how do you write and evaluate algebraic expressions… · how do you write and evaluate algebraic...

Expressions, equations, tables and graphs are used to model real-world situations.

How do you write and evaluatealgebraic expressions?

How can algebraic expressions and equationsrepresent actual situations?

Evaluate expressionsM11.A.2 .2 .1, M11.A.3 .1 .1, 2 .1 .8 .E, 2 .1 .8 .B, 2.2.8 .A

Write expressions,equations, inequalit iesM11.D.1 .1 .1, 2 .8 .8 .C

Represent functions asrules, tables, graphsM11.D.1 .1 .1, M11.D.1 .1 .2, M11.D.1 .1 .3, M11.D .

2 . 1 . 2, 2 .8 .8 .B, 2 .5 .8 .B, 2 .11 .8 .C, M8.D.1 .1 .1, M8.D.

1 . 1 . 3

How do you evaluate expressions?(ET)

How do you write expressions fromverbal models? (A)

How do you write equations andinequalities from verbal models? (ET)

What is a function and how can it berepresented with an equation, a tableof values and a graph? (ET)

PEMDAS (Order of Operations),substitution, power, base, exponent

verbal model, unit rate, , function, range, domain, input, output

Additional Information:

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Curriculum: 2009 Pequea Valley SD Curriculum PEQUEA VALLEY SD Course: Math - Algebra 8 Date: November 10, 2009 ET

Topic: Expressions, Equations and FunctionsSubject Area(s): Math

Days: 13

Grade(s): 8

Key Learning:

Unit Essential Question(s):

Concept: Concept: Concept:

Lesson Essential Question(s): Lesson Essential Question(s): Lesson Essential Question(s):

Vocabulary: Vocabulary: Vocabulary:

Attached Document(s):

Concept: Evaluate expressionsPEMDAS (Order of Operations) - substitution - power - base - exponent -

Concept: Write expressions, equations, inequalitiesverbal model -

unit rate - - -

Concept: Represent functions as rules, tables, graphsfunction - range - functiondomainrangeinputoutputdomain - input - output -

Page 1 of 1


Topic: Expressions, Equations and FunctionsSubject Area(s): Math

Days: 13

Grade(s): 8

Our real number system is infinite and can be represented in multipleways.

How can we representnumbers in multiple ways using operations and

symbols?

Graph and compare.M11.A.1 .1 .1, M11.A.1 .3 .1, M11.A.1 .3 .2, M11.A.

3 . 2 . 1, 2 .1 .8 .C, 2 .2 .8 .C, 2 .4 .8 .B, 2.1.8 .A, 2 .2 .8 .B

OperationsM11.A.2 .1 .1, 2 .4 .8 .D, 2 .1 .8 .F

Simplify.M11.D.2 .2 .1

What are the different types ofnumbers and how do you find theabsolute value of these numbers? (ET)

How do you add and subtract rationalnumbers? (A)

What are the properties that we use inmultiplying and adding numbers? (A)

How do you multiply and dividerationals? (A)

When do you use the distributiveproperty and how do you use it? (A)

What are like terms and how do youcombine them? (A)

How do you evaluate square roots andcompare them with other numbertypes? (ET)

integers, rational number, irrationalnumbers, opposites, absolute value

additive identity, additive inverse,multiplicative identity, multiplicativeinverse, reciprocal

distributive property, coefficient,constant, term, like terms


Page 1 of 1


Topic: Properties of real numbersSubject Area(s): Math

Days: 20

Grade(s): 8

Key Learning:






Concept: Graph and compare.integers - rational number - irrational numbers - opposites - absolute value -

Concept: Operationsadditive identity - additive inverse - multiplicative identity - multiplicative inverse - reciprocal -

Concept: Simplify.distributive property - coefficient - constant - term - like terms -

Page 1 of 1


Topic: Properties of real numbersSubject Area(s): Math

Days: 20

Grade(s): 8

To solve equations, you perform inverse operations to both sides ofthe equation to isolate a variable.

How do you solve equations?

Solving equationsM11.D.2 .1 .3, M11.A.2 .1 .1, M8.D.2 .1 .1

Literal equationsM11.D.2 .1 .3

What steps are used to solveequations with a variable on one side?(A)

What process do you use whenrepresenting a word problem as anequation? (A)

How can you apply equations to solvereal life problems? (ET)

What steps are used to solveequations with variables on bothsides? (A)

How do you solve equations whichcontain fractions? (A)

How do equation solving steps help usrewrite equations and formulas? (ET)

Inverse Operations, equivalentequations, Identity, complementaryand supplementary angles,corresponding, vertical and adjacentangles, alternate interior and alternateexterior angles

literal equation

Additional Information:Include angle types in this unit.

Page 1 of 1


Topic: Solving EquationsSubject Area(s): Math

Days: 17

Grade(s): 8

Key Learning:






Concept: Solving equationsInverse Operations - equivalent equations - Identity - complementary and supplementary angles - corresponding, vertical and adjacent angles - alternate interior and alternate exterior angles -

Concept: Literal equationsl iteral equation -

Page 1 of 1


Topic: Solving EquationsSubject Area(s): Math

Days: 17

Grade(s): 8

Proportions are a powerful tool for problem solving.

How can real l i fe problems bemodeled and solved using proportions?

Ratios and ProportionsM11.A.2 .1 .3, M11.A.2 .1 .1, 2 .1 .8 .D, 2 .2 .8 .D, 2 .2 .8 .E,

2 .2 .8 .F

Solving Problems withProportions2 .1 .8 .D, 2 .8 .11 .D, 2 .4 .11 .E, M11.A.2 .1 .1, M11.A.

2 . 1 . 3

What is a proportion? (A)

How do you create an equation from aproportion? (A)

How do we use proportions to solverate problems? (ET)

How can you solve percent problemsusing proportions? (ET)

How can you find the percent ofchange? (ET)

How can proportions be used to solveproblems involving similar triangles?(ET)

How can proportions be used to solvescale problems? (ET)

cross product similar triangles

Additional Information:Commission and sales tax must be included with the percent EQ.

Page 1 of 1


Topic: Solving ProportionsSubject Area(s): Math

Days: 15

Grade(s): 8

Key Learning:






Concept: Ratios and Proportionscross product -

Concept: Solving Problems with Proportionssimilar triangles -

Page 1 of 1


Topic: Solving ProportionsSubject Area(s): Math

Days: 15

Grade(s): 8

The graph of a l inear functions shows the relationship between twovariables.

What information do you needto graph a l inear function?

Graph using a table.M11.D.4 .1 .1, M11.D.2 .1 .2

Graph using interceptsM11.D.2 .1 .2

Slope and rate of changeM11.D.3 .1 .1, M11.D.3 .2 .1

What are the parts of a coordinateplane? (A)

How do you graph a linear equationusing a table? (A)

How do you use intercepts to graph alinear function? (ET)

How do you graph equations whichcontain only one variable? (A)

What is slope and how do you find it?(A)

What is "Rate of Change" and how doyou find it? (ET)

quadrant, axis, origin, ordered pair,linear function

x-intercept, y-intercept, Standard form rise, run, slope, rate of change

Graph using slopeintercept formM11.D.3 .2 .3, M11.D.2 .1 .2

Function Notation2 .8 .11 .Q

What are "m" and "b" and how do youuse them to graph linear functions? (A)

What is true about the equations oflines that are parallel? (A)

How do you use and interpret functionnotation? (A)

slope-intercept form


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Topic: Graphing Linear FunctionsSubject Area(s): Math

Days: 15

Grade(s): 8

Key Learning:









Concept: Graph using a table.quadrant - axis - origin - ordered pair - linear function -

Concept: Graph using interceptsx-intercept - y-intercept - Standard form -

Concept: Slope and rate of changerise - run - slope - rate of change -

Concept: Graph using slope intercept formslope-intercept form -

Page 1 of 1


Topic: Graphing Linear FunctionsSubject Area(s): Math

Days: 15

Grade(s): 8

Equations can be written to f it data and used to make predictionsabout the data .

How do you write the equationof a line?

write l inear equationM11.D.3 .1 .1, M11.D.3 .2 .1, M11.D.3 .2 .2, M11.D .

3 . 2 . 3, M11.D.4 .1 .1, M11.D.2 .1 .3

paral lel andperpendicular l inesM11.C.3 .1 .2, M11.D.3 .2 .3, M11.D.3 .2 .2, M11.D .

3 . 2 . 1, M11.D.4 .1 .1, M11.D.2 .1 .3

scatter plots and l inearregressionM11.D.2 .1 .3, M11.D.3 .2 .1, M11.D.3 .2 .2

How do you use slope and y-interceptto write the equation of a line? (A)

How do you write the equation of aline given two points on a line? (A)

How do you write the equation of aline given the slope and a point on theline? (A)

How do you use slope to find theequation of a parallel or perpendicularline? (A)

How do you find the equation of a lineof best fit and make a prediction onthe line of best fit? (ET)

How do you use a graphing calculatorto create a scatterplot and calculatethe linear regression equation? (ET)

parallel, perpendicular scatter plot, positive correlation,negative correlation, no correlation,line of best fit, trend line, linearregression


Page 1 of 1


Topic: Writing linear functionsSubject Area(s): Math

Days: 17

Grade(s): 8

Key Learning:






Concept: wri te l inear equation-

Concept: parallel and perpendicular l inesparallel - perpendicular -

Concept: scatter plots and linear regressionscatter plot - positive correlation - negative correlation - no correlation - line of best fit - trend line - linear regression -

Page 1 of 1


Topic: Writing linear functionsSubject Area(s): Math

Days: 17

Grade(s): 8

Linear inequalit ies and absolute value equations and inequalit ieshave unique graphs.

How are solutions to l inearinequalit ies and absolute value equations and

inequalit ies represented?

Inequalit ies in onevariablesM11.D.2 .1 .1

Absolute value equationsand inequalit iesM11.D.2 .1 .1

Inequalit ies in twovariablesM11.D.2 .1 .2

How do you graph the solution to aninequality? (A)

How do you solve an inequality? (KeyQuestion: What happens when youmultiply or divide by a negative?) (A)

How do you solve and graph thesolution to compound inequalities?(ET)

How do you solve absolute valueequations? (ET)

How do you solve and graph thesolutions to absolute valueinequalities? (ET)

How do you graph a linear inequalityin two variable? (ET)

How do you determine algebraicallyand graphically if an ordered pair is asolution? (ET)

compound inequality absolute deviation linear inequality in two variables,boundary line, boundary line


Page 1 of 1


Topic: InequalitiesSubject Area(s): Math

Days: 14

Grade(s): 8

Key Learning:






Concept: Inequalit ies in one variablescompound inequality -

Concept: Absolute value equations and inequalitiesabsolute deviation -

Concept: Inequalit ies in two variableslinear inequality in two variables - boundary line - boundary line -

Page 1 of 1


Topic: InequalitiesSubject Area(s): Math

Days: 14

Grade(s): 8

Several properties of exponents can be used to simplify expressionscontaining positive, negative and zero exponents.

Why do we need to know howto simplify exponential expressions?

products and quotientsM11.A.2 .2 .1, M11.A.2 .2 .2

zero and negativeexponentsM11.A.2 .2 .1, M11.A.2 .2 .2

scientific notationM11.A.1 .1 .2, M11.A.2 .2 .1

How can you convert betweenexponential expressions and expandednotation? (A)

What is meant by "simplifying a powerto a power", "simplifying a product ofpowers", and "simplifying a power of aproduct"? (A)

What is meant by "simplifying a powerto a power", "simplifying a product ofpowers", and "simplifying a power of aproduct"? (ET)

What is meant by "simplifying aQuotient of Powers"? (A)

What is meant by "simplifying aQuotient of Powers"? (ET)

How do you simplify expressionscontaining zero and negativeexponents? (A)

How do you simplify expressionscontaining zero and negativeexponents? (ET)

How can you convert betweenscientific and standard notation? (A)

How can you compute with numbers inscientific notation? (ET)

power, exponent, base


Page 1 of 1


Topic: Laws of ExponentsSubject Area(s): Math

Days: 20

Grade(s): 8

Key Learning:






Concept: products and quotientspower - exponent - base -

Page 1 of 1


Topic: Laws of ExponentsSubject Area(s): Math

Days: 20

Grade(s): 8

Operations can be performed on polynomials. Equations can bewritten using polynomials to allow us to solve problems.

How can we performoperations on polynomials and how can the

operations help us solve problems?

Sums, Differences andProductsM11.D.2 .2 .1

FactoringM11.A.1 .2 .1, M11.D.2 .2 .2

Solve quadraticequationsM11.D.2 .1 .5

How can polynomials be classified andidentified? (A)

How do you add and subtractpolynomials? (A)

How can sums or differences ofpolynomials be used to solveproblems? (ET)

How can multiplication withpolynomials be performed? (A)

How can area problems be solvedusing products of polynomials? (ET)

What patterns can be used to findsome products quickly? (ET)

How do you factor polynomials of theform x2 + bx + c? (A)

How do you factor polynomials of theform ax2 + bx + c? (A)

How do you use special products tofactor special polynomials? (ET)

How can terms be grouped to facilitatefactoring? (ET)

How do you use the Zero-ProductProperty? (A)

How can complete factoring be usedto solve polynomial equations? (ET)

How can you create and solve apolynomial equation that models areaand vertical motion? (ET)

binomial, trinomial, polynomial,degree, leading coefficient, monomial

FOIL root, zero of a function, perfect squaretrinomial

Additional Information:Methods for multiplying polynomials can include:1. distributive property2. columns3. FOIL4. table

Page 1 of 1


Topic: PolynomialsSubject Area(s):

Days: 25

Grade(s): 8

Key Learning:






Concept: Sums, Differences and Productsbinomial - trinomial - polynomial - degree - leading coefficient - monomial -

Concept: FactoringFOIL -

Concept: Solve quadratic equationsroot - zero of a function - perfect square trinomial -

Page 1 of 1


Topic: PolynomialsSubject Area(s):

Days: 25

Grade(s): 8

Radical expressions can be simplified. Graphs of radical equations canbe compared and applied to real l i fe situations.

How can radical equations andtheir graphs be used to model real l i fe

problems?

Graphs of radicalfunctionsM11.D.2 .1 .2

Simplify radicalexpressionsM11.A.1 .1 .3, M11.A.1 .1 .1

Operations on radicalexpressionsM11.A.2 .2 .1

How do you graph the parent squareroot function? (A)

How do operations performed on theparent square root function change itsgraph? (ET)

How do you use the Product Propertyof Radicals to simplify a radicalexpression? (A)

How do you multiply radicalexpressions? (A)

How do you use the Quotient Propertyof Radicals to simplify radicalexpressions? (A)

How do you rationalize thedenominator of a radical expression?(A)

How do you add and subtract radicalexpressions? (A)

How do you multiply radicalexpressions? (A)

What makes radical terms "liketerms"? (ET)

radical expression, radical function,square root function, parent squareroot function

simplest form of a radical expression,rationalizing the denominator,conjugates

Page 1 of 2


Topic: RadicalsSubject Area(s):

Days: 21Grade(s):

Key Learning:





Solve radical equationsM11.D.2 .1 .5

Pythagorean Theoremand related formulasM11.C.3 .1 .1, M11.C.1 .4 .1, 2 .10 .11 .B

How do you solve a radical equation?(A)

How can radical equations be used tosolve real life problems? (ET)

Why can radical equations haveextraneous solutions? (ET)

How can you find the distancebetween 2 points in the coordinateplane? (A)

How can you find the midpoint of aline segment given coordinates of itsendpoints? (A)

How can the Distance and Midpointformulas be used to solve real lifeproblems? (ET)

radical equation, extraneous solution hypotenuse, legs of a right triangle, ,midpoint, midpoint formula, distanceformula


Page 2 of 2



Days: 21Grade(s):





Concept: Graphs of radical functionsradical expression - radical function - square root function - parent square root function -

Concept: Simplify radical expressionssimplest form of a radical expression - rationalizing the denominator - conjugates -

Concept: Solve radical equationsradical equation - extraneous solution -

Concept: Pythagorean Theorem and related formulashypotenuse - legs of a right triangle - - Pythagorean Theoremmidpoint - midpoint formula - distance formula -

Page 1 of 1



Days: 21Grade(s):

Formulas and shortcuts can be used to solve problems.

What formulas and shortcutsare helpful for solving problems?

FormulasM8.A.2.2 .2, M8.B.2 .3 .1, M8.B.2 .3 .2, 2 .5 .8 .B,

2 .3 .8 .B, 2 .9 .8 .C, M8.B.2 .1 .1, M8.B.2 .1 .3, M8.B.

2 . 1 . 2, 2.3.8 .A, 2 .3 .8 .E, M8.B.1 .1 .4

Pythagorean TheoremM8.C.1 .2 .1, 2 .5 .8 .B, 2.10.8 .A

Menta l Math wi thPercentsM8.A.3.2 .1

How are formulas for area, perimeterand surface area used? (ET)

How are formulas used with anglemeasures? (ET)

How are temperature conversionsmade? (ET)

What is the Pythagorean Theorem? (A)

How can the Pythagorean Theorem beused to solve problems? (ET)

How can shortcuts be used to findpercents of numbers? (ET)

area, perimeter, surface area, simpleinterest, rate, regular polygon,irregular polygon, volume

Pythagorean Theorem, hypotenuse,leg, square root


Page 1 of 1


Topic: PSSA PrepSubject Area(s): Math

Days: 7Grade(s): 8

Key Learning:






Concept: Formulasarea - perimeter - surface area - simple interest - rate - regular polygon - irregular polygon - volume -

Concept: Pythagorean TheoremPythagorean Theorem - hypotenuse - leg - square root -

Page 1 of 1


Topic: PSSA PrepSubject Area(s): Math

Days: 7Grade(s): 8

Data can be analyzed and used to make decisions

What can we do with data?

Box and Whisker Plots2.6.8 .A, 2 .6 .8 .E, M8.E .1 .1 .3, M8.E .4 .1 .2

Scatterplots2 .6 .8 .C, M8.E .4 .1 .1, M8.E .4 .1 .2

Use of Different GraphTypes2 .4 .8 .F, 2.5.8 .A, M8.E .1 .1 .1, M8.E .1 .1 .2, M8.E .4 .1 .2

How is a Box and Whisker Plot made?(A)

What are quartiles and the IQR andwhat do they show? (ET)

What is a scatterplot? (A)

What do the types of correlation looklike and what do they mean? (A)

How can we make predictions usingdata in a scatterplot? (ET)

When is it best to use different graphtypes? (A)

When is it best to use different graphtypes? (ET)

box and whisker plot, quartiles, inter-quartile range (IQR), upper quartile,lower quartile, median

scatterplot, correlation, line of best fit circle graph, line graph

Additional Information:Students should recognize strong versus weak correlation.

Review of multiple bar graphs, stem-and-leaf plots and histograms is provided in "Class Starters" in the PSSA PrepSmartBoard file

Page 1 of 1


Topic: Data and StatisticsSubject Area(s): Math

Days: 10

Grade(s): 8

Key Learning:






Concept: Box and Whisker Plotsbox and whisker plot - quartiles - inter-quartile range (IQR) - upper quartile - lower quartile - median -

Concept: Scatterplotsscatterplot - correlation - line of best fit -

Concept: Use of Different Graph Typescircle graph - line graph -

Page 1 of 1


Topic: Data and StatisticsSubject Area(s): Math

Days: 10

Grade(s): 8

Probabil ity can be used to compare and contrast, and to makepredictions and inferences.

How can probabilty be used tomake predictions?

Simple Experimental andTheoretical Probabil ity2 .7 .8 .D, 2 .7 .8 .E, M8.E .3 .1 .1, 2 .7 .8 .B, 2 .7 .8 .C

Compound EventsM8.E .3 .2 .1, 2 .7 .8 .B, 2 .7 .8 .E, 2 .7 .8 .D

What is experimental probability andhow do you find it? (A)

How can you use experimentalprobability to make predictions? (ET)

What is theoretical probability andhow do you find it? (A)

How can you use theoreticalprobability to make predictions? (ET)

How can the total number of outcomesbe found for compound events? (A)

How do you find the probability ofcompound events? (ET)

How do you find the probability ofindependent and dependent events?(ET)

(A)

experimental probability, theoreticalprobability, outcomes, sample space

compound events, independentevents, dependent events, treediagram

Additional Information:Permutations and combinations are found using lists and tree diagrams, not factorial formulas.

Page 1 of 1


Topic: ProbabilitySubject Area(s): Math

Days: 10

Grade(s): 8

Key Learning:






Concept: Simple Experimental and Theoretical Probabil ityexperimental probability - theoretical probability - outcomes - sample space -

Concept: Compound Eventscompound events - independent events - dependent events - tree diagram -

Page 1 of 1


Topic: ProbabilitySubject Area(s): Math

Days: 10

Grade(s): 8

how do you write and evaluate algebraic expressions… · how do you write and evaluate algebraic...

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