SM1 Curriculum Notebook.docx

Linear and Exponential Core Guide
Interpret expressions for functions in terms of the situation they model. (F.LE.5)
Standard I.F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context. Limit exponential functions to those of the form f(x) = bx + k.
Concepts and Skills to Master
• Interpret the parameters in a linear function in terms of a context. Parameters include slope and y- intercept
• Interpret the parameters in an exponential function in terms of a context. Parameters include the base value and vertical shifts.
Related Standards: Current Course
Related Standards: Future Courses
I.F.IF.3, I.F.IF.4, I.F.IF.7, I.F.IF.9, I.F.BF.1b, I.F.BF.2, I.F.BF.3, I.F.LE.1, I.F.LE.2, I.F.LE.3
II.F.IF.4, II.F.IF.6, II.F.IF.7, II.F.BF.1b, II.F.BF.3, II.F.LE.3, III.F.IF.4, III.F.IF.6, III.F.IF.7, III.F.BF.1b, III.F.BF.3, III.F.LE.5
Support for Teachers
Critical Background Knowledge
• Compare proportional relationships y=mx to other linear relationships y = mx+b (7.RP.2, 8.F.3, 8.EE.5)
• Compare properties of two functions (8.F.2), interpret the equation y = mx+b (8.F.3), and interpret the
rate of change and initial value (8.F.4)
Academic Vocabulary
parameters, base value, initial value, vertical shift
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70276
I.F.LE.5


Congruence Core Guide
Build on student experience with rigid motions from earlier grades (G.CO.1-5)
Standard I.G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Concepts and Skills to Master
• Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment.
• Use prior experience with point, line, distance along a line, and distance around a circular arc to define angle,
circle, perpendicular line, and line segment.
• Demonstrate mathematical notation for each term.
Related Standards: Current Course
Related Standards: Future Courses
Most Geometry standards, I.G.CO.12, I.G.CO.13
II.G.CO.9, II.G.CO.10, II.G.CO.11
Support for Teachers
Critical Background Knowledge
• Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines (4.G.1)
• Recognize angles as geometric shapes formed wherever two rays share a common endpoint (4.MD.5)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Include the use of coordinates and absolute value to find horizontal and vertical distances (6.NS.8)
• Apply and use the Pythagorean Theorem to find distance (8.G.8)
Academic Vocabulary
angle, circle, perpendicular line, parallel line, line segment, distance, arc
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.1


Congruence Core Guide
Build on student experience with rigid motions from earlier grades (G.CO.1-5)
Standard I.G.CO.2: Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Concepts and Skills to Master
• Represent reflections, rotations and translations using a variety of media.
• Compare and contrast rigid and non-rigid transformations.
• Understand transformations as functions that take points in the plane as inputs and give other points as outputs.
Related Standards: Current Course
Related Standards: Future Courses
Geometry congruence standards (G.CO), I.G.GPE.4, I.G.GPE.5,I.F.IF.1, I.F.IF.2, I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, Prove Geometric Theorems
Support for Teachers
Critical Background Knowledge
• Identify different types of transformations (8.G.1)
• Understanddefinitionoffunction(8.F.1andI.F.IF.1)
• Describe effects of transformations using coordinates (rotations, reflections, translations, and dilations) (8.G.3)
Academic Vocabulary
plane, transformation, reflection, rotation, translation, preserve, function in terms of input and output
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.2


Congruence Core Guide
Build on student experience with rigid motions from earlier grades (G.CO.1-5)
Standard I.G.CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Concepts and Skills to Master
• Describe and identify lines of symmetry and points of rotation.
• Describe rotations and reflections which take a rectangle, parallelogram, trapezoid, or regular polygon onto itself.
Related Standards: Current Course
Related Standards: Future Courses
Geometry congruence standards (G.CO), I.G.GPE.4, I.G.GPE.5,I.F.IF.1, I.F.IF.2, I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4,
II.G.SRT.5, II.G.SRT.6, II.G.SRT.8, II.G.C.1, II.G.GPE.6
Support for Teachers
Critical Background Knowledge (Access Background Knowledge)
• Understand properties of rectangle, parallelogram, trapezoid, and regular polygons such as angle measures and side lengths (3.G.1)
• Understand lines of symmetry (4.G.3)
• Classify two dimensional figures by presence or absence of parallel or perpendicular lines (4.G.2) and other
properties (5.G.4)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Observe orientation of a figure is preserved with rotations and translations, but not with reflections (8.G.3)
Academic Vocabulary I.G.CO.3
rectangle, parallelogram, trapezoid, regular polygon, rotation, reflection, symmetry
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537


Congruence Core Guide
Build on student experience with rigid motions from earlier grades (G.CO.1-5)
Standard I.G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Concepts and Skills to Master
• Use precise definitions of angles, circles, perpendicular lines, parallel lines, and line segments to develop definitions ofrotations,reflections, andtranslations.
Related Standards: Current Course
Related Standards: Future Courses
Geometry congruence standards (G.CO), I.G.GPE.4, I.G.GPE.5,I.F.IF.1, I.F.IF.2, I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4,
II.G.SRT.5, II.G.SRT.6, II.G.SRT.8, II.G.C.1, II.G.GPE.6
Support for Teachers
Critical Background Knowledge (Access Background Knowledge)
• Recognize shapes having a given number of angles (2.G.1) and angles are formed wherever two rays share a common endpoint (4.MD.5)
• Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines (4.G.1)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Observe orientation of a figure is preserved with rotations and translations, but not with reflections (8.G.3)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments (I.G.CO.1)
I.G.CO.4 Academic Vocabulary
angle, circle, perpendicular lines, parallel lines, line segment, rotation, reflection, translation
Possible curriculum resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537


Congruence Core Guide
Build on student experience with rigid motions from earlier grades (G.CO.1-5)
Standard I.G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using,forexample,graph paper,tracingpaper,orgeometrysoftware.Specifyasequenceoftransformationsthat will carry a given figure onto another. Point out the basis of rigid motions in geometric concepts, for example, translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.
Concepts and Skills to Master
• Draw a transformed figure by performing rotations, reflections, and translations using a variety of methods.
• Identify a sequence of transformations that will carry a given figure to another.
• Understand and use rigid motions, including recognizing that translations move points a specified distance along a
line parallel to a specified line and that rotations move objects along a circular arc with a specified center through a specified angle.
Related Standards: Current Course
Related Standards: Future Courses
All Geometry congruence standards (G.CO), I.G.GPE.4, I.G.GPE.5, I.F.IF.1, I.F.IF.2, I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4,
II.G.SRT.5, II.G.SRT.6, II.G.SRT.8, II.G.C.1, II.G.GPE.6
Support for Teachers
Critical Background Knowledge
• Recognize shapes having a given number of angles (2.G.1) and angles are formed wherever two rays share a common endpoint (4.MD.5)
• Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines (4.G.1)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Observe orientation of a figure is preserved with rotations and translations, but not with reflections (8.G.3)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments (I.G.CO.1)
Academic Vocabulary
rotation, reflection, translation
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.5


Congruence Core Guide
Understandcongruenceintermsofrigidmotions.Rigidmotionsareatthefoundationofthedefinitionofcongruence. Reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems (G.CO.6-8)
Standard I.G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigidmotiononagiven figure;giventwofigures,usethedefinitionofcongruenceintermsofrigidmotionstodecide whether they are congruent.
Concepts and Skills to Master
• Transform figures using geometric descriptions of rigid motions.
• Predict the effect of rotating, reflecting or translating a given figure using prior experience with rigid motions.
• Justify the congruence of two figures using properties of rigid motions.
Related Standards: Current Course
Related Standards: Future Courses
All Geometry congruence standards (G.CO), I.G.GPE.4,I.G.GPE.5, I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4,
II.G.SRT.5, II.G.SRT.6, II.G.SRT.8, II.G.C.1, II.G.GPE.6
Support for Teachers
Critical Background Knowledge (Access Background Knowledge)
• Recognize shapes having a given number of angles (2.G.1) and angles are formed wherever two rays share a common endpoint (4.MD.5)
• Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines (4.G.1)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Observe orientation of a figure is preserved with rotations and translations, but not with reflections (8.G.3)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments (I.G.CO.1)
Academic Vocabulary
rigid motion, congruent, rotate, translate, reflect
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.6


Congruence Core Guide
Understandcongruenceintermsofrigidmotions.Rigidmotionsareatthefoundationofthedefinitionofcongruence. Reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems (G.CO.6-8)
Standard I.G.CO.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Concepts and Skills to Master
• Identify corresponding parts of two triangles.
• Showthattwotrianglesarecongruentifandonlyifcorrespondingpairsofsidesandcorrespondingpairsofangles are congruent (CPCTC).
Related Standards: Current Course
Related Standards: Future Courses
All Geometry congruence standards (G.CO), I.G.GPE.4, I.G.GPE.5,I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4, II.G.SRT.5,
II.G.SRT.6, II.G.SRT.8, II.G.C.1, II.G.GPE.4, II.G.GPE.6, III.F.TF standards.
Support for Teachers
Critical Background Knowledge
• Identify corresponding parts of geometric figures (7.G.1 and 7.G.2)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Observe orientation of a figure is preserved with rotations and translations, but not with reflections (8.G.3)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments (I.G.CO.1)
Academic Vocabulary
if and only if (iff), corresponding, rigid motion, congruent
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.7


Congruence Core Guide
Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Reason from thebasicpropertiesofrigidmotions(thattheypreservedistanceandangle),which areassumedwithoutproof.Rigidmotionsand theirassumedpropertiescanbeusedtoestablishtheusual trianglecongruencecriteria,whichcanthenbeusedtoproveother theorems (G.CO.6-8)
Standard I.G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definitionofcongruence intermsofrigidmotions.
Concepts and Skills to Master
• Identify the minimum conditions necessary for triangle congruence (ASA, SAS, and SSS).
• Understand, explain, and demonstrate why ASA, SAS, or SSS are sufficient to show congruence.
• Understand, explain, and demonstrate why SSA and AAA are not sufficient to show congruence.
• Explain the connection between ASA and AAS congruence theorems.
Related Standards: Current Course
Related Standards: Future Courses
All Geometry congruence standards (G.CO), I.G.GPE.4,I.G.GPE.5, I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4,
II.G.SRT.5, II.G.SRT.6, II.G.SRT.8, II.G.GPE.4, II.G.GPE.6, III.F.TF standards
Support for Teachers
Critical Background Knowledge
• Identify corresponding parts of geometric figures (7.G.1 and 7.G.2)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Observe orientation of a figure is preserved with rotations and translations, but not with reflections (8.G.3)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments
(I.G.CO.1)
• Use definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if
correspondingpairsofsides and corresponding pairs of angles are congruent (I.G.CO.7)
Academic Vocabulary
ASA, SAS, SSS, AAA, SSA, included angle, included side, corresponding parts
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.8


Congruence Core Guide
Make geometric constructions (G.CO.12-13)
Standard I.G.CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Emphasize the ability to formalize and defend how these constructions result in the desired objects. For example, copying a segment; copying anangle;bisectingasegment;bisectinganangle;constructingperpendicularlines, includingtheperpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Concepts and Skills to Master
• Perform the following constructions using a variety of tools and methods: copying a segment; copying an angle; bisectingasegment;bisectinganangle;constructingperpendicularlines,includingthe perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
• Explain why these constructions result in the desired objects.
• Modify an already created construction to build other constructions. Recognize that constructions develop from one another.
Related Standards: Current Course
Related Standards: Future Courses
All Geometry congruence standards (G.CO), I.G.GPE.4, I.G.GPE.5
II.G.CO.9, II.G.CO.10, II.G.CO.11, II.G.SRT.1, II.G.SRT.2, II.G.SRT.4,
II.G.SRT.5, II.G.SRT.6, II.G.SRT.8, II.G.C.1, II.G.GPE.4, II.G.GPE.6, III.F.TF
standards
Support for Teachers
Critical Background Knowledge
• Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines (4.G.1)
• Draw (using various media) geometric shapes with given conditions (7.G.2)
• Draw polygons in coordinate plane (6.G.3)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments
(I.G.CO.1)
Academic Vocabulary
segment, angle, bisect, perpendicular, parallel, construction
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537
I.G.CO.12


Congruence Core Guide
Make geometric constructions (G.CO.12-13)
Standard I.G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Concepts and Skills to Master
• Construct an equilateral triangle, a square, and a regular hexagon each inscribed in a circle.
• Modify an already created construction to build other constructions. Recognize that constructions develop from one another.
Related Standards: Current Course
Related Standards: Future Courses
All Geometry congruence standards (G.CO), I.G.GPE.4,I.G.GPE.5, I.G.GPE.7,I.F.BF.3
II.G.CO.9, II.G.CO.10, II.G.CO.11, All circle standards II.G.C,II.G.GPE.1, II.G.GPE.4,II.G.GPE.6
Support for Teachers
Critical Background Knowledge (Access Background Knowledge)
• Understand the properties of regular polygons.
• Construct congruent segments and perpendicular lines.
• Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines (4.G.1)
• Draw (using various media) geometric shapes with given conditions (7.G.2)
• Draw polygons in coordinate plane (6.G.3)
• Verify experimentally the properties of rigid transformations, showing that lines are taken to lines, line
segments are taken to line segments, angles are taken to angles, and parallel lines are taken to parallel
lines (8.G.1 a, b, c)
• Describe a sequence of rotations, reflections, and translations that exhibits congruence between two figures (8.G.2)
• Knowprecisedefinitionsandpropertiesofangles,circles,perpendicularlines,parallellines,andlinesegments (I.G.CO.1)
Academic Vocabulary
equilateral triangle, square, regular hexagon, inscribed, construction
I.G.CO.13 Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5620#71537


Expressing Geometric Properties with Equations Core Guide
Use coordinates to prove simple geometric theorems algebraically (G.GPE.4-5, 7)
StandardI.G.GPE.4:Usecoordinatestoprovesimplegeometrictheoremsalgebraically.Forexample,proveordisprove thatafiguredefinedby fourgivenpointsinthecoordinateplane isarectangle;proveordisprovethatthepoint(1,√3) liesonthecirclecenteredattheoriginand containingthepoint(0,2).
Concepts and Skills to Master
• Use coordinates to prove simple geometric theorems algebraically.
Related Standards: Current Course
Related Standards: Future Courses
I.A.CED.2; I.A.CED.3; I.A.CED.4; I.A.REI.3; I.A.REI.6, I.A.REI.10;
I.A.REI.11; I.F.IF.1; I.F.IF.4; I.F.IF.5; I.F.IF.7; I.F.IF.9; I.BF.3; All
Secondary Math I Geometry Congruence Standards
II.A.SSE.3; II.A.CED.2; II.A.REI.4; II.A.REI.7; II.G.CO.9; II.G.CO.10;
II.G.CO.11; II.G.SRT.1; II.G.SRT.2; II.G.SRT.4; II.G.SRT.5; II.G.SRT.6;
II.G.SRT.7; II.G.C.1; II.G.C.2; II.G.C.3; II.G.C.4; II.G.C.5; II.G.GPE.1; II.G.GMD.1; III.G.MG.1; III.G.MG.3; Pre Calculus G.GPE.2; Pre Calculus G.GPE.3
Support for Teachers
Critical Background Knowledge
• Compose and understand the coordinate plane (5.G.1)
• Find and position pairs of integers and other rational numbers on a coordinate plane (6.NS.6c)
• Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane
(6.NS.8)
• Draw polygons in the coordinate plane given coordinates for the vertices. Apply these techniques in the context
ofsolvingreal-worldandmathematicalproblems. (6.G.3)
• Use coordinates and absolute value to find distance between points with same x-coordinate or same y-coordinate
(6.NS.8)
• Interprettheequationy=mx+basdefiningalinearfunction,whosegraphisastraightline(8.F.3,4)
• Use similar triangles to explain why the slope m is the same between any two distinct points on a non-
verticallineinthecoordinate plane (8.EE.6)
• Apply the Pythagorean Theorem to find the distance between two points. (8.G.8)
Academic Vocabulary
Prove, theorem
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70394
I.G.GPE.4


Expressing Geometric Properties with Equations Core Guide
Use coordinates to prove simple geometric theorems algebraically (G.GPE.4-5, 7)
Standard I.G.GPE.5: Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Concepts and Skills to Master
• Prove that the slopes of parallel lines are equal.
• Prove that the product of the slopes of perpendicular lines is -1.
• Use slope criteria for parallel and perpendicular lines to solve geometric problems.
• Writetheequationofalineparallelorperpendiculartoagivenline,passingthroughagivenpoint.
Related Standards: Current Course
Related Standards: Future Courses
I.A.CED.2; I.A.REI.6; I.A.REI.10; I.F.IF.4; I.F.IF.6; I.F.IF.7; I.F.IF.9; I.F.BF.3;
I.G.CO.1; I.G.CO.3; I.G.CO.4; I.G.CO.5; I.G.GPE.4; I.G.GPE.7
II.A.SSE.3; II.A.CED.2; II.A.CED.3; II.F.IF.4; II.F.IF.6; II.F.IF.7; II.F.IF.9;
II.F.BF.3; II.G.CO.9; II.G.CO.10; II.G.CO.11; II.G.SRT.1; II.G.SRT.2;
II.G.SRT.4; II.G.SRT.5; II.G.SRT.6; II.G.SRT.7; II.G.C.2; II.G.C.3; II.G.C.4; II.G.GPE.4; III.G.MG.1; III.G.MG.3
Support for Teachers
Critical Background Knowledge
• Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane and find distance between points with the same x-coordinate or the same y-coordinate (6.NS.8)
• Interprettheequationy=mx+basdefiningalinearfunction,whosegraphisastraightline(8.F.3,4)
• Use similar triangles to explain why the slope m is the same between any two distinct points (8.EE.6)
• Apply the Pythagorean Theorem to find the distance between two points. (8.G.8)
• Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales. (I.A.CED.2)
Academic Vocabulary I.G.GPE.5
Parallel, perpendicular, reciprocal
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70394


Expressing Geometric Properties with Equations Core Guide
Use coordinates to prove simple geometric theorems algebraically (G.GPE.4-5, 7)
Standard I.G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; e.g., connectwithThe PythagoreanTheoremandthedistanceformula.
Concepts and Skills to Master
• Use the distance formula to compute perimeters of polygons and areas of triangles and rectangles.
Related Standards: Current Course
Related Standards: Future Courses
I.A.CED.2; I.A.CED.3; I.A.CED.4; I.A.REI.6; I.F.IF.4; I.F.IF.5; I.F.IF.7;
I.F.BF.3; All Secondary Math I Geometry Congruence Standards; I.G.GPE.4; I.G.GPE.5
II.A.SSE.3; II.A.CED.2; II.A.REI.4; II.A.REI.7; II.G.CO.10; II.G.CO.11;
II.G.SRT.2; II.G.SRT.4; II.G.SRT.5; II.G.SRT.6; II.G.SRT.8; II.G.C.1;
II.G.C.3; II.G.GPE.4; II.G.GPE.6; II.G.GMD.3; III.G.MG.1; III.G.MG.2;
III.G.MG.3; Pre Calculus G.GPE.2; Pre Calculus G.GPE.3
Support for Teachers
Critical Background Knowledge
• Solve real-world and mathematical problems involving perimeters of polygons (3.G.8)
• Compose and understand the coordinate plane (5.G.1) and solve problems by graphing points in all four
quadrants of the coordinate plane and use coordinates to find distance between points with same x-
coordinate or same y-coordinate (6.NS.8)
• Draw polygons in the coordinate plane given coordinates for the vertices (6.G.3)
• Solve real-world problems involving area (7.G.6)
• Interprettheequationy=mx+basdefiningalinearfunction,whosegraphisastraightline(8.F.3)
• Use similar triangles to explain why the slope m is the same between any two distinct points (8.EE.6)
• Apply the Pythagorean Theorem to find the distance between two points. (8.G.8)
AcaI.dGe.GmPicE.V7ocabulary
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70394


Interpreting Categorical and Quantitative Data Core Guide
Summarize, represent, and interpret data on a single count or measurement variable (Standards S.ID.1–3).
Standard I.S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
Concepts and Skills to Master
• Represent numerical data using dot plots, histograms, and box plots.
• Represent one or more numerical data sets on the same scale.
• Describe data sets from graphical representations.
• Recognize attributes that may be revealed by different representations (dot plots, histograms, and box plots).
Related Standards: Current Course
Related Standards: Future Courses
I.S.ID.2, I.S.ID.3, I.N.Q.1, I.N.Q.2, I.N.Q.3
III.S.ID.4, III.S.IC.1, III.S.IC.6
Support for Teachers
Critical Background Knowledge
• Display numerical data in plots on a number line, including dot plots, histograms, and box plots (6.SP.4)
• Summarize a data set using mean, median, interquartile range, and mean absolute deviation (6.SP .5c)
• Make a line plot (2.MD.9, 3.MD.4, 4.MD.1, and 5.MD.2) and draw a picture graph and a bar graph (2.MD.10 and
3.MD.3)
Academic Vocabulary
mean, median, interquartile range, center, spread, shape, dot plot, histogram, box plot, quartiles, minimum, maximum, spread, side-by-side (parallel) plots
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304
I.S.ID.1


Interpreting Categorical and Quantitative Data Core Guide
Summarize, represent, and interpret data on a single count or measurement variable (Standards S.ID.1–3).
Standard I.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Concepts and Skills to Master
• Understand standard deviation as a measure of spread. Use basic calculations to understand the concept (possibly connecting to MAD). Use technology when appropriate. (Standard deviation is applied to the normal distribution in Secondary Mathematics III.)
• Given two sets of data (numerically or graphically), identify similarities and differences in shape, center and spread.
• Compare data sets by describing the similarities and differences between their shapes, measures of center, and measures of spread.
Related Standards: Current Course
Related Standards: Future Courses
I.S.ID.1, I.S.ID.3, I.N.Q.1, I.N.Q.2, I.N.Q.3
III.S.ID.4, III.S.IC.1, III.S.IC.6
Support for Teachers
Critical Background Knowledge
• Represent numerical data in plots on a number line, including dot plots, histograms, and box plots (6.SP .4 and I.S.ID.1)
• Use measures of center and spread to draw informal inferences about two data sets (7.SP .3 and 7.SP .4)
• Summarize a data set using mean, median, interquartile range, and mean absolute deviation (6.SP .5c)
• Make a line plot (2.MD.9, 3.MD.4, 4.MD.1, and 5.MD.2) and draw a picture graph and a bar graph (2.MD.10 and
3.MD.3)
Academic Vocabulary
mean, median, interquartile range, standard deviation, center, spread, shape, dot plot, histogram, box plot, quartiles, minimum, maximum, spread, side-by-side (parallel) plots
I.S.ID.2 Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304


Interpreting Categorical and Quantitative Data Core Guide
Summarize, represent, and interpret data on a single count or measurement variable (Standards S.ID.1–3).
Standard I.S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Calculate the weighted average of a distribution and interpret it as a measure of center.
Concepts and Skills to Master
• Interpret similarities and differences between the shape, and measures of centers and spreads of data sets.
• Describe the influence of outliers on measures of center and spread.
• Calculate the weighted average (for example, determining a student’s grade when category scores are
weighted differently) and interpret it as a measure of center (balance point).
Related Standards: Current Course
Related Standards: Future Courses
I.S.ID.1, I.S.ID.2, I.N.Q.1, I.N.Q.2, I.N.Q.3
III.S.ID.4, III.S.IC.1, III.S.IC.6
Support for Teachers
Critical Background Knowledge
• Represent numerical data in plots on a number line, including dot plots, histograms, and box plots (6.SP .4 and I.S.ID.1)
• Use measures of center and spread to draw informal inferences about two data sets (7.SP .3 and 7.SP .4)
• Summarizeadatasetusingmean,median,interquartilerange(6.SP.5c),andstandarddeviation(I.S.ID.2)
• Make a line plot (2.MD.9, 3.MD.4, 4.MD.1, and 5.MD.2) and draw a picture graph and a bar graph (2.MD.10 and
3.MD.3)
Academic Vocabulary
outliers, skewed, mean, median, interquartile range, standard deviation, center, spread, shape, dot plot, histogram, box plot, quartiles, minimum, maximum, spread, side-by-side (parallel) plots
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304
I.S.ID.3


Interpreting Categorical and Quantitative Data Core Guide
Summarize, represent, and interpret data on two categorical and quantitative variables (Standard S.ID.6).
Standard I.S.ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fitalinearfunctiontothedata;usefunctionsfittedtodatatosolveproblemsinthe contextofthedata.Usegiven functions,orchooseafunctionsuggestedbythecontext. Emphasize linear and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals. Focus on situations for which linear models are appropriate.
c. Fit a linear function for scatter plots that suggest a linear association.
Concepts and Skills to Master
• Represent data on two quantitative variables on a scatter plot and describe how variables are associated.
• Given a set of bivariate data, use residuals to assess the appropriateness of a given model to
determine if the data has a linear relationship. • Findthelineofbestfitusingtechnology.
• Understand what a residual represents.
Related Standards: Current Course
Related Standards: Future Courses
I.F.IF.4, I.F.BF.1, I.F.LE.1, I.F.LE.5, I.S.ID.7, I.S.ID.8
II.F.IF.4, III.F.IF.4, III.S.IC.6
Support for Teachers
Critical Background Knowledge
• Construct and interpret scatter plots for bivariate data (8.SP.1)
• Informally fit a line (trend line) to bivariate data (8.SP.2)
• Use the equation of a linear model to solve problems in context of bivariate data (8.SP.3)
• Construct a function to model a linear relationship (8.F.4)
Academic Vocabulary
Line of best fit, residuals, bivariate data, linear model, scatter plot
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304
I.S.ID.6


Interpreting Categorical and Quantitative Data Core Guide
Interpret linear models building on students’ work with linear relationships, and introduce the correlation coefficient (Standards S.ID.7–9).
Standard I.S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Concepts and Skills to Master
• Interpret the slope in context of the situation.
• Interpret the y-intercept in context of the situation.
Related Standards: Current Course
Related Standards: Future Courses
I.F.IF.4, I.F.IF.6, I.F.IF.7, I.F.BF.1, I.F.LE.1, I.F.LE.5, I.S.ID.6, I.S.ID.8
All functions standards (throughout high school),
III.S.IC.6
Support for Teachers
Critical Background Knowledge
• Construct and interpret scatter plots for bivariate data (8.SP.1)
• Informally fit a line (trend line) to bivariate data (8.SP.2)
• Use the equation of a linear model to solve problems in context of bivariate data (8.SP.3)
• Construct a function to model a linear relationship (8.F.4)
• Determine the slope and y-intercept of a line (8.F.3)
Academic Vocabulary
slope (rate of change), y-intercept
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304
I.S.ID.7


Interpreting Categorical and Quantitative Data Core Guide
Interpret linear models building on students’ work with linear relationships, and introduce the correlation coefficient (Standards S.ID.7–9).
Standard I.S.ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
Concepts and Skills to Master
• Compute the correlation coefficient using technology.
• Interpret the direction (positive, negative, or none) and strength (strong, moderate, weak) of the
relationship based on the correlation.
Related Standards: Current Course
Related Standards: Future Courses
I.F.IF.6, I.S.ID.6, I.S.ID.7, I.S.ID.9
II.F.IF.6, III.F.IF.6
Support for Teachers
Critical Background Knowledge
• Construct and interpret scatter plots for bivariate data to investigate patterns of association (8.SP.1)
• Construct a function to model a linear relationship (8.F.4)
Academic Vocabulary
correlation coefficient, correlation, r
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304
I.S.ID.8


Interpreting Categorical and Quantitative Data Core Guide
Interpret linear models building on students’ work with linear relationships, and introduce the correlation coefficient (Standards S.ID.7–9).
Standard I.S.ID.9: Distinguish between correlation and causation.
Concepts and Skills to Master
• Understand the difference between correlation and causation.
• Using a context situation when correlation exists, determine if the correlation is a result of causation.
• Understand a strong correlation may not mean causation.
Related Standards: Current Course
Related Standards: Future Courses
I.S.ID.6, I.S.ID.7, I.S.ID.8
II.F.IF.6, III.F.IF.6
Support for Teachers
Critical Background Knowledge
• Interpret the meaning of correlation (I.S.ID.8)
Academic Vocabulary
correlation, causation
Resources
Curriculum Resources: http://www.uen.org/core/core.do?courseNum=5600#70304
I.S.ID.9


Secondary Math 1: Pacing Guide by Quarter
Quarter 1 – 46 days
MAJORCONCEPTS:SolvingLinearEquations,GraphingLinear Equations, Rate of Change
Embedded Essentials
1.N.Q.1: use units as a way to understand problems
1.N.Q.2: define appropriate quantities for the purpose of modeling
1.N.Q.3: choose a level of accuracy appropriate to limitations on measurement 1.F.IF.5: relate the domain of a function to its graph
Essentials
1.A.SSE.1a: interpret parts of an expression (terms, factors, coefficients) 1.A.CED.1: create and solve equations in
one variable (linear) 1.A.CED.2: create equations in two or more variables –graph (linear)
1. A.CED.4: rearrange formulas to highlight quantity of interest
1.A.REI.1: explain each step in solving a linear equation
1.A.REI.3a: solve one-variable equations and literal equations to highlight a variable of interest
1.A.REI.10: understand that a graph of an equation in two variables is the set of all solutions plotted in the coordinate
plane (linear)
1.F.IF.2: use function notation
1.F.IF.7a: graph linear functions and show intercepts
1.F.LE.5: interpret the parameters in a linear function in terms of a context (slope, y- intercept)
Good to Know
1.A.SSE.1b: interpret complicated expressions by viewing one or more of their parts as a single entity 1.A.CED.3: represent constraints by equations or inequalities; interpret solutions as viable or non-viable 1.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 the range.
1.F.IF.4: interpret key features of linear graphs (intercepts, increasing/decreasing, +/-, max/min, symmetries, end
behavior)
1.F.IF.5: relate the domain of a function to its graph
1.F.IF.6: calculate and interpret the average rate of change of a function over a specified interval; estimate from a graph 1.F.IF.9: compare properties of 2 linear functions, each represented in a different way (algebraically, graphically,
numerically in tables or by verbal descriptions)
1.F.LE.1a: prove linear functions grow by equal differences over equal intervals 1.F.LE.1b: recognize situations in which one quantity changes at a constant rate per unit interval relative to another
1.F.LE.2: construct linear functions given a graph, description of a relationship or two input-output pairs
Common Assessments: Developed by each PLC at each site


Quarter 2 – 45 days
MAJORCONCEPTS:WritingLinearEquations,EverythingExponential, Linear vs. Exponential, Inequalities
Essentials
1.A.CED.1: create and solve equations and inequalities in one variable (linear and exponential)
1.A.CED.2: create equations in two or more variables –graph (linear and exponential) 1.A.CED.3: represent
constraints by equations or inequalities; interpret solutions as viable or non-viable
1.A.REI.10: understand that a graph of an equation in two variables is the set of all solutions plotted in the coordinate
plane (linear and exponential)
1.A.REI.12: graph the solutions to a linear inequality
1.F.IF.6: calculate and interpret the average rate of change of a function over a specified interval; estimate from a
graph
1.F.IF.7e: graph exponential functions, showing intercepts and end behavior
1.F.IF.9: compare properties of 2 linear functions, 2 exponential functions, or linear vs exponential, each represented
in a different way (algebraically, graphically, numerically in tables or by verbal descriptions)
1.F.LE.1c: recognize situations in which a quantity grows or decays by a constant percent rate per unit interval
relative to another
1.F.LE.2: construct linear or exponential functions given a graph, description of a relationship or two input-output
pairs
1.F.LE.5: interpret the parameters in an exponential function in terms of a context (base value, vertical shifts) 1.S.ID.6a: represent data on two quantitative variables on a scatter plot and describe how they are related; fit a
linear function to the data; use fitted functions to data to solve problems in the context of the data given;
emphasize linear and exponential models
1.S.ID.7: interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of
data
Good to Know
1.A.REI.3b: solve compound inequalities, including absolute value inequalities
1.A.REI.3c: solve simple exponential equations
1.F.IF.4: interpret key features of linear and exponential graphs (intercepts, increasing/decreasing, +/-, max/min,
symmetries, end behavior)
1.F.BF.1b: write a function that describes a relationship between two quantities: combine standard function types
using arithmetic operations
1.F.BF.3: identify the effect on the graph of replacing f(x) by f(x)+k (vertical translation) 1.F.LE.1a: prove exponential functions grow by equal factors over equal intervals 1.F.LE.3: observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly
1.S.ID.6b: informally assess the fit of a function by plotting and analyzing residuals (linear)
1.S.ID.6c: fit a linear function for scatter plots that suggest a linear association
1.S.ID.8: compute (using technology) and interpret the correlation coefficient of a linear fit
1.S.ID.9: distinguish between correlation and causation Common Assessments: Developed
by each PLC at each site


Quarter 3 – 43 days
MAJOR CONCEPTS: Sequences, Systems, Stats
Essentials
1.A.CED.3: represent constraints by equations or inequalities; interpret solutions as viable or non-viable 1.A.REI.5: prove that, given a system of two equations in two variables, replacing one equation with a sum of that
equation and a multiple of the other produces a system with the same solutions
1.A.REI.6: solve systems of linear equations exactly and approximately (numerically, algebraically, graphically) 1.A.REI.11: explain why the x-coordinates of the points where the graphs of the equations intersect are the
solutions
1.F.IF.3: understand that sequences are functions, sometimes defined recursively, whose domain is a subset of
integers (arithmetic/linear and geometric/exponential)
1.S.ID.1: represent data with plots on the real number line (dot plots, histograms, and box plots)
1.S.ID.2: use statistics appropriate to the shape of the data distribution to compare center (median, mean) and
spread (IQR, range and standard deviation) of two or more data sets
1.S.ID.3: interpret differences in shape, center and spread in the context of the data sets, accounting for possible
effects of extreme data points (outliers); calculate the weighted average of a distribution and interpret it as a measure of center
Good to Know
1.A.REI.12: graph the solution to a system of linear inequalities
1.F.BF.1a: write a function that describes a relationship between two quantities: determine an explicit expression,
a recursive process, or steps for calculation from a context
1.F.BF.2: write arithmetic (linear) and geometric (exponential) sequences both recursively and with an explicit
formula
1.F.LE.2: construct linear or exponential functions, including arithmetic and geometric sequences, given a graph,
description of a relationship or two input-output pairs Common Assessments: Developed by each PLC at each site


Quarter 4 – 46 days
MAJOR CONCEPTS: Constructions, Triangle Congruencies, Transformations
Essentials
1.G.CO.5: given a geometric figure and a rotation, reflection or translation, draw the transformed figure using a
variety of media; specify a sequence of transformations that will carry a given figure onto another
1.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 two figures, use the definition of rigid motion to decide if they are congruent 1.G.CO.7: use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and
only if corresponding pairs of sides and angles are congruent
1.G.CO.8: explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions
1.G.GPE.4: use coordinates to prove simple geometric theorems algebraically focusing on lines, segments and
angles
1.G.GPE.5: prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems 1.G.GPE.7: use coordinates to compute perimeters of polygons and areas of triangles and rectangles, using the
distance formula
Good to Know
1.G.CO.1: know precise definitions of angle, circle perpendicular line, parallel line, and line segment based on the
undefined notions of point, line, distance along a line, and distance around a circular arc
1.G.CO.2: represent transformations in a plane using a variety of media; describe transformations as functions
that take points in a plane as inputs and gives other points as outputs; compare transformations that preserve
distance and angle and those that do not
1.G.CO.3: given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that
carry it onto itself
1.G.CO.4: develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines,
parallel lines and line segments
1.G.CO.12: make formal geometric constructions with a variety of tools and methods; copying a segment,
copying an angle, bisecting a segment, bisecting an angle, constructing perpendicular lines, including the
perpendicular bisector of a line segment, and constructing a line parallel to a given line through a point not on a line 1.G.CO.13: construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle
Common Assessment: SAGE


Units
Planning Guide: Jay McTighe, an expert in unit planning and author of Understanding by Design, has written four point to consider when planning units. They are presented below.
UbD Design Standards Stage 1 – To what extent does the design:
1. focus on the “Big ideas” of targeted content? Consider: are . . .
– the targeted understandings enduring, based on transferable, big ideas at the heart of the
discipline and in need of “uncoverage”?
– the targeted understandings framed as specific generalizations?
– the “big ideas” framed by questions that spark meaningful connections, provoke genuine
inquiry and deep thought, and encourage transfer?
– appropriate goals (e.g., content standards, benchmarks, curriculum objectives) identified?
– valid and unit-relevant knowledge and skills identified?
Stage 2 – To what extent do the assessments provide:
2. fair, valid, reliable and sufficient measures of the desired results? Consider: are . . .
– students asked to exhibit their understanding through “authentic” performance tasks? – appropriate criterion-based scoring tools used to evaluate student products and
performances?
– a variety of appropriate assessment formats provide additional evidence of learning? Stage 3 – To what extent is the learning plan:
3. effective and engaging? Consider: will students . . .
– know where they’re going (the learning goals), why (reason for learning the content), and
what is required of them (performance requirements and evaluative criteria)?
– be hooked – engaged in digging into the big ideas (e.g., through inquiry, research, problem- solving, experimentation)?
– have adequate opportunities to explore/experience big ideas and receive instruction to equip them for the required performance(s)?
– have sufficient opportunities to rethink, rehearse, revise, and/or refine their work based upon timely feedback?
– have an opportunity to self-evaluate their work, reflect on their learning and set future goals? Consider: the extent to which the learning plan is:
– tailored and flexible to address the interests and learning styles of all students?
– organized and sequenced to maximize engagement and effectiveness?
Overall Design – to what extent is the entire unit:
4. coherent, with the elements of all 3 stages aligned?
Grant Wiggins and Jay McTighe 2005
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Assessment Standards
SAGE
The link for further information on SAGE ELA is:
http://www.schools.utah.gov/assessment/SAGE/ELA.aspx
Purpose of Testing (from USBE testing ethics training)
The purpose of statewide assessment is for accountability.
When administered properly, standardized assessments allow students to demonstrate their abilities, knowledge, aptitude, or skills (see R277 – 404). Valid and reliable results from uniform assessments provide information used by:
Students, to determine how well they have learned the skills and curriculum they are expected to know;
Parents, to know whether their student is gaining the skills and competencies needed to be competitive and successful;
Teachers, to gauge their students’ understanding and identify potential areas of improvement in their teaching;
LEAs (districts or charter schools), to evaluate programs and provide additional support;
State, for school accountability; and
Public, to evaluate schools and districts.
As educators, we are obligated to provide students with an opportunity to demonstrate their knowledge and skills fairly and accurately.
Educators involved with the state – wide assessment of students must conduct testing in a fair and ethical manner (see Utah Code 53A-1-608; R277-404).
The best test preparation a teacher can provide is good instruction throughout the year that covers the breadth and depth of the standards for a course, using varied instructional and assessment activities tailored to individual students.
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Ethical Assessment Practices (USBE ethics training) Licensed Utah Educators should:
• Ensure students are enrolled in appropriate courses and receive appropriate instruction
• Provide instruction to the intended depth and breadth of the course curriculum
• Provide accommodations throughout instruction to eligible students as identified by an
ELL, IEP, or 504 team.
• Use a variety of assessments methods to inform instructional practices
• Introduce students to various test-taking strategies throughout the year
• Provide students with opportunities to engage with available training test to ensure that
they can successfully navigate online testing systems, and to ensure that local technology
configurations can successfully support testing.
• Use formative assessments throughout the year using high-quality, non-secure test
questions aligned to Utah Standards.
Licensed Utah Educators shall ensure that:
• An appropriate environment reflective of an instructional setting is set for testing to limit distractions from surroundings or unnecessary personnel.
• All students who are eligible for testing are tested.
• A student is not discouraged from participating in state assessments, but upon a
parent’s opt-out request (follow LEA procedures), the student is provided with a
meaningful educational activity.
• Tests are administered in-person and testing procedures meet all test administration
requirements.
• Active test proctoring occurs: walking around the room to make sure that each
student has or is logged into the correct test; has appropriate testing materials
available to them; and are progressing at an appropriate pace.
• No person is left alone in a test setting with student tests left on screen or open.
• The importance of the test, test participation, and the good faith efforts of all students
are not undermined.
• All information in the Test Administration Manual (TAM) for each test administered
is reviewed and strictly followed (see 53A-1-608; R277-404).
• Accommodations are provided for eligible students, as identified by an ELL, IEP, or
504 team. These accommodations should be consistent with accommodations
provided during instruction throughout the instructional year.
• Any electronic devices that can be used to access non-test content or to
record/distribute test content or materials shall be inaccessible by students (e.g., cell phones, recording devices, inter-capable devices). Electronic security of tests and student information must not be compromised.
• Test materials are secure before, during and after testing. When not in use, all materials shall be protected, where students, parents cannot gain access.
No one may enter a student’s computer-based test to examine content or alter a student’s response in any way either on the computer or a paper answer document for any reason.
102


Unethical Assessment Practices (USBE ethics training)
It is unethical for educators to jeopardize the integrity of an assessment or the validity of student responses.
Unethical practices include:
• Providing students with questions from the test to review before taking the test.
• Changing instruction or reviewing specific concepts because those concepts appear on
the test.
• Rewording or clarifying questions, or using inflection or gestures to help students answer.
• Allowing students to use unauthorized resources to find answers, including dictionaries,
thesauruses, mathematics tables, online references, etc.
• Displaying materials on walls or other high visibility surfaces that provide answer to
specific test items (e.g., posters, word walls, formula charts, etc.).
• Reclassifying students to alter subgroup reports.
• Allowing parent volunteers to assist with the proctoring of a test their child is taking or
using students to supervise other students taking a test.
• Allowing the public to view secure items or observe testing sessions.
• Reviewing a student’s response and instructing the student to, or suggesting that the
student should, rethink his/her answers.
• Reproducing, or distributing, in whole or in part, secure test content (e.g., taking pictures,
copying, writing, posting in a classroom, posting publically, emailing).
• Explicitly or implicitly encouraging students to not answer questions, or to engage in
dishonest testing behavior.
• Administering tests outside of the prescribed testing window for each assessment.
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Intervention Standards
PCSD MTSS/RTI Model
Provo City School District's Academic MTSS (Multi-Tiered Systems of Support) details the system for providing Tier 1, 2, and 3 instruction; interventions; and assessment to help each student receive appropriate support. It is detailed below.
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105


Unpacking the Complexity of MTSS Decision Making
Successful MTSS implementation is a highly complex process that involves the following tasks:
• Gathering accurate and reliable data
• Correctly interpreting and validating data
• Using data to make meaningful instructional changes for students
• Establishing and managing increasingly intensive tiers of support
• Evaluating the process at all tiers to ensure the system is working
106


Utah’s Multi-Tiered System of Supports USBE website:
http://www.schools.utah.gov/umtss/UMTSS-Model.aspx
107


Supplemental Resources
Provo City School District’s Instructional Model
108


• Student focus
• Educator credibility
• Meeting norms
• Professional Learning Communities (PLC)/Collaboration
• Civility policy
• Appearance and interactions
• Continual Leaning
• Testing ethics
• Research orientation
• Policy adherence
• Culture
• Safety–emotional and physical
• Physical classroom space
• Relationships
• Family connections
• Procedures
• Classroom management
• Student artifacts
• Student focus
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• Formative evaluation
• Summative evaluation
• Feedback:
• Performance of understanding
• Self-reported grades
• Student self-evaluation
• Testing ethics
• Differentiation
• Data analysis
• Response to interventions (RTI)/Multi-tiered system of success (MTSS)
• Lesson design
• Teacher clarity: share LT, share SC, share PoU
• Evidence-based instructional strategies
• Based on data
• Student engagement
• DOK – Depth of Knowledge
• Differentiation
• Student ownership of learning
• Curriculum notebook
• RTI/MTSS
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• State standards
• Curriculum map/pacing guide
• Units
• Objectives
• Curriculum Notebooks
• Course essentials
• Current
• Planning
Professional Association
The National Council of Teachers of Mathematics NCTM is the largest professional association for mathematics teachers.
Their website is at: https:// http://www.nctm.org/
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Evidence-based Pedagogical Practices
Hattie's Visible Learning
John Hattie, creator of Visible Learning, is a leading education researcher who has analyzed meta analyses in order to rank education practices (and factors) from most effective to least effective.
Hattie's list of highest ranking factors can be found at: https://visible-learning.org/hattie-ranking-influences-effect-sizes-learning-achievement/
or
https://visible-learning.org/nvd3/visualize/hattie-ranking-interactive-2009-2011- 2015.html
Hattie's original book on the topic can be found at:
https://www.amazon.com/Visible-Learning-Synthesis-Meta-Analyses- Achievement/dp/0415476186
Definitions of Hattie's factors can be found at:
https://www.amazon.com/Visible-Learning-Synthesis-Meta-Analyses- Achievement/dp/0415476186
National Reading Panel Research
The federal government commissioned a National Reading Panel to review and compile the best evidence of effective practices for reading instruction.
The full report and executive summary can be accessed at:
https://lincs.ed.gov/communications/NRP
Learning Targets
Provo City School District employs the use of learning targets, success criteria, formative assessment, and feedback. A basis of study on these topics is the book, Learning Targets, by Connie Moss and Susan Brookhart, can be found at: https://www.amazon.com/Learning-Targets-Helping-Students-Understanding- ebook/dp/B008FOKP5S.
The district has produced four videos that demonstrate elements of learning target instruction and can be found at: http://provo.edu/teachingandlearning/learning-targets-videos/
Teacher Resource Guide
Provo City School District's Teacher Resource Guide helps teachers meet the Utah Effective Teaching Standards and includes effective teaching practices. It can be found at: http://provo.edu/teachingandlearning/wp-content/uploads/sites/4/2016/01/11182016- TRG-fixed.pdf
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Glossary
Assessment Standards
College and Career Readiness
Curriculum Resources
ELA
Essential Learning Standards
Evidence-based Pedagogical Practices Intervention Standards
Language Standards
A set of criteria to guide the assessment of student learning in a course that is based on Standards/Essentials of the course; this might include formative assessment practices, summative assessments/practices, common assessment plans, feedback practices, and a schedule for testing.
The College and Career Readiness (CCR) anchor standards
and grade-specific standards are necessary complements—the former providing broad standards, the latter providing additional specificity—that together define the skills and understandings that all students must demonstrate.
The materials teachers use to plan, prepare, and deliver instruction, including materials students use to learn about the subject. Such materials include texts, textbooks, tasks, tools, and media. Sometimes organized into a comprehensive program format, they often provide the standards, units, pacing guides, assessments, supplemental resources, interventions, and student materials for a course.
English Language Arts, includes components of Reading, Writing, Speaking and Listening, and Language.
These are also known as power standards. They are particular standards/objectives/indicators that a school/district defines as critical for student learning. In fact, they are so critical that students will receive intervention if they are not learned. Essentials are chosen because they: 1. have endurance, 2. have leverage, and 3. are important for future learning.
A list of teaching strategies that are supported by adequate, empirical research as being highly effective.
A set of criteria to guide teachers to provide additional instruction to students who did not master the content in Tier 1 instruction. This might include: commercial intervention programs, teacher-developed intervention materials, diagnostic testing, RTI/MTSS processes, and a list of essential knowledge/skills that will prompt intervention if the student does not demonstrate mastery.
(L) A component of ELA Standards that focus on conventions of standard English grammar, usage, and mechanics as well as learning other ways to use language to convey meaning effectively.
(MC) Math Content Standards identify the knowledge of concepts
Math Content
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Standards
Mathematical Practice Standards
MTSS
Pacing Guide
Pathways of Progress
Performance of Understanding.
Provo Way Instructional Model
Reading Standards: Foundational Skills
SAGE
and the skills students need for college and career readiness.
The 8 Mathematical Practice Standards describe varieties of expertise that mathematics educators at all levels seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. All 8 mathematical practice standards are essential standards.
Multi-Tiered Systems of Support is an approach to academic and behavioral intervention. It is part of the intervention standards.
The order and timeline of the instruction of standards, objectives, indicators, and Essentials over the span of a course (semester or year).
(POP) An evaluation of individual student growth or improvement over time compared to other students with the same level of initial skills. It empowers educators to set goals that are meaningful, ambitious, and attainable.
(PoU). Student results that provide compelling evidence that the student has acquired the learning target. (Brookhart, 2012).
The five areas of expectations for successful instruction identified by Provo City School District.
(RF) A component of ELA Standards that focus on helping students gain a foundation where curriculum is intentionally and coherently structured to develop rich content knowledge within and across grades as well as acquiring the habits of reading independently and closely, which are essential to their future success.
Student Assessment of Growth and Excellence. This is the state end of level test for ELA and Math grades 3 – 8, and Science grades 4 – 8.
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