Ch 9 - Geometry and Measurement

Math Study Jams - EOG Questions

Formulas that you will need to know for your test.

Convert metric units of length - kilometers, meters, decimeters, centimeters, millimeters
Area of a rectangle - length x width
Area of parallelogram - base x height
Area of triangle - 1/2(base x height)
Radius - 1/2 diameter
Circumference of a circle - π x diameter
Area of a circle - π (radius squared)
Surface area of a cylinder - (Area of two circles) +2πr2 + area of rectangle A=πdh
Surface area of a triangular prism - area of 2 triangles + area of 2 same rectangles (top and bottom) + 1 smaller rectangle (side)
Volume of a rectangular prism - length x width x height
Volume of a cylinder - π x radius squared x height

Lessons

Metric Units
Converting Units in the Metric System
Perimeters and Areas of Rectangles
Areas of Parallelograms and Traingles
Circles and Circumferences
Area of a Circle
Three-Dimensional Figures and Spatial Reasoning
Surface Area of Prisms
Volumes of Rectangular Prisms
Surface Area of Volumes of Cylinders

9-1, Metric Units of Length, Mass, and Capacity

Understand ratio concepts and use ratio reasoning to solve problems.

NC.6.RP.3 Converting and Manipulating Measurements Students know the conversions facts for:

Distance in the customary system (inches, feet, yards, and miles)
The metric system units and the prefixes: milli, centi, deci, deca, hecto, kilo
Time

9-2, Converting Units in the Metric System

Understand ratio concepts and use ratio reasoning to solve problems.

NC.6.RP.3 Converting and Manipulating Measurements Students know the conversions facts for:

Distance in the customary system (inches, feet, yards, and miles)
The metric system units and the prefixes: milli, centi, deci, deca, hecto, kilo
Time

9-3, Perimeters and Areas of Rectangles

9-4, Areas of Parallelograms and Triangles

Solve real-world and mathematical problems involving area, surface area, and volume.

NC.6.G.1 Create geometric models to solve real-world and mathematical problems to:

Find the area of triangles by composing into rectangles and decomposing into right triangles.
Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles.

9-5, Circles and Circumference

Not on EOG

Circumference = pi x diamater

Circumference = 2 x pi x radius

9-6, Area of a Circle

Not on EOG

Area of a Circle = pi x radius squared

9-7, Three-Dimensional Figures and Spatial Reasoning

Prism: a three-dimensional figure with two parallel and congruent faces that are polygons. The faces are called bases.

9-8, Surface Areas of Prisms

Solve real-world and mathematical problems involving area, surface area, and volume.

NC.6.G.2 Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems.

How to Find Surface Area of Right Rectangular Prism

Multiply top and bottom
Left and right
Front and back
Then, add them all.

9-8 - Drawing a Net

Solve real-world and mathematical problems involving area, surface area, and volume.

NC.6.G.4

Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use nets to find the surface area of these figures.
Apply these techniques in the context of solving real world and mathematical problems.

Polygons in the Coordinate Plane

Solve real-world and mathematical problems involving area, surface area, and volume.

NC.6.G.3 Use the coordinate plane to solve real-world and mathematical problems by:

Drawing polygons in the coordinate plane given coordinates for the vertices.
Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

NC.6.NS.6 Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane.

b. On a coordinate plane

Understand signs of numbers in ordered pairs as indicating locations in quadrants.
Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Find and position pairs of rational numbers on a coordinate plane.

Reflection

Opposite Image - Mirror Reflection

Transformation

Rotation

Translation

Slide

9-9, Volumes of Rectangular Prisms

Solve real-world and mathematical problems involving area, surface area, and volume.

How to Find Volume of Right Rectangular Prism

Multiply length x width x height
Multiply base (length x width) x height

9-10, Surface Areas and Volumes of Cylinders

Solve real-world and mathematical problems involving area, surface area, and volume.

NC.6.G.4 Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use nets to find the surface area of these figures. Apply these techniques in the context of solving real world and mathematical problems.

Draw polygons on Coordinate Plane

NC.6.G.3 Use the coordinate plane to solve real-world and mathematical problems by:

Drawing polygons in the coordinate plane given coordinates for the vertices.
Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

What you must be able to do...

NC.6.G.1 Create geometric models to solve real-world and mathematical problems to:

• Find the area of triangles by composing into rectangles and decomposing into right triangles.

• Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles.

NC.6.G.3 Use the coordinate plane to solve real-world and mathematical problems by:

• Drawing polygons in the coordinate plane given coordinates for the vertices.

• Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

NC.6.G.4 Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use nets to find the surface area of these figures.

Apply these techniques in the context of solving real world and mathematical problems.