Polygons. 5 sides 5 angles. pentagon. no no R90. Name
|
|
|
- Joshua Moore
- 7 years ago
- Views:
Transcription
1 Lesson 11.1 Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number of angles that it has. Congruent figures have the same size and shape. In a regular polygon, all sides are congruent and all angles are congruent. Classify the polygon below. Polygon Sides Angles Vertices Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon How many sides does this polygon have? How many angles does this polygon have? Name the polygon. pentagon Are all the sides congruent? Are all the angles congruent? no no 5 sides 5 angles So, the polygon above is a pentagon. It is not a regular polygon. Name each polygon. Then tell whether it is a regular polygon or not a regular polygon T 3.. G H Y U N U X T O E F S R V W S R Q P R90
2 Lesson 11.2 Triangles You can classify triangles by the length of their sides and by the measure of their angles. Classify each triangle. Use a ruler to measure the side lengths. equilateral triangle All sides are the same length. isosceles triangle Two sides are the same length. scalene triangle All sides are different lengths. Use the corner of a sheet of paper to classify the angles. acute triangle All three angles are acute. obtuse triangle One angle is obtuse. The other two angles are acute. right triangle One angle is right. The other two angles are acute. Classify the triangle according to its side lengths. It has two congruent sides. The triangle is an isosceles triangle. Classify the triangle according to its angle measures. It has one right angle. The triangle is a right triangle. Classify each triangle. Write isosceles, scalene, or equilateral. Then write acute, obtuse, or right in mi 1 mi 5 in in. 15 mi 10 m 10 m m R91
3 Lesson 11.3 Quadrilaterals You can use this chart to help you classify quadrilaterals. quadrilateral sides parallelogram quadrilateral opposite sides are parallel opposite sides are congruent trapezoid quadrilateral exactly one pair of parallel sides rectangle parallelogram right angles 2 pairs of perpendicular sides rhombus parallelogram congruent sides square rhombus rectangle Classify the figure. The figure has sides, so it is a quadrilateral. The figure has exactly one pair of parallel sides, so it is a trapezoid. quadrilateral, trapezoid Classify the quadrilateral in as many ways as possible. Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid R92
4 Lesson 11. Three-Dimensional Figures A polyhedron is a solid figure with faces that are polygons. You can identify a polyhedron by the shape of its faces. A is a polyhedron with one polygon base. The lateral faces of a are triangles that meet at a common vertex. triangular The base and faces are triangles. A prism is a polyhedron with two congruent polygons as bases. The lateral faces of a prism are rectangles. triangular prism The two bases are triangles. rectangular The base is a rectangle. rectangular prism All faces are rectangles. square The base is a square. square prism or cube All faces are squares. pentagonal The base is a pentagon. pentagonal prism The two bases are pentagons. hexagonal The base is a hexagon. hexagonal prism The two bases are hexagons. A solid figure with curved surfaces is not a polyhedron. cone The one base is a circle. cylinder sphere There is no base. The two bases are circles. Classify the solid figure. Write prism,, cone, cylinder, or sphere. The solid figure has one base. The rest of its faces are triangles. So, the solid figure is a. Classify each solid figure. Write prism,, cone, cylinder, or sphere R93
5 Lesson 11.5 Unit Cubes and Solid Figures A unit cube is a cube that has a length, width, and height of 1 unit. You can use unit cubes to 1 unit build a rectangular prism. 1 unit 1 unit Count the number of cubes used to build the rectangular prism. The length of the prism is made up of The width of the prism is made up of The height of the prism is made up of unit cubes. unit cubes. unit cube. The number of unit cubes used to build the rectangular prism is 16. Count the number of unit cubes used to build each solid figure unit cubes unit cubes 3.. unit cubes unit cubes R9
6 Lesson 11.6 Understand Volume The volume of a rectangular prism is equal to the number of unit cubes that make up the prism. Each unit cube has a volume of 1 cubic unit. Find the volume of the prism. 1 unit cube 5 1 cubic inch Step 1 Count the number of unit cubes in the bottom layer of the prism. There are There are There is 1 2 unit cubes that make up the length of the first layer. unit cubes that make up the width of the first layer. unit cube that makes up the height of the first layer. So, altogether, there are unit cubes that make up the bottom layer of the prism. Step 2 Count the number of layers of cubes that make up the prism. The prism is made up of layers of unit cubes. Step 3 Find the total number of cubes that fill the prism. Multiply the number of layers by the number of cubes in each layer unit cubes Each unit cube has a volume of 1 cubic inch. So, the volume of the prism is 2 3 1, or cubic inches. Use the unit given. Find the volume ft cm 5 ft 3 ft 6 cm 3 cm Each cube 5 1 cu ft Each cube 5 1 cu cm Volume 5 cu R95 Volume 5 cu
7 Lesson 11.7 Estimate Volume You can estimate the volume of a larger box by filling it with smaller boxes. Mario packs boxes of markers into a large box. The volume of each box of markers is 15 cubic inches. Estimate the volume of the large box. Markers Markers Markers Markers The volume of one box of markers is 15 cubic inches. Use the box of markers to estimate the volume of the large box. The large box holds layers of boxes of markers, a top layer and a bottom layer. Each layer contains 10 boxes of markers. So, the large box holds about , or 20 boxes of markers. Multiply the volume of 1 box of markers by the estimated number of boxes of markers that fit in the large box So, the volume of the large box is about cubic inches. Estimate the volume. 1. Each box of toothpaste has a volume of 25 cubic inches. 2. Volume of case: 80 cu cm Toothpaste Toothpaste Toothpaste Toothpaste Toothpaste Toothpaste There are boxes of toothpaste in the large box. The estimated volume of the large box Volume of large box: is cubic inches. R96
8 Lesson 11.8 Volume of Rectangular Prisms Jorge wants to find the volume of this rectangular prism. He can use cubes that measure 1 centimeter on each side to find the volume. Step 1 The base has a length of 2 centimeters and a width of 3 centimeters. Multiply to find the area of the base. Base Base 5 6 cm 2 Step 2 The height of the prism is centimeters. Add the number of cubes in each layer to find the volume. Remember: Each layer has 6 cubes. 2 cm 2 3 cm cm 3 Step 3 Count the cubes. cubes Multiply the base and the height to check your answer. Volume 5 3 Volume cubic centimeters So, the volume of Jorge s rectangular prism is 2 cubic centimeters. Find the volume cm 3 cm 2 cm 2. 2 ft 5 ft 2 ft Volume: Volume: in. 3 cm 6 cm 3 cm Volume: Volume: R97
9 Lesson 11.9 Algebra Apply Volume Formulas You can use a formula to find the volume of a rectangular prism. Volume 5 length 3 width 3 height V 5(l 3 w) 3 h Find the volume of the rectangular prism. Step 1 Identify the length, width, and height of the rectangular prism. 9 3 length 5 in. width 5 in. height 5 in. Step 2 Substitute the values of the length, width, and height into the formula. V 5 (l 3 w) 3 h V 5 ( 9 3 ) 3 Step 3 Multiply the length by the width. V 5 (9 3 3) 3 V 5 3 Step Multiply the product of the length and width by the height. V So, the volume of the rectangular prism is cubic inches. 9 in. 3 in. Find the volume ft 2. 8 cm 12 ft ft 8 cm 8 cm V 5 V 5 R98
10 Lesson Problem Solving Compare Volumes A company makes aquariums that come in three sizes of rectangular prisms. The length of each aquarium is three times its width and depth. The depths of the aquariums are 1 foot, 2 feet, and 3 feet. What is the volume of each aquarium? Read the Problem What do I need to find? I need to find the volume of each aquarium. What information do I need to use? I can use the formula for volume, V 5 l 3 w 3 h, or V 5 B 3 h. I can use 1 ft, 2 ft, and 3 ft as the depths. I can use the clues the length is three times the width and depth. How will I use the information? I will use the volume formula and a table to list all of the possible combinations of lengths, widths, and depths. Solve the Problem Think: The depth of an aquarium is the same as the height of the prism formed by the aquarium Length (ft) Width (ft) Depth, or Height (ft) Volume (cu ft) So, the volumes of the aquariums are 3 cubic feet, 2 cubic feet, and 81 cubic feet. 1. Jamie needs a bin for her school supplies. A blue bin has a length of 12 inches, a width of 5 inches, and a height of inches. A green bin has a length of 10 inches, a width of 6 inches, and a height of 5 inches. What is the volume of the bin with the greatest volume? 2. Suppose the blue bin that Jamie found had a length of 5 inches, a width of 5 inches, and a height of 12 inches. Would one bin have a greater volume than the other? Explain. R99
11 Lesson Find Volume of Composed Figures A composite figure is a solid made up of two or more solids. To find the volume of a composite figure, first find the volume of each solid that makes up the figure. Then find the sum of the volumes of the figures. Find the volume of the composite figure at right. Step 1 Break apart the composite figure into two rectangular prisms. Label the dimensions of each prism. Prism 1 Prism 2 8 in. 20 in. 8 in. 8 in. 20 in. 8 in. Step 2 Find the volume of each prism. Prism 1 Prism 2 V 5 (l 3 w) 3 h 8 V 5 (l 3 w) 3 h 20 8 V V V in. 3 V 5 60 in. 3 Step 3 Find the sum of the volumes of the two prisms. Volume of Prism 1 1 Volume of Prism 2 5 Volume of Composite Figure 128 in in in. 3 So, the volume of the composite figure is 768 in Volume of Composite Figure 5 Volume of Composite Figure Find the volume of the composite figure ft 2. 7 in. 10 ft 8 ft 12 ft 1 in. 8 ft 28 ft ft 6 in. 3 in. V 5 V 5 R100
Target To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
Shape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
Chapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
Grade 8 Mathematics Geometry: Lesson 2
Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
Angles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
Grade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse
Algebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
UNIT H1 Angles and Symmetry Activities
UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)
Area of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
Area of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
Lateral and Surface Area of Right Prisms
CHAPTER A Lateral and Surface Area of Right Prisms c GOAL Calculate lateral area and surface area of right prisms. You will need a ruler a calculator Learn about the Math A prism is a polyhedron (solid
of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.
Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:
Line Segments, Rays, and Lines
HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw
Geometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
12 Surface Area and Volume
12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids
2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?
MATH 206 - Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of
12-1 Representations of Three-Dimensional Figures
Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular
Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures
SHAPE NAMES Three-Dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two-Dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]
MENSURATION. Definition
MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters
Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
Solids. Objective A: Volume of a Solids
Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular
Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons
Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons I. ABSTRACT This unit contains lessons that focus on geometric
Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
Geometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
Geometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes
Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
SA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
CBA Volume: Student Sheet 1
CBA Volume: Student Sheet 1 For each problem, decide which cube building has more room inside, or if they have the same amount of room. Then find two ways to use cubes to check your answers, one way that
Estimating Angle Measures
1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle
2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
Filling and Wrapping: Homework Examples from ACE
Filling and Wrapping: Homework Examples from ACE Investigation 1: Building Smart Boxes: Rectangular Prisms, ACE #3 Investigation 2: Polygonal Prisms, ACE #12 Investigation 3: Area and Circumference of
Geometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
Finding Volume of Rectangular Prisms
MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.
MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.
MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units
SURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
Activity Set 4. Trainer Guide
Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons
CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining
3D shapes. Level A. 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite. 2. What is another name for 3-D shapes?
Level A 1. Which of the following is a 3-D shape? A) Cylinder B) Octagon C) Kite 2. What is another name for 3-D shapes? A) Polygon B) Polyhedron C) Point 3. A 3-D shape has four sides and a triangular
Unit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
Shapes & Designs Notes
Problem 1.1 Definitions: regular polygons - polygons in which all the side lengths and angles have the same measure edge - also referred to as the side of a figure tiling - covering a flat surface with
2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
Geometry Notes VOLUME AND SURFACE AREA
Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate
Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain
AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent
Lesson 1.1 Building Blocks of Geometry
Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.
Conjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical
TEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM
7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in
B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3
45 Volume Surface area measures the area of the two-dimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space
Which two rectangles fit together, without overlapping, to make a square?
SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has
Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?
Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is
SOLIDS, NETS, AND CROSS SECTIONS
SOLIDS, NETS, AND CROSS SECTIONS Polyhedra In this section, we will examine various three-dimensional figures, known as solids. We begin with a discussion of polyhedra. Polyhedron A polyhedron is a three-dimensional
Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
Quick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book
GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18
Geometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.
Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional
Conjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
Discovering Math: Exploring Geometry Teacher s Guide
Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
MATH STUDENT BOOK. 6th Grade Unit 8
MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF
What You ll Learn. Why It s Important
These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why
How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure?
Middletown Public Schools Mathematics Unit Planning Organizer Subject Mathematics Grade/Course Grade 7 Unit 3 Two and Three Dimensional Geometry Duration 23 instructional days (+4 days reteaching/enrichment)
Applications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
Lesson 9.1 The Theorem of Pythagoras
Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius
Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
12 Surface Area and Volume
CHAPTER 12 Surface Area and Volume Chapter Outline 12.1 EXPLORING SOLIDS 12.2 SURFACE AREA OF PRISMS AND CYLINDERS 12.3 SURFACE AREA OF PYRAMIDS AND CONES 12.4 VOLUME OF PRISMS AND CYLINDERS 12.5 VOLUME
Problem of the Month: William s Polygons
Problem of the Month: William s Polygons The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
GEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
Shapes Bingo. More general matters which apply to the use of this unit are covered on the next page.
Shapes Bingo Shapes Bingo This unit provides the material for practicing some basic shape identification in the context of the well-known game of Bingo. Directions on how to play Bingo are not given here.
Math 5th grade. Create your own number and explain how to use expanded form to show place value to the ten millions place.
Number Properties and Operations Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop
Area. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
Geometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
Course 2 Summer Packet For students entering 8th grade in the fall
Course 2 Summer Packet For students entering 8th grade in the fall The summer packet is comprised of important topics upcoming eighth graders should know upon entering math in the fall. Please use your
Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:
Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in. Three Dimensions It is called three-dimensional or 3D because there are three dimensions: width,
37 Basic Geometric Shapes and Figures
37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
Area is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
Geometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement
GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
IWCF United Kingdom Branch
IWCF United Kingdom Branch Drilling Calculations Distance Learning Programme Part 2 Areas and Volumes IWCF UK Branch Distance Learning Programme - DRILLING CALCULATIONS Contents Introduction Training objectives
9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
The GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
angle attribute Figure 1 4 right angles opposite sides parallel Lesson 14 5 Lesson 14 4 Vocab
Vocab angle attribute 006_055_G4_VisV_101741.indd Page F46 2/13/10 11:27:36 PM u-s014 /Volumes/114/GO00403/GO00403_Natl_Visual_Voca_Cards_G4%0 Figure 1 4 right angles opposite sides parallel endpoint hexagon
Geometry: Classifying, Identifying, and Constructing Triangles
Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
ISAT Mathematics Performance Definitions Grade 4
ISAT Mathematics Performance Definitions Grade 4 EXCEEDS STANDARDS Fourth-grade students whose measured performance exceeds standards are able to identify, read, write, represent, and model whole numbers
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
Area & Volume. 1. Surface Area to Volume Ratio
1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.
G3-33 Building Pyramids
G3-33 Building Pyramids Goal: Students will build skeletons of pyramids and describe properties of pyramids. Prior Knowledge Required: Polygons: triangles, quadrilaterals, pentagons, hexagons Vocabulary:
Illinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other