Core Curriculum for 8th-Grade Mathematics

8/23/2019 Core Curriculum for 8th-Grade Mathematics

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College-Career Ready Common Core Standards/PA Common CorePlanning and Scheduling Timeline

3rd QuarterMath: 8th Grade

1

In the beginning of this quarterstudentunknown side of right triangles by solvingdimensional figures, and compare and co

By the end of this quarterstudents will bTheorem. They will be able to construct sitransformations on a coordinate plan and i

able to find the unknown side of a right triathe Pythagorean Theorem. They will be amidpoint between two points. The terms stsimilar, congruent, proportional, ratio,coordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte

will determine if a triangle isroportions. They will reviewtrast rotations, reflections, a

e able to solve real life problilar and congruent two-dime

dentify specific points as an

ngle within another figure anle to use the distance formuludents should learn to use wotations, reflections, translheorem, hypotenuse, rightance, midpoint, midpoint

ce area, kite/quadrilateral, lertical angles, perpendiculx.

a right triangle and find theproperties of various two-d translations.

ms using the Pythagoreannsional figures in a series ofrdered pair. Students will be

solve real world problems usingto determine distance and the

ith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,

formula, right angle, radius,ine symmetry, net,ar lines, perpendicular

Performance Descriptor/ EligibleContent

PA Common CoreStandards

What will it mean for thestudent?

Performance Descriptor

2.3.8.A.2Understand and apply congruencesimilarity, and geometric transformationsusing various tools.

Eligible ContentM08.C-G.1.1.1Identify and apply properties of rotations,reflections, and translations.

Example: Angle measures are preservedin rotations, reflections, and translations.

2.3 Geometry

CCRS.8.G.2CCRS.8.G.3CCRS.8.G.4

Students will be able to Identify

and apply properties of rotations,reflections and translations.

Performance Descriptor2.3.8.A.2Understand and apply congruencesimilarity, and geometric transformationsusing various tools.

Eligible ContentM08.C-G.1.1.2Given two congruent figures, describe asequence of transformations that exhibitsthe congruence between them.

2.3 GeometryCCRS.8.G.2CCRS.8.G.3CCRS.8.G.4

Students will be able todetermine congruence usingvarious tools.


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Standards of Mathematical Practice

solving them; Use appropriate tools stand quantitatively; Model with mathemrepeated reasoning.

Non-Negotiables: Make sense of pro

ategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere in

ructure; Reason abstractlyexpress regularity in

How will students apply t eir knowledge and skills? Textual References and

Proficient: Advanced:

Resources

Sample Task:

Describe the effects of translations,rotations, and reflections on two-dimensional figures usingcoordinates.ExplainInvestigate

Sample Task:

Compare and contrast the effects oftranslations, rotations, and reflectionson two or more two-dimensionalfigures.InvestigateAnalyze

See Schoolnet for Internet

links and resources.Use this space forplanning.

Sample Task:Determine congruence throughinvestigations obtained fromrotations, reflections, andtranslations.Draw conclusionsConstruct

Sample Task:Describe a sequence that exhibitscongruence of two-dimensionalfigures using rotations, reflections,and translations.ExplainSynthesize


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In the beginning of this quarterstudents

unknown side of right triangles by solvingdimensional figures, and compare and con


to find the unknown side of a right trianglePythagorean Theorem. They will be able tmidpoint between two points. The terms stsimilar, congruent, proportional, ratio, rcoordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte

will determine if a triangle is

roportions. They will reviewtrast rotations, reflections, an

e able to solve real life probleilar and congruent two-dime

dentify specific points as an o

within another figure and soluse the distance formula to

udents should learn to use wiotations, reflections, translheorem, hypotenuse, righttance, midpoint, midpointe area, kite/quadrilateral, l

ertical angles, perpendiculx.

right triangle and find the

roperties of various two-d translations.

ms using the Pythagoreannsional figures in a series ofrdered pair. Students will be able

e real world problems using thedetermine distance and theith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,ormula, right angle, radius,

ine symmetry, net,ar lines, perpendicular





2.3.8.A.2Understand and apply congruence,similarity, and geometric transformationsusing various tools.

Eligible ContentM08.C-G.1.1.3Describe the effect of dilation,translations, rotations, and reflections ontwo-dimensional figures, usingcoordinates.

2.3 Geometry


Students will be able to describe

the effect of dilation, translations,rotations and reflections on two-dimensional figures.

Performance Descriptor2.3.8.A.1Apply the concepts of volume ofcylinders, cones, and spheres to solvereal world and mathematical problems.

Eligible ContentM08.C-G.1.1.4Given two similar two-dimensionalfigures, describe a sequence oftransformations that exhibits the similarity

between them.


Students will be able todetermine a similar twodimensional figure in a sequenceof transformations.


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solving them; Use appropriate tools stand quantitatively; Model with matherepeated reasoning.




tructure; Reason abstractlyexpress regularity in



Resources

Sample Task:

Investigate the effects of dilation,translations, rotations, and reflectionsof two-dimensional figures on acoordinate grid, using coordinates toexplain sequences.Draw conclusionsConstruct

Sample Task:

Explain and justify the effects ofdilation, translations, rotations, andreflections of 2-dimensional figureson a coordinate grid, usingcoordinates to explain sequences.AnalyzeProve



Sample Task:Distinguish a similar two-dimensional figure within a group oftransformed figures.ExamineDifferentiate

Sample Task:Design a series of similar twodimensional figures in a sequence oftransformations using proportionalreasoning.CreateSynthesize


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unknown side of right triangles by solvingdimensional figures, and compare and co

By the end of this quarterstudents will bTheorem. They will be able to construct sitransformations on a coordinate plan and ito find the unknown side of a right trianglePythagorean Theorem. They will be able tmidpoint between two points. The terms ssimilar, congruent, proportional, ratio,coordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte


proportions. They will reviewtrast rotations, reflections, a


dentify specific points as anwithin another figure and solo use the distance formula toudents should learn to use wotations, reflections, translheorem, hypotenuse, rightance, midpoint, midpoint


a right triangle and find the

properties of various two-d translations.

ms using the Pythagoreannsional figures in a series ofrdered pair. Students will be ablee real world problems using thedetermine distance and theith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,ormula, right angle, radius,






2.3.8.A.3Understand and apply the PythagoreanTheorem to solve problems.

Eligible ContentM08.C-G.2.1.1Apply the converse of the Pythagoreantheorem to show a triangle is a righttriangle.

2.3 Geometry


Students will be able to

determine if a triangle is a righttriangle by applying a^2 + b^2 =c^2

Performance Descriptor2.3.8.A.3Understand and apply the PythagoreanTheorem to solve problems.

Eligible ContentM08.C-G.2.1.2Apply the Pythagorean theorem todetermine unknown side lengths in righttriangles in real-world and mathematicalproblems in two and three dimensions.


Students will be able to apply thePythagorean Theorem todetermine unknown side lengthsin right triangles in real world andmathematical problems in twoand three dimensions.


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solving them; Use appropriate tools stand quantitatively; Model with mathemrepeated reasoning.




ructure; Reason abstractlyexpress regularity in



Resources

Sample Task:

Apply the converse to determine iftriangles are right triangles in thecontext of a word problem.ExamineApply

Sample Task:

Compare two triangles in the contextof a word problem and apply theconverse of the Pythagoreantheorem to determine if eithertriangular figure is a right triangle.EvaluateProveInvestigate



Sample Task:Solve various problems in real lifecontext involving right triangles byusing the Pythagorean theorem tofinding leg a, b, and c (hypotenuse).ApplyConstruct

Sample Task:Determine the unknown side of aright triangle associated with anothertwo-dimensional figure where a givenside must be deduced from the otherfigure.Draw conclusionsEvaluate


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By the end of this quarterstudents will bTheorem. They will be able to construct sitransformations on a coordinate plan and ito find the unknown side of a right trianglePythagorean Theorem. They will be able tmidpoint between two points. The terms ssimilar, congruent, proportional, ratio,coordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte








ms using the Pythagoreannsional figures in a series ofrdered pair. Students will be ablee real world problems using thedetermine distance and theith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,ormula, right angle, radius,






2.3.8.A.2Understand and apply the PythagoreanTheorem to solve problems.

Eligible ContentM08.C-G.2.1.3Apply the Pythagorean theorem to findthe distance between two points in acoordinate system

2.3 Geometry


Students will be able to apply the

Pythagorean Theorem todetermine unknown side lengthswithin a coordinate grid.

Performance Descriptor2.3.8.A.1Apply the concept of volume of cylinders,

cones, and spheres to solve real worldand mathematical problems.

Eligible ContentM08.C-G.3.1.1Apply formulas for the volumes of cones,cylinders, and spheres to solve real-worldand mathematicalproblems. Formulas will be provided.M8.B.2.2.1Calculate the surface area of cubes andrectangular prisms (Formula provided onthe reference sheet).

M8.B.2.2.3Determine the appropriate type ofmeasurement (circumference, perimeter,area, surface area, volume) for a givensituation (e.g., which measurement isneeded to determine the amount ofcarpeting for a room)

2.3 GeometryCCRS.8.G.9

Students will be able to solvereal-world and mathematicalproblems involving volume of

cylinders, cones and spheres,determine surface area of ofcubes and rectangular prismsand select the appropriate type ofmeasurement for a givensituation.


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Standards of Mathematical Practicesolving them; Use appropriate tools stand quantitatively; Model with matherepeated reasoning.

Non-Negotiables: Make sense of prorategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere inructure; Reason abstractlyexpress regularity in



Resources

Sample Task:Determine the unknown side (in theform of a line segment) of righttriangles placed on coordinate grids.ApplySolve

Sample Task:Determine the unknown side (in theform of a line segment) of a righttriangle and determine thecoordinates of a point when the righttriangle is transformed at a specificpoint.Apply conceptsVerify

See Schoolnet for Internetlinks and resources.Use this space forplanning.

Sample Task:Solve problems involving volume(cylinders, cones, and spheres),

surface area of cubes andrectangular prisms with oneconversion (i.e inches to feet), andexplain rationale for selectingappropriate measurement for a realworld problem.ApplyConstruct

Sample Task:Investigate and solve practicalproblems (volume of cylinders,

cones, and spheres) and surfacearea of cubes and rectangularprisms. Describe how changing onemeasured attribute of a figure affectsthe volume and surface area(Include one conversion). Given asituation, create a question todetermine perimeter, area, surfacearea, circumference, surface area,and/or volume. (e.g What is thedistance around the pool? How muchwater is required to fill the pool)Analyze

Prove


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By the end of this quarterstudents will bTheorem. They will be able to construct si

transformations on a coordinate plan and ito find the unknown side of a right trianglePythagorean Theorem. They will be able tmidpoint between two points. The terms ssimilar, congruent, proportional, ratio,coordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte








ms using the Pythagoreannsional figures in a series of

rdered pair. Students will be ablee real world problems using thedetermine distance and theith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,ormula, right angle, radius,






2.4.5.A.1Solve problems using conversions withina given measurement system.

Eligible ContentM8.B.1.1.1Convert among metric measurements(milli, centi, kilo using meter, liter andgram) (table of equivalency provided onthe reference sheet).M8.B.1.1.2Convert customary measurements up to

2 units above or below the given unit(e.g., inches to yards, pints to gallons)(table of equivalency provided on thereference sheet).M8.B.1.1.3Convert time up to 2 units above orbelow given unit (e.g., seconds to hours).M8.B.1.1.4Convert from Fahrenheit to Celsius orCelsius to Fahrenheit (formulas providedon the reference sheet).

2.4 Measurement, Data

and ProbabilityCCRS.5.MD.1

Students will be able to perform

conversions within the metricsystem and within the customarysystem including scalemeasurements, between units oftime and between units oftemperature.


2.3.8.A.1Apply the concepts of volume ofcylinders, cones, and spheres to solvereal-world and mathematical problems.Eligible ContentM8.C.1.1.1Match the three-dimensional figure withits net (cube, cylinder, cone, prism,pyramid). Any measurements usedshould be consistent in the stem andanswer choices.

2.3 Geometry

CCRS.8.G.9

Students will be able to

determine the net of cylinders,cones, prisms, and pyramids.


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Non-Negotiables: Make sense of proategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere intructure; Reason abstractlyexpress regularity in



Resources

Sample Task:Compare, contrast, and convertunits of measure between differentmeasurement systems (UScustomary or metric (SI)) anddimensions including temperature tosolve problems.AnalyzeEvaluate

Sample Task:Justify procedures involving realworld problems between customary,metric and dimensions includingtemperature .ProveInvestigate


Sample Task:

Distinguish between nets of threedimensional figures.CompareContrast

Sample Task:

Construct and explain thedifferences between nets of threedimensional figures.FormulateDesign


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to find the unknown side of a right trianglePythagorean Theorem. They will be able tmidpoint between two points. The terms stsimilar, congruent, proportional, ratio,coordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte


roportions. They will reviewtrast rotations, reflections, a




udents should learn to use wotations, reflections, translheorem, hypotenuse, rightance, midpoint, midpoint





e real world problems using thedetermine distance and theith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,





Performance Descriptor2.3.7.A.2Visualize and represent geometric figuresand describe the relationships betweenthem.Eligible ContentM8.B.2.1.1Determine the total number of degrees inthe interior angles of a polygon in 3 - 8sided figures (formula provided on thereference sheet).M8.B.2.1.2Determine the measurement of oneinterior angle of a regular polygon (3-8

sided polygons, formula provided on thereference sheet).M8.B.2.1.3Determine the number of sides of apolygon given the total number ofdegrees in the interior angles (3-8sided polygons, formula provided on thereference sheet).


Students will be able to examinepolygons to determine number ofdegrees in an angle using aformula or pattern in the contextof a real world problem.


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solving them; Use appropriate tools stand quantitatively; Model with matherepeated reasoning.




tructure; Reason abstractlyexpress regularity in



Resources

Sample Task:

Formulate patterns and useformulas to determine the number ofdegrees in interior angles of regularpolygons.SolveConstruct

Sample Task:

In the context of problems, explainthe differences between the degreesfor interior angles when the polygonis altered.InvestigateProve




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to find the unknown side of a right trianglePythagorean Theorem. They will be able tmidpoint between two points. The terms stsimilar, congruent, proportional, ratio,coordinates, converse of Pythagoreanequilateral triangle, scalene triangle, dicircumference, diameter, volume, surfaparallelogram, parallel lines, adjacent,bisector, rhombus, trapezoid, and verte


roportions. They will reviewtrast rotations, reflections, a




udents should learn to use wotations, reflections, translheorem, hypotenuse, rightance, midpoint, midpoint





e real world problems using thedetermine distance and theith increasing precisions are:ations, dilation, sequence,triangle, isosceles triangle,






2.3.7.A.2Visualize and represent geometric figuresand describe the relationships betweenthem.

Eligible ContentM8.C.1.1.2Define, identify and/or use properties ofangles formed by intersecting lines(complementary, supplementary,adjacent and/or vertical angles).M8.C.1.1.3Define, identify and/or use properties ofangles formed when two parallel lines arecut by a transversal (alternate interior,alternate exterior, verticalcorresponding).

2.3 Geometry

CCRS.7.G.1CCRS.7.G.3

Students will be able to make

conjectures usingcomplementary, supplementary,adjacent, and verticalrelationships and determinemeasurement of angles usingtransversals and parallel lines.


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Non-Negotiables: Make sense of proategically; Look for and make use of satics; Attend to precision; Look for and

blems and persevere intructure; Reason abstractlyexpress regularity in



Resources

Sample Task:Determine the measurement ofunknown angles using properties ofintersecting lines.ExamineAssess

Sample Task:Justify reasoning for an unknownangles using several properties ofangels using including transversalsand parallel lines.ExplainAnalyze



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Core Curriculum for 8th-Grade Mathematics

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Transcript of Core Curriculum for 8th-Grade Mathematics