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Use variables in expressions describing geometric quantities (e.g., P=2w + 2l, Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an
AF AF
3.1
A=1/2bh, C=πd…the formulas for perimeter of a rectangle, area of a 3.4
item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand
triangle, and the circumference of a circle, respectively) that the slope of the line equals the quantities.
Compare weights, capacities, geometric measures, times, and temperatures within and between
AF GM
3.2
Express in symbolic form simple relationships arising from geometry. 1.1
measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic
centimeters).
GM Understand the concept of a constant such as pi; know the formulas for the GM
Construct and read drawings and models made to scale.
1.1 circumference and area of a circle. 1.2
Know common estimates of p (3.14; 22/7) and use these values to estimate and Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g.,
GM GM
1.2
calculate the circumference and the area of circles; compare with actual 1.3
person-days) to solve problems; check the units of the solutions; and use dimensional analysis
measurements. to check the reasonableness of the answer.
Know and use the formulas for the volume of triangular prisms and cylinders Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and
GM GM2
1.3
(area of base x height); compare these formulas and explain the similarity .1
the surface area and volume of basic three-dimensional figures, including rectangles,
between them and the formula for the volume of a rectangular solid. parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
GM Identify angles as vertical, adjacent, complementary, or supplementary and GM2 Estimate and compute the area of more complex or irregular two-and three-dimensional
2.1 provide descriptions of these terms. .2 figures by breaking the figures down into more basic geometric objects.
Compute the length of the perimeter, the surface area of the faces, and the volume of a three-
GM Use the properties of complementary and supplementary angles and the sum GM2 dimensional object built from rectangular solids. Understand that when the lengths of all
2.2 of the angles of a triangle to solve problems involving an unknown angle. .3 dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the
scale factor and the volume is multiplied by the cube of the scale factor.
Draw quadrilaterals and triangles from given information about them (e.g., a Relate the changes in measurements with a change of scale to the units used (e.g., square
GM GM2
2.3
quadrilateral having equal sides but no right angles, a right isosceles .4
inches, cubic feet) and to conversions between units (1 square foot=144 square inches or [1ft2]
triangles). = [144 in2 ], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals,
GM3
angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of
.1
circles) by using a compass and straightedge.
GM3 Understand and use coordinate graphs to plot simple figures, determine lengths and areas
.2 related to them, and determine their image under translations and reflections.
Know and understand the Pythagorean theorem and its converse and use it to find the length
GM3 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, GM3
of the missing side of a right triangle and the lengths of other line segments and, in some
.5 and cones. .3
situations, empirically verify the Pythagorean Theorem by direct measurement.
Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) Demonstrate and understanding of conditions that indicate two geometrical figures are
GM3 GM3
and describe how two or more objects are related in space (e.g., skew lines, the possible ways congruent and what congruence means about the relationships between the sides and angles of
.6 .4
three planes might intersect). the two figures.
GM1 GM1
Derive & Calculate Area of Polygons Compare between measurement systems (weight, capacity, time, temp., & geo measure)
.1 .1
GM1 GM1
Construct & Compute Rectangular Prism Surface Area Scale Drawing
.2 .2
GM1 GM1
Volume of Rectangular Solids Convert of complex units, calculate & use rates (dimensional analysis)
.3 .3
GM1 GM2
Area, Perimeter & Volume: Use Correct Units Using formulas: area, perimeter, surface area & volume
.4 .1
GM2 GM2
Measure, ID, & Draw Geometric Figures Area of complex geometric figures
.1 .2
GM2 GM2
Sum of the Angles: Triangle, Rectangle Compute: perimeter, area, volume, with scale
.2 .3
GM2 GM2
Draw 2-D Objects from 3-D Figures Relate & change complex units with scale
.3 .4
GM3
ID & construct basic elements of geometric figures
.1
GM1 GM3
Pi + Circumference & Area of a Circle (know formulas) Plot simple figures & find Area +Translation & Reflection
.1 .2
GM1 GM3
Area & Circumference of a Circle Pythagorean Theorem
.2 .3
GM1 GM3
Volume (know formulas) Similarity & Congruence
.3 .4
GM2 GM3
ID & Describe Geometric Parts, Adjacent & Vertical Construct 3D geometric models
.1 .5
GM2 GM3
Complementary & Supplementary Angles ID & Describe: elements & relationships of geometric objects in space
.2 .6
GM2
Draw Quadrilaterals & Triangles from Information Given
.3
GM1
Volume (know formulas)
.3
GM2
ID & Describe Geometric Parts, Adjacent & Vertical
.1
GM2
Complementary & Supplementary Angles
.2
GM2
Draw Quadrilaterals & Triangles from Information Given
.3
