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Poyen School |
| Number and Operations |
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Solve problems
The learner will be able to read, write, compare and solve problems, with and without appropriate technology, including numbers less than 1 in scientific notation.
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Convert scientific and standard notation
The learner will be able to convert between scientific notation and standard notation, including numbers from zero to one.
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Compare and order real numbers
The learner will be able to compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate).
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Real number classifications: subsets
The learner will be able to understand and justify classification of numbers in the real number system.
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Two-step equations
The learner will be able to apply the addition, subtraction, multiplication, and division properties of equality to two-step equations.
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Inverse and identity properties
The learner will be able to understand and apply the inverse and identify properties.
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Inverse relationships
The learner will be able to use inverse relationships (addition and subtraction, multiplication and division, squaring and square roots) in problem solving situations.
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Order of operations
The learner will be able to apply rules (conventions) for order of operations to rational numbers.
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Operations with rational numbers
The learner will be able to model and develop addition, subtraction, multiplication and division of rational numbers. (Example: -8 1/2 + 2 3/4).
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Rational numbers: multi-step problems
The learner will be able to compute, with and without appropriate technology, with rational numbers in multi-step problems.
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Solve muti-step problems
The learner will be able to solve, with and without appropriate technology, multi-step problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil).
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Estimation to solve problems
The learner will be able to use estimation to solve problems involving rational numbers; including ratio, proportion, percent (increase or decrease) then judge the reasonableness of solutions.
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Factorization of algebraic expressions
The learner will be able to apply factorization to find LCM and GCF of algebraic expressions. Example: See 2004 Arkansas Mathematics Frameworks for specific examples of algebraic factorization applications.
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Approximate square roots
The learner will be able to calculate and find approximations of square roots with appropriate technology.
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Solve real world percent problems
The learner will be able to solve, with and without technology, real world percent problems including percent of increase or decrease.
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| Algebraic Concepts |
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Nth term of a pattern
The learner will be able to find the nth term in a pattern or a function table.
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Describe patterns
The learner will be able to using real world situations, describe patterns in words, tables, pictures, and symbolic representations.
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Represent 2 operation functions
The learner will be able to interpret and represent a two operation function as an algebraic equation. (Example: y = 2x + 1).
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Independent/dependent variables
The learner will be able to use table, graphs, and equations to identify independent/dependent variables (input/output).
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Solve/graph two-step equations/inequal
The learner will be able to solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology.
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Solve/graph linear equations
The learner will be able to solve and graph linear equations (in the form y = mx + b).
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Translate to algebraic
The learner will be able to translate sentences into algebraic equations and inequalities and combine like terms within polynomials.
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Write/evaluate algebraic expressions
The learner will be able to write and evaluate algebraic expressions using rational numbers.
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Graph/equation relationships
The learner will be able to describe, with and without appropriate technology, the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change (rise/run) and y-intercept in real-world problems.
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Represent linear relationships
The learner will be able to represent, with and without appropriate technology, linear relationships concretely, using tables, graphs, and equations.
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Independent/dependent variables
The learner will be able to differentiate between independent/dependent variables given a linear relationship context.
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Represent exponential/quadratic function
The learner will be able to represent, with and without appropriate technology, simple exponential and/or quadratic functions using verbal descriptions, tables, graphs and formulas and translate among these representations.
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Use/analyze graphs
The learner will be able to use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost).
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| Geometry |
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Properties of geometric shapes
The learner will be able to form generalizations and validate conclusions about properties of geometric shapes.
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Properties 2-D vs 3-D
The learner will be able to make, with and without appropriate technology, and test conjectures about characteristics and properties between two-dimensional figures and three-dimensional objects (Example: circle vs. cylinder, square vs. cube).
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Apply geometric concepts
The learner will be able to determine appropriate application of geometric ideas and relationships, such as congruence, similarity, and the Pythagorean theorem, with and without appropriate technology.
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Transformations
The learner will be able to determine a transformation's line of symmetry and compare the properties of the figure and its transformation.
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Draw the results of transformations
The learner will be able to draw the results of translations and reflections about the x and y axis and rotations of objects about the origin.
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Link geometric/algebraic representations
The learner will be able to use coordinate geometry to explore the links between geometric and algebraic representations of problems (lengths of segments/distance between points, slope/perpendicular-parallel lines).
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Isometric drawings
The learner will be able to using isometric dot paper interpret and draw different views of buildings.
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| Measurement |
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Measurement units and tools
The learner will be able to understand, select and use with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area, and volume to solve real world problems.
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Equivalent measures
The learner will be able to describe and apply equivalent measures using a variety of units within the same system of measurement.
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Measure with precision
The learner will be able to draw and apply measurement skills with fluency to appropriate levels of precision.
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Volume and surface area
The learner will be able to solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology.
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Apply proportions
The learner will be able to apply proportional reasoning to solve problems involving indirect measurements, scale drawings or rates.
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Distance on coordinate plane
The learner will be able to find the distance between two points on a coordinate plane using the Pythagorean theorem.
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Area of irregular shapes
The learner will be able to estimate and compute the area of irregular two-dimensional shapes.
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| Data Analysis and Probability |
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Conduct investigations
The learner will be able to design and conduct investigations which include 1. Adequate number of trials 2. Unbiased sampling 3. Record-keeping.
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Appropriate display of data
The learner will be able to explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit).
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Use data from charts, plots and graphs
The learner will be able to interpret or solve real-world problems using data from charts, line plots, stem-and-leaf plots, double-bar graphs, line graphs, box-and-whisker plots, scatter plots, frequency tables or double line graphs.
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Reliability of data
The learner will be able to compare and contrast the reliability of data sets with different size populations (Example: 40/80 vs 40/800).
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Measures of central tendency and spread
The learner will be able to analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread.
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Create data set from central tendency
The learner will be able to given at least one of the measures of central tendency create a data set.
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Outliers
The learner will be able to describe how the inclusion of outliers affects those measures (central tendency/spread).
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Make conjectures about data sets
The learner will be able to use observations about differences between sets of data to make conjectures about the populations from which the data was taken.
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Probability: compound events
The learner will be able to compute, with and without appropriate technology, probabilities of compound events, using organized lists, tree diagrams, and logic grid.
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Make predictions:theoretical probability
The learner will be able to make predictions based on theoretical probabilities, desigen and conduct an experiment to test the predictions, compare the actual results to the predicted results, and explain differences. Example: Suggested materials for simulations are: polyhedra die, random number table, and technology.
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