Bryants leave town for a vacation, they put their dog Tyco in a kennel. The kennel charges $15 for a first-day flea bath and $5 per day. The equation t = 15 + 5d relates the total charge t to the number of days d. Graph the equation.

Charles’ Law states that when the pressure is constant, the volume of a gas is directly proportional to the temperature on the Kelvin scale. Write an equation for each situation and solve. If the volume of a gas is 35 ft3 at 290K, what is the volume at 350 K? Student Journal

Name______

Date______

Topic______

______

Response______

______

I. Audience/General

 Algebra I  2-50 minute sessions

II. Concept

 Parallel and Perpendicular Lines

III. Objective

 SWBAT determine whether lines are parallel  SWBAT determine whether lines are perpendicular

 Introductory Activity o Show a road map. o Pick two roads at a time and talk about how they run into each other. o Pick two that are parallel. o What is special about them? o Is there a name for that? Parallel o What other things do we see everyday that are parallel? o Go back to the map and pick out two streets that are perpendicular. o Is there anything special about these two? o What are they called when they have 90-degree angles? Perpendicular o What other things do we see everyday that are perpendicular?

 Developmental Activity o Looking at these parallel and perpendicular lines, are they still linear equations? o Lets first look at two parallel lines. o We know that they run next to each other and never touch by looking at them. o Lets write the equations for two. o Draw two lines on a graph and write the equation of both. o Is there anything significant about the two equations? o They have the same slope o If I wanted to write an equation of a third line that was also parallel, what could it be? o We know the slope, so all we have to do is pick a different y- intercept. o Lets look at two perpendicular lines. o Draw two perpendicular lines on a graph and figure out the equations for both. o Is there anything significant about the two equations? o The slopes are the negative reciprocal o So what would be another linear equation that is perpendicular to equation one? o Answer any questions that the students have over slope, slope- intercept form, parallel, or perpendicular lines. o Have students get into their groups. o Pass out a graph paper to each group. o We are going to drawing blueprints. o Your group will receive a card that tells you what you are to draw. o Your graph most contain all parts stated on the card. o Use a separate piece of graph paper for each part. o All lines must have the equation with it. o Remember parallel and perpendicular tricks. o Any extras you would like to add to the blue prints will be creativity points. o Day 2 o Students should take the first 15 minutes to get everything together. o Groups will take turns presenting the blueprints they created.

 Concluding Activity

o We have talked a lot about using slope within architecture and construction. o However, there are several other occupations that will encounter the use of slope.

V. Evaluation

 Homework: In your journal write about another career choice that would use slope, also add in how they would use slope. It does not have to be the career of your choice it can be anything.

VI. Extension  Talk about what some of the next steps would be in the construction of the blueprint your group designed.  Pointing out other times when mathematics plays a large role in the process.

VII. Materials

 Road Map  Overhead o Graph Paper  Large Graph Paper, four per group  Topic Card, one per group  Colored Pencils  Student’s journal Blueprint Card Topics

1. Design the front layout of your dream house. Your dream house has to have a garage, it can be attached to the house or not. The outline and the door is all that needs to have an equation.

2. You have just started a new company and you want your office building to look great, so you decide to design the front of it yourself. You also want your front desk in a special place so you design your entranceway. (You only need equations for the front of the building)

3. You want to redesign your bedroom and your parents are going to pay for the whole thing. Show what the layout of your new room would be. (You must have the important items, a bed and a dresser, labeled with an equation) 4. You are on a team to design a new roller coaster that will be coming out in two years. Your team needs to come up with five different hill sizes. You will only need to label the up and down hill path with an equation, do not worry about where they meet. (Similar to what we did in class) Put together all of the hills to show what the roller coaster would look like. (Equations are not needed on this section)

5. You are building a bike track. Design five different ramps that will be placed on the track. Show the layout of the track all together, this section does not need equations. Student Journal

Name______

Date______

Topic______

______

Response______

______

I. Audience/General

II. Concept

 Line of Best Fit

III. Objective

 SWBAT write the equation for a line of best fit and use it to make predictions.

 Introductory Activity o Have students get into their groups. o Pass out Score Card worksheets, one for each student. o Give each group a basket with a foam ball in it. o Today we are going to play some basketball.

 Developmental Activity o Students will take turns taking ten shots. o Shots will be made from the same distance every time. o Distance should be about the length of four desks. o Each student will keep track of how many shots they make each time. o Each student should have five turns. o Go ahead and start, remember to fill in all your data. o When students have finished, they should return to their seat. o Pass out graph paper, one for each student. o Students are to create a graph and plot the data they have just gathered. o Place an example on the board. o If you had perfect accuracy with a straight line, however for most of us a straight line will not touch every point. o This is where we use a line of best fit. o Define Line of Best Fit: it is a straight-line draw through data that best represents the trend o Lets go ahead and draw a line of best fit through our data. o Now that we have a straight line, can we come up with a linear equation? o Find the slope. o If our y-intercept is a whole number, what form can we use? o Slope-intercept. o If our y-intercept is not a whole number, what form can we use? o Point-slope. o We have our linear equation. o If I asked you to repeat this five more times, how many would you be likely to make then? o Think back to functions, can we plug 10 into the equation and get an estimated answer?

 Concluding Activity o We used the line of best fit to predict our accuracy in basketball. o What else could you use this for? o Discuss jobs and daily life.

V. Evaluation

 Homework: Complete Scatter Plot worksheet, if the extension is completed then the correlation of the graph should be labeled.

VII. Extension

 Define Positive Correlation: If your line of best fit has a positive slope, which means that the more attempts you have the better you are shooting.  Define Negative Correlation: If your line of best fit has a negative slope, which means that the more attempts you have the worse you are shooting.  Define No Correlation: If your line of best fit has no slope, which means that the more attempts you, have your shooting accuracy never changed.

VIII. Materials

 Worksheet o Score Card o Graph paper, one per student o Scatter Plot  Basket, one per group  Foam Ball, one per group Players Name______

Turn 1 2 3 4 5 Number Baskets Made

Players Name______

Turn 1 2 3 4 5 Number Baskets Made

Players Name______

Turn 1 2 3 4 5 Number Baskets Made Scatter Plots

Name ______Date ______

Create a scatter plot for the following tables using a separate sheet of graph paper.

1. Test Scores Students 1 2 3 4 5 6 7 8 9 Study Time 20 65 30 90 45 30 80 50 35 (min) Test Score 60 85 70 100 88 77 90 82 80

2. Life Expectancy (years) Year 190 191 192 193 194 195 196 197 198 199 of 0 0 0 0 0 0 0 0 0 0 Birth Life 47. 50. 54.1 59. 62. 68. 69. 70. 73. 75. Exp. 3 0 7 9 2 7 8 7 4 (years )

3. Garbage Recycled (pounds per person) Year 1960 1965 1970 1975 1980 1985 1990 Garbage 0.18 .019 .023 0.25 0.35 0.38 0.70 Recycled Post-Assessment of Linear Equations and Graphs

1. Slope 1 2 3 4 5

2. Rate of Change 1 2 3 4 5

3. Slope-Intercept Form 1 2 3 4 5

4. Linear Equation 1 2 3 4 5

5. Y-Intercept 1 2 3 4 5

6. X-Intercept 1 2 3 4 5

7. Standard Form 1 2 3 4 5

8. Point-Slope Form 1 2 3 4 5

9. Parallel Lines 1 2 3 4 5

10. Perpendicular Lines 1 2 3 4 5

11. Reciprocal 1 2 3 4 5

12. Scatter Plots 1 2 3 4 5

13. Line of Best Fit 1 2 3 4 5

14. Correlation 1 2 3 4 5

15. Translations 1 2 3 4 5 Directions: Answers the following questions to the best of your ability. Please show your work.

1. Find the slope between (2, 11) and ( 5, 7).

2. What is the slope of the line y = 4x + 1?

3. Can a horizontal line have a slope?

4. What is the y-intercept of the line y = -2x - 7.

5. Write the following line in slope-intercept form –5x – y = 13 6. Draw two perpendicular lines.

7. Draw two parallel lines.

8. What is the negative reciprocal of -2?

9. Draw a line representing a positive correlation.

10. Translate the graph y  x up 2. References

Algebra 1 Explorations and Applications. Illinois: McDougal Littell Inc., 1997.

Algebridge Constructing Numerical Equations. Janson Publications, Inc., 1990.

Chapter 2 Support File Solving Equations. Massachusetts: Prentice Hall, 2004.

Cord Algebra 1 Mathematics in Context. Michigan: School Zone Publishing Company, 2000.

Glencoe Algebra 1, Integration, Application, Connections. New York: McGraw-Hill, 1997.

Glencoe Algebra 1, Real-World Application Transparencies and Masters. New York: McGraw-Hill.

Kennedy and Thomas. A Tangle of Mathematical Yarns. Vol. 4. 1981.

Math Grade 6. Massachusetts: Prentice Hall, 2004.

Pearson Prentice Hall. 2004. Feb 2004. http://www.phschool.com.

Prentice Hall Algebra Tools For A Changing World. Massachusetts: Prentice Hall, 1998.

Prentice Hall Mathematics Algebra 1. Massachusetts: Pearson Education Inc., 2004.

Prentice Hall Mathematics Hands-On Activities. Massachusetts: Pearson Education Inc., 2004.

Southwestern Algebra 1 An Integrated Approach. Ohio: South-Western Educational Publishing, 1997.

Success Building Masters. Massachusetts: Prentice Hall Inc. p. 44.

Thompson. Hands-On Algebra! Ready-to-Use Games & Activities for Grades 7-12. Jossey-Bass, 1998.