Download Geometry - AMTNYS!

Crosswalk (Math, K-8)
2005 NYS Core Curriculum → 2010 Common Core
Geometry
Concept /
Skill
2005 NYS Core Curriculum
Shapes (2-D): 1.G.2 - Recognize, name, describe, create,
Identification &
Classification
1.G.5 2.G.2 -
3.G.1 -
4.G.1 -
sort, and compare two-dimensional
and three-dimensional shapes
Recognize geometric shapes and
structures in the environment
Identify and appropriately name twodimensional shapes: circle, square,
rectangle, and triangle (both regular
and irregular)
Define and use correct terminology
when referring to shapes (circle,
triangle, square, rectangle, rhombus,
trapezoid, and hexagon)
Identify and name polygons,
recognizing that their names are
related to the number of sides and
angles (triangle, quadrilateral,
pentagon, hexagon, and octagon)
Shapes (2-D): K.G.1 - Describe characteristics and
Characteristics
relationships of geometric objects
2.G.3 - Compose (put together) and
decompose (break apart) twodimensional shapes
4.G.1 - Identify and name polygons,
recognizing that their names are
related to the number of sides and
angles (triangle, quadrilateral,
pentagon, hexagon, and octagon)
2010 Common Core
K.G.1 - Describe objects in the environment using names of shapes, and
describe the relative positions of these objects using terms such
as above, below, beside, in front of, behind, and next to.
K.G.2 - Correctly name shapes regardless of their orientations or overall
size (squares, circles, triangles, rectangles, hexagons, cubes,
cones, cylinders, and spheres).
K.G.3 - Identify shapes as two-dimensional (lying in a plane, “flat”) or
three-dimensional (“solid”) (squares, circles, triangles, rectangles,
hexagons, cubes, cones, cylinders, and spheres).
2.G.1 - Recognize and draw shapes having specified attributes, such as
a given number of angles or a given number of equal faces.5
Identify triangles, quadrilaterals, pentagons, hexagons, and
cubes.
3.G.1 - Understand that shapes in different categories (e.g., rhombuses,
rectangles, and others) may share attributes (e.g., having four
sides), and that the shared attributes can define a larger category
(e.g., quadrilaterals). Recognize rhombuses, rectangles, and
squares as examples of quadrilaterals, and draw examples of
quadrilaterals that do not belong to any of these subcategories.
4.G.2 - Classify two-dimensional figures based on the presence or
absence of parallel or perpendicular lines, or the presence or
absence of angles of a specified size. Recognize right triangles
as a category, and identify right triangles.
5.G.3 - Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that
category. For example, all rectangles have four right angles and
squares are rectangles, so all squares have four right angles.
5.G.4 - Classify two-dimensional figures in a hierarchy based on
properties.
K.G.5 - Model shapes in the world by building shapes from components
(e.g., sticks and clay balls) and drawing shapes.
K.G.6 - Compose simple shapes to form larger shapes. For example,
“Can you join these two triangles with full sides touching to make
a rectangle?”
1.G.1 - Distinguish between defining attributes (e.g., triangles are closed
and three-sided) versus non-defining attributes (e.g., color,
orientation, overall size); build and draw shapes to possess
defining attributes.
1.G.2 - Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or threedimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.4
2.G.1 - Recognize and draw shapes having specified attributes, such as
a given number of angles or a given number of equal faces.5
Identify triangles, quadrilaterals, pentagons, hexagons, and
cubes.
Shapes (2-D): PK.G.1- Match shapes, first with same size
Similarity &
Congruence
Brian Cohen
K.G.2 and orientation, then with different
sizes and orientation
1.G.1 - Match shapes and parts of shapes to K.G.4 justify congruency
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Correctly name shapes regardless of their orientations or overall
size (squares, circles, triangles, rectangles, hexagons, cubes,
cones, cylinders, and spheres).
Analyze and compare two- and three-dimensional shapes, in
different sizes and orientations, using informal language to
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2.G.1 - Experiment with slides, flips, and
turns to compare two-dimensional
shapes
3.G.2 - Identify congruent and similar figures
describe their similarities, differences, parts (e.g., number of
sides and vertices/“corners”) and other attributes (e.g., having
sides of equal length).
8.G.2 - Understand that a two-dimensional figure is congruent to another
if the second can be obtained from the first by a sequence of
rotations, reflections, and translations; given two congruent
figures, describe a sequence that exhibits the congruence
between them.
Shapes (2-D): 4.G.3 - Find perimeter of polygons by adding 3.MD.8 -Solve real world and mathematical problems involving perimeters
Perimeter
sides
5.G.1 - Calculate the perimeter of regular
and irregular polygons
Shapes (2-D): 4.G.4 - Find the area of a rectangle by
Area
Brian Cohen
of polygons, including finding the perimeter given the side
lengths, finding an unknown side length, and exhibiting
rectangles with the same perimeter and different areas or with
the same area and different perimeters.
4.MD.3 -Apply the area and perimeter formulas for rectangles in real
world and mathematical problems. For example, find the width of
a rectangular room given the area of the flooring and the length,
by viewing the area formula as a multiplication equation with an
unknown factor.
counting the number of squares
needed to cover the rectangle
6.G.2 - Determine the area of triangles and
quadrilaterals (squares, rectangles,
rhombi, and trapezoids) and develop
formulas
6.G.3 - Use a variety of strategies to find the
area of regular and irregular
polygons
3.MD.5 -Recognize area as an attribute of plane figures and understand
concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is
said to have “one square unit” of area, and can be used to
measure area.
b. A plane figure which can be covered without gaps or
overlaps by n unit squares is said to have an area of n
square units.
3.MD.6 - Measure areas by counting unit squares (square cm, square m,
square in, square ft, and improvised units).
3.MD.7 -Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side
lengths by tiling it, and show that the area is the same as
would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world
and mathematical problems, and represent whole-number
products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a
rectangle with whole-number side lengths a and b + c is
the sum of a × b and a × c. Use area models to represent
the distributive property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear
figures by decomposing them into non-overlapping
rectangles and adding the areas of the non-overlapping
parts, applying this technique to solve real world problems.
4.MD.3 -Apply the area and perimeter formulas for rectangles in real
world and mathematical problems. For example, find the width of
a rectangular room given the area of the flooring and the length,
by viewing the area formula as a multiplication equation with an
unknown factor.
5.NF.4 - Apply and extend previous understandings of multiplication to
multiply a fraction or whole number by a fraction.
b. Find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction
side lengths, and show that the area is the same as would
be found by multiplying the side lengths. Multiply fractional
side lengths to find areas of rectangles, and represent
fraction products as rectangular areas.
6.G.1 - Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these
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techniques in the context of solving real-world and mathematical
problems.
7.G.6 - Solve real-world and mathematical problems involving area,
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right
prisms.
Shapes (2-D): 4.N.8 - Recognize and generate equivalent
Fractions of a
whole
fractions (halves, fourths, thirds,
fifths, sixths, and tenths) using
manipulatives, visual models, and
illustrations
Shapes (2-D): 6.G.5 - Identify radius, diameter, chords and
Circles (parts)
circumference of a circle, using the
appropriate formula
6.G.8 - Calculate the area of a sector of a
circle, given the measure of a central
angle and the radius of the circle
6.G.9 - Understand the relationship between
the circumference and the diameter
of a circle
7.G.1 - Calculate the radius or diameter,
given the circumference or area of a
circle
Shapes (3-D): PK.G.2- Informally play with solids (e.g.,
Identification
building blocks)
1.G.2 - Recognize, name, describe, create,
sort, and compare two-dimensional
and three-dimensional shapes
1.G.5 - Recognize geometric shapes and
structures in the environment
3.G.3 - Name, describe, compare, and sort
three-dimensional shapes: cube,
cylinder, sphere, prism, and cone
Shapes (3-D): 3.G.4 - Identify the faces on a threeCharacteristics
Brian Cohen
Not directly addressed
central angles of a circle
6.G.6 - Understand the relationship between
the diameter and radius of a circle
Shapes (2-D): 6.G.7 - Determine the area and
Circles (area &
circumference)
1.G.3 - Partition circles and rectangles into two and four equal shares,
describe the shares using the words halves, fourths, and
quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand
for these examples that decomposing into more equal shares
creates smaller shares.
2.G.2 - Partition a rectangle into rows and columns of same-size squares
and count to find the total number of them.
2.G.3 - Partition circles and rectangles into two, three, or four equal
shares, describe the shares using the words halves, thirds, half
of, a third of, etc., and describe the whole as two halves, three
thirds, four fourths. Recognize that equal shares of identical
wholes need not have the same shape.
3.G.2 - Partition shapes into parts with equal areas. Express the area of
each part as a unit fraction of the whole. For example, partition a
shape into 4 parts with equal area, and describe the area of each
part as 1/4 of the area of the shape.
dimensional shape as twodimensional shapes
4.G.5 - Define and identify vertices, faces,
and edges of three-dimensional
7.G.4 - Know the formulas for the area and circumference of a circle and
use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle.
K.G.1 - Describe objects in the environment using names of shapes, and
describe the relative positions of these objects using terms such
as above, below, beside, in front of, behind, and next to.
K.G.2 - Correctly name shapes regardless of their orientations or overall
size (squares, circles, triangles, rectangles, hexagons, cubes,
cones, cylinders, and spheres).
K.G.3 - Identify shapes as two-dimensional (lying in a plane, “flat”) or
three-dimensional (“solid”) (squares, circles, triangles, rectangles,
hexagons, cubes, cones, cylinders, and spheres).
2.G.1 - Recognize and draw shapes having specified attributes, such as
a given number of angles or a given number of equal faces.5
Identify triangles, quadrilaterals, pentagons, hexagons, and
cubes.
K.G.5 - Model shapes in the world by building shapes from components
(e.g., sticks and clay balls) and drawing shapes.
7.G.3 - Describe the two-dimensional figures that result from slicing
three-dimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids.
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shapes
7.G.3 - Identify the two-dimensional shapes
that make up the faces and bases of
three-dimensional shapes (prisms,
cylinders, cones, and pyramids)
Shapes (3-D): 6.G.4 - Determine the volume of rectangular
Volume
prisms by counting cubes and
develop the formula
6.M.1 - Measure capacity and calculate
volume of a rectangular prism
7.G.2 - Calculate the volume of prisms and
cylinders, using a given formula and
a calculator
4.MD.2 -Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects,
and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements
given in a larger unit in terms of a smaller unit. Represent
measurement quantities using diagrams such as number line
diagrams that feature a measurement scale.
5.MD.3 -Recognize volume as an attribute of solid figures and understand
concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said
to have “one cubic unit” of volume, and can be used to
measure volume.
b. A solid figure which can be packed without gaps or
overlaps using n unit cubes is said to have a volume of n
cubic units.
5.MD.4 -Measure volumes by counting unit cubes, using cubic cm, cubic
in, cubic ft, and improvised units.
5.MD.5 -Relate volume to the operations of multiplication and addition and
solve real world and mathematical problems involving volume.
a. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and
show that the volume is the same as would be found by
multiplying the edge lengths, equivalently by multiplying the
height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the
associative property of multiplication.
b. Apply the formulas V = l × w × h and V = b × h for
rectangular prisms to find volumes of right rectangular
prisms with whole-number edge lengths in the context of
solving real world and mathematical problems.
c. Recognize volume as additive. Find volumes of solid
figures composed of two non-overlapping right rectangular
prisms by adding the volumes of the non-overlapping parts,
applying this technique to solve real world problems.
6.G.2 - Find the volume of a right rectangular prism with fractional edge
lengths by packing it with unit cubes of the appropriate unit
fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism.
Apply the formulas V = l w h and V = b h to find volumes of right
rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.
7.G.6 - Solve real-world and mathematical problems involving area,
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right
prisms.
8.G.9 - Know the formulas for the volumes of cones, cylinders, and
spheres and use them to solve real-world and mathematical
problems.
Shapes (3-D): 7.G.4 - Determine the surface area of prisms 6.G.4 - Represent three-dimensional figures using nets made up of
Surface Area
Brian Cohen
and cylinders, using a calculator and
a variety of methods
7.M.11 - Estimate surface area
rectangles and triangles, and use the nets to find the surface
area of these figures. Apply these techniques in the context of
solving real-world and mathematical problems.
7.G.6 - Solve real-world and mathematical problems involving area,
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right
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prisms.
Geometric
Relationships:
Positions
Geometric
Relationships:
Properties
Geometric
Relationships:
Lines & Angles
K.G.5 - Understand and use ideas such as
over, under, above, below, on,
beside, next to, and between
K.G.1 - Describe objects in the environment using names of shapes, and
describe the relative positions of these objects using terms such
as above, below, beside, in front of, behind, and next to.
PK.S.4- Describe the attributes of objects
K.G.2 - Sort groups of objects by size and
size order (increasing and
decreasing)
2.G.4 - Group objects by like properties
Not directly addressed
4.G.2 - Identify points and line segments
when drawing a plane figure
4.G.6 - Draw and identify intersecting,
perpendicular, and parallel lines
4.G.7 - Identify points and rays when
drawing angles
4.G.8 - Classify angles as acute, obtuse,
right, and straight
4.G.1 - Draw points, lines, line segments, rays, angles (right, acute,
obtuse), and perpendicular and parallel lines. Identify these in
two-dimensional figures.
8.G.1 - Identify pairs of vertical angles as
7.G.5 - Use facts about supplementary, complementary, vertical, and
congruent
adjacent angles in a multi-step problem to write and solve simple
8.G.2 - Identify pairs of supplementary and
equations for an unknown angle in a figure.
complementary angles
8.G.5 - Use informal arguments to establish facts about the angle sum
8.G.3 - Calculate the missing angle in a
and exterior angle of triangles, about the angles created when
supplementary or complementary
parallel lines are cut by a transversal, and the angle-angle
pair
criterion for similarity of triangles. For example, arrange three
8.G.4 - Determine angle pair relationships
copies of the same triangle so that the sum of the three angles
when given two parallel lines cut by a
appears to form a line, and give an argument in terms of
transversal
transversals why this is so.
8.G.5 - Calculate the missing angle
measurements when given two
parallel lines cut by a transversal
8.G.6 - Calculate the missing angle
measurements when given two
intersecting lines and an angle
Geometric
Relationships:
Constructions
Geometric
Relationships:
Quadrilaterals
Brian Cohen
8.G.0
Construct the following, using a
straight edge and compass:
segment congruent to a segment,
angle congruent to an angle,
perpendicular bisector, & angle
bisector
7.G.2 - Draw (freehand, with ruler and protractor, and with technology)
geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing when
the conditions determine a unique triangle, more than one
triangle, or no triangle.
5.G.4 - Classify quadrilaterals by properties
of their angles and sides
5.G.5 - Know that the sum of the interior
angles of a quadrilateral is 360
degrees
7.G.7 - Find a missing angle when given
angles of a quadrilateral
3.G.1 - Understand that shapes in different categories (e.g., rhombuses,
rectangles, and others) may share attributes (e.g., having four
sides), and that the shared attributes can define a larger category
(e.g., quadrilaterals). Recognize rhombuses, rectangles, and
squares as examples of quadrilaterals, and draw examples of
quadrilaterals that do not belong to any of these subcategories.
4.G.2 - Classify two-dimensional figures based on the presence or
absence of parallel or perpendicular lines, or the presence or
absence of angles of a specified size. Recognize right triangles
as a category, and identify right triangles.
5.G.3 - Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that
category. For example, all rectangles have four right angles and
squares are rectangles, so all squares have four right angles.
5.G.4 - Classify two-dimensional figures in a hierarchy based on
properties.
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Geometric
Relationships:
Triangles (angles)
Geometric
Relationships:
Triangles (similarity
& congruence)
Geometric
Relationships:
Triangles
(Pythagorean
Theorem)
Geometric
Relationships:
Scale
5.G.6 - Classify triangles by properties of
3.G.1 their angles and sides
5.G.7 - Know that the sum of the interior
angles of a triangle is 180 degrees
5.G.8 - Find a missing angle when given two
angles of a triangle
4.G.2 -
Understand that shapes in different categories (e.g., rhombuses,
rectangles, and others) may share attributes (e.g., having four
sides), and that the shared attributes can define a larger category
(e.g., quadrilaterals). Recognize rhombuses, rectangles, and
squares as examples of quadrilaterals, and draw examples of
quadrilaterals that do not belong to any of these subcategories.
Classify two-dimensional figures based on the presence or
absence of parallel or perpendicular lines, or the presence or
absence of angles of a specified size. Recognize right triangles
as a category, and identify right triangles.
5.G.3 - Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that
category. For example, all rectangles have four right angles and
squares are rectangles, so all squares have four right angles.
5.G.4 - Classify two-dimensional figures in a hierarchy based on
properties.
8.G.5 - 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. For example, arrange three
copies of the same triangle so that the sum of the three angles
appears to form a line, and give an argument in terms of
transversals why this is so.
5.G.2 - Identify pairs of similar triangles
7.G.1 - Solve problems involving scale drawings of geometric figures,
5.G.3 - Identify the ratio of corresponding
including computing actual lengths and areas from a scale
sides of similar triangles
drawing and reproducing a scale drawing at a different scale.
5.G.9 - Identify pairs of congruent triangles
Appears in the following high school conceptual category:
5.G.10 - Identify corresponding parts of
 Geometry
congruent triangles
6.G.1 - Calculate the length of corresponding
sides of similar triangles, using
proportional reasoning
7.G.5 - Identify the right angle, hypotenuse, 8.G.6 - Explain a proof of the Pythagorean Theorem and its converse.
and legs of a right triangle
8.G.7 - Apply the Pythagorean Theorem to determine unknown side
7.G.6 - Explore the relationship between the
lengths in right triangles in real-world and mathematical problems
lengths of the three sides of a right
in two and three dimensions.
triangle to develop the Pythagorean 8.G.8 - Apply the Pythagorean Theorem to find the distance between two
Theorem
points in a coordinate system.
7.G.8 - Use the Pythagorean Theorem to
determine the unknown length of a
side of a right triangle
7.G.9 - Determine whether a given triangle is
a right triangle by applying the
Pythagorean Theorem and using a
calculator
7.R.9 - Use mathematics to show and
7.G.1 - Solve problems involving scale drawings of geometric figures,
understand physical phenomena
including computing actual lengths and areas from a scale
(e.g., make and interpret scale
drawing and reproducing a scale drawing at a different scale.
drawings of figures or scale models
of objects)
7.M.1 - Calculate distance using a map scale
8.R.9 - Use mathematics to show and
understand physical phenomena
(e.g., make and interpret scale
drawings of figures or scale models
of objects)
Transformational K.G.3 - Explore vertical and horizontal
Brian Cohen
K.G.2 - Correctly name shapes regardless of their orientations or overall
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Geometry:
Orientation &
Informal
Transformations
orientation of objects
1.G.3 - Experiment with slides, flips, and
turns of two-dimensional shapes
2.G.5 - Explore and predict the outcome of
slides, flips, and turns of twodimensional shapes
size (squares, circles, triangles, rectangles, hexagons, cubes,
cones, cylinders, and spheres).
K.G.4 - Analyze and compare two- and three-dimensional shapes, in
different sizes and orientations, using informal language to
describe their similarities, differences, parts (e.g., number of
sides and vertices/“corners”) and other attributes (e.g., having
sides of equal length).
Transformational K.G.4 - Manipulate two- and threedimensional shapes to explore
Geometry:
Symmetry
4.G.3 - Recognize a line of symmetry for a two-dimensional figure as a
line across the figure such that the figure can be folded along the
symmetry
line into matching parts. Identify line-symmetric figures and draw
1.G.4 - Identify symmetry in two-dimensional
lines of symmetry.
shapes
2.G.6 - Explore line symmetry
3.G.5 - Identify and construct lines of
symmetry
5.G.11 - Identify and draw lines of symmetry
of basic geometric shapes
Transformational 8.G.7 - Describe and identify transformations 8.G.1 - Verify experimentally the properties of rotations, reflections, and
in the plane, using proper function
translations:
Geometry:
Transformations
notation (rotations, reflections,
translations, and dilations)
8.G.8 - Draw the image of a figure under
rotations of 90 and 180 degrees
8.G.9 - Draw the image of a figure under a
reflection over a given line
8.G.10 - Draw the image of a figure under a
translation
8.G.11 - Draw the image of a figure under a
dilation
8.G.12 - Identify the properties preserved and
not preserved under a reflection,
rotation, translation, and dilation
a. Lines are taken to lines, and line segments to line
segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G.2 - Understand that a two-dimensional figure is congruent to another
if the second can be obtained from the first by a sequence of
rotations, reflections, and translations; given two congruent
figures, describe a sequence that exhibits the congruence
between them.
8.G.3 - Describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates.
8.G.4 - Understand that a two-dimensional figure is similar to another if
the second can be obtained from the first by a sequence of
rotations, reflections, translations, and dilations; given two similar
two-dimensional figures, describe a sequence that exhibits the
similarity between them.
Coordinate
Geometry:
5.G.12 - Identify and plot points in the first
quadrant
5.OA.3 - Generate two numerical patterns using two given rules. Identify
apparent relationships between corresponding terms. Form
ordered pairs consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a coordinate plane. For
example, given the rule “Add 3” and the starting number 0, and
given the rule “Add 6” and the starting number 0, generate terms
in the resulting sequences, and observe that the terms in one
sequence are twice the corresponding terms in the other
sequence. Explain informally why this is so
5.G.1 - Use a pair of perpendicular number lines, called axes, to define a
coordinate system, with the intersection of the lines (the origin)
arranged to coincide with the 0 on each line and a given point in
the plane located by using an ordered pair of numbers, called its
coordinates. Understand that the first number indicates how far
to travel from the origin in the direction of one axis, and the
second number indicates how far to travel in the direction of the
second axis, with the convention that the names of the two axes
and the coordinates correspond (e.g., x-axis and x-coordinate, yaxis and y-coordinate).
5.G.2 - Represent real world and mathematical problems by graphing
points in the first quadrant of the coordinate plane, and interpret
coordinate values of points in the context of the situation.
6.RP.3 - Use ratio and rate reasoning to solve real-world and
mathematical problems, e.g., by reasoning about tables of
Plotting Points
Brian Cohen
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equivalent ratios, tape diagrams, double number line diagrams,
or equations.
a. Make tables of equivalent ratios relating quantities with
whole-number measurements, find missing values in the
tables, and plot the pairs of values on the coordinate
plane. Use tables to compare ratios.
Coordinate
Geometry:
Area & Perimeter
Coordinate
Geometry:
Graphing
Inequalities
Coordinate
Brian Cohen
5.G.13 - Plot points to form basic geometric
shapes (identify and classify)
6.G.3 - 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.
6.G.10 - Identify and plot points in all four
quadrants
6.NS.6 - Understand a rational number as a point on the number line.
Extend number line diagrams and coordinate axes familiar from
previous grades to represent points on the line and in the plane
with negative number coordinates.
b. Understand signs of numbers in ordered pairs as indicating
locations in quadrants of the coordinate plane; recognize
that when two ordered pairs differ only by signs, the
locations of the points are related by reflections across one
or both axes.
c. Find and position integers and other rational numbers on a
horizontal or vertical number line diagram; find and
position pairs of integers and other rational numbers on a
coordinate plane.
6.NS.8 - Solve real-world and mathematical problems by graphing points
in all four quadrants of the coordinate plane. Include use of
coordinates and absolute value to find distances between points
with the same first coordinate or the same second coordinate.
5.G.14 - Calculate perimeter of basic
Not directly addressed
geometric shapes drawn on a
coordinate plane (rectangles and
shapes composed of rectangles
having sides with integer lengths and
parallel to the axes)
6.G.11 - Calculate the area of basic polygons
drawn on a coordinate plane
(rectangles and shapes composed of
rectangles having sides with integer
lengths)
7.G.10 - Graph the solution set of an
inequality (positive coefficients only)
on a number line (See 7.A.5)
8.G.19 - Graph the solution set of an
inequality on a number line
6.EE.8 - Write an inequality of the form x > c or x < c to represent a
constraint or condition in a real-world or mathematical problem.
Recognize that inequalities of the form x > c or x < c have
infinitely many solutions; represent solutions of such inequalities
on number line diagrams.
7.EE.4 - Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and
inequalities to solve problems by reasoning about the quantities.
b. Solve word problems leading to inequalities of the form px
+ q > r or px + q < r, where p, q, and r are specific
rational numbers. Graph the solution set of the inequality
and interpret it in the context of the problem. For example:
As a salesperson, you are paid $50 per week plus $3 per
sale. This week you want your pay to be at least $100.
Write an inequality for the number of sales you need to
make, and describe the solutions.
8.G.13 - Determine the slope of a line from a
graph and explain the meaning of
8.EE.6 - Use similar triangles to explain why the slope m is the same
between any two distinct points on a non-vertical line in the
page 8 of 9
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Geometry:
Graphing Linear
Equations
Coordinate
Geometry:
Quadratics
Brian Cohen
slope as a constant rate of change
coordinate plane; derive the equation y = mx for a line through
8.G.14 - Determine the y-intercept of a line
the origin and the equation y = mx + b for a line intercepting the
from a graph and be able to explain
vertical axis at b.
the y-intercept
8.EE.8 - Analyze and solve pairs of simultaneous linear equations.
8.G.15 - Graph a line using a table of values
a. Understand that solutions to a system of two linear
8.G.16 - Determine the equation of a line
equations in two variables correspond to points of
given the slope and the y-intercept
intersection of their graphs, because points of intersection
8.G.17 - Graph a line from an equation in
satisfy both equations simultaneously.
slope-intercept form (y = mx + b)
b. Solve systems of two linear equations in two variables
8.G.18 - Solve systems of equations
algebraically, and estimate solutions by graphing the
graphically (only linear, integral
equations. Solve simple cases by inspection. For example,
solutions, y = mx + b format, no
3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x +
vertical/horizontal lines)
2y cannot simultaneously be 5 and 6.
8.G.20 - Distinguish between linear and
c. Solve real-world and mathematical problems leading to
nonlinear equations ax2 + bx + c; a=1
two linear equations in two variables. For example, given
(only graphically)
coordinates for two pairs of points, determine whether the
line through the first pair of points intersects the line
through the second pair.
8.F.3 - Interpret the equation y = mx + b as defining a linear function,
whose graph is a straight line; give examples of functions that
are not linear. For example, the function A = s2 giving the area of
a square as a function of its side length is not linear because its
graph contains the points (1,1), (2,4) and (3,9), which are not on
a straight line.
8.F.4 - Construct a function to model a linear relationship between two
quantities. Determine the rate of change and initial value of the
function from a description of a relationship or from two (x, y)
values, including reading these from a table or from a graph.
Interpret the rate of change and initial value of a linear function in
terms of the situation it models, and in terms of its graph or a
table of values.
8.G.21 - Recognize the characteristics of
quadratics in tables, graphs,
equations, and situations
Appears in the following conceptual categories of the Mathematics
Standards for High School:
 Number and Quantity
 Algebra
 Functions
 Statistics and Probability
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