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Dallas School District |
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K-12 Curriculum |
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Elementary Mathematics - Grade 5 |
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Number Sentence: Choose/Apply
The learner will be able to
choose and apply appropriate methods, including physical materials, to obtain solutions to number sentences and describe the method of solution.
| Strand |
Source |
Activities |
| Number Sentence |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.G |
Classroom
Home
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Equations: Describe
The learner will be able to
use information given in equations inequalities tables of graphs in the description of a realistic scenario.
| Strand |
Source |
Activities |
| Equations |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.F |
Classroom
Home
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Expressions: Create
The learner will be able to
create expressions that represent mathematical situations using physical objects and combinations of symbols and numbers.
| Strand |
Source |
Activities |
| Expressions |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.D |
Classroom
Home
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Algorithms: Develop/Apply
The learner will be able to
develop and apply algorithms to obtain solutions to word problems that involve adding, subtracting, and/or multiplying with fractions and mixed numbers that include like and unlike denominators.
| Strand |
Source |
Activities |
| Algorithms |
PA: Academic Standards, January 16, 1999, Grade 5, p.4,2.2.5.B, p.4,2.2.5.C |
Classroom
Home
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Algorithms: Develop/Apply
The learner will be able to
develop and apply algorithms to obtain solutions to word problems that involve adding, subtracting, and/or multiplying with decimals with and without regrouping.
| Strand |
Source |
Activities |
| Algorithms |
PA: Academic Standards, January 16, 1999, Grade 5, p.4,2.2.5.B |
Classroom
Home
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Rates: Explain Relationship/Time
The learner will be able to
explain the relationship between rates of change and time.
| Strand |
Source |
Activities |
| Rates |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.D |
Classroom
Home
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Variable
The learner will be able to
understand the basic concept of a variable as representing an unknown quantity.
| Strand |
Source |
Activities |
| Variable |
PA: System of School Assessment, 1997, Grade 5, p.12,#5 week tested: 30. |
Classroom
Home
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Variable: Solving For
The learner will be able to
manipulate a given formula to solve for a specific variable.
| Strand |
Source |
Activities |
| Variable |
PA: System of School Assessment, 1997, Grade 5, p.12,#5 week tested: 30. |
Classroom
Home
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Algorithms: Describe
The learner will be able to
describe algorithms for multiplication and division.
| Strand |
Source |
Activities |
| Algorithms |
PA: Academic Standards, January 16, 1999, Grade 5, p.5,2.2.5.H |
Classroom
Home
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Computation: Select
The learner will be able to
select a suitable computational strategy.
| Strand |
Source |
Activities |
| Computation |
PA: Academic Standards, January 16, 1999, Grade 5, p.5,2.2.5.I |
Classroom
Home
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Symbols: Explain
The learner will be able to
explain the application of combinations of symbols and numbers in expressions, equations, and inequalities.
| Strand |
Source |
Activities |
| Symbols |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.E |
Classroom
Home
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Calculus and Pre-Calculus
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Apply Calculus Concepts: Max/Min
The learner will be able to
determine maximum and minimum.
| Strand |
Source |
Activities |
| Applying Calculus Concepts |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.C |
Classroom
Home
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Bar Graphs: Recognize Values
The learner will be able to
recognize least and greatest values illustrated in bar graphs and circle graphs.
| Strand |
Source |
Activities |
| Bar Graphs |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.B |
Classroom
Home
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Decimal Notation
The learner will be able to
identify and use decimal notation.
| Strand |
Source |
Activities |
| Decimals |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Fraction Notation
The learner will be able to
evaluate fraction notation in context as part of a whole, in division, or as a ratio.
| Strand |
Source |
Activities |
| Fractions |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Problem Solving: Fractions
The learner will be able to
apply fraction representations to solve real-world problems.
| Strand |
Source |
Activities |
| Problem Solving |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Functions: Generate/Relate
The learner will be able to
use tables of data to generate functions and relate data to corresponding graphs and functions.
| Strand |
Source |
Activities |
| Functions |
PA: Academic Standards, January 16, 1999, Grade 5, p.14,2.8.5.I |
Classroom
Home
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Figures: Construct/Geoboard
The learner will be able to
create two-and three-dimensional shapes and figures using geoboards.
| Strand |
Source |
Activities |
| Figures: Construct |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.E |
Classroom
Home
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Representations: Create/Mental Image
The learner will be able to
create a mental image of constructed and/or altered shapes.
| Strand |
Source |
Activities |
| Figures: Representations |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Figures: Name/Identify
The learner will be able to
identify, name, and/or apply properties of geometric figures.
| Strand |
Source |
Activities |
| Figures |
PA: Academic Standards, January 16, 1999, Grade 5, p.17,2.9.5.L |
Classroom
Home
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Figures: Identify/Properties
The learner will be able to
recognize geometric shapes and/or know the properties they may possess.
| Strand |
Source |
Activities |
| Figures |
PA: System of School Assessment, 1997, Grade 5, p.11,#3C week tested: 30. |
Classroom
Home
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Circle: Radius/Diameter
The learner will be able to
recognize the radius and diameter of a circle and measure them.
| Strand |
Source |
Activities |
| Circles |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.C |
Classroom
Home
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Planes/Points/Lines: Apply Concepts
The learner will be able to
apply the ideas of planes, points, and/or lines in one, two, and/or three dimensions.
| Strand |
Source |
Activities |
| Planes/Points/Lines |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.I |
Classroom
Home
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Logic: Interpret Statements
The learner will be able to
analyze and/or understand statements that are constructed with the specific language of logic, including the terms all, every, none, some, and/or many.
| Strand |
Source |
Activities |
| Logic |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.E |
Classroom
Home
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Properties: Define
The learner will be able to
define the elementary properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres, and cylinders.
| Strand |
Source |
Activities |
| Properties of Figures |
PA: Academic Standards, January 16, 1999, Grade 5, p.17,2.9.5.J |
Classroom
Home
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Lines/Angles: Identify/Apply
The learner will be able to
identify real-world examples of different types of lines and angles and apply them in problem solving or creative projects.
| Strand |
Source |
Activities |
| Lines/Angles/Polygons |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Figures: Describe/Constructing
The learner will be able to
give word descriptions of how geometric shapes are constructed.
| Strand |
Source |
Activities |
| Figures: Describe |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.D |
Classroom
Home
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Vocabulary: Compose/Definitions
The learner will be able to
compose definitions for familiar geometric figures.
| Strand |
Source |
Activities |
| Figures: Vocabulary |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.A |
Classroom
Home
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Solids: Real-World
The learner will be able to
identify three-dimensional solids in his/her environment.
| Strand |
Source |
Activities |
| Three-Dimensional Solids |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.F |
Classroom
Home
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Shapes: Circle
The learner will be able to
identify a circle.
| Strand |
Source |
Activities |
| Two-Dimensional Shapes |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.C |
Classroom
Home
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Right Triangle: Create/Geoboard
The learner will be able to
use a geoboard to create right triangles.
| Strand |
Source |
Activities |
| Triangles |
PA: Academic Standards, January 16, 1999, Grade 5, p.18,2.10.5.B |
Classroom
Home
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Triangles: Compare
The learner will be able to
make comparisons of triangles based upon their sides or angles.
| Strand |
Source |
Activities |
| Triangles |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.B |
Classroom
Home
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Triangles: Classify
The learner will be able to
classify triangles according to their side lengths and angle measures.
| Strand |
Source |
Activities |
| Triangles |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.B |
Classroom
Home
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Circles: Measure
The learner will be able to
measure circles.
| Strand |
Source |
Activities |
| Circles |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.C |
Classroom
Home
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Transformation: Interpret
The learner will be able to
develop interpretations of transformations of figures in the coordinate plane.
| Strand |
Source |
Activities |
| Transformations |
PA: Academic Standards, January 16, 1999, Grade 5, p.17,2.9.5.K |
Classroom
Home
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Tessellations: Create
The learner will be able to
create tessellations.
| Strand |
Source |
Activities |
| Tessellations |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.G |
Classroom
Home
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Inductive/Deductive: Conclusions
The learner will be able to
form inductive and deductive conclusions within mathematical contexts.
| Strand |
Source |
Activities |
| Reasoning |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.C |
Classroom
Home
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Point/Line/Plane: Represent
The learner will be able to
draw representations of the undefined terms (point, line, and plane) of geometry.
| Strand |
Source |
Activities |
| Planes/Points/Lines |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.I |
Classroom
Home
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Rotation: Analyze/Line Segments
The learner will be able to
study the rotations of line segments.
| Strand |
Source |
Activities |
| Rotations |
PA: Academic Standards, January 16, 1999, Grade 5, p.17,2.9.5.K |
Classroom
Home
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Constructions: 2-D
The learner will be able to
construct two-dimensional shapes through the use of physical materials.
| Strand |
Source |
Activities |
| Constructions |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.E |
Classroom
Home
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Constructions: 3-D
The learner will be able to
construct three-dimensional shapes through the use of physical materials.
| Strand |
Source |
Activities |
| Constructions |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.E |
Classroom
Home
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Quadrilaterals: Classify
The learner will be able to
classify quadrilaterals based upon their sides or angles.
| Strand |
Source |
Activities |
| Quadrilaterals |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.B |
Classroom
Home
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Quadrilaterals: Compare
The learner will be able to
make comparisons of quadrilaterals based upon their sides or angles.
| Strand |
Source |
Activities |
| Quadrilaterals |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.B |
Classroom
Home
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Integers: Computing
The learner will be able to
perform computations involving integers through the use of models, manipulatives, and/or rules.
| Strand |
Source |
Activities |
| Integers |
PA: Academic Standards, January 16, 1999, Grade 5, p.18,2.10.5.A |
Classroom
Home
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Mathematical Concepts: Communication
The learner will be able to
demonstrate concepts in many different ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams and models.
| Strand |
Source |
Activities |
| Communication |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.C |
Classroom
Home
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Modeling: Multiplication
The learner will be able to
illustrate the idea of multiplication as area, volume, array, change in size, rate factor, and/or repeated addition through the use of concrete models as well as pictorial and algebraic representations.
| Strand |
Source |
Activities |
| Mathematical Modeling |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.F |
Classroom
Home
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Models: Fractions/Decimals
The learner will be able to
illustrate fractions and decimals using models.
| Strand |
Source |
Activities |
| Mathematical Modeling |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.D |
Classroom
Home
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Units: Tools
The learner will be able to
choose the most suitable tools and units in problem solving situations that may require estimation and measurement, and relate methods used in problem solving using technology as appropriate.
| Strand |
Source |
Activities |
| Units |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Units
The learner will be able to
obtain solutions to and approximate suitable answers for problems that use metric and/or customary measurement units.
| Strand |
Source |
Activities |
| Units |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Accuracy
The learner will be able to
demonstrate that mathematical operations can represent a variety of problem situations.
| Strand |
Source |
Activities |
| Accuracy |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.C |
Classroom
Home
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Measurement Concepts: Add/Subtract
The learner will be able to
perform addition and/or subtraction with measurement values, including weight and/or length.
| Strand |
Source |
Activities |
| Measurement Concepts |
PA: Academic Standards, January 16, 1999, Grade 5, p.6,2.3.5.E |
Classroom
Home
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Tools: Choose/Apply
The learner will be able to
choose and apply standard tools to measure the size of shapes to the given degree of accuracy, including length, width, perimeter, and area.
| Strand |
Source |
Activities |
| Tools/Instruments |
PA: Academic Standards, January 16, 1999, Grade 5, p.6,2.3.5.B |
Classroom
Home
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Measurement Processes: Estimate
The learner will be able to
approximate, refine, and confirm specified measurements of objects.
| Strand |
Source |
Activities |
| Measurement Processes |
PA: Academic Standards, January 16, 1999, Grade 5, p.6,2.3.5.C |
Classroom
Home
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Length: Convert
The learner will be able to
convert units of length within either the standard or metric system.
| Strand |
Source |
Activities |
| Length |
PA: Academic Standards, January 16, 1999, Grade 5, p.6,2.3.5.D |
Classroom
Home
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Area: Estimate
The learner will be able to
estimate area as the sum of area of tiles.
| Strand |
Source |
Activities |
| Area |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.E |
Classroom
Home
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Perimeter/Area: Relationship/Triangles
The learner will be able to
explain the relationship between the perimeter and area of triangles.
| Strand |
Source |
Activities |
| Perimeter/Area/Volume |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.H |
Classroom
Home
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Perimeter/Area: Relationship/Quad
The learner will be able to
explain the relationship between the perimeter and area of quadrilaterals.
| Strand |
Source |
Activities |
| Perimeter/Area/Volume |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.H |
Classroom
Home
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Perimeter/Area: Relationship/Circles
The learner will be able to
explain the relationship between the perimeter and area of circles.
| Strand |
Source |
Activities |
| Perimeter/Area/Volume |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.H |
Classroom
Home
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Perimeter/Area/Volume: Exact/Estimate
The learner will be able to
find or estimate the area, perimeter, and volume of shapes as necessary.
| Strand |
Source |
Activities |
| Perimeter/Area/Volume |
PA: System of School Assessment, 1997, Grade 5, p.11,2 week tested: 30. |
Classroom
Home
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Volume: Estimate
The learner will be able to
estimate volume as the sum of volumes of cubes.
| Strand |
Source |
Activities |
| Volume |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.E |
Classroom
Home
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Measurement: Appropriate Instrument/Unit
The learner will be able to
use the most appropriate instrument and unit to measure.
| Strand |
Source |
Activities |
| Measurement: Exploring |
PA: Academic Standards, January 16, 1999, Grade 5, p.6,2.3.5.A |
Classroom
Home
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Measurement: Select Units/Tools
The learner will be able to
select suitable units and tools to measure quantities.
| Strand |
Source |
Activities |
| Measurement: Application |
PA: Academic Standards, January 16, 1999, Grade 5, p.6,2.3.5.A |
Classroom
Home
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Communicating: Relationships
The learner will be able to
explain the relationship between the size of the unit of measurement and the approximation of the areas and volumes.
| Strand |
Source |
Activities |
| Communicating Measurement Concepts |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.F |
Classroom
Home
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Conversion: Between Systems
The learner will be able to
solve problems which require converting units of measurement between systems.
| Strand |
Source |
Activities |
| Converting |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Number Forms: Negative Numbers
The learner will be able to
apply the simple concepts of negative numbers (e.g. number line, temperature).
| Strand |
Source |
Activities |
| Number Forms |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.F |
Classroom
Home
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Number Theory Concepts: Develop/Apply
The learner will be able to
develop and apply number theory concepts to illustrate numbers in many different ways (e.g. primes, factors, multiples and composites).
| Strand |
Source |
Activities |
| Number Theory |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.G |
Classroom
Home
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Expanded Notation: Whole Numbers
The learner will be able to
write whole numbers in expanded notation.
| Strand |
Source |
Activities |
| Expanded Notation |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.A |
Classroom
Home
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Primes/Composites: Describe
The learner will be able to
describe the idea of prime and composite numbers.
| Strand |
Source |
Activities |
| Prime/Composite Numbers |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.E |
Classroom
Home
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Multiples
The learner will be able to
demonstrate an understanding of multiples.
| Strand |
Source |
Activities |
| Multiples |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Factors: Applications
The learner will be able to
understand and use factors.
| Strand |
Source |
Activities |
| Factors |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Number Theory: Renaming
The learner will be able to
use number theory concepts to rename a number quantity.
| Strand |
Source |
Activities |
| Number Theory |
PA: Academic Standards, January 16, 1999, Grade 5, p.2,2.1.5.B |
Classroom
Home
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Pattern Concepts: Applying
The learner will be able to
apply an understanding of mathematical patterns to deal with number systems, operations, and forms.
| Strand |
Source |
Activities |
| Patterns |
PA: System of School Assessment, 1997, Grade 5, p.12,#5 week tested: 30. |
Classroom
Home
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Estimation: Apply/Problems
The learner will be able to
apply estimation methods to many different problems including time and money problems.
| Strand |
Source |
Activities |
| Estimation |
PA: Academic Standards, January 16, 1999, Grade 5, p.5,2.2.5.G |
Classroom
Home
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Pattern: Identify/Duplicate/Continue
The learner will be able to
identify, duplicate, continue, create, and describe patterns, sequences and relationships orally, numerically, symbolically and graphically, using many different materials.
| Strand |
Source |
Activities |
| Patterns: Identify/Describe/Continue |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.A |
Classroom
Home
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Pattern: Rules
The learner will be able to
identify and describe rules for given patterns.
| Strand |
Source |
Activities |
| Patterns: Determining Rules |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.C |
Classroom
Home
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Pattern: Connect/Geometric Relations
The learner will be able to
connect patterns to geometric relations and elementary number skills.
| Strand |
Source |
Activities |
| Patterns: Geometric |
PA: Academic Standards, January 16, 1999, Grade 5, p.13,2.8.5.B |
Classroom
Home
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Quantity: Compare
The learner will be able to
make comparisons of quantity of numbers.
| Strand |
Source |
Activities |
| Quantity |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.A |
Classroom
Home
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Comparison: Numbers
The learner will be able to
compare numbers.
| Strand |
Source |
Activities |
| Comparison |
PA: Academic Standards, January 16, 1999, Grade 5, p.19,2.11.5.A |
Classroom
Home
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Estimation: Evaluate Reasonableness
The learner will be able to
evaluate the reasonableness of sums, differences, products, and quotients of whole number operations by using a variety of estimation strategies.
| Strand |
Source |
Activities |
| Estimation |
PA: Academic Standards, January 16, 1999, Grade 5, p.4,2.2.5.E |
Classroom
Home
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Estimation
The learner will be able to
use estimation in solving problems.
| Strand |
Source |
Activities |
| Estimation |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Rounding: Demonstrate Skills
The learner will be able to
demonstrate the skills necessary to round numbers.
| Strand |
Source |
Activities |
| Rounding |
PA: Academic Standards, January 16, 1999, Grade 5, p.4,2.2.5.D |
Classroom
Home
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Rounding: Estimation
The learner will be able to
relate rounding skills to estimating possible outcomes of equations and estimations of size.
| Strand |
Source |
Activities |
| Rounding |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
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Magnitude: Compare
The learner will be able to
make comparisons of the magnitudes of numbers.
| Strand |
Source |
Activities |
| Magnitude |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.A |
Classroom
Home
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Mean/Median/Mode/Range: Describe
The learner will be able to
apply the concepts of mean, median, mode, and/or range to make descriptions of data, justifying their actions, if necessary.
| Strand |
Source |
Activities |
| Average/Median/Mode/Range |
PA: Academic Standards, January 16, 1999, Grade 5, p.9,2.6.5.B |
Classroom
Home
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Probability of Events: Analyzing
The learner will be able to
analyze the probability of events to determine their dependence or independence, and study the probability of compound events.
| Strand |
Source |
Activities |
| Probability |
PA: System of School Assessment, 1997, Grade 5, p.12,#4 week tested: 30. |
Classroom
Home
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Probability
The learner will be able to
illustrate and/or display probability measures as rational numbers.
| Strand |
Source |
Activities |
| Probability |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.C |
Classroom
Home
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Data: Organize/Display
The learner will be able to
organize and illustrate data using pictures, tallies, tables, charts, bar graphs, and circle graphs.
| Strand |
Source |
Activities |
| Data |
PA: Academic Standards, January 16, 1999, Grade 5, p.9,2.6.5.A |
Classroom
Home
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Predictions: Check/Confirm
The learner will be able to
apply models, number facts, properties and relationships to check and confirm predictions and explain reasoning.
| Strand |
Source |
Activities |
| Predictions |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.B |
Classroom
Home
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Probability/Statistics: Problem Solving
The learner will be able to
understand and use basic probability and statistics concepts to solve both real-world and theoretical problems.
| Strand |
Source |
Activities |
| Probability/Statistics |
PA: System of School Assessment, 1997, Grade 5, p.12,#4 week tested: 30. |
Classroom
Home
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Venn Diagram: Sort
The learner will be able to
use Venn diagrams to sort data.
| Strand |
Source |
Activities |
| Venn Diagram |
PA: Academic Standards, January 16, 1999, Grade 5, p.9,2.6.5.C |
Classroom
Home
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Probability: Determine
The learner will be able to
identify the probability of an event involving "and", "or" or "not".
| Strand |
Source |
Activities |
| Probability |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.G |
Classroom
Home
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Probability: Simple Event
The learner will be able to
determine the probability of a simple event.
| Strand |
Source |
Activities |
| Probability |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.E |
Classroom
Home
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Probability: Predict
The learner will be able to
predict the probability a situation will occur based on the analysis of data.
| Strand |
Source |
Activities |
| Probability |
PA: Academic Standards, January 16, 1999, Grade 5, p.9,2.6.5.D |
Classroom
Home
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Data: Create/Defend Conclusions
The learner will be able to
create and defend simple conclusions that are based on data.
| Strand |
Source |
Activities |
| Data |
PA: Academic Standards, January 16, 1999, Grade 5, p.9,2.6.5.E |
Classroom
Home
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Predictions: Simulations
The learner will be able to
perform simulations with physical devices to predict the probability of the occurring of an event.
| Strand |
Source |
Activities |
| Predictions |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.A |
Classroom
Home
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Statistics: Quantify Issues
The learner will be able to
quantify issues using statistics.
| Strand |
Source |
Activities |
| Statistics |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.F |
Classroom
Home
|
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Tree Diagrams
The learner will be able to
use tree diagrams to represent possible outcomes.
| Strand |
Source |
Activities |
| Counting Methods |
PA: Academic Standards, January 16, 1999, Grade 5, p.12,2.7.5.J |
Classroom
Home
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Combinations: Find All
The learner will be able to
determine all combinations and arrangements that have a limited number of variables.
| Strand |
Source |
Activities |
| Combinations |
PA: Academic Standards, January 16, 1999, Grade 5, p.12,2.7.5.I |
Classroom
Home
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Experiments: Pattern
The learner will be able to
identify patterns formed as a result of an experiment.
| Strand |
Source |
Activities |
| Experiments |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.F |
Classroom
Home
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Experiments: Describe
The learner will be able to
describe the relationship between experimental results and the mathematical expectations.
| Strand |
Source |
Activities |
| Experiments |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.D |
Classroom
Home
|
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Impossible/Certain Events: Predict
The learner will be able to
predict and identify why some outcomes are certain, more likely, less likely, equally likely or impossible.
| Strand |
Source |
Activities |
| Impossible/Certain Events |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.H |
Classroom
Home
|
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Trees: Create
The learner will be able to
make tree diagrams.
| Strand |
Source |
Activities |
| Trees |
PA: Academic Standards, January 16, 1999, Grade 5, p.12,2.7.5.J |
Classroom
Home
|
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Probability Concepts: Spinners
The learner will be able to
identify the fairness of the design of a spinner.
| Strand |
Source |
Activities |
| Probability Concepts |
PA: Academic Standards, January 16, 1999, Grade 5, p.11,2.7.5.B |
Classroom
Home
|
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Irrelevant/Necessary Information
The learner will be able to
recognize superfluous and/or needed information in problem solving situations.
| Strand |
Source |
Activities |
| Irrelevant/Necessary Information |
PA: Academic Standards, January 16, 1999, Grade 5, p.7,2.4.5.D |
Classroom
Home
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Solution: Communicate Process
The learner will be able to
communicate the mathematical processes used to solve a problem.
| Strand |
Source |
Activities |
| Solution |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.A |
Classroom
Home
|
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Solutions: Extend/Generalize
The learner will be able to
connect, extend, and generalize solutions to problems to other ideas, problems and situations in mathematics.
| Strand |
Source |
Activities |
| Solution |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.D |
Classroom
Home
|
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Strategies: Choose/Apply/Justify
The learner will be able to
choose, apply, and justify the methods, materials, and strategies used to obtain solutions to problems.
| Strand |
Source |
Activities |
| Strategies |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.E |
Classroom
Home
|
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Analyzing Problems: Describe
The learner will be able to
use suitable mathematical terms, vocabulary, language symbols and graphs to clearly describe problem solutions.
| Strand |
Source |
Activities |
| Analyzing Problems |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.B |
Classroom
Home
|
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Problem Solving: Planned Process
The learner will be able to
plan a process to solve a problem and implement that plan.
| Strand |
Source |
Activities |
| Problem Solving |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.A |
Classroom
Home
|
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Necessary Information
The learner will be able to
identify the information needed to solve a problem.
| Strand |
Source |
Activities |
| Irrelevant/Necessary Information |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.A |
Classroom
Home
|
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Solution: Reasonableness
The learner will be able to
evaluate the reasonableness of a given solution.
| Strand |
Source |
Activities |
| Solution |
PA: Academic Standards, January 16, 1999, Grade 5, p.8,2.5.5.A |
Classroom
Home
|
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Word Problems: Operations/Whole Numbers
The learner will be able to
obtain solutions to elementary word problems involving operations with whole numbers.
| Strand |
Source |
Activities |
| Word Problems |
PA: Academic Standards, January 16, 1999, Grade 5, p.4,2.2.5.A |
Classroom
Home
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Word Problems: Create
The learner will be able to
create word problems involving the four basic operations with whole numbers.
| Strand |
Source |
Activities |
| Word Problems |
PA: Academic Standards, January 16, 1999, Grade 5, p.4,2.2.5.A |
Classroom
Home
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Real Numbers and the Coordinate Plane
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Coordinate Geometry: Locating
The learner will be able to
use coordinates to find points in two and/or three dimensions.
| Strand |
Source |
Activities |
| Coordinate Geometry |
PA: Academic Standards, January 16, 1999, Grade 5, p.14,2.8.5.H |
Classroom
Home
|
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Coordinate Plane: Identify Points
The learner will be able to
identify points on a coordinate plane.
| Strand |
Source |
Activities |
| Coordinate Geometry |
PA: Academic Standards, January 16, 1999, Grade 5, p.14,2.8.5.H |
Classroom
Home
|
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Calculator: Fraction
The learner will be able to
show the ability to use fraction calculators to confirm conjectures and computations, and investigate complex problem-solving situations.
| Strand |
Source |
Activities |
| Calculator Operations |
PA: Academic Standards, January 16, 1999, Grade 5, p.5,2.2.5.F |
Classroom
Home
|
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Geometry: Constructions
The learner will be able to
make geometric constructions using computer software.
| Strand |
Source |
Activities |
| Geometry |
PA: Academic Standards, January 16, 1999, Grade 5, p.16,2.9.5.E |
Classroom
Home
|
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Operations: Add/Subtract/Multiply/Divide
The learner will be able to
add, subtract, multiply, and divide whole numbers within the context of numerical problems.
| Strand |
Source |
Activities |
| Operations |
PA: System of School Assessment, 1997, Grade 5, p.11,#1 week tested: 30. |
Classroom
Home
|
|
Algebraic Concepts: Relationships
The learner will be able to
create graphs, charts, tables, rules, and equations to represent algebraic relationships and patterns.
| Strand |
Source |
Activities |
| Algebraic Concepts |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Computation: Across Forms
The learner will be able to
perform computations with whole numbers, fractions, decimals, integers, and rational numbers.
| Strand |
Source |
Activities |
| Computation |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Equations/Expressions: Analyzing
The learner will be able to
demonstrate an understanding of equations and expressions by determining patterns in equations and expressions, by finding missing elements, by matching equations and expressions to models, manipulatives, and pictures, and by distinguishing between expressions and equations by explaining their purposes.
| Strand |
Source |
Activities |
| Equations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sentences: Relating to Real-World
The learner will be able to
explore expressions, equations, and inequalities involving whole numbers, fractions, decimals, and integers within the context of real-world scenarios, identify relationships between the variables and coefficients, and articulate how each relates to a corresponding real-world problem (in coordinate geometry, measurement, career fields, etc.).
| Strand |
Source |
Activities |
| Relating Number Sentences/Problems |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
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Number Sentences: Relating to Real-World
The learner will be able to
explore expressions, equations, and inequalities involving whole numbers, fractions, decimals, and integers within the context of real-world scenarios, analyze equations by identifying relationships between the variables and coefficients, and articulate how each relates to corresponding real-world problems.
| Strand |
Source |
Activities |
| Relating Number Sentences/Problems |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Operational Symbols: Reasoning
The learner will be able to
evaluate number sentences such as 348 x 1.5 ? 353, 45 x 1/2 ? 90, and 1/4 x 1/2 ? 8/1, replace the question marks with appropriate comparison symbols (<, =, >), and justify the symbol with a written or oral explanation.
| Strand |
Source |
Activities |
| Operations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Operations: Inverse Relationships
The learner will be able to
demonstrate the inverse relationship of addition/subtraction and multiplication/division to solve problems, and to explain and justify a solution, and read a real-world scenario requiring multiplication, identify the nature of the problem, key elements, and the operation needed, set up the equation, solve the equation, and understand how to divide to prove the solution.
| Strand |
Source |
Activities |
| Operations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Problem Solving: Manipulatives
The learner will be able to
demonstrate an understanding of equations by reading or listening to a given scenario, and creating manipulatives to represent the scenario.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Translate Problems: Two Variables
The learner will be able to
translate a given real-world scenario (delivered orally or in a written prompt) into an equation or inequality with two variables, use order of operations to solve the equation, and apply inverse operations to check the answer.
| Strand |
Source |
Activities |
| Relating Number Sentences/Problems |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Analyzing: Graphical Forms
The learner will be able to
demonstrate the ability to interpret graphical forms of data by articulating the details, facts, and concepts presented in the forms, and by evaluating the reasonableness of specific graphical forms given the types of information presented in the forms and the specific target audiences.
| Strand |
Source |
Activities |
| Analyzing/Evaluating Graphical Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Analyzing: Graphical Forms
The learner will be able to
demonstrate the ability to interpret graphical forms of data by evaluating graphical forms in the following areas: accuracy, organization, and appropriateness of the forms given a specific audience and purpose.
| Strand |
Source |
Activities |
| Analyzing/Evaluating Graphical Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Communicating: Graphical Forms/Creating
The learner will be able to
communicate complex ideas effectively by creating graphical forms of data, including collecting data from a variety of sources, consolidating raw data, and selecting appropriate elements of the data to organize and include in a logical graphical form.
| Strand |
Source |
Activities |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Graphical Forms/Creating
The learner will be able to
communicate complex ideas effectively by creating graphical forms of data including collecting data from a variety of sources, consolidating raw data, and selecting appropriate elements of the data to organize and include in a logical graphical form (diagrams, tables, charts, bar graphs, line graphs, pictographs, etc.).
| Strand |
Source |
Activities |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Graphical Forms/Solution
The learner will be able to
use graphical forms to show a solution to a probability problem, to provide visual or condensed representation of an idea, to explain mathematical concepts, and to express real-world situations such as population variance, grades, marketing materials, sports statistics, and cultural trends.
| Strand |
Source |
Activities |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Graphical Forms/Solution
The learner will be able to
use graphical forms to show a solution to a problem, to provide visual representation of an idea, and to explain concepts.
| Strand |
Source |
Activities |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Graphical Forms/Solution
The learner will be able to
use graphical forms to show a solution to a problem, to provide visual representation of an idea, to explain concepts, and to express real-world situations.
| Strand |
Source |
Activities |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Connecting: Forms
The learner will be able to
connect concepts relating decimals, whole numbers, fractions, and percents by demonstrating how these number forms are used to communicate place value, ordinality, and money amounts, and to evaluate the reasonableness of a given problem and solution.
| Strand |
Source |
Activities |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Problem Solving: Application
The learner will be able to
use manipulatives, calculators, and symbols to solve real-world scenario problems which call for the rounding, addition, subtraction, multiplication, and division of decimals. This process includes evaluating a given problem scenario, identifying the problem, determining the relevant elements and the required operation, setting up a number sentence, and solving the problem.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Problem Solving: Application
The learner will be able to
use manipulatives, calculators, symbols, and diagrams to solve real-world scenario problems which call for the rounding, addition, subtraction, multiplication, and division of decimals. This process includes evaluating a given problem scenario, identifying the problem, determining the relevant elements and the required operation, setting up a number sentence, solving the problem, and using inverse operations to check the solution.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Problem Solving: Application
The learner will be able to
use manipulatives, calculators, symbols, mental math, and diagrams to solve real-world scenario problems which call for the rounding, addition, subtraction, multiplication, and division of decimals. This process includes evaluating a given problem scenario, identifying the problem, determining the relevant elements and the required operation (without being cued about the operation the problem would require), setting up a number sentence, solving the problem, and using inverse operations to check the solution.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Problem Solving: Application
The learner will be able to
evaluate, solve, and justify solutions for real-world mathematical problems which include ambiguous circumstances.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Connecting: Using Fractions
The learner will be able to
make connections between the functions of numerators and the functions of denominators by exploring fractions (i.e., drawing conclusions about fractions a/b, b/c, c/b, a/c, b/a, and c/a, when a > b > c).
| Strand |
Source |
Activities |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Number Sense: Forms
The learner will be able to
have an intuitive sense of fractions, the portions they represent, their relationship to whole numbers, decimals, percents, and physical models of fractions, and how fractions are used to solve problems and to communicate in real-world scenarios.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
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Number Sense: Forms/Applications
The learner will be able to
relate fractions to concrete objects, to real-world events, to other number forms (whole numbers, decimals, percents), and incorporate the language of fractions to describe proportions in daily events and across the curriculum.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sense: Using Fractions
The learner will be able to
have an intuitive sense of fractions, the portions they represent, and how fractions are used to solve problems and to communicate proportions and ideas in real-world settings.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sense: Using Fractions
The learner will be able to
analyze a bar graph (created by another student) and interpret the bars by naming the represented fractions.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sense: Using Fractions
The learner will be able to
demonstrate an understanding of fractions and the ability to represent fraction concepts in different mediums by analyzing a bar graph.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sense: Using Fractions
The learner will be able to
understand when it is appropriate to express proportions with fractions, and interpret whether a fraction in a given situation is being expressed as a part of a whole, a ratio, a divisor, or an operator.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sense: Using Fractions
The learner will be able to
demonstrate a sense of fractions, and the ability to represent fraction concepts in different mediums by designing and creating bar graphs which express how specific fractions compare to a given whole.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Number Sense: Using Venn Diagrams
The learner will be able to
create Venn diagrams which demonstrate how specific fractions relate to one another, and name fractions which meet the criteria of all three circles, which meet the criteria of only two circles, and which don't fit into any of the circles.
| Strand |
Source |
Activities |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Problem Solving
The learner will be able to
demonstrate a sense of how operations with fractions manipulate numbers by recognizing a real-world situation which calls for specific operations (addition, subtraction, multiplication, or division) with fractions, evaluating the situation, articulating the nature and elements of the problem, and solving the problem without being cued that the calculations involved would require fractions.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Problem Solving
The learner will be able to
recognize a real-world situation which calls for operations (addition, subtraction, multiplication, or division) with fractions, evaluate the situation, articulate the nature and elements of the problem, and solve the problem without being cued that the calculations involved would require fractions.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Problem Solving
The learner will be able to
recognize a real-world situation which calls for operations (addition, subtraction, multiplication, or division) with fractions (without being cued that the calculations involved would require a specific operation), evaluate the situation, articulate the nature and elements of the problem, solve the problem, and use inverse operations to check the solution.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Angle Measurements
The learner will be able to
study angle measurement by analyzing three circles, each divided by a different number of wedges, and four angles of different sizes, and count the number of wedges from each circle to determine how many fit into each angle measure.
| Strand |
Source |
Activities |
| Lines/Angles/Polygons |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Combining Figures
The learner will be able to
analyze the properties of geometric figures by predicting the properties of two or more combined figures.
| Strand |
Source |
Activities |
| Combine/Partition/Transform |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Combining: Figures
The learner will be able to
predict what will occur when two geometric shapes are adjoined, combine the shapes, and study the new shape.
| Strand |
Source |
Activities |
| Combine/Partition/Transform |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Spatial Sense
The learner will be able to
develop spatial sense by speaking, writing, and using models and diagrams to explain such terms and concepts as transformation, congruency, similarity, points, lines, and the properties of two- and three-dimensional figures.
| Strand |
Source |
Activities |
| Communicating Spatial Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Spatial Sense
The learner will be able to
develop spatial sense by speaking, writing, and using models and diagrams to explain transformations, congruency, similarity, angles, lines, line segments, points, and the properties of two- and three-dimensional figures.
| Strand |
Source |
Activities |
| Communicating Spatial Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Communicating: Spatial Sense
The learner will be able to
develop spatial sense by speaking, writing, designing flow charts, and using models and diagrams to explain transformations, congruency, similarity, angles, lines, line segments, points, parallelism, perpendicularity, and the properties of two- and three-dimensional figures.
| Strand |
Source |
Activities |
| Communicating Spatial Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Connecting: Geometry Applications
The learner will be able to
make connections involving topics of geometry, their applications in mathematics and science, and how geometry is used by professionals in a variety of career fields.
| Strand |
Source |
Activities |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Connecting: Geometry/Algebra
The learner will be able to
apply geometric concepts to solve problems in algebra by solving systems of equations through graphing, analyzing range, domain, functions, and intercepts, by finding an equation of a line given a graphical representation, and by exploring number sentence relationships to coordinate graphs (numerical coefficients, slopes, and the y and x intercepts).
| Strand |
Source |
Activities |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Connecting: Geometry/Algebra
The learner will be able to
apply geometric concepts to solve problems in algebra by solving systems of equations through graphing, analyzing range, domain, functions, and intercepts, by finding the equation of the line given a graphical representation, and by exploring relationships, numerical coefficients, slopes, and the y and x intercepts.
| Strand |
Source |
Activities |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
Classroom
Home
|
|
Constructions: Pyramids/Prisms
The learner will be able to
construct pyramids and prisms by analyzing patterns in the number of vertices, faces, and edges in triangular, square, pentagonal, and hexagonal pyramid shapes, and realize the relationship that exists between vertices, faces and edges, specifically, Euler's theorem: V + F = E + 2.
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Activities |
| Constructions |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Exploring: Quadrilateral
The learner will be able to
explore properties of quadrilaterals by drawing quadrilaterals on geopaper divided into 3 x 3 sections (9 dots), discussing the different types of quadrilaterals drawn, and making predictions about how each type of quadrilateral will change if turned one quarter, one half, three quarters, etc.
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Source |
Activities |
| Exploring Spatial Concepts |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Logic: Proving Validity
The learner will be able to
test the validity of possible solutions by utilizing inverse operations, truth tables, and other methods.
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Source |
Activities |
| Logic |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Patterns: Comparing
The learner will be able to
study the geometric patterns found in art forms from a variety of cultures (rugs, lace, jewelry, pottery, and architecture), draw conclusions about typical patterns, and compare the patterns of different cultures.
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Source |
Activities |
| Geometric Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Patterns: Writing Expressions
The learner will be able to
explore borders, and create expressions, by determining the number of square units on a piece of grid paper (8 squares x 8 squares), and finding the number of square units on the border of the grid paper.
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Source |
Activities |
| Geometric Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Proving: Geometric Models
The learner will be able to
use models to prove the validity of a solution to a problem involving geometric properties, and use models found in the classroom to explore and estimate measurements of various geometric figures.
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Source |
Activities |
| Geometric Proofs/Theorems |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Spatial Thinking: Properties
The learner will be able to
show an awareness of the spatial properties of figures by investigating how to cover a flat surface by using one or more geometric figures, by identifying and drawing similar figures, and by drawing solids made with cubes on triangle dot paper.
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Source |
Activities |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Triangles: Pythagorean Theorem/Applying
The learner will be able to
explore implications of the Pythagorean theorem by creating a table which communicates the lengths of the two legs and the hypotenuse of a given set of right triangles, extend the table to include the lengths of the legs squared, analyze the extended table for patterns, and conjecture about the Pythagorean theorem pattern a (squared) + b (squared) = c (squared), and the theorem's converse.
| Strand |
Source |
Activities |
| Lines/Angles/Polygons |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Triangles: Relating/Applying
The learner will be able to
investigate the following triangle issues: the relationship between equilateral, isosceles, and scalene triangles, the nature of triangles as rigid figures (they cannot be shifted without being broken), and how triangles are used in real-world scenarios (e.g., to support tripods used by surveyors and photographers).
| Strand |
Source |
Activities |
| Lines/Angles/Polygons |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Problem Solving: Application
The learner will be able to
recognize real-world situations which call for operations with integers, and apply an understanding of integers to solve problems in such areas as temperature, coordinate geometry, number lines, algebra, and statistics, and analyze real-world scenarios, set up number sentences, and solve problems.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Problem Solving: Application
The learner will be able to
recognize real-world situations which call for operations with integers, and apply an understanding of integers to solve problems in such areas as temperature, coordinate geometry, number lines, algebra, and statistics and analyze real-world scenarios (without being cued with formulas, sample problems, or other means of communicating a particular number form or operation), determine the nature of the problem and relevant elements, set up a number sentence, solve the problem, and use inverse operations to check the solution.
| Strand |
Source |
Activities |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Math as Reasoning: Analyzing
The learner will be able to
analyze reasoning processes used in dealing with spatial sense, proportions, and graphs.
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Source |
Activities |
| Reasoning |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Math as Reasoning: Deductive/Inductive
The learner will be able to
employ deductive and inductive reasoning techniques to make conjectures, to validate his/her own line of thinking, and to deal with the introduction of new mathematics concepts.
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Source |
Activities |
| Reasoning |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Mathematical Connections
The learner will be able to
make mathematical connections among mathematics topics, across the curriculum, and in day to day life.
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Source |
Activities |
| Connections |
National Council of Teachers of Mathematics (NCTM), March, 1989, Eighth Grade |
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Mathematical Connections
The learner will be able to
understand mathematics as an integration of number forms, systems, relationships, ideas, and topics, and use each of th
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