Download Math Practice Standards:

LUSD MATHEMATICS: Geometry
MEASUREMENT TOPICS
Score: CL K – MT: Identify and describe shapes.
CL 1 – MT: Reason with shapes and their attributes.
CL 2 – MT: Reason with shapes and their attributes.
Learner Coach: Learner creates (with LF input/feedback) a learning plan aligned to a Learning Target and assists a (learning facilitator selected) peer in obtaining Level 3 proficiency.
4.0 •
3.0
2.0
1.0
•
Challenge Task: Learner completes a Level 4 task aligned to a single learning target. The learner must earn a proficient or higher on the scoring rubric or assessment criteria.
•
Integrated Project: Learner completes a Level 4 project aligned to several learning targets within the subject matter. The learner must earn a proficient or higher on the scoring rubric.
•
Integrated Cross Curricular Project: Learner designs (with LF input/feedback) and completes an interdisciplinary project. The learner must earn a proficient or higher on the scoring rubric.
 Identify shapes as two-dimensional (flat) or three-dimensional (solid).
 Distinguish between defining attributes versus non-defining attributes, build  Draw shapes having specified attributes, such as a given number of angles
(M.K.G.3)
and draw shapes to possess defining attributes. (M.1.G.1)
or a given number of equal faces. (M.2.G.1)
 Analyze and compare two- and three-dimensional shapes, in different sizes
 Compose two-dimensional shapes or three-dimensional shapes to create a
 Partition circles and rectangles into two, three, or four equal shares,
and orientations, using informal language to describe their similarities,
composite shape, and compose new shapes from the composite shape.
describe the shares using the words halves, thirds, half of, a third of, etc.,
differences, parts and other attributes. (M.K.G.4)
(M.1.G.2)
and describe the whole as two halves, three thirds, four fourths. (M.2.G. 3)
 Compose simple shapes to form larger shapes. (M.K.G.6)
 Partition circles and rectangles in two and four equal shares. Understand
that decomposing into more equal shares creates smaller shares. (M.1.G.3)
 Know and use the terms: shapes, two-dimensional, flat, three-dimensional,  Know the terms: defining attribute, shape, closed, side, two-dimensional,
 Know the terms: attributes, angles, sides, faces, triangles, quadrilaterals,
solid, closed figure, attributes, triangles, squares, circles, rectangles,
three-dimensional, angles, faces, rectangle, square, triangle, trapezoid,
hexagons, pentagons, cubes, equal shares, whole, half, thirds, fourths, row,
trapezoids, hexagons, cubes, cones, cylinders, and spheres, corners, vertex,
compose (composite), half-circle, quarter-circle, prism, cylinder, cone,
column
vertices, edges, sides, faces, compose, decompose
sphere, cube, rectangular prism, rhombus, quadrilateral, equal shares,
 Partition a rectangle into rows and columns of same-size squares and count
 Describe objects in the environment using names of shapes, and describe
halves, fourths, quarters, partition, whole, half of, fourth of, quarter of
to find the total number of them. (M.2.G. 2)
the relative positions of these objects using terms such as above, below,
beside, in front of, behind, and next to. (M.K.G.1)
 Correctly name shapes regardless of their orientations or overall size.
(M.K.G.2)
 Model shapes in the world by building shapes from components (e.g., sticks
and clay balls) and drawing shapes. (M.K.G.5)
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
Math Practice Standards:
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.3: Construct a viable argument and critique
the reasoning of others.
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.7: Look for and
make use of structure.
MP.8: Look for and express regularity in repeated reasoning.
1|Page
DRAFT – August 2013
LUSD MATHEMATICS: Geometry
MEASUREMENT TOPICS
Score: CL 3 – MT: Reason with shapes and their attributes.
4.0
3.0
2.0
1.0
CL 4 – MT: Draw and identify lines and angles, and classify
shapes by the properties of their lines and angles.
CL 5 – MT: Graph points on the coordinate plane to solve
real-world and mathematical problems.
•
Learner Coach: Learner creates (with LF input/feedback) a learning plan aligned to a Learning Target and assists a (learning facilitator selected) peer in obtaining Level 3 proficiency.
•
Challenge Task: Learner completes a Level 4 task aligned to a single learning target. The learner must earn a proficient or higher on the scoring rubric or assessment criteria.
•
Integrated Project: Learner completes a Level 4 project aligned to several learning targets within the subject matter. The learner must earn a proficient or higher on the scoring rubric.
•
Integrated Cross Curricular Project: Learner designs (with LF input/feedback) and completes an interdisciplinary project. The learner must earn a proficient or higher on the scoring rubric.
 Understand that shapes in different categories may share attributes, and
 Classify two-dimensional figures based on the presence or absence of
 Represent real world and mathematical problems by graphing points in the
that the shared attributes can define a larger category. (M.3.G.1)
parallel or perpendicular lines, or the presence or absence of angles of a
first quadrant of the coordinate plane, and interpret coordinate values of
 Partition shapes into parts with equal areas. Express the area of each part
specified size. (M.4.G.2)
points in the context of the situation. (M.5.G.2)
as a unit fraction of the whole. (M.3.G.2)
 Identify line-symmetric figures and draw lines of symmetry. (M.4.G.3)
 Know and use the terms: attribute, quadrilateral, rectangle, rhombus,
 Know and use the terms point, line, line segment, ray, angle, right angle,
 Know and use the terms ordered pair, quadrant, coordinate plane,
square, parallelogram, trapezoid, area, unit fraction, partition
acute angle, obtuse angle, perpendicular lines, parallel lines, right triangle,
 Use a pair of perpendicular number lines, called axes, to define a coordinate
two dimensional figures, equilateral triangle, equiangular triangle, isosceles
system, with the intersection of the lines (the origin) arranged to coincide
triangle, scalene triangle, quadrilaterals, rhombus, square, rectangle,
with the 0 on each line and a given point in the plane located by using an
parallelogram, trapezoid,
ordered pair of numbers, called its coordinates. Understand that the first
 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and
number indicates how far to travel from the origin in the direction of one
perpendicular and parallel lines. Identify these in two-dimensional figures.
axis, and the second number indicates how far to travel in the direction of
(M.4.G.1)
the second axis, with the convention that the names of the two axes and
the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and ycoordinate). (M.5.G.1)
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
Math Practice Standards:
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.3: Construct a viable argument and critique the
reasoning of others. MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.7: Look for and make use
of structure.
MP.8: Look for and express regularity in repeated reasoning.
2|Page
DRAFT – August 2013
LUSD MATHEMATICS: Geometry
MEASUREMENT TOPICS
Score: CL 5 – MT: Classify two-dimensional figures into categories
CL 6 – MT: Solve real-world and mathematical problems
CL 7 – MT: Draw, construct, and describe geometrical figures
based on their properties.
involving area, surface area, and volume.
and describe the relationships between them.
Learner Coach: Learner creates (with LF input/feedback) a learning plan aligned to a Learning Target and assists a (learning facilitator selected) peer in obtaining Level 3 proficiency.
4.0 •
3.0
2.0
1.0
•
Challenge Task: Learner completes a Level 4 task aligned to a single learning target. The learner must earn a proficient or higher on the scoring rubric or assessment criteria.
•
Integrated Project: Learner completes a Level 4 project aligned to several learning targets within the subject matter. The learner must earn a proficient or higher on the scoring rubric.
•
Integrated Cross Curricular Project: Learner designs (with LF input/feedback) and completes an interdisciplinary project. The learner must earn a proficient or higher on the scoring rubric.
 Classify two-dimensional figures in a hierarchy based on properties.
 Find the area of triangles, quadrilaterals, and polygons by composing into
 Solve problems involving scale drawings of geometric figures, including
(M.5.G.4)
rectangles or decomposing into triangles and other shapes; apply these
computing actual lengths and areas from a scale drawing and reproducing a
techniques in the context of solving real-world and mathematical problems.
scale drawing at a different scale. (M.7.G.1)
(M.6.G.1)
 Apply the formulas V=lwh and V=Bh to find volumes of right rectangular
prisms with fractional edge lengths in the context of solving real-world and
mathematical problems. (M.6.G.2)
 Draw polygons in the coordinate plane given coordinates for the vertices;
use coordinates to find the length of a side joining points with the same first
coordinate or the same second coordinate. Apply these techniques in the
context of solving real-world and mathematical problems. (M.6.G.3)
 Know and use the terms: hierarchy, attribute, category, subcategory, two-  Know and use the terms: polygon, triangle, right triangle, quadrilateral,
 Know and use the terms: angles, angle measure, dimensions, acute,
dimensional, polygon, rhombus, quadrilateral, trapezoid, kite,
parallelogram, trapezoid, rhombus, scalene triangle, isosceles triangle,
obtuse, right, protractor, scale drawing, scale, plane, perpendicular, base
parallelogram,
equilateral triangle, obtuse triangle, acute triangle, area, square unit,
 Draw (freehand, with ruler and protractor, and with technology) geometric
 Understand that attributes belonging to a category of two-dimensional
decomposing shapes, formulas, right rectangular prism, base, height, area,
shapes with given conditions. Focus on constructing triangles from three
figures also belong to all subcategories of that category. (M.5.G.3)
volume, cubic unit, unit fraction, fractional edge lengths, vertex/vertices,
measures of angles or sides, noticing when the conditions determine a
sides, length, coordinate plane, coordinate pairs, coordinates, polygon
unique triangle, more than one triangle, or no triangle. (M.7.G.2)
 Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and
right rectangular pyramids. (M.7.G.3)
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
Math Practice Standards:
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.3: Construct a viable argument and critique the
reasoning of others. MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.7: Look for and make use of
structure. MP.8: Look for and express regularity in repeated reasoning.
3|Page
DRAFT – August 2013
LUSD MATHEMATICS: Geometry
MEASUREMENT TOPICS
Score: CL 7 – MT: Solve real-life and mathematical problems
CL 8 – MT: Understand congruence and similarity using
CL 8– MT: Understand and apply the Pythagorean Theorem.
involving angle measure, area, surface area, and volume.
physical models, transparencies, or geometry software.
Learner Coach: Learner creates (with LF input/feedback) a learning plan aligned to a Learning Target and assists a (learning facilitator selected) peer in obtaining Level 3 proficiency.
4.0 •
3.0
2.0
1.0
•
Challenge Task: Learner completes a Level 4 task aligned to a single learning target. The learner must earn a proficient or higher on the scoring rubric or assessment criteria.
•
Integrated Project: Learner completes a Level 4 project aligned to several learning targets within the subject matter. The learner must earn a proficient or higher on the scoring rubric.
•
Integrated Cross Curricular Project: Learner designs (with LF input/feedback) and completes an interdisciplinary project. The learner must earn a proficient or higher on the scoring rubric.
 Know the formulas for the area and circumference of a circle and use them
 Understand that a two-dimensional figure is congruent to another if the
 Apply the Pythagorean Theorem to determine unknown side lengths in right
to solve problems; give an informal derivation of the relationship between
second can be obtained from the first by a sequence of rotations,
triangles in real-world and mathematical problems in two and three
the circumference and area of a circle. (M.7.G.4)
reflections, and translations; given two congruent figures, describe a
dimensions. (M.8.G.7)
 Use facts about supplementary, complementary, vertical, and adjacent
sequence that exhibits the congruence between them. (M.8.G.2)
 Apply the Pythagorean Theorem to find the distance between two points in
angles in a multi-step problem to write and solve simple equations for an
 Understand that a two-dimensional figure is similar to another if the second
a coordinate system. (M.8.G.8)
unknown angle in a figure. (M.7.G.5)
can be obtained from the first by a sequence of rotations, reflections,
 Solve real-world and mathematical problems involving area, volume and
translations, and dilations; given two similar two-dimensional figures,
surface area of two- and three-dimensional objects composed of triangles,
describe a sequence that exhibits the similarity between them. (M.8.G.4)
quadrilaterals, polygons, cubes, and right prisms. (M.7.G.6)
 Use informal arguments to establish facts about the angle sum and exterior
angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles.
(M.8.G.5)
 Know and use the terms: radius, diameter, circumference, area, pi (π),
 Know and use the terms: congruent, transformation, reflection, rotation,
 Know and use the terms: Pythagorean Theorem, leg, hypotenuse,
circle, diameter, supplementary angles, complementary angles, vertical
translation, line of reflection, corresponding, angle, degree, measure of an
converse, right triangle, base, height,
angles, adjacent angles, linear pairs of angles, length, width, height,
angle, measure of a line segment, rotate, reflect, translate, line segment,
 Explain a proof of the Pythagorean Theorem and its converse. (M.8.G.6)
altitude, area, surface area, volume, triangle, quadrilateral, square,
 Verify experimentally the properties of rotations, reflections, and
rectangle, parallelogram, trapezoid, cube, right prism
translations. (M.8.G.1)
 Describe the effect of dilations, translations, rotations, and reflections on
two-dimensional figures using coordinates. (M.8.G.3)
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
With help, learner has a partial understanding of some of the score 2.0
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
elements and some of the score 3.0 elements.
Math Practice Standards:
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.3: Construct a viable argument and critique the
reasoning of others. MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.7: Look for and make use of
structure. MP.8: Look for and express regularity in repeated reasoning.
4|Page
DRAFT – August 2013
LUSD MATHEMATICS: Geometry
MEASUREMENT TOPICS
Score: CL 8 – MT: Solve real-world and mathematical problems
involving volume of cylinders, cones, and spheres.
4.0
3.0
2.0
1.0
•
Learner Coach: Learner creates (with LF input/feedback) a learning plan
aligned to a Learning Target and assists a (learning facilitator selected) peer in
obtaining Level 3 proficiency.
•
Challenge Task: Learner completes a Level 4 task aligned to a single
learning target. The learner must earn a proficient or higher on the scoring
rubric or assessment criteria.
•
Integrated Project: Learner completes a Level 4 project aligned to
several learning targets within the subject matter. The learner must earn a
proficient or higher on the scoring rubric.
•
Integrated Cross Curricular Project: Learner designs (with LF
input/feedback) and completes an interdisciplinary project. The learner must
earn a proficient or higher on the scoring rubric.
 Know the formulas for the volumes of cones, cylinders, and spheres and use
them to solve real-world and mathematical problems. (M.8.G.9)

Know and use the terms: cylinder, cone, sphere, volume, radius, height, Pi
, diameter, area, base
With help, learner has a partial understanding of some of the score 2.0 elements
and some of the score 3.0 elements.
Math Practice Standards:
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.3: Construct a viable argument and critique
the reasoning of others.
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.7: Look for and
make use of structure.
MP.8: Look for and express regularity in repeated reasoning.
5|Page
DRAFT – August 2013