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Number, Number Sense and Operations
A. Represent and compare numbers less than 0 through familiar applications and extending the number line.
B. Compare, order and convert among fractions, decimals and percents.
C. Develop meaning for percents, including percents greater than 100 and less than 1.
D. Use models and pictures to relate concepts of ratio, proportion and percent.
E. Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.
F. Apply number system properties when performing computations.
G. Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations.
H. Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.
I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.
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Measurement
A. Select appropriate units to measure angles, circumference, surface area, mass and volume, using:
o U.S. customary units; e.g., degrees, square feet, pounds, and other units as appropriate;
o metric units; e.g., square meters, kilograms and other units as appropriate.
B. Convert units of length, area, volume, mass and time within the same measurement system.
C. Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.
D. Select a tool and measure accurately to a specified level of precision.
E. Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature.
F. Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.
G. Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.
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Geometry and Spatial Sense
A. Identify and label angle parts and the regions defined within the plane where the angle resides.
B. Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.
C. Specify locations and plot ordered pairs on a coordinate plane.
D. Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.
E. Use proportions to express relationships among corresponding parts of similar figures.
F. Describe and use the concepts of congruence, similarity and symmetry to solve problems.
G. Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.
H. Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.
I. Identify and draw three-dimensional objects from different views (top, side, front and perspective).
J. Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.
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