Asbury Park High School
Unit Plan
Department: Mathematics
Course: Algebra 1 – [2011-2012 yr]
Unit designation: #1 Algebraic Foundations
Anticipated timeframe: Days 10
Desired Outcomes
Standards 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
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
Essential Questions:
 How can you represent quantities, patterns and
relationships?

How are properties related to Algebra?
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
relationships
Assessment Evidence
Performance Tasks:
Other Evidence:
 Class quizzes (including graphing calculator
 Class Discussions
assessment)
 Group work
 Class work
 Homework
 Dynamic Activity
 Technology integration (Math XL practice); ALEKS
 Authentic Assessment “Pull it together” p. 67
 Unit test
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 Plan
Anticipated 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.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 School
Unit Plan
Department: Mathematics
Course: Algebra 1 – [2011-2012 yr]
Unit designation: #2 Solving Equations
Anticipated timeframe: Days 10
Desired Outcomes
Standards 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:
Essential Questions:
 Equivalent equations each have the same solution(s)
 Can equations that appear to be different, be equivalent?
 Inverse operations are used to solve equations
 How can one solve equations?
 Properties of equality can be used repeatedly to
 What kinds of relationships can proportions represent?
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
Learners will know:
Learners will be able to:
 1-step & 2-step equations in one variable
 Solve 1-step equations by using inverse operations
 Inverse (or opposite) operations
 Solve 2-step equations by forming a set of simpler
equivalent equations
 Multi-step equations

Combine like terms
 “Like terms”
 Solve single variable equations with a variable on both
 Variables on both sides
sides
 No solution/ all solutions/ one solution

Recognize equations for which there exists no solution
 Properties of equality (+, - , *. ÷ )
 Solve an equations for which the solution set is all real
 Literal equations (more than 1 variable)
#s
 Rates; ratios; proportions (is/of = %/100)

Rewrite a literal equation (isolate the y variable)to ease
 Percent change (percent increase or
finding solutions
decrease)=difference/original value
 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 Evidence
Performance Tasks:
Other Evidence:
 Class quizzes
 Class Discussions
 Classwork
 Group work
 Dynamic Activities
 Homework
 Authentic Assessment “Pull it together” p. 151
 Technology integration (Math XL practice); ALEKS
 Unit test
 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 Plan
Anticipated 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.com
Other 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 School
Unit Plan
Department: Mathematics
Course: Algebra 1 – [2011-2012 yr]
Unit designation: #3 Solving Inequalities
Anticipated timeframe: Days 9
Desired Outcomes
Standards 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:
Essential Questions:
 Inequalities are used to represent a range of
 Can inequalities that appear to be different, be
acceptable solutions to a given problem
equivalent?
 Single-variable inequalities can be expressed
 How can one solve inequalities?
graphically using a number line
 How do you represent relationships between unequal
 Equivalent inequalities each have the same solutions
quantities?
 Sets are the basis of mathematical language (an
 How can one visually demonstrate values that are
element is either included in the set or it is not)
common elements to 2 sets? 3 sets?
 To solve an absolute value equation, you isolate the
abs value expression first, then write equivalent linear
equations.
Learners will know:
Learners will be able to:
 Inequality symbols
 Solve 1-step inequalities by using inverse operations
 Inequality graphs (inclusive and exclusive of
 Solve 2-step inequalities by forming a set of simpler
endpoints)
equivalent equations
 Solving inequalities using “Properties of Equality”+,-  Recognize inequality symbols and accurately use to
,*,÷
describe a situation
 Compound inequalities
 Create an algebraic inequality model given a verbal
example
 Absolute value equations
 Solve multi-step inequalities using +, -, *, ÷
 Unions and intersections of sets
 Solve compound inequalities
 The empty set
 Solve absolute value equations
 Set notation EX: Set X = {x| x is divisible by 2};
 Work with sets
Aᴗ B



sets
Venn diagrams
Complement of a set

Graphically demonstrate union and intersection of sets
Assessment Evidence
Performance Tasks:
Other Evidence:
 Class quizzes
 Class Discussions
 Classwork
 Group work
 Dynamic Activities
 Homework
 Authentic Assessment “Pull it together” p. 221
 Technology integration (Math XL practice); ALEKS
 Unit test
 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 Plan
Anticipated 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
 Day 8
 Day 9
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]
Unit 3 review; Additional teacher-prepared Venn diagram practice p.221-230 text
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.com
Other 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 School
Unit Plan
Department: Mathematics
Course: Algebra 1
Unit designation: #5Graph Linear Inequality
Anticipated timeframe: Days 14
Desired Outcomes
Standards 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
algebraic
inequalities because most problems do not yield a
single
solution, 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)
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
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 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 using
linear 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 inequalities
Assessment 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 plot
Authentic 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 Plan
Anticipated 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;reallifeelevation.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 School
Unit Plan
Department: Mathematics
Course: Algebra 1
Unit designation: #6Systems of Eqn’s/Inequality
Anticipated timeframe: Days 14
Desired Outcomes
Standards 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
solutions
Enduring Understandings:
Essential Questions:
 There are 4 basic ways to solve a system of
 If two trains are in the same town at the exact same time,
equations. Knowing the advantages & disadvantages
do they have to crash? Why or why not?
of each method of solving systems of
 If you have to babysit your sibling and you want to go to
equations/inequalities, helps one become a more
the mall for 2 hours with friends, how can you satisfy
efficient problem-solver.
both need and want, responsibly?
 Linear systems are used daily by corporations to help  How does someone prove (s)he is independent?
them make productive, cost-saving decisions
Learners will know:
Learners will be able to:
 What comprises a system of equations/inequalities
 graph a system of linear equations/inequalities (graph
paper & TI-84’s)
 Definition of half-plane; consistent & inconsistent
-determine if the boundaries are/are not part of the
system;
solution set
Linearly dependent & linearly dependent system;
substitution; system solution; coefficient; determinant  describe & identify domain and range of system solution
 Cramer’s Rule
 create an algebraic model of a real-life situation using
systems
 4 ways to solve a system( graph, substitution, linear
of linear equations/ inequalities
combination, guess and check)
 compare and contrast linearly dependent & independent
 By sight if boundary is included or excluded in
systems
solution set
 solve a system using substitution, graphing, linear
 One solution, all solutions, no solution
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 Evidence
Performance Tasks:
Other Evidence:
 Class quizzes(including graphing calculator
 Class Discussions
assessment)
 Group work
 Classwork& activities
 Homework
 Unit test
 Technology integration= TI-84’s
 Graphing inequality functions practice “y=” and plot;
using the shade above/below feature
Authentic 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 Plan
Anticipated 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
Littell
Helpful 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 School
Unit Plan
Department: Mathematics
Course: Algebra 1
Unit designation: #7 Exponents & exp. functions
Anticipated timeframe: Days 8
Desired Outcomes
Standards 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 modeling
Transfer 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. functions
Enduring Understandings:
Essential Questions:
 Scientific notation is used frequently to condense the  What are some abbreviations we use when texting
representation of very large and very small numbers,
friends?
using exponents in this manner is efficient
 Would it be useful to be able to abbreviate long
 Exponents are used to simplify expressions, they are
numbers?/How can we ensure everyone uses the same
short-hand multiplication
code?
 Exponential growth and decay functions are used to
 What do we mean by the word decay?
model real-life situations and to make predictions on
 Why doesn’t 52 = 10?
future prices/increases or depreciation and losses
Learners will know:
 Multiplication properties of exponents
 Division properties of exponents
 Scientific notation
 Formula for exponential growth/ exponential decay
 Zero power property
 Vocabulary: power, base, growth factor, exponential
function
Learners will be able to:
 Apply multiplication properties of exponents to 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 Evidence
Other Evidence:
 Class Discussions
 Group work
 Homework
 Technology integration= TI-84’s
Authentic Assessment: Exponential decay Assessment
Performance Tasks:
 Class quizzes (including graphing calculator
assessment)
 Classwork & activities
 Unit test
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 lifeexpectancy 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 Plan
Anticipated 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 School
Unit Plan
Department: Mathematics
Course: Algebra 1
Unit designation: #8 Radicals & Quadratics
Anticipated timeframe: Days 12
Desired Outcomes
Standards 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 modeling
Transfer 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:
Essential Questions:
 Quadratic equations model many real-life situations
 How can we use a picture of a square to solve a square
(ex: trajectories like balls thrown; area- dimension
root?
options, etc)
 How can we draw a picture to represent the path of a ball
 Predictions can be made for real-life situations using
thrown up
quadratics
(think a basketball)? Where is the ball at time zero?
 Square roots are the solution for the length of a side
 Why can’t distance be negative? If we get a negative
of a square,
value as a root to a quadratic- modeling area, what
given the area as the radicand
should we do?
Learners will know:
Learners will be able to:
 Square roots of perfect squares
 Solve and simplify radical expressions
 Approximate values of non-perfect squares up to 100  Utilize a function graph to estimate square roots up to
100
 Definitions: radical , radicand, root, real root, axis of
 Graph a quadratic using TI-84’s and identify roots
symmetry, parabola, vertex, extraneous
root
 Recognize the direction a parabola opens given a
quadratic in standard form
 Factoring formulas for quadratics with leading
 Solve for the roots of a quadratic using factoring (when
coefficient = 1
leading coefficient is 1)
 Quadratic formula
 Solve for the roots of a quadratic using quadratic
formula
 Determine the number of real roots using the
 Discriminant b2- 4ac
discriminant given a quadratic in standard form
 Location of quadratic term, linear term, constant of
 Recognize if a root is extraneous (using area
quadratic in standard form
typequadratic problems)
Assessment Evidence
Performance Tasks:
Other Evidence:
 Class quizzes (including graphing calculator
 Class Discussions
assessment)
 Group work
 Classwork & activities
 Homework
 Unit 8 test
 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 Plan
Anticipated 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 School
Unit Plan
Department: Mathematics
Course: Algebra 1
Unit designation: #10 Probability & statistics
Anticipated timeframe: Days 10
Desired Outcomes
Standards 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 independent
Transfer 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:
Essential Questions:
 Measures of central tendency: mean (average),
 What do we mean by deviation?
median(central value in an ordered set), mode (most
 Why do you think companies use surveys?
frequently appearing value)are used to compare and
 How does a basketball coach use statistics (% free
analyze data.
throws)
 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.
Learners will know:
Learners will be able to:
 Mean, median, mode are measures used to compare
 Calculate mean, median, mode of a data set
data
 Locate outliers if they exist in a data set, calculate &
 Outliers can impact the validity of measures of
compare mean, median and mode without the impact of
central tendency
an outlier
 What a sample is (random, convenience, with
 Read a description of aw survey and recognize if it
observational bias)
contains bias or random
 All professional sports utilize statistics
 Calculate RBI’s for baseball, yardage per game for
football, % successful shots for basketball
 What is a bell curve or “normal curve”
 Make predictions based upon probability
 What is standard deviation and variance





Analyze information from a “normal curve”-what 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 distribution
Assessment Evidence
Performance Tasks:
Other Evidence:
 Class quizzes (including graphing calculator
 Class Discussions
assessment)
 Group work
 Classwork & activities
 Homework
 Unit 10 test
 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 Plan
Anticipated 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
Independent vs. dependent events
Compound probability
Theoretical probability vs. Experimental probability
Law of large numbers
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 School
Unit Plan
Department: Mathematics
Course: Algebra 1
Unit designation: #11 Geometry connections
Anticipated timeframe: Days 10
Desired Outcomes
Standards 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:
Essential Questions:
 The sum of the squares of the 2 legs of a right triangle  How can we measure distance across a lake or through a
always equal the square of the hypotenuse.
mountain?
 Pythagorean theorem is one of the most useful tools
 When is it important to find the exact middle point of
from geometry and is used regularly in building &
something?
construction
 How could you find the length of a line if it is not
 Transformations (reflections. rotations, translations)
graphed on a coordinate plane?
preserve the original shape of the object and are used
in many patterns in real-world
Learners will know:
Learners will be able to:
 Pythagorean theorem a2 + b2 = c2 is used to
 apply the Pythagorean formula to find the length of a
determine if a triangle is right or to find a missing
missing edge of a rt. Triangle
edge of a right triangle
 utilize the converse of the Pythagorean theorem (if
 Distance formula –used to calculate the distance
a2+b2≠c2 therefore, the triangle is not a right triangle)
between any two points given their coordinates
 apply Pythagorean theorem to any triangle to decide if
 Midpoint formula –used to calculate the midpoint of
the triangle is acute or obtuse if a2 + b2 < c2 or a2 + b2>
any line segment given the coordinates of their two
c2
endpoints
 determine the midpoint of any segment given the
 Interior angle sum for a triangle (angle a + angle b +
coordinates of the two endpoints utilizing midpoint
angle c=1800) can be used to calculate an unknown
formula
angle measure if two are known
 determine the distance between any two points given the
 Transformations: reflections, rotations, translationsx and y coordinates of the two endpoints
(motions which preserve the size and shape of the
 Apply the interior angle sum postulate (angle a + angle b
pre-image)
+ angle c = 1800) to solve for a missing angle; also
 Hypotenuse (always located across from rt. Angle)utilizing balancing equations to solve for a missing angle
where is it located and why is it so important that we
given as an algebraic expression (ex. 3x + 5 is angle “c”)
can label it in a right triangle?
 Perform various transformations on rigid objects and
 Legs of a right triangle ( how can we always
decide where the image results in the coordinate plane
distinguish them from the hypotenuse?; what is their
 Perform transformations on a line segment and
role in Pythagorean Theorem?)
determine the effect on each of the coordinates.
 Right triangle (one angle must = 900) vs. acute ▲vs.  Fold the platonic solids out of paper to get a visual of
obtuse ▲
each face
 Platonic solids- what are the names of all 5, and what  Create unique tessellations using transformations on a
do their nets look like? How can one fold paper to
rectangle or parallelogram
construct a platonic solid? What separates them from  Visualize the 3-D object formed from the rotation of a 2other polyhedron?
D shape (ex: rt triangle rotated around y axis yields a
 Tessellations (tile a surface)- (the sum of the angles at
cone; a rectangle rotated about the y axis yields a
the convergence of the shapes must be 3600); regular
cylinder
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).
Assessment Evidence
Performance Tasks:
Other Evidence:
 Class quizzes (including graphing calculator
 Class Discussions
assessment)
 Group work
 Classwork & activities
 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 Plan
Anticipated 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 )