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Poyen School |
| Number and Operations |
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Ratio/proportions/percents
The learner will be able to relate, with and without models and pictures, concepts of ratio, proportion, and percent, including percents less than 1 and greater than 100.
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Place value/powers of 10/scientific not.
The learner will be able to demonstrate, with and without appropriate technology, an understanding of place value using powers of 10 and write numbers greater than one in scientific notation.
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Scientific and standard notation
The learner will be able to convert between scientific notation and standard notation using numbers greater than one.
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Mixed number/decimal/percent equivalents
The learner will be able to find decimal and percent equivalents for mixed numbers and explain why they represent the same value.
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Integers, fractions, decimals, mixed #
The learner will be able to compare and represent integers, fractions, decimals, and mixed numbers and find their approximate location on a number line.
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Subsets of real number system
The learner will be able to recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers).
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Distributive property
The learner will be able to apply the distributive property of multiplication over addition or subtraction to simplify computations with integers, fractions, and decimals.
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One-step equations
The learner will be able to apply the addition, subtraction, multiplication, and division properties of equality to one-step equations with integers, fractions, and decimals.
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Order of operations
The learner will be able to apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets, or exponents.
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Operations with integers
The learner will be able to model and develop addition, subtraction, multiplication, and division of integers.
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Integers & positive rational numbers
The learner will be able to compute, with and without appropriate technology, with integers and positive rational numbers using real-world situations to solve problems.
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Multi-step problems
The learner will be able to solve with and without appropriate technolgy, multi-step problems using a variety of methods and tools (i.e., objects, mental computation, paper and pencil).
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Estimation: determine reasonable answer
The learner will be able to determine when an estimate is sufficient and use estimation to decide whether answers are reasonable in problems including fractions and decimals.
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Factorization, LCM, GCF
The learner will be able to apply factorization, LCM, and GCF to solve problems using more than two numbers and explain the solution.
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Absolute value, exponents, square roots
The learner will be able to represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents, and square roots (for perfect squares) with and without appropriate technology.
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Real world percent problems
The learner will be able to solve, with and without technology, real world percent problems. (Example: I = PRT).
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| Algebraic Concepts |
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Function table with two operations
The learner will be able to create and complete a function table (input/output) using a given rule with two operations.
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Patterns
The learner will be able to identify and extend patterns in real world situations.
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Rule for 2 operation function table
The learner will be able to interpret and write a rule for a two-operation function table (Example: multiply by 2 and add 1).
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Linear equations and inequalities
The learner will be able to solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology.
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Linear equations with integers
The learner will be able to solve simple linear equations using integers and graph on a coordinate plane. Example: Use a T chart.
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Translate phrases to algebraic
The learner will be able to translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like terms.
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Write and evaluate algebraic expressions
The learner will be able to write and evaluate algebraic expressions using positive rational numbers.
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Linear equations on coordinate plane
The learner will be able to use tables and graphs to represent linear equations by plotting, with and without appropriate technology, points in a coordinate plane.
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Data table to plot linear equations
The learner will be able to represent, with and without appropriate technology, linear equations by plotting and graphing points in the coordinate plane using all four quadrants given data in a table from a real world situation.
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Function table with 2 operations
The learner will be able to create and complete a function table (input/output) using a given rule with two operations in real world situations.
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Rates of change
The learner will be able to use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of change.
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| Geometry |
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Geometric figures
The learner will be able to identify, draw, classify, and compare geometric figures using models and real world examples.
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Geometric properties
The learner will be able to investigate geometric properties and their relationships in one, two, and three dimensions models, including convex and concave polygons.
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Pairs of angles
The learner will be able to recognize the pairs of angles formed and the relationship between the angles including two intersecting lines and parallel lines cut by a transversal (vertical, supplementary, complementary, corresponding, alternate interior, alternate exterior angles and linear pair).
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Sum of measures of interior angles
The learner will be able to use paper or physical models to determine the sum of the measures of interior angles of triangles and quadrilaterals.
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Concept of pi
The learner will be able to model and develop the concept that pi is the ratio of the circumference to the diameter of any circle. Use symbolism for pi.
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Properties of similar figures
The learner will be able to develop the properties of similar figures (ratio of sides and congruent angles).
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Transformations
The learner will be able to examine the congruence, similarity, and line or rotational symmetry of objects using transformations.
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Translations and Reflections
The learner will be able to perform translations and reflections of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).
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Plot points in coordinate plane
The learner will be able to plot points in the coordinate plane.
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Plot points to form geometric figure
The learner will be able to plot points that form the vertices of a geometric figure and draw, identify, and classify the figure.
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Build 3-D solid from net
The learner will be able to build three-dimensional solids from two-dimensional patterns (nets).
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Cubes: Orthographic views
The learner will be able to construct a building out of cubes from a set of views (front, top, side).
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| Measurement |
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Units & tools for measurement
The learner will be able to understand, select, and use the appropriate units and tools (metric and customary) to measure length, weight, mass and volume to the required degree of accuracy for real world problems.
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Relationships among measurement units
The learner will be able to understand relationships among units within the same system.
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Perimeter/Area
The learner will be able to find different areas for a given perimeter and find a different perimeter for a given area.
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Elapsed time
The learner will be able to solve real world problems involving two or more elapsed times, counting forward and backward (calendar and clock).
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Draw and measure distance
The learner will be able to draw and measure distance to the nearest mm and 1/16 inch accurately.
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Area and circumference
The learner will be able to develop and use strategies to solve problems involving area of a trapezoid and circumference and area of a circle.
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Surface area and volume
The learner will be able to derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials.
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Congruent and similar triangles
The learner will be able to apply properties (scale factors, ratio, and proportion) of congruent or similar triangles to solve problems involving missing lengths and angle measures.
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Distance and midpoint on a number line
The learner will be able to find the distance between two points on a number line and locate the midpoint.
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Area of irregular shapes
The learner will be able to estimate and compute the area of more complex or irregular two-dimensional shapes by dividing them into more basic shapes.
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| Data Analysis and Probability |
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Questioning and samples
The learner will be able to identify different ways of selecting samples and compose app |