Math: Geometry & Measurement Flip Chart

Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Geometry & Measurement Geometry & Measurement Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-3004 \|xiBAHBDy01263kzU Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Geometry & Measurement Polygons Area, Volume & Perimeter Congruence, Transformation & Symmetry Lines, Angles & Circles Surface Area of Solid Figures Area & Circ umference of Circles Customary & Metric Units of Measurement Collecting & Displaying Data Problem Solving Strategies

Solid Figures – objects that have length, width, and height. Lines & Line Segments Triangles & Polygons Angles Quadrilaterals rectangular prism cube line line segment right angle 90º right triangle (90º) square rectangle parallelogram rhombus trapezoid acute triangle ( < 90º) obtuse triangle (one angle > 90º) equilateral triangle (all sides equal) isosceles triangle (two sides equal) scalene triangle (no sides equal) hexagon (6 sides) acute angle < 90º obtuse angle > 90º Polygon parallel lines intersecting lines ray point pyramid cone cylinder sphere • Lines and line segments make up shapes and solid figures. • A triangle has three sides. • A polygon is any closed plane figure made up of three or more sides. • An angle is formed by two rays that share the same end point or vertex. corner or vertex edge vertex 3 cm 3 cm 5 cm 7 cm right angle ray ray face • The faces of these solid figures are polygons. • The perimeter is the distance around a figure. • Volume is the space inside a solid figure. Volume = 8 cubic units Perimeter: Volume: Area: Area = 4 + 4 + 4 = 12 squares Perimeter = 3 + 5 + 3 + 7 = 18 cm © C opyright NewPath Learning. All Rights Reserved. 93-4309 www.newpathlearning.com Geometry & Measurement

\|xiBAHBDy01647sz\ Solid Figures – objects that have length , width , and height . Lines & Line Segments Triangles & Polygons Angles Quadrilaterals rectangular prism cube pyramid cone cylinder sphere • Lines and line segments make up shapes and solid fi ur . • A has three sides. • A is any closed plane figure made up of three or more sides. • An angle is formed by two rays that share the same end point or vertex. 3 cm 3 cm 5 cm 7 cm • The faces of these solid figures are polygons . • The perimeter is the a figure. • Volume is the a solid figure. Volume = 8 cubic units Perimeter: Volume: Area: Area = = squares + + Perimeter = = 18cm + + + © C opyright NewPath Learning. All Rights Reserved. 93-4309 www.newpathlearning.com Geometry & Measurement Key Vocabulary Terms • angle • area • corner • edge • face • geometry • height • length • line • line segment • measurement • perimeter • polygon • quadrilaterals • solid figure • triangle • vertex • volume • width

Draw a Picture Read & understand Reflect & check Use your strategy to solve the problem 1 Plan 2 3 4 The Four-Step Method Strategies Make a Graph or Table Find a Pattern Work Backward Write a Number Sentence Day Number of Butterflies N u m b e r o f S tu d e n ts Monday Tuesday Wednesday Thursday 14 8 20 26 ? $ 7 m $ 16 $ 16 $ 7 m Day 1 243 miles 168 miles 212 miles allowance candy drink Day 2 $ 16 – $ 7 = m $ 16 – $ 7 = $ 9 m = $ 9 Day 3 ? • What do I need to find? • Identify and underline clue words • Look for something that changes in a predictable way. • Identify the steps in a problem and work backward doing the reverse of each step. • Make a graph or a table to compare information and to see patterns. • Write a number sentence and solve it to find the missing part. • Did I answer the question? • Is my answer probable? • Which strategy do I use? • Draw a picture • Find a pattern • Make a graph or table • Write a number sentence • Work backwards TOTAL ? – $ 3 – $ 2 • Draw a picture when the problem describes some action. ? + $ 3 + $ 2 $ 5 $ 5 money left allowance candy drink money left Clue Words Clue Words Addition Subtraction Multiplication Division • sum • total • in all • difference • how much more • product • total • times • share • average • quotient © Copyright NewPath Learning. All Rights Reserved. 93-4310 www.newpathlearning.com Problem-Solving Strategies

\|xiBAHBDy01661ozX Draw a Picture Read & understand Reflect & check Use your strategy to solve the problem 1 Plan 2 3 4 The Four-Step Method Strategies Make a Graph or Table Find a Pattern Work Backward Write a Number Sentence N u m b e r o f S tu d e n ts Monday Tuesday Wednesday Thursday 14 8 20 26 ? $ 7 m $ 16 $ 16 $ 7 m Day 1 243 miles 168 miles 212 miles allowance candy drink Day 2 $ 16 – $ 7 = m $ 16 – $ 7 = $ 9 m = $ 9 Day 3 ? • What do I need to find? • Identify and underline clue words • Look for something that changes in a predictable way. • Identify the steps in a problem and work backward doing the reverse of each step. • Make a graph or a table to compare information and to see pattern s . • Write a number sentence and solve it to find the missing part . • Did I answer the question? • Is my answer probable? • Which strategy do I use? • Draw a picture • Find a pattern • Make a graph or table • Write a number sentence • Work backwards TOTAL – $ 3 $ 10 – $ 2 • Draw a picture when the problem describes some action . + $ 3 + $ 2 $ 5 money left allowance candy drink money left Clue Words Clue Words Addition Subtraction Multiplication Division Key Vocabulary Terms • addition • product • average • quotient • difference • share • division • strategy • graph • subtraction • how much more • sum • in all • table • multiplication • times • number sentence • total • pattern • • • • • • • • • • • Day Number of Butterflies Problem-Solving Strategies © Copyright NewPath Learning. All Rights Reserved. 93-4310 www.newpathlearning.com

equilateral triangle isosceles triangle right triangle obtuse triangle acute triangle scalene triangle square rectangle parallelogram rhombus trapezoid Triangles – Polygons with three sides Quadrilaterals – Polygons with four sides vertex side • Polygons are plane figures (flat shapes) with three or more sides. • A polygon is made by joining line segments. Each line segment is a side. • A vertex is the point where the sides meet. Polygon equilateral triangle isosceles triangle right triangle obtuse triangle acute triangle scalene triangle square rectangle parallelogram rhombus trapezoid © Copyright NewPath Learning. All Rights Reserved. 93-4405 www.newpathlearning.com Polygons All three sides have equal length One of the angles is a right angle (90º) All three angles are acute angles (less than a right angle) One of the angles is an obtuse angle (greater than a right angle) At least two sides have equal length A four-sided polygon with two pairs of parallel sides Four sides of equal length and four right angles A four-sided polygon with four right angles A four-sided polygon with one pair of parallel sides Opposite sides are parallel and all four sides have equal length All three sides have different lengths

\|xiBAHBDy01659lz[ Key Vocabulary Terms • acute triangle • rectangle • equilateral triangle • rhombus • isosceles triangle • right triangle • line segment • scalene triangle • obtuse triangle • side • parallelogram • square • plain figure • trapezoid • polygon • triangle • quadrilateral • vertex Triangles – Polygons with three sides Quadrilaterals – Polygons with four sides • Polygons are (flat shapes) with three or more sides. • A polygon is made by joining . Each line segment is a . • A is the point where the sides meet. © Copyright NewPath Learning. All Rights Reserved. 93-4405 www.newpathlearning.com Polygons All three sides have length One of the angles is a angle (90º) All three angles are angles (less than a right angle) One of the angles is an angle (greater than a right angle) At least two sides have length A four-sided polygon with two pairs of sides Four sides of length and four angles A four-sided polygon with four angles A four-sided polygon with one pair of sides Opposite sides are and all four sides have length All three sides have lengths

Volume = length x width x height Perimeter = 2 + 2w Perimeter = (2 x length) + (2 x width) Area = length x width Volume = 36 cubic feet Area = 45 square feet Perimeter = 42 meters P = 14 + 7 + 14 + 7 = 42m Perimeter Volume Area Area formula Volume formula Perimeter formula width (w) height (h) width (w) width (w) width (w) width (w) 5ft 4ft 3ft 3ft 9ft A = l x w A = 9 x 5 A = 45 V = x w x h V = 4 x 3 x 3 V = 36 P = 2 + 2 P = 2(14) + 2(7) P = 28 + 14 P = 42 7m 7m 14m 14m Area is the number of square units needed to cover the inside of a figure. Volume is the number of cubic units that fill up a solid figure. Perimeter is the distance around a plane figure. To find the perimeter you may also add the lengths of all sides. Volume = x w x h Area = x w length ( ) length ( ) length ( ) length ( ) length ( ) © Copyright NewPath Learning. All Rights Reserved. 93-4407 www.newpathlearning.com Area, Volume & Perimeter

Volume = cubic feet Area = square feet Perimeter = meters P = + + + = Perimeter Volume Area 5ft 4ft 3ft 3ft 9ft A = l x w A = 9 x 5 A = 45 V = x w x h V = 4 x 3 x 3 V = 36 P = 2 + 2 P = 2(12) + 2(6) P = 24 + 12 P = 36 7m 7m 14m 14m Area is the number of s needed to cover the inside of a figure. Volume is the number of that fill up a solid figure. Perimeter is the a plane figure. To find the perimeter you may also add the lengths of all sides. Volume = length x width x height Perimeter = (2 x length) + (2 x width) Area = length x width Volume formula Perimeter formula width (w) width (w) Area formula Area = x Volume = x x Perimeter = + length ( ) length ( ) Key Vocabulary Terms • area • solid figure • cubic unit • plane figure • height • square unit • length • volume • perimeter • width • side © Copyright NewPath Learning. All Rights Reserved. 93-4407 www.newpathlearning.com Area, Volume & Perimeter \|xiBAHBDy01640tz]

1 2 3 4 5 6 7 8 9 cm -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 -40 -20 0 20 40 60 80 100 120 140 160 180 200 1 2 3 4 5 6 7 Inch 1 mL One Gallon MILK One Quar t 1,000 mg total mass 5 grams 1 gram 500 mg 500 mg Customary Units Metric Units Degrees Celsius (ºC) are metric units of temperature. Degrees Fahrenheit (ºF) are customary units of temperature. Length Capacity Weight Temperature Length Capacity Mass Temperature The Customary System of Measurement is used primarily in the United States. The Metric System of Measurement is used primarily in most parts of the world. It is a base-ten system. Comparing Metric & Customary Measures Length Capacity Weight & Mass 1 in. = 2.54 cm 1 m ≈ 39.37 in. 1 m ≈ 1.09 yd 1 km ≈ 0.6 mi 1 mi ≈ 1.6 km 1 L ≈ 1.06 qt 1 gal ≈ 3.8 L 1 oz ≈ 28 g 1 kg ≈ 2.2 lb 12 inches (in.) 1 foot (ft) 1 centimeter (cm) 10 millimeters (mm) 1,000 milliliters (mL) 10 centimeters (cm) 10 decimeters 1,000 meters 1 decimeter (dm) 1 meter (m) 1 kilometer (km) 3 feet 1 yard (yd) 36 inches 1 yard 1,760 yards 1 mile (mi) 5,280 feet 1 mile 2 cups 1 pint (pt) 1 liter (L) 1 liter (L) 10 deciliters (dL) 1,000 milligrams (mg) 1 gram (g) 1,000 grams 1 kilogram (kg) 16 ounces (oz) 1 pound (lb) 2,000 pounds 1 ton (T) 2 pints 1 quart (qt) 4 cups 1 quart 32ºF water freezes 0ºC water freezes 212ºF water boils 98.6ºF normal body temperature 100ºC water boils 37ºC normal body temperature 4 quarts 1 gallon (gal) IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII © Copyright NewPath Learning. All Rights Reserved. 93-4410 www.newpathlearning.com Customary & Metric Units of Measurement

1 2 3 4 5 6 7 8 9 cm -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 -40 -20 0 20 40 60 80 100 120 140 160 180 200 1 2 3 4 5 6 7 Inch 1,000 mg total mass 500 mg 500 mg Customary Units Metric Units Degrees Celsius (ºC) are metric units of temperature. Degrees fahrenheit (ºF) are customary units of temperature. Length Capacity Weight Temperature Length Capacity Mass Temperature The Customary System of Measurement is used primarily in the United States. The Metric System of Measurement is used primarily in most parts of the world. It is a base-ten system. Comparing Metric & Customary Measures Length Capacity Weight & Mass 1 in. = 2.54 cm 1 m ≈ 39.37 in. 1 m ≈ 1.09 yd 1 km ≈ 0.6 mi 1 mi ≈ 1.6 km 1 L ≈ 1.06 qt 1 gal ≈ 3.8 L 1 oz ≈ 28 g 1 kg ≈ 2.2 lb 1 foot (ft) 1 centimeter (cm) 1 decimeter (dm) 1 meter (m) 1 kilometer (km) 1 yard (yd) 1 yard 1 mile (mi) 1 mile 1 pint (pt) 1 liter (L) 10 deciliters (dL) 1 gram (g) 1 kilogram (kg) 1 pound (lb) 1 ton (T) 1 quart (qt) 1 quart water freezes water freezes water boils normal body temperature water boils normal body temperature 1 gallon (gal) IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Key Vocabulary Terms • capacity • Celsius • centimeter • customary units • deciliter • decimeter • Fahrenheit • foot • gallon • gram • kilogram • kilometer • length • liter • mass • meter • metric units • mile • milligram • milliliter • millimeter • pint • pound • quart • ton • weight • yard 5 grams 1 gram © Copyright NewPath Learning. All Rights Reserved. 93-4410 www.newpathlearning.com Customary & Metric Units of Measurement \|xiBAHBDy01643kzU

Tables Collecting data • You can collect data (information) from other people using polls and surveys. • Scientists collect data from experiments. • Tables and graphs help us organize and interpret collected information. The mean is the average of a set of numbers. To find the mean, add all the numbers in the set and divide the sum by the number of items in the set. The median is the middle number when the data are in numerical order. The mode is the number that occurs most often in a set of data. Bike Color No. of Gears Price Ranger Outdoor Tourist Starburst Mountain Silver 5 10 $240 $295 $325 12 $375 $225 15 6 Blue Red Black White Types of Bikes Sold at the Bike Shop Mean Median Mode 20 ÷ 5 = 4 The mean is 4 The median is 6 The mode is 5 2, 3, 3, 6, 8, 10, 12 3, 5, 5, 5, 6, 6, 8, 9 middle number Frequency Table A frequency table shows the totals of the tally marks. A bar graph is one way of showing data that can be counted. Each segment in a circle graph represents a fraction of a set of data. A line graph presents a set of data collected over time using line segments. Months Months Number of bikes sold Number of Bikes A stem-and-leaf plot shows data arranged by place value. 3 + 5 + 2 + 6 + 4 Line Graph Circle Graph Bar Graph Stem–and–Leaf Plot Ranger Bike Tally Total Outdoor Tourist Starburst Mountain RangerOutdoorT ourist Starburst Mountain 0 1 2 3 4 5 6 7 8 9 10 Total 20 10 2 1 4 3 10 20 30 40 50 60 10 20 30 40 50 60 January F ebruaryM ar ch M ay A pril June July A ugust 15, 20, 28, 31, 35, 46, 49, 52 (arranged from least to greatest) Stem (tens digit) Leaf (ones digit) Mountain (10 bikes) 5 08 15 69 2 1 2 3 4 5 Outdoor (4 bikes) Ranger (3 bikes) Starburst Tourist(1 bike) To find the number of gears of the Starburst bike, look across the Starburst row until it meets the Gear column. The headings tell us what data is in each column. The title tells us what the table is about. Height of the bars shows how many of each bike sold (2 bikes) © Copyright NewPath Learning. All Rights Reserved. 93-4501 www.newpathlearning.com Collecting & Displaying Data

\|xiBAHBDy01641qzZ Tables The is the average of a set of numbers. To find the mean, add all the numbers in the set and divide the sum by the number of items in the set. The median is the when the data are in numerical order. The mode is the number that occurs in a set of data. Bike Color No. of Gears Price Ranger Outdoor Tourist Starburst Mountain Silver 5 10 $240 $295 $325 12 $375 $225 15 6 Blue Red Black White Types of Bikes Sold at the Bike Shop Mean Median Mode ÷ = The mean is 4 The median is 6 The mode is 5 2, 3, 3, 6, 8, 10, 12 3, 5, 5, 5, 6, 6, 8, 9 middle number Frequency Table A frequency table shows the totals of the tally marks. A bar graph is one way of showing data that can be counted. Each segment in a circle graph represents a fraction of a set of data. A line graph presents a set of data collected over time using line segments. Months Number of bikes sold Number of Bikes A stem-and-leaf plot shows data arranged by place value. 3 + 5 + 2 + 6 + 4 Key Vocabulary Terms • bar graph • circle graph • column • data • frequency table • graph • heading • line graph • mean • median • mode • poll • stem-and-leaf plot • survey • table • title Line Graph Circle Graph Bar Graph Stem–and–Leaf Plot Ranger Bike Tally Total Outdoor Tourist Starburst Mountain RangerOutdoorT ourist Starburst Mountain 0 1 2 3 4 5 6 7 8 9 10 Total 10 20 30 40 50 60 January F ebruaryM ar ch M ay A pril June July A ugust 15, 20, 28, 31, 35, 46, 49, 52 (arranged from least to greatest) Stem (tens digit) Leaf (ones digit) To find the number of gears of the Starburst bike, look across the Starburst row until it meets the Gear column. The headings tell us what data is in each column. The tells us what the table is about. © Copyright NewPath Learning. All Rights Reserved. 93-4501 www.newpathlearning.com Collecting & Displaying Data

Congruence & Similarity Symmetry 1 line of symmetry 4 lines of symmetry line of symmetry mirror placed through the middle of letter A 3 lines of symmetry Transformations – Flips, Slides & Turns The three main transformations are: • The reflected part of letter A on the mirror looks exactly the same as the original part. • Similar figures are identical in shape, but not in size. • A figure has line of symmetry if it can be folded or reflected into two congruent parts that fit on top of each other. The fold line or line of reflection is called the line of symmetry. • Shapes can be congruent if one of them has been transformed by sliding, flipping or turning. • The figure is moved along a straight line. • The figure is flipped over a line creating a mirror image. • The figure is moved around a point. • Congruent figures are identical in both shape and size. © Copyright NewPath Learning. All Rights Reserved. 93-4509 www.newpathlearning.com Slide or Translation Flip or Reflection Turn or Rotation A A A B B B C C1 B1 A1 D1 D C C mirror image Congruence, Transformations & Symmetry

Congruence & Similarity Symmetry 1 line of symmetry 4 lines of symmetry 3 lines of symmetry Transformations – Flips, Slides & Turns The three main transformations are: • Similar figures are identical in , but not in . • A figure has line of symmetry if it can be folded or reflected into parts that fit on top of each other. The fold line or line of reflection is called the . • Shapes can be congruent if one of them has been transformed by , or . . • Congruent figures are in both and . © Copyright NewPath Learning. All Rights Reserved. 93-4509 www.newpathlearning.com Slide or Translation Flip or Reflection Turn or Rotation A A B B C D C Congruence, Transformations & Symmetry Key Vocabulary Terms • congruent • flip • fold line • line of reflection • line of symmetry • reflection • rotation • shape • similar • size • slide • symmetry • transformation • translation • turn \|xiBAHBDy01642nzW

Circles & Related Figures AB is a radius AC is a diameter EF is a cord ∠DBC is a center angle A E C 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 Lines Angles Measuring Angles Drawing Angles right angle straight angle acute angle obtuse angle right angle A D G H E F I An angle is made up of two rays that share the same endpoint called the vertex. A straight angle forms a straight line. A right angle forms a square corner. Place the center point of the protractor over the vertex (corner) of the angle. Draw the ray DF. Place the center point of the protractor on the end point of the ray. Line up the ray DF so that it passes through the 0º mark of the protractor. Make a mark at 115º and label it E. Draw ray DE from the end point of ray DF to the mark you made at 115º. Place the protractor so that ray AC is over the base line of the protractor and passes through the 0º mark. Read the measure where the other ray AB crosses the protractor. An acute angle is less than a right angle. An obtuse angle is greater than a right angle. A ray is part of a line with one endpoint and goes on forever in the other direction. A line segment is part of a line between two endpoints. A line is a straight collection of points that extend in two opposite directions without end. A point is a location in space. AB CD BAC • point A • point B AB CD AB CD A A B D C B C interior exterior side A B D A B C D E F A B D C Line Segment Line Ray Angle Point Measure ∠BAC Draw ∠EDF of 115º B D F center The measure of ∠BAC is 65º Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 Step 4 Step 5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 A center point B C © Copyright NewPath Learning. All Rights Reserved. 93-4510 www.newpathlearning.com Lines, Angles & Circles

\|xiBAHBDy01650sz\ Circles & Related Figures AB is a AC is a EF is a ∠DBC is a A E C 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 Lines Angles Measuring Angles Drawing Angles A D G H E F I Define: Example: Define: Example: Define: Example: Define: Example: Define: Example: Place the center point of the protractor over the vertex (corner) of the angle. Place the protractor so that ray AC is over the base line of the protractor and passes through the 0º mark. Read the measure where the other ray AB crosses the protractor. Line Segment Line Ray Angle Point Measure ∠BAC Draw ∠EDF of 115º B D F center The measure of ∠BAC is 65º Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 Step 4 Step 5 Key Vocabulary Terms • acute angle • angle • circle • cord • diameter • line • line segment • obtuse angle • point • protractor • radius • ray • right angle • straight angle • straight line • vertex 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14 0 15 0 16 0 17 0 18 0 18 0 17 0 16 0 15 0 14 0 13 0 120 110 100 90 80 70 60 50 40 30 20 10 0 A center point B C © Copyright NewPath Learning. All Rights Reserved. 93-4510 www.newpathlearning.com Lines, Angles & Circles

S 9 x 6(3.14) + 2 x 9(3.14) • Solid figures are 3-dimensional figures that have length, width, and height. • The surface area of a solid figure is the sum of the areas of all its surfaces or faces. • A net is a pattern made to show each face of a solid figure flat. Surface Area of a Prism Surface Area of a Cylinder Surface Area of a Pyramid flattened cube rectangular prism 6 in. 3 ft 9 ft 8 in. 5 ft 6 ft h 5 ft 8 in. pyramid cylinder flattened cylinder r h flattened pyramid triangular face flattened prism cube front top side • Use the formula A = • w to find the area of each face. Face A : A = 6 x 4 = 24 Face B : A = 8 x 6 = 48 Face C : A = 8 x 4 = 32 Face D : A = 8 x 6 = 48 Face E : A = 8 x 4 = 32 Face F : A = 6 x 4 = 24 S = 85 ft2 S = S2 + 4 x ( b • h ) S = 25 + 4 x 15 S = 25 + 60 S 226.08 ft2 S = h x (2 r) + 2 x ( r2) S 9 x 18.84 + 2 x 28.26 S 169.56 + 56.52 4 in. 4 in. 6 in. F A E B C D A C E B D Surface Area (S) = area of square (A) + 4 x (area of triangular face) Surface Area (S) = area of lateral surface + 2 x (area of each base) 1 2 S = 52 + 4 ( x 5 x 6 ) 1 2 lateral surface base circumference of base r base r S = 9 x 6 + 2 x 9 S = 9 x (2 x x 3) + 2 x ( x 32) S © Copyright NewPath Learning. All Rights Reserved. 93-4609 www.newpathlearning.com Surface Areas of Solid Figures top face side face side face front face opposite to front face bottom face

• Solid figures are that have length, width, and height. • The surface area of a solid figure is the of the of all its surfaces or . • A is a pattern made to show each face of a solid figure flat. Surface Area of a Prism Surface Area of a Cylinder Surface Area of a Pyramid flattened cube rectangular prism 6 in. 3 ft 9 ft 8 in. 5 ft 6 ft h 5 ft 8 in. pyramid cylinder flattened cylinder r h flattened pyramid triangular face flattened prism cube front top side • Use the formula A = • w to find the area of each face. Face A : A = 6 x 4 = 2 4 Face B : A = 6 x 4 = Face C : A = 6 x 4 = Face D : A = 6 x 4 = Face E : A = 6 x 4 = Face F : A = 6 x 4 = S = 85 ft2 S = S2 + 4 x ( b • h) S = 5 + 4 x 15 S = 25 + 60 S 226.08 ft2 4 in. 4 in. 6 in. F A E B C D A C E B D Surface Area (S) = area of square (A) + 4 x (area of triangular face) Surface Area (S) = area of lateral surface + 2 x (area of each base) 1 2 S = 52 + 4 ( x 5 x 6 ) 1 2 lateral surface base circumference of base r base r Key Vocabulary Terms • base • circumference • cylinder • face • lateral area • prism • pyramid • solid figure • surface area S 9 x 6 ( 3.14 ) + 2 x 9 ( 3.14 ) S = h x (2 r) + 2 x ( r2) S 9 x 18.84 + 2 x 28.26 S 169.56 + 56.52 S = 9 x 6 + 2 x 9 S = 9 x ( 2 x x 3 ) + 2 x ( x 32) © Copyright NewPath Learning. All Rights Reserved. 93-4609 www.newpathlearning.com Surface Areas of Solid Figures top face side face side face front face opposite to front face bottom face \|xiBAHBDy01686rzu

C = d or 2 r C = r 2 Area of a Circle Circumference of a Circle A E AB is a diameter AD, DB, and DC are radii EF is a cord B D C F center diameter circle D circumference radius chord • A circle is a plane figure formed by a set of points that are equal distance from a fixed point within it, called the center. • The diameter of a circle is the distance across the inside of a circle through the center. It is twice the measure of a radius. • The radius is half the measure of a diameter. It is a line segment with one end point at the center of the circle and the other endpoint on the edge of the circle. • The circumference of a circle is the distance around it. • A chord is a line segment that connects any two points on a circle. • The area of a circle is the space contained within the circumference. • The ratio of the circumference of a circle to the diameter of a circle is approximately equal to 3.14 or . This ratio is called Pi ( ) and is the same for all circles. 22 7 d = 12 in. ; A = ? d = 12 A = r 2 A 3.14 • (6) 2 A 3.14 • 36 A 113.04 in.2 C = 2 r C 2 • 3.14 • 5 C 31.4 ft r = 6 r = r = 5 ft ; C = ? d 2 r = 12 2 12 in. 5 ft C = d C 3.14 • 10 C 31.4 ft d = 10 ft ; C = ? • • • © Copyright NewPath Learning. All Rights Reserved. 93-4610 www.newpathlearning.com Area & Circumference of Circles

\|xiBAHBDy01665mzV C = d or 2 r C = r 2 Area of a Circle Circumference of a Circle A E AB is a diameter AD, DB, and DC are radii EF is a cord B D C F circle D • A circle is a formed by a set of points that are equal distance from a fixed point within it, called the . • The of a circle is the distance across the inside of a circle through the . It is twice the measure of a . • The is half the measure of a . It is a line segment with one end point at the center of the circle and the other endpoint on the edge of the circle. • The of a circle is the distance around it. • A is a line segment that connects any two points on a circle. • The of a circle is the space contained within the circumference. • The ratio of the circumference of a circle to the diameter of a circle is approximately equal to or . This ratio is called and is the same for all circles. d = 12 in. ; A = ? d = 12 A = r 2 A 3.14 • ( 6 ) 2 A 3.14 • 36 A 113.04 in2 C = 2 r C 2 • 3.14 • 5 C 31.4 ft. r = 6 r = r = 5 ft ; C = ? r = 12 in. 5 ft C = d C 3.14 • 10 C 31.4 ft. d = 10 ft ; C = ? • • • Key Vocabulary Terms • area • center • chord • circle • circumference • diameter • pi ( ) • plane figure • radius © Copyright NewPath Learning. All Rights Reserved. 93-4610 www.newpathlearning.com Area & Circumference of Circles

Math: Geometry & Measurement

Mathematics, Grade 6

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