Geometry and Measurement (G) - Concepts - Oregon

Level 1

Beginning ABE Literacy

Level 2

Beginning ABE

Level 3

Low Intermediate ABE

Level 4

High Intermediate ABE

Geometry and Measurement (G) - Concepts

G1.1 Read, write, interpret, G2.1 Read, write, interpret, G3.1 Read, write, interpret, and G4.1 Read, write, interpret, and apply a variety of

and apply very simple types and apply simple types of apply common types of concepts common mathematical concepts and skills.

of concepts and skills.

concepts and skills.

and skills.

a. Analyze and compare two- a. Recognize and draw shapes a. Use the four operations to a. Solve real-world and mathematical problems by

and three-dimensional

having specified attributes, solve word problems involving graphing points in all four quadrants of the

shapes, in different sizes such as a given number of distances, intervals of time,

coordinate plane. Include use of coordinates and

and orientations, using

angles or a given number of liquid volumes, masses of

absolute value to find distances between points

informal language to

equal faces. Identify

objects, and money, including with the same first coordinate or the same second

describe their similarities, triangles, quadrilaterals,

problems involving simple

coordinate.

differences, parts. For example, number of sides

pentagons, hexagons, and cubes.

benchmark fractions or decimals, ( ?, ?, ? and 0.25,

b. Use informal arguments to establish facts about:

and vertices/corners and other attributes such as having sides of equal length.

b. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word

0.50, 0.75) and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

? angle sums and exterior angles of triangles ? angles created when parallel lines are cut by

a transversal ? angle-angle criterion for similarity of

b. Develop benchmark

problems involving addition b. Represent measurement

triangles

estimates for common units and subtraction of time

quantities using diagrams such For example, arrange three copies of the same

of measure. For example, intervals in minutes, e.g., by as number line diagrams,

triangle so that the sum of the three angles appears

length of inch is about the representing the problem thermometers, and gauges that to form a line, and give an argument in terms of

length of end of thumb to first knuckle; length of a cm is about the width of aa pinkie fingernail.

c.

on a number line diagram. feature a measurement scale.

Measure and estimate liquid c. Recognize angles as two rays

volumes and masses of

that share a common endpoint.

objects using units of grams

transversals of why this is so. c. Use informal arguments to establish facts about:

? angle sums and exterior angles of triangles

c. Recognize that a given

(g), kilograms (kg), and liters d. Define a degree as 1/360 of a

and exterior angles of triangles

measurement consists of (l).

circle.

? the angles created when parallel lines are

more small units than large units. For example, one yard contains 36 inches, but only 3 feet.

d.

Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are

e. Know that a full rotation around a circle is 360 degrees and each degree is used to measure angles.

cut by a transversal ? the angle-angle criterion for similarity of

triangles

For example:

d. Read and write time. For example, hours and minutes; day of month, year and temperature (Fahrenheit or Celsius)

given in the same units. For

example, by using drawings f. An angle that turns through n

(such as a beaker with a one-degree angles is said to have

measurement scale) to an angle measure of n degrees.

represent the problem.

g. Draw representations of points,

? arrange three copies of the same triangle so that the sum of the three angles appears to form a line

? give an argument in terms of transversals of why this is so

e. Develop benchmark estimates for common units of measure. For example, weight of a gram is about

lines, line segments, rays,

d. Conjecture, develop and justify the formula for

angles (right, acute, obtuse),

volume of a cube or rectangular solid based on the

and perpendicular and parallel formula for area

lines. Identify these in two-

the same as the weight of a

e. Develop and write simple informal geometric

small paper clip; length of dimensional figures.

cm is about half the length of an inch.

h. Make conjectures about the formulas for simple two-

f. Recognize area as an

dimensional shapes. For

attribute of plane figures and example, since a rectangle can

understand concepts of area be cut into two equal triangles,

measurement.

the area of the triangle can be

a. A square with side length 1 unit, called "a unit

found by creating the rectangle it came from.

square," is said to have i. Recognize volume as an

"one square unit" of area, attribute of solid figures and

and can be used to

understand concepts of volume

measure area.

measurement.

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.

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

g. Relate area to the

packed without gaps or

operations of multiplication overlaps using n unit cubes is

and addition.

said to have a volume of n

h. Recognize area as additive. cubic units.

Find areas of rectilinear j. Measure volumes by counting

figures by decomposing

unit cubes, using cubic cm,

them into non-overlapping cubic in, cubic ft. and

rectangles and adding the improvised units.

areas of the non-overlapping parts, applying this technique to solve real world problems.

k.

Relate volume to the operations of multiplication and addition and solve real world and mathematical

i. Find areas of shapes

problems involving volume.

composed of 2 or more rectangles by adding the of the component parts.

areas

l.

Use a pair of perpendicular number lines, called axes, to define a coordinate system,

proofs. For example, the Pythagorean Theorem and explain the reasoning behind them

j. Describe the difference

with the intersection of the

between square units and

lines (the origin) arranged to

linear units and when each is coincide with the 0 on each line

used.

and a given point in the plane

k. Interpret simple coordinates contained in coordinate planes and maps using an

located by using an ordered pair of numbers, called its coordinates.

eight-point compass rose m. Understand that the first

with secondary directions. number indicates how far to

For example, southwest;

travel from the origin in the

southeast; northeast.

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. For

example, x-axis and x-

coordinate, y-axis and y-

coordinate.

n. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

o. Use the attributes of polygons to name them, identifying categorical relationships such as all squares are parallelograms and all equilateral triangles are also isosceles.

p. Represent three-dimensional figures using nets made up of 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.

q. Measure and compare radius, diameter, and circumference of a circle and informally develop an equation for determining the diameter or circumference For example, C is about 3d, so pi is about 3.

Level 5

Low ASE

Level 6

High ASE

Level 7

Transition

Strand: Geometry and Measurement (G)

G5.1 Read, write, interpret, and apply a wide G6.1 Read, write, interpret, and apply a

variety of mathematical concepts and skills variety of challenging mathematical

using technology strategically.

concepts and skills using technology

strategically.

G7.1 Read, write, interpret, and apply a wide variety of challenging mathematical concepts and skills using technology strategically.

a. Use precise definitions of angle, circle,

a. Use the definitions of trigonometric ratios a. Read trig tables or use scientific

perpendicular line, parallel line, and line

to find the sine, cosine, and tangent of the calculator to find trig ratios to solve

segment, based on the undefined notions of acute angles of a right triangle.

trigonometric equations.

point, line, distance along a line, and distance around a circular arc.

b. Develop and write simple informal geometric proofs. For example, the

b. Use trig functions to illustrate periodic phenomenon. For example, sound and

b. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Pythagorean Theorem and explain the reasoning behind them.

c. Create and explain rotations and

light waves.

c. Use an appropriate right-angle trigonometric model to solve real-life

c. Conjecture and develop formulas for finding reflections of rectangles, trapezoids, and problems. For example figuring out

area of different polygons and explain their parallelograms.

how to space stairs leading to a deck.

relationships.

d. Write simple proofs of theorems in

d. Develop and prove formulas for prisms and cylinders.

geometric situations. For example, theorems about triangles, congruent figures, similar figures, lines, and

e. Create simple rotations of rectangles and describe how they are rotated.

perpendicular bisectors of line segments.

e. Compare, describe, and create transformations, rotations, and reflections of regular polygons, rectangles, parallelograms, and trapezoids.

Level 1

Beginning ABE Literacy

Level 2

Beginning ABE

Level 3

Low Intermediate ABE

Level 4

High Intermediate ABE

Strand: Geometry and Measurement (G) - Procedures

G1.2 Select and apply a few G2.2 Select and apply a few

simple procedures.

simple procedures.

G3.2 Select and apply

G4.2 Select and apply a

procedures, using technology variety of procedures, using

strategically.

technology strategically.

a. Compose two-dimensional c shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles) or three-dimensional 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.

b. Find the perimeter of simple shapes using concrete objects

a. Apply the area and perimeter a. Solve problems involving

formulas for rectangles in real scale drawings of

world and mathematical

geometric figures,

problems. For example, find including computing actual

the width of a rectangular

lengths and areas from a

room given the area of the

scale drawing.

flooring and the length, by viewing the area formula as a multiplication equation with

b. Reproduce a scale drawing using a different scale.

an unknown factor.

c. Know the formulas for the

b. Measure angles in wholenumber degrees using a

area and circumference of a circle.

protractor. Sketch angles of d. Give an informal derivation

specified measure.

of the relationship

C. Find the measure of an angle in a diagram made of two adjacent angles given the sum

between the circumference and area of a circle.

of one of the angles.

e. Use facts about

d. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

e. Convert standard measurement units within a given measurement system. For example, convert 5 cm to 0.05 m, and use these conversions in solving multistep, real world problems.

f. 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.

f.

Find the volume of a right rectangular prism whose sides are whole numbers packing it

g.

Describe the sequence rotations, reflections, and/or translations

of

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