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DSCYF EDUCATION UNIT

K-U-D (Know, Understand, Do) Chart

Grade/Course Algebra 2

Unit Title: Unit 1: Expressions, Equations, and Inequalities

Content Standards:A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Know Understand Do(Note: concepts, facts, formulas, key vocabulary)

Algebraic expressions and equations reflect patterns.

Properties of real numbers

Vocabulary:algebraic expression, numerical expression, constant, variable, mathematical quantity, opposite, additive inverse, multiplicative inverse, reciprocal, evaluate, term, constant term, like terms, coefficient, inverse operations, solution of an equation, literal equation, compound inequality , absolute value

(Big idea, large concept, declarative statement of an enduring understanding)

Real numbers are related in systems and subsets.

(Skills, competencies)

Write expressions to represent patterns in pictures, tables, and graphs

Identify properties of real numbers

Apply the Properties of Equality and Properties of Inequality to solve equations

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Unit Essential Question: How do equations help you solve real-world problems?

Key Learning: Expressions, Equations, and Inequalities

Lesson Essential Question 1 Lesson 1 Vocabulary

1.1 Patterns and Expressions

How can patterns in pictures, tables, and graphs be used to interpret algebraic expressions and equations?

algebraic expression, numerical expression, constant, variable, mathematical quantity


1.2 Properties of Real Numbers

How can properties of real numbers be used to simplify and solve expressions and equations involving real numbers?

opposite, additive inverse, multiplicative inverse, reciprocal


1.3 Algebraic Expressions

How are the properties of equality and inequality applied to solve equations and inequalities?

evaluate, term, constant term, like terms, coefficient


1.4 Solving Equations

What is your plan for solving multi-step problems?

inverse operations, solution of an equation, literal equation


1.5 Solving Inequalities compound inequality



How do you solve an inequality?


1.6 Absolute Value Equations and Inequalities

How is it possible to have two answers for the same problem?

absolute value

extraneous solution

Major Unit Assignment

Name Class DatePrentice Hall Algebra 2 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.74

Chapter 1 Project: Buy the HourBeginning the Chapter ProjectHave you had your first job yet? If so, you were probably paid an hourly wage. Theamount of money you earned for each hour you worked may have been the minimumWage. This amount, set by the U.S. Department of Labor, is the minimum amount forOne hour of work an employer is allowed to pay to employees who meet certain specific criteria. Each state may set its own minimum wage, but where federal and state lawsset different rates, the employer is required to pay the greater of the two amounts to allemployees to whom the conditions of the federal law apply.*

In this project, you will write expressions that model amounts of money earned. You willwrite equations and inequalities to determine the number of hours that must be workedto satisfy certain conditions. You will also research the current federal and state minimumwage laws.

ActivitiesActivity 1: ResearchingResearch the current federal minimum wage. Then find out whether the state inwhich you live has set its own minimum wage. If so, what is that wage?



_______________

Select a state other than the state in which you live. Research the minimum wage for thatstate. You might find it helpful to contact the U.S. Department of Labor and statelabor commissioners, or to use the Internet to find this data. What state did you select? ________What is that state’s minimum wage? ________

Activity 2: ModelingSuppose you earn the minimum wage determined in Activity 1 for the state other than your own.Suppose that next week you plan to work h hours. Write an expression that models theamount of money (M) you will earn. ________________________________________

Suppose that your friend earns the same hourly wage that you earn, but worksin a job for which he receives tips. Write an expression that models yourfriend’s total earnings for a week during which he works n hours and receives$15 in tips. ____________________________________________Then, evaluate the expression for n = 10 and explain what this number means. ______________________________ explanation: _______________________________________________________________________

Write an expression that models the sum of your earnings for 3 weeks and your friend’searnings for 2 weeks if you each work r hours per week and your friend receives $15 intips per week. Simplify the expression. ________________________________________________

Write an expression that models the difference between your earningsand your friend’s earnings for a week during which you work h hours, yourfriend works n hours, and your friend earns t dollars in tips. (Hint: Be sure toconsider the fact that you do not know who earns more money!) ___________________________*Source: http://www.dol.gov/dol/topic/wages/minimumwage.htm

Activity 3: SolvingRound numbers of hours to the nearest tenth if necessary.Suppose that last week your employer gave you a $.50/h raise and a $20bonus as a reward for good work. You earned a total of $80 for the week. Letx represent the number of hours you worked that week. Write an equation tomodel this situation. Then solve your equation and explain the meaning ofyour solution.

Equation:______________________________________________Solution: ________________________Explanation: _____________________________________________



Suppose your friend (still earning minimum wage) receives $20 in tips, and that you(earning $.50/h more than your friend) have earned the same amount of money at theend of a week during which you worked the same number of hours as your friend. Writean equation to model this situation. Then solve your equation and explain the meaningof your solution.

Equation:______________________________________________Solution: ________________________Explanation: _____________________________________________

Suppose that your friend wants to earn at least $95 next week and he expectsto earn $15 in tips. Write an inequality that models this situation. Then solveand graph your inequality. Explain the meaning of your solution.

Inequality: ________________________________________Solution: ________________________Explanation: _____________________________________________Graph:

Finishing the ProjectThe answers to the activities should help you to complete your project. Youshould prepare a presentation for the class describing your results. Yourpresentation should include the data you researched; the expressions, equations,and inequality you used to model the given situations; and the graph of yourinequality.

Reflect and ReviseAsk a classmate to review your project. After you have reviewed each other’spresentations, decide if your work is clear, complete, and convincing. If needed,make changes to improve your presentation.

Extending the ProjectResearch the minimum wages set by other states. If they differ from the minimumwage of your state, determine possible factors that might contribute to thedifferences. Find out what conditions might exist that would allow an employer topay an employee less than the federal minimum wage.

Name Class DatePrentice Hall Algebra 2 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.76Chapter 1 Project Manager: Buy the HourGetting StartedRead the project. As you work on the project, you will need a calculator andmaterials on which you can record your results and make calculations. Keep all of



your work for the project in a folder.Checklist Suggestions☐ Activity 1: researching minimum wages ☐ Select a state in which you are interested.

☐ Activity 2: writing algebraic expressions ☐ Substitute reasonable values for the variables to determine if the expressions make sense.

☐ Activity 3: writing and solving equations ☐ Check that your answers are reasonable.

and inequalities

☐ algebraic models ☐ Have you defined the variables in your expressions, equations, and inequality? How does the graph of an equation differ from the graph of an inequality? What does this mean in terms of your solution?

Student Scoring Rubric4 The expressions, the equations, and the inequality are correct. The graph andall calculations are accurate. Explanations are thorough and well thoughtout. The presentation is clear and complete.

3 The expressions, the equations, and the inequality have minor errors. Thegraph and calculations are mostly correct. The explanations and presentationlack detail or contain small errors.

2 The expressions, the equations, and the inequality have major errors.The graph and calculations contain minor errors. The explanation andpresentation contain minor inaccuracies.

1 The expressions, the equations, and the inequality are not correct. The graphis not accurate. Calculations contain major errors or are incomplete. Theexplanations and presentation are inaccurate or incomplete.

0 Major elements of the project are incomplete or missing.

Teacher’s Evaluation of the Project

Chapter Project Rubric

Student Name: ____________________________________________________

CATEGORY3 2 1 0

Developing persevered to completed most needed key hints needed extensive



Autonomy- The student

complete the project without help

of the problem without help

to solve the problem

guidance to work the problem

The Solution Process – The students work

showed

a complete and appropriate solution process

an appropriate solution process that is almost complete

an appropriate process that is partially complete

an inappropriate process or no evidence of a process

The Conclusion/Answer

– The student’s answer is an

accurate conclusion, supported by valid evidence and reasons, appropriate to this problem and context

inaccurate but logical conclusion, supported by evidence and reasoning but incorrect due to minor factual error (in details of problem, in computation, recall of formula, etc.) or minor mistake in reasoning

inaccurate but logical conclusion that overlooks or gets wrong significant (about the problem, the rule, computation, etc.).

inappropriate conclusion, not supported by facts and logic, or there is no conclusion

Student Assessments(How students will indicate learning and understanding of the concepts in the unit.

Note: Can have multiple assessments, one on each page.)

Unit Topic:

TitlePerformance Task

Description Performance Task 1:Your Basil Metabolic Rate (BMR) is the measure of how many calories you burn if you rest all day. Physicians and other health professionals use this rate as an important tool for determining a person’s daily caloric needs. The Harris-Benedict Formula is commonly used to calculate BMR for an individual.

The formulas are slightly different for males and females. A female’s



BMR can be expressed as 655 more than the sum of 4.35 times her weight (lb.) and 4.7 times her height (in.) and then less 4.7 times her age (years). The formula for a male is 66 more than 6.23 times his weight (lb.) plus the product of 12.7 and his height (in.) minus 6.8 times is age (years).

a. Use w = weight, h = height, and a= age to write the formula for the BMR of a female and the formula for the BMR of a male. Female BMR = __________________________ Male BMR = __________________________

b. Calculate your BMR. ______ What does that tell you? ____________________________________________c. Look at each term of the formula. Make a conjecture about what happens to you BMR as you get older, and why. _____________________________________________________________________________________________________________

d. Which term of the expression affects the BMR the most? Explain.__________________________________________________________________________________________________________

e. What is the weight of a 16 year-old male with a BMR of 2600 and a height of 5 feet 10 inches? Show or explain your work. _______ _______________________________________________________________________________________________________________________________________________________________

Performance Task 2:

Find all possible values of a and b in the figures, given the following conditions: * figure I is a rectangle with sides length a and width b, * figure 2 is an isosceles triangle with 2 congruent sides 2a and the

base b, * the perimeters of the two figures are equal * the rectangle has an area between 80 and 100 square units, * the values of a and b are integers.Drawn the figures.

Show your work

Time (In Days) 2Differentiation

You may choose to assign one problem to some students rather than both. You may want to provide pictures of the figures in Task 2. You may want to allow students to work with a partner or a group. Some



students may need assistance setting up the formulas in Task 1.

Revise/Review

Resources & Materials Paper, calculator, ruler, folder for keeping materials together,

internet for researching Task 1

Performance Task Rubric

Student Name: ____________________________________________________

CATEGORY 3 2 1 0Developing

Autonomy- The student

persevered to complete the project without help

completed most of the problem without help

needed key hints to solve the problem

needed extensive guidance to work the problem

The Solution Process – The students work

showed

a complete and appropriate solution process

an appropriate solution process that is almost complete

an appropriate process that is partially complete

an inappropriate process or no evidence of a process

The Conclusion/Answer

– The student’s answer is an

accurate conclusion, supported by valid evidence and reasons, appropriate to this problem and context

inaccurate but logical conclusion, supported by evidence and reasoning but incorrect due to minor factual error (in details of problem, in computation, recall of formula, etc.) or minor mistake in reasoning

inaccurate but logical conclusion that overlooks or gets wrong significant (about the problem, the rule, computation, etc.).

inappropriate conclusion, not supported by facts and logic, or there is no conclusion

Research: Performance Task (Essay) Students’ Names: ________________________________________

CATEGORY 5-4 3 2 1



Quality of Information (Double weighting)

Information clearly relates to the main topic and answers the question. It includes salient examples, lucid analysis and clear links to the question.

Information relates to the main topic and answers the question. It includes some salient examples, analysis and links to the question.

Information has a tenuous link to the main topic.Some details and/or examples are given, but might be irrelevant to the question.

Information has little or nothing to do with the main topic.

Organization (Half weighting)

Information is very organized with well-constructed paragraphs and very clear main points.

Information is organized with well-constructed paragraphs and clear main point.

Information is organized, but paragraphs are not well-constructed, and the main point is unclear.

The information appears to be disorganized.

Introduction The introduction consists of a very good argument, and outlines briefly the factors to be examined, and is very consistent with the essay.

The introduction consists of a good argument, and outlines briefly the factors to be examined, and is consistent with the essay.

The introduction consists of a rather weak argument, and outlines briefly the factors to be examined, but is not very consistent with the essay.

The introduction does not have an argument, and does not outline the factors to be examined.

Conclusion The conclusion deals fully with the requirements of the question, and is very consistent with the essay.

The conclusion deals with the requirements of the question, and is consistent with the essay.

The conclusion deals partially with the requirements of the question, but is not very consistent with the essay.

The conclusion does not deal with the requirements of the question, and is not consistent with the essay.

Mechanics (Half weighting)

No grammatical, spelling or punctuation errors.

Almost no grammatical, spelling or punctuation errors

A few grammatical, spelling, or punctuation errors.

Many grammatical, spelling, or punctuation errors.

Sources All sources (information and graphics) are accurately documented in the desired format.

All sources (information and graphics) are accurately documented, but a few are not in the desired format.

All sources (information and graphics) are accurately documented, but many are not in the desired format.

Some sources are not accurately documented.

Total marks: _________/ 30 Learning Goals for this Lesson: 1.1 Patterns and ExpressionsUse patterns in pictures, tables, and graphs to interpret algebraic expressions and equations

Standards: Reviews A.SSE.3 Choose and produce an equivalent form of an expression to reveal and



explain properties of the quantity represented by the expression.

Students Will KnowHow to use patterns in pictures, tables, and graphs to interpret algebraic expressions and equations

Students Will Be Able To:Use patterns in pictures, tables, and graphs to interpret algebraic expressions and equations

Lesson Essential Question: How can patterns in pictures, tables, and graphs be used to interpret algebraic expressions and equations?

Activating Strategy: Getting Ready! P.4 You are playing a video game. You reach a locked gate. The lock is a square with nine sections. You can make a key by placing a red or yellow block in each section. Near the gate is a carving of a pattern of squares. (All Getting Ready problems are available on the textbook website)

Key vocabulary to preview and vocabulary strategy: STRATEGYalgebraic expression, numerical expression, constant, variable, mathematical quantity

Lesson InstructionLearning Activity 1: Work through Problem 1on p.4 with the students. You may prompt them to see how the number of sides is changing from one figure to the next. The next figure would have to have 7 sides (aka heptagon).

Assessment Prompt for Learning Activity 1: Got It? P.4 Look at the figures from left to right. What is the pattern? Draw the next figure in the pattern. Turn to your shoulder partner and compare. Explain how you figured it out.

Graphic Organizer Table for Learning Activity 2 Table for Learning Activity 3

Learning Activity 2: Read through the paragraph at the top of p.5. Write the key concepts on the board with the definitions. Ask students for examples of each. Have them write the examples in the notebooks.

Explain to students that tables are an effective way to organize data and discover patterns. They work much like an “input/output” machine. Adding a process column to the middle allows you to “see” what is happening inside the machine.

Work through the toothpick problem, Problem 2 on p. 5. Create a table to correspond with the information provided. Ask the students to identify what is happening inside the machine. Use this information to determine how many toothpicks will be in the 20th figure. Then, write an expression to describe how many toothpicks will be in the nth figure.

Assessment Prompt for Learning Activity 2: Got It? P.5. How many tiles will be in the 25th figure in this pattern (it begins with four and adds two each time). Have students make a table to represent this data, with a process column. Tell students, “Share with your partner to review your tables. Raise

Assignment:p.8 #9-23 odd and 25-35



your hands if they are the same.” Ask if anyone can give the mathematical expression to describe the process.

Learning Activity 3: Work through Problem 3 with the students. Aquarium You want to set up an aquarium and need to determine what size tank to buy. The graph shows tank sizes using a rule that relates capacity of the tank to the combined lengths of the fish it can hold.

If you want five 2 inch platys, four 1 inch guppies, and a 3 inch loach. Which is the smallest tank you can buy: 15-gallon, 20-gallon, or 25-gallon? Use a table to find the answer, with a process column. Walk the students through the process in the middle of page 6 demonstrating how to find the solution.

Assessment Prompt for Learning Activity 3: Got It? p.6 3. The graph shows the total cost of platys at the aquarium shop. Use a table to answer the questions. A. How much do 6 platys cost? B. How much do 10 platys cost? C. Why is the graph in problem 3 a line while this graph is a set of points? Compare your answer with your partner’s.________________________________________________________________

Have the students work in pairs to complete the Lesson Check on page 7. After 10 minutes, call on students at random to describe a rule for each pattern.

Give each pair of students a few Post-It notes to records their responses to items 8 through 15. Have the students post their responses on the board for you to check quickly.

Summarizing Strategy: Exit Slip: Have the students record answers to items 36 and 37 on p.9.

Learning Goals for this Lesson: 1.2 Properties of real Numbers

Order real numbers.Identify and use properties of real numbers

Standards: Reviews N.RN.3 Explain why sums and products of rational numbers are rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.

Students Will Know:

The set of real numbers has special subsets.

Students Will Be Able To:Order real numbers.Identify and use properties of real numbers



Properties of numbers are relationships that are true for all real numbers, except for zero, in one case.

Lesson Essential Question: How can properties of real numbers be used to simplify and solve expressions and equations involving real numbers?

Activating Strategy: Getting Ready p.11 You use emoticons in text messages to help you communicate. Six emoticons are shown on p.11. How can a set be described that includes five of them, but not the 6 th?

Key vocabulary to preview and vocabulary strategy: Have students work with a partner to create a definition and example for each of the vocabulary terms listed below. Monitor students as they work. Then ask some of them to share their work with the class.

opposite, additive inverse, multiplicative inverse, reciprocal

Lesson Instruction: Remind students that the set of numbers has several special subsets of numbers related in particular ways.

Learning Activity 1: Show the students the diagram on the top of p.12 to describe the subsets of real numbers. Distribute the graphic organizer on Real Numbers to the students. Allow them to write the definition of each subset . Ask the students to work with a partner to write another 2 examples for each subset. Allow each pair of students to place one of their examples on the large picture on the board. Make sure to discuss that each example belongs not only to its subset but all those below it as well.

Work with Problem 1 with the students to answer the multiple choice question: Your school is sponsoring a charity race. Which set of numbers does not contain the number of people p who participate in the race?

a. natural numbers c. rational numbersb. integers d. irrational numbers

Assessment Prompt for Learning Activity 1: Got It p.12 In problem 1, if each participant made a donation of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised?



Learning Activity 2: Draw a number line on the board with integers from negative 3 to positive 3. Have the students place the numbers -5/2, √2, and 2.66666…

Assessment Prompt for Learning Activity 2: Have the students add the numbers √3, -1.4444, and 1/3 to the number line. Compare your answers with your shoulder partner.

Assignment: p.15 #10-40, 42-48 even, 58-66 even

Learning Activity 3: Ordering Real Numbers, when comparing two numbers greater than, or less than signs are more useful than a number line. To compare √17 and 3.8 it is helpful to use the perfect square closest to 17…16 Walk the students through the fact that √16 = 4 and since 17 is larger than 16. Therefore, √17 must be larger than 4 and thus larger than 3.8. So, 3.8 < √17

Assessment Prompt for Learning Activity 3: Have the students complete Got It on p.13 to compare √26 and 6.25 using < or >. Then, if a< b and b < c, compare a and c using < or >. Thumbs up if a is bigger. Thumbs up if c is bigger. (If all agree, have students explain to their neighbor how they knew.) (If there is a mixture of responses, ask for student explanations.)

--------------------------------------------------------------------------------------------------------Learning Activity 4: Review the vocabulary at the top of p. 14: opposite or additive inverse of a number is –a. The sum of a number and its opposite is zero. The reciprocal or multiplicative inverse of a non-zero number is 1/a; the product of them is 1.

Have the students complete the foldable as shown to write the properties of real numbers the definitions and examples.

Ask the students to identify which property is illustrated by each of the following examples:

a. (-2/3) (-3/2) = 1b. ( 3 x 4 ) x 5 = ( 4 x 3 ) x 5

http://mathequalslove.blogspot.com/2012/08/algebra-2-week-1-inb-pictures.html



Assessment Prompt for Learning Activity 4: Got It? p.14 Have the students use the foldable to determine which property is illustrated by the equation 3 ( g + h ) + 2g = ( 3g + 3h ) + 2g. What property of real numbers allows us to justify that a + [ 3 + (-a)] = 3 Tell your neighbor your answer.

Summarizing Strategy: Exit Slip: There are grouping symbols in the equation ( 5 + w ) + 8 = ( w + 5 ) + 8 but it does not illustrate the Associative Property of Addition. How is it different? What property is illustrated?

Learning Goals for this Lesson: 1.3 Algebraic ExpressionsSolve equations and simplify expressions using properties of equality.

Standards: Reviews A.SSE.1.a Interpret parts of an expression such as terms, factors, and coefficients.

Students Will KnowHow the properties of equalities are applied to solve equations.

Students Will Be Able ToSolve equations and simplify expressions using properties of equality.

Lesson Essential Question: How are the properties of equality and inequality applied to solve equations and inequalities?

Activating Strategy: Getting Readyp.18 Work the following problem with the class. During summer vacation, you work two jobs. You walk three dogs several times a week, and you work part-time as a receptionist at a hair studio. You earn $8 per hour as a receptionist and $20 per week per dog. Your weekly schedule (shown in the chart below) is the same each week. How much will you earn in 10 weeks? Explain.

Monday Tuesday Wednesday Thursday Friday SaturdayWalk dogs 8-9am

Studio 1-5pm Studio 1-5pm

Walk dogs 8-9am

Studio 1-5pm Studio 1-5pm

Walk dogs 8-9am

Studio Noon-4pm

Key vocabulary to preview and vocabulary strategy: STRATEGY

evaluate, term, constant term, like terms, coefficient

Lesson Instruction

Learning Activity 1: Lead the students through Problem 1, p.18, Which algebraic expression models the word phrase “seven fewer than a number t?” Ask the students what operation is usually represented by the word “fewer.”

Graphic Organizer



The choices are: a) t+7 b) -7t c) t-7 d) 7-t Seven fewer than suggests subtraction. Begin with the number t and subtract 7. Therefore the correct response is “c,” t-7.

To model a situation with an algebraic expression, do the following:

Identify the actions that suggest operations. Define one or more variables to represent the unknown(s) Represent the actions using the variables and the operations.

Allow the students to create a foldable brainstorming of all the words they can think of they signify mathematical operations. Allow them 5 minutes to work in a group of 3 or 4 then ask for volunteers to read a word of his/her paper. The other students are to put a check on their paper if they have the same word. If they do not have the word they should add it to their paper. Continue until all words have been read, and all students have a good list of words. You may need to prompt some of them… quotient….

Assessment Prompt for Learning Activity 1: Got It? P.18 Which algebraic expression models the word phrase “two times the sum of a and b.” The choices are: f) a+b g) 2a+b h) 2 (a+b) i) a+2b Shout out your answer on the count of three… 1,2, 3 Discuss results… If necessary have students explain what each of the expressions means in words.

Addition Subtraction

Multiplication Division

Activity 5:

Fold paper in four columns or create chart as attached to plan to have columns for property, shown w/symbol, example with numbers, and description in words

Learning Activity 2: Guide the students through Problem 2 on p.19 You start with $20 and save $6 each week. What algebraic expression models the total amount you save? (You may want to ask what this would look like on a graph… starts at 20, positive y-intercept, and goes up by 6 each week, positive slope, linear, constant rate of change)

Assessment Prompt for Learning Activity 2: Got It? p.19 You had $150, but you are spending $2 each day. What algebraic expression models this situation? Compare your response with your partner’s. Raise your hands if they are the same.

Assignment:

p. 22 # 11 – 37, 39 - 60

Learning Activity 3: Guide the students through Problem 3 A and B on p. 19 to evaluate the algebraic expressions by substituting in the given value for each variable. Remind the students of PEMDAS (the order of operations).

Assessment Prompt for Learning Activity 3: Got It? p.19 Have the students compute the value of the expression 2¿¿ if x=6 and y= -3. Will the value of the expression change if the parentheses are removed? Explain to your partner.



________________________________________________________________

Learning Activity 4: Guide the students through writing the algebraic expression to determine the total number of points a football teams scored with 3 touchdowns (6pts. Each), 2 extra point kicks (1 point each), and 4 field goals (3 pts. each)? Follow the plan on p. 20 to emphasize the Know Need and Plan for solving problems. Remind the students that they will encounter problems that are more challenging and must be prepared to write down the problem and steps.

Assessment Prompt for Learning Activity 4: In basketball, teams can score by making 2 point shots, three point shots, or 1 point free throws. What algebraic expression models the total number of points a team scores in a game? If a team makes 10 2 point shots, 5 three point shots, and 7 free throws, how many points does in score in all? Write your answer on a post-it and pass it to your left. If the answer is correct, post it on the board.--------------------------------------------------------------------------------------------------------Learning Activity 5: Have the students identify the following from the expression: -4ax + 7w – 6: terms, coefficients, constant terms, and like terms

Remind them from algebra 1 what it means to “combine like terms”!

Have the students work with a partner to complete the table for Learning Activity 5 (attached at the end of this packet, or make a foldable) to write the list of properties listed on p. 21 with the symbols, examples, and words for each.

Utilizing the properties, work through problems 5A & B on p. 21 with the students

A. 7x2 + 3y2+ 2y2 - 4x2

B. –(3k + m) + 2(k – 4m)

Assessment Prompt for Learning Activity 5: Have the students complete Got it? on p. 21 Combine like terms. What is a simpler form of each expression? -4 j2- 7k + 5j + j2 b. –(8a + 3b) + 10(2a -5b)

Summarizing Strategy: Exit Quiz… You have a summer job detailing cars. You charge $5 to wash a car, $25 to wax a car, and $2 to vacuum a car.

1. What algebraic expression models the amount you can earn? 2. If you wash 8 cars, wax 2 cars, and vacuum 6 cars, how much money will you earn in all?



Learning Goals for this Lesson: 1.4 Solving Equations Standards: A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Students Will Know

Properties of numbers and equality can be used to solve an equation by finding increasingly simpler equations that have the same solution as the original equation.

Important properties of equality include reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication and division.

Students Will Be Able To: Solve equations in one step, multi-step, identity, and no solution

Lesson Essential Question: What is your plan for solving multi-step problems?

Activating Strategy:

Key vocabulary to preview and vocabulary strategy

inverse operations, solution of an equation, literal equation

Lesson Instruction

Learning Activity 1

Review the vocabulary word: equation

Review the EQ and the Essential Understanding

Give students the Cornell Notes page and have them record the following information for the Properties of Equality.

Graphic Organizer:Graphic Organizer: Word Problem Organizer

http://img.docstoccdn.com/ thumb/orig/20485139.png

Or (see attached at the end of the unit: Solving Word Problems

http://img.docstoccdn.com/thumb/orig/20485139.png

http://img.docstoccdn.com/thumb/orig/20485139.png

http://www.ebstc.org/TechLit/notes/cornellbasic.jpg



Assessment Prompt for Learning Activity 1 - Solving for a variable, using the properties we learned:

In your Collaborative Pairs, 1’s and 2’s: Think Ink Share

1’s solve: 12b = 18

Graphic Organizer) Or http://jackiemurphy21.files.wordpress.com/2013/02/solve.jpg

http://jackiemurphy21.files.wordpress.com/2013/02/solve.jpg

http://jackiemurphy21.files.wordpress.com/2013/02/solve.jpg



Work should be similar to this:

12b=18

12b/12= 18/12

b= 1 ½ or 1.5

2’s solve: -3a=-15

Work should be similar to this:

-3a = -15

-3a/-3 = -15/-3

a= 5

After you have students share the answers, have them discuss which properties were used to figure out the answer. Share answers with the larger group.

Learning Activity 2

Show students this problem, in their Pairs.

Have students explain to their partner how you solve an equation with the variable on both sides of the equal sign. Share answers and show students the remainder of the problem’s solution. Ask students why they think you have to put the variable on one side.

Do activity sheet attached at the end of the unit (marked Lesson

Assignment



1.4)

Assessment Prompt for Learning Activity 2

The Got it problem #3 (see the Activity Sheet marked Lesson 1.4)

They will also need another copy of the Graphic Organizer for Problem Solving.

Learning Activity 3

Have students take notes:

Try this problem in Collaborative Pairs:


With a Partner, solve this problem:

The first half of a play is 35 minutes longer than the second half of the play. If the entire play is 155 minutes long, how long is the first half of the play? Write an equation to solve the problem.

Summarizing Strategy: : Exit Ticket



Independently, solve these problems on a sheet of lined paper. This is your ticket out the door.

Part 1: Make a plan and solve this problem.

The length of a rectangle is 3cm greater than its width. The perimeter is 24cm. What are the dimensions of the rectangle?

(Answer: width= 4.5cm, length = 7.5cm)

Part 2: Find and explain the error(s) in the steps shown:

Error Analysis

12x +10=-2

12x = 8

X= 8/12 or 2/3

(Answer: the second line is incorrect, subtract 10 from each side)

Learning Goals for this Lesson: 1.5 Solving Inequalities Standards: A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Students Will Know

Just as properties of equality can be used to solve equations, properties of inequality and be used to solve inequalities.

Properties of numbers and inequality can be used to solve an inequality by finding increasingly simpler inequalities that have the same solution as the original inequality.

Students Will Be Able To

Create equations and inequalities in one

variable and use them to solve problems.

Lesson Essential Question: How do you solve an inequality?


Here are the number line graphs of two different inequalities.



Compare and contrast the two inequalities and graphs that are shown above.

Similarities Differences


Frayer

compound inequality

Compound inequalities are two inequalities joined by the word and or by the word or. Inequalities joined by the word and

are called conjunctions. Inequalities joined by the word or are disjunctions. You can represent compound inequalities using

words, symbols or graphs.

Lesson Instruction

Learning Activity 1

Interactive Learning: Solve It!

Question: You want to download some new songs on your MP3 player. Each song will use about 4.3 MB of space. The amount of storage space on your MP3 is shown at the right. At most how many songs can you download? Explain. (Hint: 1 GB=1000MB)

Purpose: To distinguish between situations that involve equations and those that involve inequalities

Process: Students may

Multiply 7.8 by 1000 to find the number of available

Words like “at most” and “at least” suggest a relationship in which two

Graphic Organizer

Frayer Vocab. (see attached templates)Compound Inequality

Compare and Contrast Chart (Activating Strategy)



quantities may not be equal. You can represent such a relationship with a

ESSENTIAL UNDERSTANDING: Just as you use properties of equations, you can use properties of inequality to solve inequalities.

Cornell Notes see Templates






Using collaborative pairs, solve this problem to check your understanding.

What is the solution of -2(x+9) +5 ≥ 3? Graph the solution.

Learning Activity 2

Assignment




Compare and Contrast the two plans

Plan 1 Plan 2



Learning Activity 3


Summarizing Strategy

Learning Goals for this Lesson: 1.6 Absolute Value Equations and Inequalities Standards: A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Students Will Know

Absolute value is nonnegative

Opposites have the same absolute value, so an absolute value equation can have two solutions

Students Will Be Able To

Solve and write equations and inequalities involving absolute value

Lesson Essential Question: How is it possible to have two answers for the same problem?


Introduce Absolute Value with this song/video (36 sec.)

https://www.youtube.com/watch?v=gT-Be1OE5Ug&feature=player_embedded

https://www.youtube.com/watch?v=gT-Be1OE5Ug&feature=player_embedded



Complete a Frayer model, teacher guiding the process

(see attached template)


absolute value

extraneous solution

Lesson Instruction

Learning Activity 1

Lead the students through the Solve It! problem at the beginning of the lesson. http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=scoViewer&internalId=131112100000200&isHtml5Sco=false&fromTab=DONETAB

You are riding in an elevator and decide to find out how far it travels in 10 min. You start on the third floor and record each trip in a table. Each floor is 12ft high. How far did the elevator travel in all? Justify your answer.

Allow students to discuss the problem and how they think the question can be solved. Let them work together to try and solve it. Allow sharing of the answers. Then, reveal the answer.

Then work on Problem 1 together using this resource:

http://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=scoViewer&internalId=131112100000201&isHtml5Sco=false&fromTab=DONETAB

Have partners look at the problem and see if they can figure out how to solve it.

Go over it together.


(TE pg 42 Got It #1)

In your math notebook, record the following problem. Solve the problem.

Graphic Organizer

Frayer (see attached templates)









Then hold your hand up so I can check your answer.

What is the solution of 2 │x+9│+3 = 7? Graph the solution

Learning Activity 2

Put the following problems on pieces of paper and allow pairs of students to draw one. Have them solve it and share the answers with the class (using the Smart Board, doc. Camera, or white board.) Have students include the Answer Check by substituting the answer in place of the variable.

1. 2. 3.

4. 5. 6.

Note Taking:

The distance on the number line cannot be negative. Therefore, some absolute value equations, such as │x│=-5, have no solution. It is important to check the possible solutions of an absolute value equation. One or more of the possible solutions may be extraneous.

An extraneous solution is a solution derived from an original equation that is not a solution pf the original equation.

Problem 3 (TE pg43) Checking for extraneous solutions

What is the solution of │3x+2│= 4x+5? Check for extraneous solutions.

Step 1: Rewrite the problem as two equations. And solve each equation.

3x+2=4x+5 or 3x+2=1(4x-5)

-x=3 x=-1

Check your answer by substituting the answer.

Since x=-3 does not satisfy the original equation, -3 in an extraneous solution, The only solution to the equation is x=-1.

Assignment

Complete this lesson review: (with a partner)

Complete this worksheet https://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-318813-2-01/media/HSM12CC_A2/Chapter_1/HSM12CC_A2_01_06_CM.pdf

3 6 7 14x 3 2 1 21d

https://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-318813-2-01/media/HSM12CC_A2/Chapter_1/HSM12CC_A2_01_06_CM.pdf






With a partner, solve this problem and Check for extraneous solutions.

Make sure you students use the Opposite of a Sum Property when simplying.

(TE pg 43 Got It?)

What is the solution of │5x-2│=7x+14? Check for extraneous solutions.

Learning Activity 3

Take Notes: Inequality

The solutions of the absolute value inequality │x│<5 include values greater than -5 and less than 5.

This is the compound inequality x>-5 and x<5, which you can write as -5 <x <5. So, │x│ < 5 means x is between -5 and 5.

(Draw a number line to graph -5 to 5)

You can write an absolute value inequality as a compound inequality without value symbols.

(Problem 4 TE pg 43)

Solving the Absolute Value Inequality │A│<b

What is the solution of │2x-1│<5? Graph the solution.

Plan out and discuss the problem together:

Is this an “and” problem or an “or” problem? Why?

2x-1 is less than 5 and greater than -5. It is an “and” problem.

│2x - 1│<5

-5 < 2x – 1 < 5

-4 <2x <6

-2 <x <3



Take Notes: Concept Summary Use the Smart Board, white board, or projector to show students this table and have them copy it into their notes.

Symbols Definition Graphing│x│= a The distance from x to

0 is a units.Draw number line to demonstrate

│x│< a {│x│≤ a} The distance from x to 0 is less than a units.

Draw number line to demonstrate

│x│ >a {│x│≥ a} The distance from x to 0 is greater than a units.

Draw number line to demonstrate


With a partner find the solution and graph it:

│3x-4│ ≤ 8? Graph the solution.

Summarizing Strategy

Ticket Out the Door:

Explain what it means for a solution of an equation to be extraneous.



Cornell Notes templates





http://mathequalslove.blogspot.com/2012/08/algebra-2-week-1-inb-pictures.html



Lesson 1.6

Definition Picture to represent the word

Examples Non-Examples

Absolute Value


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