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 their properties 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, proportions, or indirect measurements.
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3.1.A1B
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applying the Pythagorean Theorem, e.g., indirect measurements, map reading/distance, or diagonals.
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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 triangles and quadrilaterals related to (2.4.K1h):
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3.1.K2A
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sum of the interior angles of any triangle is 180°;
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3.1.K2B
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sum of the interior angles of any quadrilateral is 360°;
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3.1.K2C
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parallelograms have opposite sides that are parallel and congruent, opposite angles are congruent;
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3.1.K2D
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rectangles have angles of 90°, sides may or may not be equal;
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3.1.K2E
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rhombi have all sides equal in length, angles may or may not be equal;
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3.1.K2F
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squares have angles of 90°, all sides congruent;
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3.1.K2G
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trapezoids have one pair of opposite sides parallel and the other pair of opposite sides are not parallel;
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3.1.K2H
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kites have two distinct pairs of adjacent congruent sides.
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3.1.K3
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recognizes and describes the rotational symmetries and line symmetries that exist in two-dimensional figures (2.4.K1h), e.g., draw a picture with a line of symmetry in it. Explain why it is a line of symmetry.
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3.1.K4
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recognizes and uses properties of corresponding parts of similar and congruent triangles and quadrilaterals to find side or angle measures using standard notation for similarity (~) and congruence (2.4.K1h).
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3.1.K5
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knows and describes Triangle Inequality Theorem to determine if a triangle exists (2.4.K1h).
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3.1.K6
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uses the Pythagorean theorem to (2.4.K1h):
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3.1.K6A
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determine if a triangle is a right triangle,
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3.1.K6B
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find a missing side of a right triangle where the lengths of all three sides are whole numbers.
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3.1.K7
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recognizes and compares the concepts of a point, line, and plane.
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3.1.K8
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describes the intersection of plane figures, e.g., two circles could intersect at no point, one point, two points, or all points.
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3.1.K9
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describes and explains angle relationships:
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3.1.K9A
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when two lines intersect including vertical and supplementary angles;
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3.1.K9B
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when formed by parallel lines cut by a transversal including corresponding, alternate interior, and alternate exterior angles.
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3.1.K10
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recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc (Ç) and circle (8) (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 (2.4.A1a) by ($):
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3.2.A1A
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converting within the customary and the metric systems, e.g., James added 30 grams of sand to his model boat that weighed 2 kg before it sank. With the sand included, what is the total weight of his boat?
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3.2.A1B
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finding perimeter and area of circles, squares, rectangles, triangles, parallelograms, and trapezoids; e.g., Jane jogs on a circular track with a radius of 100 feet. How far would she jog in one lap?
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3.2.A1C
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finding the volume and surface area of rectangular prisms, e.g., how much paint would be needed to cover a box with dimensions of 3 feet by 4 feet by 5 feet?
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3.2.K1
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determines and uses rational number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, area, and surface area using standard and nonstandard units of measure (2.4.K1a) ($).
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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, perimeter, area, surface area, and angle measurements (2.4.K1a) ($).
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3.2.A2
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estimates to check whether or not measurements or calculations for length, weight, volume, temperature, time, perimeter, area, and surface area in real world problems are reasonable and adjusts original measurement or estimation based on additional information (a frame of reference) (2.4.A1a) ($), e.g., to check your calculation in finding the area of the floor in the kitchen; you count how many foot-square tiles there are on the floor.
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3.2.A3
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uses ratio and proportion to measure inaccessible objects (2.4.A1c), e.g., using the length of a shadow to measure the height of a flagpole.
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3.2.K3
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converts within the customary system and within the metric system.
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3.2.K4
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estimates the measure of a concrete object in one system given the measure of that object in another system and the approximate conversion factor (2.4.K1a), e.g., a mile is about 2.2 kilometers; how far is 2 miles?
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3.2.K5
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uses given measurement formulas to find (2.4.K1h):
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3.2.K5A
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area of parallelograms and trapezoids;
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3.2.K5B
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surface area of rectangular prisms, triangular prisms, and cylinders;
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3.2.K5C
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volume of rectangular prisms, triangular prisms, and cylinders.
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3.2.K6
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recognizes how ratios and proportions can be used to measure inaccessible objects (2.4.K1c), e.g., using shadows to measure the height of a flagpole.
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3.2.K7
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calculates rates of change, e.g., speed or population growth.
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3.3
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The student recognizes and applies transformations on geometric figures in a variety of situations.
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3.3.A1
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generalizes the impact of transformations on the area and perimeter of any two-dimensional geometric figure (2.4.A1a), e.g., enlarging by a factor of three triples the perimeter (circumference) and multiplies the area by a factor of nine.
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3.3.K1
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identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure (2.4.K1a).
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3.3.K2
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describes a reflection of a given two-dimensional figure that moves it from its initial placement (preimage) to its final placement (image) in the coordinate plane over the x- and y-axis (2.4.K1a,i).
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3.3.A2
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describes and draws a two-dimensional figure after undergoing two specified transformations without using a concrete object.
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3.3.A3
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investigates congruency, similarity, and symmetry of geometric figures using transformations (2.4.A1g).
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3.3.K3
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draws (2.4.K1a):
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3.3.K3A
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three-dimensional figures from a variety of perspectives (top, bottom, sides, corners);
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3.3.K3B
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a scale drawing of a two-dimensional figure;
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3.3.K3C
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a two-dimensional drawing of a three-dimensional figure.
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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 (2.4.K1a).
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3.3.A4
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uses a scale drawing to determine the actual dimensions and/or measurements of a two-dimensional figure represented in a scale drawing (2.4.A1h).
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3.4
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The student uses an algebraic perspective to examine the geometry of two dimensional figures in a variety of situations.
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3.4.A1
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represents, generates, and/or solves distance problems (including the use of the Pythagorean theorem, but not necessarily the distance formula) (2.4.A1a), e.g., a student lives five miles west and three miles north of school and another student lives 4 miles south and 7 miles east of school. What is the shortest distance between the students’ homes (as the crow flies)?
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3.4.K1
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uses the coordinate plane to (2.4.K1a):
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3.4.K1A
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list several ordered pairs on the graph of a line and find the slope of the line;
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3.4.K1B
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recognize that ordered pairs that lie on the graph of an equation are solutions to that equation;
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3.4.K1C
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recognize that points that do not lie on the graph of an equation are not solutions to that equation;
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3.4.K1D
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determine the length of a side of a figure drawn on a coordinate plane with vertices having the same x- or y-coordinates;
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3.4.K1E
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solve simple systems of linear equations.
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3.4.K2
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uses a given linear equation with integer coefficients and constants and an integer solution to find the ordered pairs, organizes the ordered pairs using a T-table, and plots the ordered pairs on a coordinate plane (2.4.K1e-g).
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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, d-g), e.g., given a situation: make a T-table, define the algebraic relationship, and graph the ordered pairs. The T-table can be represented as – as an algebraic relationship -2x=5.
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3.4.K3
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examines characteristics of two-dimensional figures on a coordinate plane using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology (2.4.A1g).
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