Standard
Benchmark
Indicator | Description | Lesson Plans | Thinkfinity | Resources |
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3
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The student uses geometric concepts and procedures in a variety of situations.
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3.1
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The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations.
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3.1.A1
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solves real-world problems by (2.4.A1a):
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3.1.A1A
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using the properties of corresponding parts of similar and congruent figures, e.g., scale drawings, map reading, or proportions;
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3.1.A1B
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applying the Pythagorean Theorem, e.g., when checking for square corners on concrete forms for a foundation, determine if a right angle is formed by using the Pythagorean Theorem;
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3.1.A1C
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using properties of parallel lines, e.g., street intersections.
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3.1.K1
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recognizes and compares properties of two-and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology (2.4.K1h).
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3.1.K2
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discusses properties of regular polygons related to (2.4.K1g-h):
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3.1.K2A
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angle measures,
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3.1.K2B
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diagonals.
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3.1.A2
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uses deductive reasoning to justify the relationships between the sides of 30°-60°-90° and 45°-45°-90° triangles using the ratios of sides of similar triangles (2.4.A1a).
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3.1.A3
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understands the concepts of and develops a formal or informal proof through understanding of the difference between a statement verified by proof (theorem) and a statement supported by examples (2.4.A1a).
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3.1.K3
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recognizes and describes the symmetries (point, line, plane) that exist in three-dimensional figures (2.4.K1h).
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3.1.K4
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recognizes that similar figures have congruent angles, and their corresponding sides are proportional (2.4.K1h).
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3.1.K5
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uses the Pythagorean Theorem to (2.4.K1h):
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3.1.K5A
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determine if a triangle is a right triangle,
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3.1.K5B
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find a missing side of a right triangle.
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3.1.K6
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recognizes and describes (2.4.K1g-h):
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3.1.K6A
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congruence of triangles using: Side-Side-Side (SSS), Angle-Side-Angle (ASA), Side-Angle-Side (SAS), and Angle-Angle-Side (AAS);
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3.1.K6B
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the ratios of the sides in special right triangles: 30°-60°-90° and 45°-45°-90°.
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3.1.K7
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recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut by a transversal (2.4.K1h).
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3.1.K8
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recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles (2.4.K1h).
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3.2
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The student estimates, measures, and uses geometric formulas in a variety of situations.
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3.2.A1
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solves real-world problems by (2.4.A1a) ($):
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3.2.A1A
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converting within the customary and the metric systems, e.g., Marti and Ginger are making a huge batch of cookies and so they are multiplying their favorite recipe quite a few times. They find that they need 45 tablespoons of liquid. To the nearest ¼ of a cup, how many cups would be needed?
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3.2.A1B
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finding the perimeter and the area of circles, squares, rectangles, triangles, parallelograms, and trapezoids, e.g., a track is made up of a rectangle with dimensions 100 meters by 50 meters with semicircles at each end (having a diameter of 50 meters). What is the distance of one lap around the inside lane of the track?
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3.2.A1C
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finding the volume and the surface area of rectangular solids and cylinders, e.g., a car engine has 6 cylinders. Each cylinder has a height of 8.4 cm and a diameter of 8.8 cm. What is the total volume of the cylinders?
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3.2.A1D
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using the Pythagorean theorem, e.g., a baseball diamond is a square with 90 feet between each base. What is the approximate distance from home plate to second base?
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3.2.A1E
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using rates of change, e.g., the equation w = –52 + 1.6t can be used to approximate the wind chill temperatures for a wind speed of 40 mph. Find the wind chill temperature (w) when the actual temperature (t) is 32 degrees. What part of the equation represents the rate of change?
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3.2.K1
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determines and uses real number approximations (estimations) for length, width, weight, volume, temperature, time, distance, perimeter, area, surface area, and angle measurement using standard and nonstandard units of measure (2.4.K1a) ($).
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3.2.K2
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selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate real number representations for length, weight, volume, temperature, time, distance, area, surface area, mass, midpoint, and angle measurements (2.4.K1a) ($).
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3.2.A2
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estimates to check whether or not measurements or calculations for length, weight, volume, temperature, time, distance, perimeter, area, surface area, and angle measurement in real-world problems are reasonable and adjusts original measurement or estimation based on additional information (a frame of reference) (2.4.A1a) ($).
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3.2.A3
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uses indirect measurements to measure inaccessible objects (2.4.A1a), e.g., you are standing next to the railroad tracks and a train passes. The number of cars in the train can be determined if you know how long it takes for one car to pass and the length of time the whole train takes to pass you.
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3.2.K3
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approximates conversions between customary and metric systems given the conversion unit or formula (2.4.K1a).
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3.2.K4
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states, recognizes, and applies formulas for (2.4.K1h) ($):
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3.2.K4A
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perimeter and area of squares, rectangle, and triangles;
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3.2.K4B
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circumference and area of circles; volume of rectangular solids.
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3.2.K5
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uses given measurement formulas to find perimeter, area, volume, and surface area of two- and three-dimensional figures (regular and irregular) (2.4.K1h).
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3.2.K6
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recognizes and applies properties of corresponding parts of similar and congruent figures to find measurements of missing sides (2.4.K1a).
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3.2.K7
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knows, explains, and uses ratios and proportions to describe rates of change (2.4.K1d) ($), e.g., miles per gallon, meters per second, calories per ounce, or rise over run.
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3.3
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The student recognizes and applies transformations on two and three dimensional figures in a variety of situations
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3.3.A1
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analyzes the impact of transformations on the perimeter and area of circles, rectangles, and triangles and volume of rectangular prisms and cylinders (2.4.A1f), e.g., reducing by a factor of ½ multiplies an area by a factor of ¼ and multiplies the volume by a factor of 1/8, whereas, rotating a geometric figure does not change perimeter or area.
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3.3.K1
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describes and performs single and multiple transformations [refection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on two- and three-dimensional figures (2.4.K1a).
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3.3.K2
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recognizes a three-dimensional figure created by rotating a simple two-dimensional figure around a fixed line (2.4.K1a), e.g., a rectangle rotated about one of its edges generates a cylinder; an isosceles triangle rotated about a fixed line that runs from the vertex to the midpoint of its base generates a cone.
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3.3.A2
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describes and draws a simple three-dimensional shape after undergoing one specified transformation without using concrete objects to perform the transformation (2.4.A1a).
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3.3.A3
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uses a variety of scales to view and analyze two- and three-dimensional figures (2.4.A1g).
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3.3.K3
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generates a two-dimensional representation of a three-dimensional figure (2.4.K1a).
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3.3.K4
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determines where and how an object or a shape can be tessellated using single or multiple transformations and creates a tessellation (2.4.K1a).
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3.3.A4
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analyzes and explains transformations using such things as sketches and coordinate systems (2.4.A1a).
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3.4
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The student uses an algebraic perspective to analyze the geometry of two- and three- dimensional figures in a variety of situations.
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3.4.A1
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represents, generates, and/or solves real-world problems that involve distance and two-dimensional geometric figures including parabolas in the form ax2 + c (2.4.A1e), e.g., compare the heights of 2 different objects whose paths are represented h1(t) = 3t² + 1 and h2(t) = ½t² + 4 (where h represents the height in feet and t represents elapsed time in seconds) after 5 seconds.
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3.4.K1
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recognizes and examines two- and three-dimensional figures and their attributes including the graphs of functions on a coordinate plane using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology (2.4.K1f).
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3.4.K2
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determines if a given point lies on the graph of a given line or parabola without graphing and justifies the answer (2.4.K1f).
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3.4.A2
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translates between the written, numeric, algebraic, and geometric representations of a real-world problem (2.4.A1a-e) ($), e.g., given a situation, write a function rule, make a T-table of the algebraic relationship, and graph the order pairs.
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3.4.A3
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recognizes and explains the effects of scale changes on the appearance of the graph of an equation involving a line or parabola (2.4.A1g).
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3.4.K3
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calculates the slope of a line from a list of ordered pairs on the line and explains how the graph of the line is related to its slope (2.4.K1f).
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3.4.K4
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finds and explains the relationship between the slopes of parallel and perpendicular lines (2.4.K1f), e.g., the equation of a line 2x + 3y = 12. The slope of this line is -2/3. What is the slope of a line perpendicular to this line?
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3.4.A4
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analyzes how changes in the constants and/or leading coefficients within the equation of a line or parabola affects the appearance of the graph of the equation (2.4.A1e).
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3.4.K5
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uses the Pythagorean Theorem to find distance (may use the distance formula) (2.4.K1f).
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3.4.K6
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recognizes the equation of a line and transforms the equation into slope-intercept form in order to identify the slope and y-intercept and uses this information to graph the line (2.4.K1f).
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3.4.K7
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recognizes the equation y = ax2 + c as a parabola; represents and identifies characteristics of the parabola including opens upward or opens downward, steepness (wide/narrow), the vertex, maximum and minimum values, and line of symmetry; and sketches the graph of the parabola (2.4.K1f).
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3.4.K8
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explains the relationship between the solution(s) to systems of equations and systems of inequalities in two unknowns and their corresponding graphs (2.4.K1f), e.g., for equations, the lines intersect in either one point, no points, or infinite points; and for inequalities, all points in double-shaded areas are solutions for both inequalities.
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