Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #1 Algebraic FoundationsCourse: Algebra 1 – [2011-2012 yr] Anticipated timeframe: Days 10

Desired OutcomesStandards addressed: A-CED 1 create equations and inequalities in one variable and use them to solve problems A-CED 2 create equations in two or more variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales A-CED 3 represent constraints by equations or inequalities and by systems of equations and/or inequalities and

interpret solutions as viable or non-viable options in a modeling contex A-REI 10 understand that the graph of an equation in two variables is the set of all its solutions plotted in the

coordinate plane A-REI 12 graph the solutions of a linear inequality in 2 variables as a half-plane A-SSE 1a interpret parts of an expression, such as terms , factors & coefficients N-RN 3 explain why the sum or product of two rational numbers is rational; that the sum of a rational number

and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational

Transfer Goals: Apply order of operations to simplify and solve problems Recognize, describe and apply properties of real numbers to simplify problems Perform numeric operations involving real-life problems

Enduring Understandings: Fluency and flexibility in the algorithms and

properties that rule numeric operations are essential for accurate computations (necessary for problem solving)

Patterns can be used to make predictions of future behavior

Exponents are just short-hand for multiplication

Essential Questions: How can you represent quantities, patterns and

relationships?

How are properties related to Algebra?

Learners will know: Variables & expressions Order of operations (PEMDAS) What defines a rational number “Density of rational numbers” Properties of real numbers: commutative +/*,

associative+,distributive mult. over +, identity +/*,Inverse +/*

“Fundamental theorem of arithmetic”-all positive integers are prime or a product of prime numbers

Patterns, graphs Equations

Learners will be able to: Transform rational numbers from one form to

another Simplify expressions using exponents Apply order of operations to simplify expressions Write algebraic expressions Classify, graph and compare real numbers(order real

numbers) Find and estimate square roots Identify and use properties of real numbers Find sums and differences of real numbers(adding

signed #’s) Find products and quotients of real numbers (*/÷

signed #’s) Apply the distributive property (use for mental math) Solve equations using: mental math, tables,

substitution Use tables, graphs and equations to describe

relationshipsAssessment Evidence

Performance Tasks: Class quizzes (including graphing calculator

Other Evidence: Class Discussions

assessment) Class work Dynamic Activity Authentic Assessment “Pull it together” p. 67 Unit test

Group work Homework Technology integration (Math XL practice); ALEKS

Authentic Assessment: p. 67 Text #1 – you are a riding stable manager, write an expression for cost of feeding horses#3 you are purchasing gifts for 10 people . Each person gets a CD or DVD. Write an expression for number of DVD’s bought. Write expression for cost of CD’s & cost of DVD’s. Write an expression for total cost.

VOCAB: absolute value, additive inverse, algebraic inverse, algebraic expression, base, coefficient, constant, counterexample, deductive reasoning, distributive property, element of a set, equation, equivalent expressions, evaluate, exponent, inductive reasoning, inequality, integer, irrational number, like terms, multiplicative inverse, natural number, numerical expression, open sentence, opposite, order of operations, perfect square, power, quantity, radical, radicand, rational number, real number, reciprocal, set, simplify, solution of an equation, square root, subset, term, variable, whole number

Learning PlanAnticipated daily sequence of activities:

Day 1 Game “Rules of Play” & diagnostic p. 1 text & p. 799-803 Skills handbook Day 2 Variables & Expressions/ order of operations p. 2-15 text ** [step pneumonic device for order of

op’s] Day 3 Ordering real numbers; Estimating square roots p. 16-22 text **[string taped around room, sticky

notes with square roots given to students to place between integers from 1 to 15] Day 4 Properties of real numbers & mid-chpt. Quiz p. 23-29 text Day 5 Adding and subtracting real numbers p. 30-37 text **[Card activity: red cards represent negative

#’s, black cards represent positive numbers, played in pairs, each student turns over a card and then sum the 2 cards. Same color, add the values, different colors= subtract lower number from higher (abs. value)] **[construction paper number lines, use bingo chips or pennies to jump rt for positive values, left for negative values. Always start each turn at zero. (teacher creates problems ex: -2 + 5 = )]

Day 6 Multiplying and dividing real numbers p. 38-45 text **[ students copy chart ++ = + - - = + 2 same signs multiplied always equal a positive. - + = - + - = - 2 different signs multiplied always equal a negative]

Day 7 Distributive Property p. 46-52 text **[ Algebra Tile activity to demonstrate distribution-kids work in pairs] **[ teacher makes cut out shapes of apples, bananas, carrots and uses play dollars to represent constants. Shapes are attached to magnet to allow for demonstration of distribution on a white board . EX: 3 ( 2a + 1) means you have 3 piles with 2 apples and 1 dollar in each pile. Have student draw a horizontal line for each pile, then place the correct # objects and dollars in each pile, then tally total objects (variable) & total constants. Good activity for ELL- can also be done on desktops with no need for magnets, can use rulers to be each pile)

Day 8 Solving Equations: mental math, using tables, writing simple equations, estimation p. 53-59 text **[can use “hands on equations”kit- but stress mental math vs. inverse operations at this point] Day 9 Patterns, equations & graphs(use patterns to make predictions) & Review for Unit 1 test p. 60-76 text **[Number cube game p. 60 text – also good for traditional ed students] Day 10 Unit 1 test; authentic assessment p. 67 text; Unit 2 readiness diagnostic p. 77 text

** [ ] - denotes suggested activities for Spec needs students as well as ELL students. Activities will be more tactile and visual to aid in comprehension. These activities & suggestions are also applicable to traditional ed. Students.Anticipated resources:

TEXT – PEARSON ALGEBRA 1 – common core; Text McDougall Littell Alg. 1 , 2004 edtn; “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall Littell

Helpful websites: www.classzone.com; www.NJDOE ; Kuta Software.comOther Supplementals: HSPA “a collection of activities”(Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #2 Solving EquationsCourse: Algebra 1 – [2011-2012 yr] Anticipated timeframe: Days 10

Desired OutcomesStandards addressed: 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 A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at

previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI 3 solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

NQ 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays

NQ 2 define appropriate quantities for the purpose of descriptive modeling NQ 3 choose a level of accuracy appropriate to limitations on measurement when reporting quantities ASSE interpret the structure of expressions (terms, factors, coefficients)

Transfer Goals: Represent real-life situations with algebraic equations, then solve and evaluate equations Use proportions & percents to solve real-world problems Calculate percent increase/decrease & use to make decisions

Enduring Understandings: Equivalent equations each have the same

solution(s) Inverse operations are used to solve equations Properties of equality can be used repeatedly to

isolate a variable (whatever you do to “one side”, you do to “the other side”)

Ratios can be written and unit rates used to compare quantities and solve problems (proportions are 2 equal ratios: a/b = c/d; cross-product is used to solve for a variable

Essential Questions: Can equations that appear to be different, be

equivalent? How can one solve equations? What kinds of relationships can proportions

represent?

Learners will know: 1-step & 2-step equations in one variable Inverse (or opposite) operations Multi-step equations “Like terms” Variables on both sides No solution/ all solutions/ one solution Properties of equality (+, - , *. ÷ ) Literal equations (more than 1 variable) Rates; ratios; proportions (is/of = %/100) Percent change (percent increase or

decrease)=difference/original value

Learners will be able to: Solve 1-step equations by using inverse operations Solve 2-step equations by forming a set of simpler

equivalent equations Combine like terms Solve single variable equations with a variable on

both sides Recognize equations for which there exists no

solution Solve an equations for which the solution set is all

real #s Rewrite a literal equation (isolate the y variable)to

ease finding solutions Rewrite a geometric formula to highlight a different

variable Convert units and rates; write ratios to compare

quantities Solve and apply proportions (apply for similar

figures; solve %) Calculate percent change

Assessment EvidencePerformance Tasks: Class quizzes Classwork Dynamic Activities Authentic Assessment “Pull it together” p. 151 Unit test

Other Evidence: Class Discussions Group work Homework Technology integration (Math XL practice); ALEKS Notebook

Authentic Assessment: p. 151 Text #1 – Solve an equation using symbols only, no numbers. Justify each step.#3 your family is renting a truck to move . There is a fixed rental cost plus an additional , variable cost per mile driven. In addition, there is a gasoline expense. Calculate the total cost of the move using the map provided to estimate total driving distance.

VOCAB: Addition property of equality, conversion factor, cross-products, Cross-products property, Division property of equality, equivalent equations, formula, identity, inverse operations, isolate, literal equation, Multiplication property of equality, percent error, percent change, percent increase, percent decrease, proportion, rate, ratio, relative error, scale, scale drawing, scale model, similar figures, Subtraction property of equality, unit analysis, unit rate

Learning PlanAnticipated daily sequence of activities: Day 1 Solving 1-step & 2-step equations p. 80-93 text **[ Algebra tile activity p. 80 text] Day 2 Solving multi-step equations p. 94-101 text ** [Algebra tiles activity p. 101 ] Day 3 Solving equations with variables on both sides p. 102-108 text **[“hands on equations” kit – also p. 105

copy solution summary charts] Day 4 Linear Modeling (literal equations); rewriting formulas to isolate a different variable p. 109-114 text Day 5 Mid-chpt. Quiz; rates, ratios & conversions p. 116-123 text **[Unit Rate activity: have students cut out

5 examples of sales that are specials ex: 3 tuna cans for 1.99, then calculate the unit rate & glue advertisement & unit rate calculation onto construction paper and post around the room ]

Day 6 Solving proportions p. 124-129 text **[ teach cross product rhyme: up and left, multiply and drop it left; up and right, multiply and drop it right ] **[pneumonic “same level”, “same label” EX: 5 bagels/

3 dollars= 10 bagels/ 6 dollars Day 7 Proportions & similar figures p. 130-136 text **[ Have students create a scaled model using graph paper- “APPLY – B” p. 135 text – copy and label all lengths and widths in inches and /or feet] Day 8 Percents p. 137-143 text **[ Visualizing Percents activity: give students sheets with 9 of “10 by 10” grids. Students note there are 100 equal boxes in each grid so each box represents 1%. If a jacket costs $200, what

is 1 %? (break the $200 evenly into the 100 boxes, so each box = $_____(ans:$2). Ask critical thinking type Questions EX: if the jacket is 5% off ( that means 5 boxes), how many dollars are saved? 20% off? 50%

off=1/2 Day 9 Calculating Percent increase/ decrease; Unit 2 test review p. 144-160 text **[students design an index card % change= difference/original, then decorate the card and add to

notebook, ELL students write in their own language] Day 10 Unit 2 test; authentic assessment p. 151 text; Unit 3 readiness diagnostic p. 161 text

** [ ] - denotes suggested activities for Spec needs students as well as ELL students. Activities will be more tactile and visual to aid in comprehension. These activities & suggestions are also applicable to traditional ed. Students.

Anticipated resources: TEXT – PEARSON ALGEBRA 1 – common core; Text McDougall Littell Alg. 1 , 2004 edtn; “Meas Up” WB;

HSPA Coach WB; ALG1 resource WB McDougall Littell

Helpful websites: www.classzone.com; www.NJDOE ; Kuta Software.com; purpleMath; Math.comOther Supplementals: HSPA “a collection of activities”; ALEKS individualized math program; Pearson “MATHXL”

program; On-line access to stepped-out problems “On-line Problems”(Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #3 Solving InequalitiesCourse: Algebra 1 – [2011-2012 yr] Anticipated timeframe: Days 9

Desired OutcomesStandards addressed: A-CED 1 create equations and inequalities in one variable and use them to solve problems

A-CED 3 represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable

options in a modeling context

A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at previous step, starting from the

assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI 3 solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

NQ 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in

formulas; choose and interpret the scale and the origin in graphs and data displays Transfer Goals: Represent real-life situations using single-variable inequalities Accurately graph a single-variable equation, noting whether the endpoint is or is not included in the solution set Solve absolute value equations, understanding that absolute value is a measure of distance from zero(cannot ever =

neg. value)Enduring Understandings: Inequalities are used to represent a range of

acceptable solutions to a given problem Single-variable inequalities can be expressed

graphically using a number line Equivalent inequalities each have the same

solutions Sets are the basis of mathematical language (an

element is either included in the set or it is not) To solve an absolute value equation, you isolate

the abs value expression first, then write equivalent linear equations.

Essential Questions: Can inequalities that appear to be different, be

equivalent? How can one solve inequalities? How do you represent relationships between unequal

quantities? How can one visually demonstrate values that are

common elements to 2 sets? 3 sets?

Learners will know: Inequality symbols Inequality graphs (inclusive and exclusive of

endpoints) Solving inequalities using “Properties of

Equality”+,-,*,÷ Compound inequalities Absolute value equations Unions and intersections of sets The empty set Set notation EX: Set X = {x| x is divisible by

2}; Aᴗ B

Learners will be able to: Solve 1-step inequalities by using inverse operations Solve 2-step inequalities by forming a set of simpler

equivalent equations Recognize inequality symbols and accurately use to

describe a situation Create an algebraic inequality model given a verbal

example Solve multi-step inequalities using +, -, *, ÷ Solve compound inequalities Solve absolute value equations Work with sets

sets Venn diagrams Complement of a set

Graphically demonstrate union and intersection of sets

Assessment EvidencePerformance Tasks: Class quizzes Classwork Dynamic Activities Authentic Assessment “Pull it together” p. 221 Unit test

Other Evidence: Class Discussions Group work Homework Technology integration (Math XL practice); ALEKS Notebook

Authentic Assessment: p. 221 Text #1 – You are the store manager for camping supplies. Regular prices of tents are $68 to $119. The sale has all tents marked 10%-25% off. Construct a sign to depict the new cost range of tents on sale. Option #2 : Given 2 shapes with variable range of heights, use area restriction to determine integer values for x that satisfy the inequality given. Option #3 You are framing a piece of art of fixed dimensions 12 in x 18 in. You want to add a matting of equal width “x” around the print. Your restriction is that you only have a length of wood 80 in long to construct the frame. Draw a sketch to imitate this situation. Calculate the dimensions of that frame that allows for the maximum enclosed area. Explain your thought process.

VOCAB: complement of a set, compound inequality, disjoint sets, empty set, equivalent inequalities, intersection of sets, interval notation, roster form, set-builder notation, solution of an inequality, union, universal set

Learning PlanAnticipated daily sequence of activities: Day 1 Writing and graphing single-variable inequalities p. 162-170 text **[ Create Cards from construction

paper or oak tag: <, > , ≤, ≥ and also some cards with values EX: 2, -5, 4, -1, 0 , etc. The student represents the variable. Act out the inequalities and have the rest of the group graph on individual white boards. Mnemonic – “If the point touches the variable, go left” (the variable is less than the value); “if the open side touches the variable, go right (the variable is greater than the value). Ensure that you set up situations to practice variables on both the left and right of the values EX x>2, -3>x. Also “if equal bar, color in the included endpoint”; “no bar, empty endpoint (endpoint is not a member of the solution set]]

Day 2 Solving inequalities using addition/ subtraction p. 171-177 text ** [Use “undo” technique and railroad tracks to visually emphasize the “fulcrum” or center of a balance. Provide numerous opportunities for students to practice. EX: x + 3 < 7 . Three has been added to the variable, so you must subtract to “undo”.

-3 -3 (subtraction property of equality is reason) x < 4 means x represents all values less than, but not equal to 4 or “ x is less

than 4”] Day 3 Solving inequalities using multiplication/ division p. 178-184 text **[“Investigating inequalities” p. 333 McDougall Alg 1 text. Activity has students start with a true statement such as 2 < 5, then multiply both

sides by -1 to see why it is a necessary task to “flip the inequality” whenever one mult./divides by a negative value to preserve a true statement]

Day 4 Solving multi-step inequalities; mid-chpt. quiz p. 185-193 text **[Algebra tile activity p. 185 text] Day 5 Working with sets (complements, empty set, universal set) p. 194-199; 214-220 text **[Complement,

“think complete” ex: If x represents the set of all odd numbers, the complement of x would be all even numbers to yield a “complete” set of all counting numbers. Have students come up with additional examples. If a set is comprised of all adults (over 18), the complement would be____________? (Ans: all youth ie. Those under 18)

For ELL students, you can respresent the class using the universal symbols for girls and boys to show a set and its complement. For more challenged students, teacher provides the set, students provide the complement]

Day 6 Compound inequalities p. 200-206 text **[ Included boundary, color the endpoint dot; excluded boundary, endpoint is an empty dot. Have students construct a chart in NB’s x < ; x ≥ ; x > ;

x ≤ . You can also include the graph picture with the variable on the right if necessary] Day 7 Absolute value equations and inequalities p. 207-213 text **[ Demonstrate absolute value as the distance

from zero. | 5 | is represented as 5 units from zero. Use a ruler to show distance is never negative, so 5 units from zero is either +5 or -5. -5 0 5 . Assign students at least 3 more abs. values to

represent using | 5 units | 5 units | a number line. Ex: | 3 |, | 7 |, | 10 | . Students can swap with partner for agreement/ correction] Day 8 Unit 3 review; Additional teacher-prepared Venn diagram practice p.221-230 text Day 9 Unit 3 test ; authentic assessment; Unit 3 readiness diagnostic p. 221,231 text

** [ ] - denotes suggested activities for Spec needs students as well as ELL students. Activities will be more tactile and visual to aid in comprehension. These activities & suggestions are also applicable to traditional ed. Students.Anticipated resources:

TEXT – PEARSON ALGEBRA 1 – common core; Text McDougall Littell Alg. 1 , 2004 edtn; “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall Littell

Helpful websites: www.classzone.com; www.NJDOE ; Kuta Software.com; purpleMath; Math.comOther Supplementals: HSPA “a collection of activities”; ALEKS individualized math program; Pearson “MATHXL” program; On-line access to stepped-out problems “On-line Problems”

(Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #5Graph Linear InequalityCourse: Algebra 1 Anticipated timeframe: Days 14

Desired OutcomesStandards addressed: A-CED 1create equations and inequalities in one variable and use them to solve problems A-CED 3represent constraints by equations or inequalities and by systems of equations and/or inequalities and

interpret solutions as viable or non-viable options in a modeling context A-REI 1explain each step in solving a simple equation as following from the equality of numbers asserted at the

previous step A-REI 3 solve linear equations and inequalities in one variable A-REI 10understand that the graph of an equation in two variables is the set of all its solutions plotted in the

coordinate plane A-REI 12 graph the solutions of a linear inequality in 2 variables as a half-plane F-IF 7b graph piecewise-defined functions including step functions and absolute value functions N-Q 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and

interpret the scale and the origin in graphs and data displays

Transfer Goals: graph linear inequalities using various techniques and strategies and incorporating technology graph and describe absolute value functions, realizing that transformations are similar to those of linear equations

Enduring Understandings: many real-life situations can be modeled using

algebraicinequalities because most problems do not yield a singlesolution, rather a range of acceptable solutions

boundaries can be either inclusive or exclusive depending on whether the boundary meets the conditions for the inequality (is or is not included in the solution set)

Essential Questions: How is sound produced? (do all creatures hear the

same?)

How do we see colors? ( what is the visible spectrum to humans?)

Why are different sea creatures found at different elevations?

Learners will know: Inequality symbols > , < , ≥ , ≤ Definition of half-plane Absolute value function Compound inequalities Definition of linear inequality Continuous function Piecewise-defined function boundaries inverse operations

Learners will be able to: graph a linear inequality (graph paper & TI-84’s) describe & identify domain and range of a linear

inequality create an algebraic model of a real-life situation

usinglinear inequalities

graph an absolute value function graph a piecewise defined function recognize translations of absolute value functions verify solution points of a given inequality and

understand that the half-plane represents all possible solutions

solve 1-step, 2-step and multi-step inequalitiesAssessment Evidence

Performance Tasks: Class quizzes(including graphing calculator

assessment) Classwork Unit test

Other Evidence: Class Discussions Group work Homework Technology integration= Ti-84’s

Graphing inequality functions practice “y=” and plotAuthentic Assessment:Comparing Cell Phone plans: You are an investigative reporter for Consumer Reports Magazine. Your job is to present a break-down of what “deals” the various major cell phone corporations are offering. In order to present the information in the most user-friendly manner, you and your teams will create graphs showing amount of minutes and cost per month for service. You assign one team to research Verizon costs, one team to check out AT&T, another team to inquire about SPRINT and lastly a team to investigate Vonage. Each team will compile data on service charges for #minutes cell use per month (ex: 200 minutes, 400 min, 1,000 minutes & unlimited minutes if offered) from the internet, newspaper ad or call to a representative . Each team will create a step graph to show the boundaries and included/excluded endpoints. You have 10 days to complete your report and present a graph with the results. Once done each team will present their findings and you will discuss which company your magazine wishes to endorse overall and which company you will endorse at each # minutes level. Finally, you will present a written, brief report to your publisher regarding your final results.

Learning PlanAnticipated daily sequence of activities: Day 1,2 Investigating Inequalities ( 1 & 2 steps)p. 333 Text; p. 277,278 “Meas Up” WB; p. 334-339 Text Day 3,4 Solving Compound Inequalities p. 346-352 Text (explain upper and lower bounds;real-

lifeelevation.346) Day 5 Solving absolute value equations p. 353 ; calculator activity p. 359 text Day 6,7 Solving absolute value inequalities p. 354-358 text Day 8-10 Graphing linear inequalities in 2 variables p. 360-366; calculator activity p. 376 Day 11,12 Graph piecewise-defined functions Day 13 Unit 5 Review p. 384-389 Text Day 14 Unit 5 Test

Anticipated resources: Text McDougall Littell Alg. 1 , 2004 edtn; “Measuring Up” WB; HSPA Coach WB; ALG1 resource WB

McDougall Littell

Helpful websites: www.classzone.com; www.NJDOE; Other Supplementals: HSPA “a collection of activities”; ReteachingCopymasters Passport to Algebra & Geometry, 2002 McDougall Littell;

(Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #6Systems of Eqn’s/InequalityCourse: Algebra 1 Anticipated timeframe: Days 14

Desired OutcomesStandards addressed: A-CED 2 create equations in two or more variables to represent relationships between quantities; graph equations on

coordinate axes with labels& scales A-CED 3 represent constraints by equations or inequalities and by systems of equations and/or inequalities and

interpret solutions as viable or non-viable options in a modeling context A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at the

previous step A-REI 6 solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two

variables A-REI 10 understand that the graph of an equation in two variables is the set of all its solutions plotted in the

coordinate plane A-REI 11 explain why the “x” coordinates of the points where the graphs of two equations f(x)=y & g(x)=y intersect

are the solutions of the equation f(x)=g(x); find thesolutions approximately (using technology to graph the functions), make tables of values or find successive approximations

A-REI 12 graph the solutions of a linear inequality in 2 variables as a half-plane NVM 6 use matrices to represent and manipulate data A-SSE 1a interpret parts of an expression such as terms, factors and coefficients A-SSE 3 choose and produce an equivalent form of an expression to reveal and explain properties of the quantity

represented by the expression F-BF 1 write a function that describes a relationship between two quantities NQ 2 define appropriate quantities for the purpose of descriptive modeling F-IF 1 understand that a function from one set (domain) to another set (range) assigns to each element of the

domain exactly one element of range F-IF 4 for a function that models a relationship between two quantities, interpret key features of the graph and

tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.

F-IF 5 relate the domain of a graph to its function and, where applicable, to the quantitative relationship it describes (ex: + integers describe time-domain)

F-IF 7 graph functions expressed symbolically and show key features of the graph, by hand and/or technology (ex: intercepts, slope, intersections)

N-Q 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret the scale and the origin in graphs and data displays

Transfer Goals: Solve systems of linear equations /inequalities using various techniques and strategies and incorporating

technology Model real-life situations utilizing systems of equations/inequalities and making decisions based on the algebraic

solutionsEnduring Understandings: There are 4 basic ways to solve a system of

equations. Knowing the advantages & disadvantages of each method of solving systems of equations/inequalities, helps one become a more efficient problem-solver.

Linear systems are used daily by corporations to help them make productive, cost-saving decisions

Essential Questions: If two trains are in the same town at the exact same

time, do they have to crash? Why or why not? If you have to babysit your sibling and you want to

go to the mall for 2 hours with friends, how can you satisfy both need and want, responsibly?

How does someone prove (s)he is independent?

Learners will know: Learners will be able to:

What comprises a system of equations/inequalities Definition of half-plane; consistent & inconsistent

system;Linearly dependent & linearly dependent system; substitution; system solution; coefficient; determinant

Cramer’s Rule 4 ways to solve a system( graph, substitution,

linear combination, guess and check) By sight if boundary is included or excluded in

solution set One solution, all solutions, no solution

graph a system of linear equations/inequalities (graph paper & TI-84’s)-determine if the boundaries are/are not part of the solution set

describe & identify domain and range of system solution

create an algebraic model of a real-life situation using systems of linear equations/ inequalities

compare and contrast linearly dependent & independent systems

solve a system using substitution, graphing, linear combination

verify solution points of a given inequality system and understand that intersection of the half-planes represents all possible solutions

apply Cramer’s rule to solve systems of eqn’s& determine ║lines

Assessment EvidencePerformance Tasks: Class quizzes(including graphing calculator

assessment) Classwork& activities Unit test

Other Evidence: Class Discussions Group work Homework Technology integration= TI-84’s Graphing inequality functions practice “y=” and plot;

using the shade above/below featureAuthentic Assessment: You are the CEO of Apple Inc. A smaller, less expensive version of the I-pad is almost finished in the research &development department. Your company has already invested 4 million dollars developing this new technology. Each unit will cost $115 to manufacture. Based on surveys and sales of similar devices, your marketing department has suggested a selling price of $400 each. To ensure profitability of this product at the suggested price, you complete the following investigations:

Define variables for the quantities that are changing in the manufacturing of the new device. Units produced=___;Cost=____

Write an equation for the cost to manufacture the new product Marketing dept. has stated that projected sales should be 1,000,000 units globally in the 1st year. You are not sure.

-you calculate the cost to manufacture 200,000; 500,000 and 1,000,000 units 200,000 500,000 1,000,000

Define variables for the quantities that are changing in the sales of the new device. Units sold=___; Income=______

Write an equation to calculate the income generated from sales of this new device How much income will Apple Inc. receive for selling 200,000; 500,000 and 1,000,000 units?

200,000 500,000 1,000,000

For each of the prior functions, you identify the slope & y-intercept and explain their meaning/ significance- Cost to manufacture slope: y-intercept:

- Income from sales slope: y-intercept: Graph your 2 functions on graph paper (you also use your TI-84 to confirm).

What does the point of intersection of the two lines represent?_____________________________ Explain what the points to the left of the intersection represent.____________________________ Explain the points to the right of the ntersection.____________________________________

Decide if you feel comfortable with the $400 selling price,write a one paragraph justification. Then, come up with

a new catchy name for the new, smaller I-pad device. Sketch a sales advertisement (must include a picture and list of features for the device.)

Learning PlanAnticipated daily sequence of activities: Day 1 Solving Systems Linear eqn. Graphing -“think &discuss”p. 395 text;p. 398-404 Text Day 2,3 Substitution method Solving systems p. 405-410 Text Day 4,5 Linear combinations p. 411-416 Text Day 6,7 Cramer’s Rule “Learning Cramer’s Rule Activity”; p.426-430 text (write each in standard form, then

apply Cramer’s rule) Day 8,9 Systems of linear inequalities p. 432-438 text Day 10-12 Pre-HSPA testing/ Mixed Practice-choose best method to solve system.p. 418-424T(testing students as

HW) Day 13 Unit 6 Review p. 384-389 Text Day 14 Unit 6 Test

Anticipated resources: Text McDougall Littell Alg. 1 , 2004 edtn; “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall

LittellHelpful websites: www.classzone.com; www.NJDOE; www.hsunlimited.com/worksheets; www.kuta software.com

Other Supplementals: HSPA “a collection of activities”; ReteachingCopymasters Passport to Algebra & Geometry, 2002 McDougall Littell

(Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #7 Exponents & exp. functionsCourse: Algebra 1 Anticipated timeframe: Days 8

Desired OutcomesStandards addressed: A-CED 2 create equations in two or more variables to represent relationships between quantities; graph equations on

coordinate axes with labels & scales A-CED 3 represent constraints by equations or inequalities and by systems of equations and/or inequalities and

interpret solutions as viable or non-viable options in a modeling context A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at the

previous ste A-REI 10 understand that the graph of an equation in two variables is the set of all its solutions plotted in the

coordinate plane S-ID 6 represent data on two quantitative variables on a scatter plot and describe how the variables are related;

fit a function to the data; use functions fitted to data to solve problems in the context of the data. Emphasize linear, quadratic and exponential model

F-LE 1 distinguish between situations that can be modeled with linear functions and with exponential functions F-LE 2 construct linear and exponential functions, given a graph, a description of a relationship, or 2 input-output

pairs (including reading from a table) A-SSE 1a interpret parts of an expression such as terms, factors and coefficients A-SSE 2 use the structure of an expression to identify ways to rewrite it F-BF 1 write a function that describes a relationship between two quantities F-IF 1 understand that a function from one set (domain) to another set (range) assigns to each element of the

domain exactly one element of range F-IF 4 for a function that models a relationship between two quantities, interpret key features of the graph and

tables in terms of the quantities and Sketch graphs showing key features given a verbal description of the relationship.

F-IF 5 relate the domain of a graph to its function and, where applicable, to the quantitative relationship it describes (ex: + integers describe time-domain)

F-IF 7 graph functions expressed symbolically and show key features of the graph, by hand and/or technology (ex: intercepts, slope, intersections)

N-Q 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret the scale and the origin in graphs and data displays

N-Q 2 define appropriate quantities for the purpose of descriptive modelingTransfer Goals: Simplify expressions utilizing multiplication and division properties of exponents Apply scientific notation to represent very large and very small numbers Model real-life situations employing exponential growth and exponential decay functions; making predictions

based upon these exp. functionsEnduring Understandings: Scientific notation is used frequently to condense

the representation of very large and very small numbers, using exponents in this manner is efficient

Exponents are used to simplify expressions, they are short-hand multiplication

Exponential growth and decay functions are used to model real-life situations and to make predictions on future prices/increases or depreciation and losses

Essential Questions: What are some abbreviations we use when texting

friends? Would it be useful to be able to abbreviate long

numbers?/How can we ensure everyone uses the same code?

What do we mean by the word decay? Why doesn’t 52 = 10?

Learners will know: Multiplication properties of exponents

Learners will be able to: Apply multiplication properties of exponents to

Division properties of exponents Scientific notation Formula for exponential growth/ exponential

decay Zero power property Vocabulary: power, base, growth factor,

exponential function

simplify expressions Apply division (quotient) rules to simplify

expressions Utilize scientific notation to simplify representation

of small and large numbers Transcribe a number written in scientific notation to

standard representation Construct exponential growth and decay models to

solve real-life problems and also to make predictions on future values

Assessment EvidencePerformance Tasks: Class quizzes (including graphing calculator

assessment) Classwork & activities Unit test

Other Evidence: Class Discussions Group work Homework Technology integration= TI-84’s

Authentic Assessment: Exponential decay Assessment

You have just purchased a used BMW with 60,000miles for $12,000. It has a depreciation rate of 6% annually based upon average mileage usage. Complete a chart to display the value of your car after 2 years, 5 years, 7 years, 10 years. Graphically display your data using a coordinate grid (or graph paper). Use your graph to make a prediction of your car’s value after 12 years and 15 years (you may not use your calculator or the formula, your estimate is solely to be graph based). Write a one page essay explaining how long you should keep your used BMW. (consider milage accumulation, parts replacement costs , value of car vs. cost of repairs, etc). You may wish to utilize the internet for information on life-expectancy of BMW cars and repair costs. Was the purchase a good one compared with other car manufacturers? Do BMW’s retain their value for a long time?

Learning PlanAnticipated daily sequence of activities:

Day 1 Review multiplication properties of exponents - text p. 448-455; Measuring Up Wb p. 9-12,15 Day 2 Zero and negative power property p. 456-462 text Day 3 Quotient power property and power of quotient property p. 463-469 text Day 4 Scientific Notation p. 470-475Text; Measuring up Wb p. 27-34 Day 5 Exponential Growth functions p. 476-482 text Day 6 Exponential Decay functions p. 483-492 text / start authentic assessment Day 7 Unit 7 Review – p. 493-496 text/ research authentic assessment on internet (or have them bring as HW) Day 8 Unit 7 Test p. 497-499 text /wrap up authentic assessment, write analysis essay

Anticipated resources: Text McDougall Littell Alg. 1 , 2004 edtn; “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall

Littell Helpful websites: www.classzone.com; www.NJDOE ; www.hsunlimited.com/worksheets; www.kuta

software.com; math.com/worksheets Other Supplementals: HSPA “a collection of activities”; Reteaching Copymasters Passport to Algebra &

Geometry, 2002 McDougall Littell (Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #8 Radicals & QuadraticsCourse: Algebra 1 Anticipated timeframe: Days 12

Desired OutcomesStandards addressed: A-CED 2 create equations in two or more variables to represent relationships between quantities; graph equations on

coordinate axes with labels & scales A-CED 3 represent constraints by equations or inequalities and by systems of equations and/or inequalities and

interpret solutions as viable or non-viable options in a modeling context A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at the

previous step A-REI 10 understand that the graph of an equation in two variables is the set of all its solutions plotted in the

coordinate plane S-ID 6 represent data on two quantitative variables on a scatter plot and describe how the variables are related; fit

a function to the data; use functions fitted to data to solve problems in the context of the data. Emphasize linear, quadratic and exponential models

F-LE 1 distinguish between situations that can be modeled with linear and exponential functions F-LE 2 construct linear and exponential functions, given a graph, a description of a relationship, or 2 input-output

pairs (including reading from a table) F-LE 3 observe using graphs and tables that a quantity increasing exponentially eventually exceeds a

quantity increasing linearly, quadratically A-SSE 1a interpret parts of an expression such as terms, factors and coefficients F-BF 1 write a function that describes a relationship between two quantities F-IF 1 understand that a function from one set (domain) to another set (range) assigns to each element of the

domain exactly one element of range F-IF 4 for a function that models a relationship between two quantities, interpret key features of the graph and

tables in terms of the quantities and Sketch graphs showing key features given a verbal description of the relationship.

F-IF 5 relate the domain of a graph to its function and, where applicable, to the quantitative relationship it describes (ex: + integers describe time-domain)

F-IF 8 use the process of factoring in a quadratic function to show zeros, extreme values and symmetry of the graph and interpret in terms of a context

F-IF 7 graph functions expressed symbolically and show key features of the graph, by hand and/or technology (ex: intercepts, slope, intersections); graph linear and quadratic functions and show intercepts, maxima, minima

N-Q 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret the scale and the origin in graphs and data displays

N-Q 2 define appropriate quantities for the purpose of descriptive modelingTransfer Goals: Solve square roots; Mentally estimate value of non-perfect square roots; simplify radical expressions Solve quadratics using factoring and quadratic formula methods Model real-life situations utilizing quadratic functions

Enduring Understandings: Quadratic equations model many real-life

situations (ex: trajectories like balls thrown; area- dimension options, etc)

Predictions can be made for real-life situations using quadratics

Square roots are the solution for the length of a side of a square,given the area as the radicand

Essential Questions: How can we use a picture of a square to solve a

square root? How can we draw a picture to represent the path of a

ball thrown up(think a basketball)? Where is the ball at time zero?

Why can’t distance be negative? If we get a negative value as a root to a quadratic- modeling area, what should we do?

Learners will know: Square roots of perfect squares Approximate values of non-perfect squares up to

100 Definitions: radical , radicand, root, real root,

axis of symmetry, parabola, vertex, extraneous root

Factoring formulas for quadratics with leading

coefficient = 1 Quadratic formula

Discriminant b2- 4ac Location of quadratic term, linear term, constant

of quadratic in standard form

Learners will be able to: Solve and simplify radical expressions Utilize a function graph to estimate square roots up

to 100 Graph a quadratic using TI-84’s and identify roots Recognize the direction a parabola opens given a

quadratic in standard form Solve for the roots of a quadratic using factoring

(when leading coefficient is 1) Solve for the roots of a quadratic using quadratic

formula Determine the number of real roots using the

discriminant given a quadratic in standard form Recognize if a root is extraneous (using area

typequadratic problems)

Assessment EvidencePerformance Tasks: Class quizzes (including graphing calculator

assessment) Classwork & activities Unit 8 test

Other Evidence: Class Discussions Group work Homework Technology integration= TI-84’s

Authentic Assessment: You are designing a parking lot for a new middle school. The total area cannot exceed 10000 sq yards and must be designed around the athletic field ( the field is included in the 10000 sq yd total). If the field is 120 yds by 40 yds, design some possible parking lot layouts so that the length of the total lot is 20 yards longer than the width. The principal had stipulated that the athletic field must touch one side of the edges of the lot. Draw and label a diagram, determine what the possible lengh and widths of the lot can be. Write a short paragraph stating which design you favor (you must give at least two options)

Learning PlanAnticipated daily sequence of activities: Day 1 Review perfect squares, mental estimation of square roots, generate a function chart to help estimate

values for all square roots up to radicand of 100 -sq. root graph activity, Measuring Up Wb p. 13,14,16

Day 2 Simplifying radicals p. 511,512 text Day 3 Simplifying radical expressions p. 513-516 text Day 4,5 Investigating graphs of quadratics (direction of opening, vertex, axis symmetry, roots )p. 517-524 Text Day 6 Solving quadratics utilizing factoring (product of 2 sums, product of 2 differences)-factoring

supplemental activity Day 7 Solving quadratics factoring method (product of a sum and difference);applications Day 8,9 Solving quadratics (quadratic formula)-p. 533-539 text Day 10 Use discriminants to determine # of real roots p. 541-547 text Day 11 Unit 8 review p. 562-564 (avoid quadratic inequality questions); compare linear,exp, quad eqns p.

554,557 Day 12 Unit 8 Test

Anticipated resources:

Text McDougall Littell Alg. 1 , 2004 edtn; “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall Littell

Helpful websites: www.classzone.com; www.NJDOE ; www.hsunlimited.com/worksheets; www.kuta software.com, math.com/worksheets

Other Supplementals: HSPA “a collection of activities”; Reteaching Copymasters Passport to Algebra & Geometry, 2002 McDougall Littell (Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #10 Probability & statisticsCourse: Algebra 1 Anticipated timeframe: Days 10

Desired OutcomesStandards addressed: A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step A-REI 12 graph the solutions of a linear inequality in 2 variables as a half-plane A-SSE1a interpret parts of an expression such as terms, factors and coefficients NQ 2 define appropriate quantities for the purpose of descriptive modeling N-Q 1 use units as a way to understand problems and to guide the solution of multi-step problems; choose and

interpret the scale and the origin in graphs and data displays S-ID 2 use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread

(standard deviation) of two or more data sets S-ID 3 interpret differences in shape, center and spread in the context of the data sets, accounting for the possible

effects of extreme data points (outliers) S-ID 4 use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population

percentages . Recognize that there are data sets for which such a procedure is not appropriate. S-IC 1 understand statistics as a process for making inferences about population parameters based on a random

sample from that population. S-IC 3 recognize the purposes of and differences among sample surveys, experiments, and observational studies;

explain how randomization relates to each. S-CP 2 understand that two events A and B are independent if the probability of A & B occurring together is the

product of their probabilities and use this characterization to determine if they are independentTransfer Goals: Utilize measures of central tendency to analyze data Make predictions of outcomes based upon theoretical and experimental probability Understand that samples can contain bias and that organizations can alter data (use it to mislead the consumer) Recognize and apply normal curve in statistical analysis

Enduring Understandings: Measures of central tendency: mean (average),

median(central value in an ordered set), mode (most frequently appearing value)are used to compare and analyze data.

Varying intervals & presenting a “broken graph” will alter a graph’s appearance

Many data sets fall into a normal curve ( the majority of data points cluster about the mean)

The spread effects the “flatness” of a normal curve.

Essential Questions: What do we mean by deviation? Why do you think companies use surveys? How does a basketball coach use statistics (% free

throws)

Learners will know: Mean, median, mode are measures used to

compare data Outliers can impact the validity of measures of

central tendency What a sample is (random, convenience, with

observational bias) All professional sports utilize statistics What is a bell curve or “normal curve” What is standard deviation and variance Independent vs. dependent events

Learners will be able to: Calculate mean, median, mode of a data set Locate outliers if they exist in a data set, calculate &

compare mean, median and mode without the impact of an outlier

Read a description of aw survey and recognize if it contains bias or random

Calculate RBI’s for baseball, yardage per game for football, % successful shots for basketball

Make predictions based upon probability Analyze information from a “normal curve”-what

Compound probability Theoretical probability vs. Experimental

probability Law of large numbers

data is within 1, 2 or 3 standard deviations from the mean?

Calculate variance (both types = sample & population)

Utilize variance to calculate standard deviation Make inferences based upon the percentages

contained within a normal distributionAssessment Evidence

Performance Tasks: Class quizzes (including graphing calculator

assessment) Classwork & activities Unit 10 test

Other Evidence: Class Discussions Group work Homework Probability Project

Authentic Assessment: 1)You have been hired as the quality control officer for Mattel for the board game division. Your job is to ensure that all playing pieces are fair ( the spinners, the dice and any other tossed polyhedron.) You set up a field test to test every 100th item on the assembly line. The team project leader supervises the trials and reports back to you. Each test is done enough times to see that the experiments are approaching theoretical probability. The data is collected, then analyzed and lastly presented to you for approval. (teachers –there is a probability project that includes this as well as with other probability extensions .2) Sports stats – you are a sports journalist for the NY TIMES and are writing a piece about your favorite sport. Select a famous sports figure from your favorite team and calculate at least 3 statistics about that person. You can google how to calculate 3 different stats (ex: ERA’s and RBI’s for a baseball figure).

Learning PlanAnticipated daily sequence of activities: Day 1 Sample Populations and Bias -p. 336-345 HSPA COACH WB Day 3 Effects of outliers/ measures of central tendency p. 182-189 “Measure Up” WB Day 4,5 Variance and standard deviation p. 358 – 362 “HSPA COACH” WB (also check on-line for activities) Day 6 Normal distribution (Bell curve)p. 363 -368 “HSPA COACH” WB; p. 422 Open-ended Day 7 Experimental probability project – data collection & analysis ( activity prepared) Day 8 Margin of error in data analysis & statistics used in sports (see activity sheet for some suggested stats

by sports) Day 9 combinations/permutations review on TI – 84’s & Unit 10 Review Day 10 Unit 10 Test

Anticipated resources: “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall Littell

Helpful websites: www.classzone.com; www.NJDOE ; math.com .hsunlimited.com/worksheets; www.kuta software.com

Other Supplementals: HSPA “a collection of activities”

(Supplementals as well as manipulatives will be available at a central location within APHS )

Asbury Park High SchoolUnit Plan

Department: Mathematics Unit designation: #11 Geometry connectionsCourse: Algebra 1 Anticipated timeframe: Days 10

Desired OutcomesStandards addressed: A-REI 1 explain each step in solving a simple equation as following from the equality of numbers asserted at the

previous step A-SSE 1a interpret parts of an expression such as terms, factors and coefficients G-CO 2 represent transformations in the plane using transparencies; describe transformations as functions that

take points in the plane as inputs and give other points as outputs G-CO 3 given a rectangle, parallelogram, trapezoid or regular polygon, describe the rotations and reflections that

carry it onto itself G-CO 5 given a geometric figure and a rotation, reflection or translation, draw the transformed figure using

graph paper, tracing paper or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO 6 use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given 2 figures, use the definition of congruence in terms of rigid motion to decide if they are congruent

G-CO 12 make formal geometric constructions with a variety of tools and methods (compass, straight edge,string, reflective devices, paper folding, dynamic geometric software, etc.)

G-GPE 7 use coordinates to compute perimeters of polygons and areas of triangles and rectangles( e.g. using distance formula)

G-SRT 8 use trigonometric ratios and Pythagorean theorem to solve right triangles in applied problems G-GMD 4 identify the shapes of two dimensional cross-sections of three dimensional objects, and identify three

dimensional objects that are the result of a rotation of a two dimensional object

Transfer Goals: Apply Pythagorean theorem to solve real world problems Utilize distance and midpoint formulas to solve problems Complete transformations and determine the new location of the object

Enduring Understandings: The sum of the squares of the 2 legs of a right

triangle always equal the square of the hypotenuse. Pythagorean theorem is one of the most useful

tools from geometry and is used regularly in building & construction

Transformations (reflections. rotations, translations) preserve the original shape of the object and are used in many patterns in real-world

Essential Questions: How can we measure distance across a lake or

through a mountain? When is it important to find the exact middle point

of something? How could you find the length of a line if it is not

graphed on a coordinate plane?

Learners will know: Pythagorean theorem a2 + b2 = c2 is used to

determine if a triangle is right or to find a missing edge of a right triangle

Distance formula –used to calculate the distance between any two points given their coordinates

Midpoint formula –used to calculate the midpoint of any line segment given the coordinates of their two endpoints

Interior angle sum for a triangle (angle a + angle b + angle c=1800) can be used to calculate an unknown angle measure if two are known

Transformations: reflections, rotations, translations- (motions which preserve the size and shape of the pre-image)

Hypotenuse (always located across from rt. Angle)-where is it located and why is it so important that we can label it in a right triangle?

Legs of a right triangle ( how can we always distinguish them from the hypotenuse?; what is their role in Pythagorean Theorem?)

Right triangle (one angle must = 900) vs. acute ▲vs. obtuse ▲

Platonic solids- what are the names of all 5, and what do their nets look like? How can one fold paper to construct a platonic solid? What separates them from other polyhedron?

Tessellations (tile a surface)- (the sum of the angles at the convergence of the shapes must be 3600); regular tessellations vs. semi-regular tessellations- what is the difference?; how to create a unique tessellation utilizing transformations (given any shape that would normally tessellate a plane).

Learners will be able to: apply the Pythagorean formula to find the length of a

missing edge of a rt. Triangle utilize the converse of the Pythagorean theorem (if

a2+b2≠c2 therefore, the triangle is not a right triangle) apply Pythagorean theorem to any triangle to decide

if the triangle is acute or obtuse if a2 + b2 < c2 or a2 + b2> c2

determine the midpoint of any segment given the coordinates of the two endpoints utilizing midpoint formula

determine the distance between any two points given the x and y coordinates of the two endpoints

Apply the interior angle sum postulate (angle a + angle b + angle c = 1800) to solve for a missing angle; also utilizing balancing equations to solve for a missing angle given as an algebraic expression (ex. 3x + 5 is angle “c”)

Perform various transformations on rigid objects and decide where the image results in the coordinate plane

Perform transformations on a line segment and determine the effect on each of the coordinates.

Fold the platonic solids out of paper to get a visual of each face

Create unique tessellations using transformations on a rectangle or parallelogram

Visualize the 3-D object formed from the rotation of a 2-D shape (ex: rt triangle rotated around y axis yields a cone; a rectangle rotated about the y axis yields a cylinder

Assessment EvidencePerformance Tasks: Class quizzes (including graphing calculator

assessment) Classwork & activities

Other Evidence: Class Discussions Group work Homework Tessellation construction/ creativity Folded polyhedron constructions (3dimension

visualization)Authentic Assessment: You are a graphic designer and working on a new project. You are designing a mural for the Metropolitan Museum of Art in NYC. You are to create an interesting tessellation utilizing at least 4 colors . The shape is to be a recognizable object. You must start with either a rectangle or a parallelogram. Your mural will be the gateway to a new Escher prints section of the museum. You have two days to complete the draft. Your “puzzle piece must interlock with all others. There must be no gaps and no overlaps ( or you will lose the commission to another artist). The chief director for commissioned works will be the person you report to.

Learning PlanAnticipated daily sequence of activities: Day 1 Pythagorean theorem & converse P. 737 “investigation” & p. 728-744 text Alg 1 Day 2 Distance and midpoint formulas p. 745- 751 Alg 1 text Day 3 Interior angle sum of a triangle – Worksheets from geometry supplemental WB also HSPA COACH Day 4 Transformations of rigid shapes & lines (what is the impact on the x,y coordinates) HSPA COACH Day 5,6 Tessellation creation – activity may start with any rectangle, parallelogram or equilateral triangle or hexagon Day 7 Platonic solids and cross-sections –nets downloaded from internet(each student colors,cuts & folds one);

teacher demonstration rotating a rt. triangle to yield a cone and rotating a rectangle to yield a cylinder Day 8,9 Final Exam review Day 10 Final Exam Alg 1

Anticipated resources: “Meas Up” WB; HSPA Coach WB; ALG1 resource WB McDougall Littell Helpful websites: www.classzone.com; www.NJDOE ; math.com .hsunlimited.com/worksheets; www.kuta

software.com

Other Supplementals: HSPA “a collection of activities”

(Supplementals as well as manipulatives will be available at a central location within APHS )