Surface Area and Volume

Save this PDF as:

Size: px
Start display at page:

Transcription

1 1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly

2 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish between area, surface area and volume when questions are presented to them as figures drawn and dimensions labeled. They should be able to calculate any given word problem. Students should be able to transfer information into everyday real world situations. What are the objectives for this unit? Students should be able to:. Find the area of a rectangle, trapezoid or right triangle, given its dimensions.. Find the area of a rectangle, trapezoid or right triangle in real contexts/word problems.. Identify the commutative property of multiplication.. Find the surface area of a rectangular solid, given the dimensions.. Find the surface area of a rectangular solid in real contexts/word problems.. Find the volume of a rectangular solid, given its dimensions.. Find the volume of a rectangular solid in real contexts/word problems.. Use the TI-73 calculator

3 3 Standards for the Unit NYS Standard #3: Students will understand mathematics and become mathematically confident by communicating and reasoning, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry. NYS Standards Key Ideas Addressed: KI #1 - Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence and construct an argument. KI #3 - Students use mathematical operations and relationships among them to understand mathematics. KI #4 - Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating and connecting mathematical information and relationships. KI #5 - Students use measurement in both metric and English measurement to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data. NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 3-C - Use grouping symbols to clarify the intended order of operations. 3-D - Apply the associative, commutative and distributive properties. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use measurements in real-world situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons.

4 4 Resources: The University of Chicago School of Mathematics Project Transition Mathematics. Scott, Foresman and Co., 1998, pg , Middle School Math:Course 3 McDougal Littell, Inc., 2004, pg Math Topics, Grades 7 8, Measurements, Geometry, Area, Probability and Graphing. Instructional Fair, Inc., pg

5 5 Materials Needed: notebooks and pencils rulers 4 graphic organizers (included) ETA Alphashapes, (2-D shapes, including rectangles, triangles and trapezoids) ETA Relational GeoSolids, (3-D shapes, plastic solids, small and large, 3 sets, total of 24 solids) 3-D shapes of various boxes covered in construction paper TI-73 graphing calculator TI Viewing Screen 12 plastic tangrams sets 1-cm graph paper 7 worksheets (included) 9 homework assignments (included) Answers to homework (included) boxes from candy/raisins (enough for the entire class, same size boxes, approximately 12) Aluminum trays 8 oz plastic cups of water paper towels Answer keys for worksheets and homework assignments textbook

6 6 Prerequisite Skills/Knowledge: Eighth grade students will have completed a review of area, volume, 2-dimensional and 3-dimensional concepts in both 6 th and 7 th grades. Parameters: Class time consists of 45-minute periods, 5 days a week. Each class has approximately 25 to 29. Computer use for students is limited to word processing and set games on 9/30 computers. Internet access and other computer program tools not available at present time.

7 7 DAY 1 - Area of Polygons NYS Standards Performance Indicators: 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: pencils, paper, calculators, TI-73 and TI viewing screen, 4 sizes per group of rectangles, squares, triangles and trapezoids with the sides measured and labeled in inches, cm, mm or labeled in other units not drawn to scale made of construction paper/graph paper (approximately 12 sets), graphic organizer #1 to classify shapes, ETA Alphashapes Warm-Up: Write a list of at least ten geometric shapes seen daily, classify the shapes into the following categories: squares, rectangles, triangles, others Procedures: 1. To review the warm-up students will work with the person they sit next to and will generate a list of at least 10 geometric shapes they see in various environments. Then students will classify the shapes into the four categories listed in the warm-up (see attached graphic organizer #1). We will review this as a group by listing the categories on the overhead and calling on students to state an item and which category it falls into. 2. Discuss the shapes suggested by students, lead students review to ideas of area and 2- dimensional figures and then have students copy notes on area of polygons that include the following information: -definitions of polygons, quadrilaterals, rectangles, triangles, trapezoids -examples of each shape and formulas for area of squares, rectangles, triangles and trapezoids -use of commutative property of multiplication -use ETA Alphashapes as examples 3. Review the concepts of units squared using 1 cm graph paper and encourage the generalized idea of other square units of measurement. 4. Students will practice activities finding the area of squares, rectangles, triangles and trapezoids that are cut out of construction paper as well as graph paper. Each pair of students will receive an envelope of 4 shapes. The units dimensions will be provided on each shape. Students will write out the following three steps for each shape: the area formula used, the substitution of dimensions, and areas labeled in units squared.

8 8 5. After approximately 15 minutes of group work, review a few of the shapes students have found the area of, stress the ideas of square units, using an overhead version of the chart students have. Homework: page 472, # 1 5

9 9 DAY 2 - Area of Polygons NYS Standards Performance Indicators: 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: pencils, notebooks, rulers, calculators, TI-73 and TI viewing screen, graphic organizer #2 to review definitions and formulas, various shapes of rectangles, squares, triangles, trapezoids that do not have the sides measured and labeled, worksheet #1 to complete during activity Warm-Up: -Complete graphic organizer on definitions, words to know, area formula, perimeter formula. -Post answers to homework. After checking off completed homework students will check their answers. Procedures: 1. To review the warm-up students will work independently on graphic organizers listing facts about each shape (see attached graphic organizer #2). We will review this as a group by completing organizers on the overhead and calling on students to complete them. Review any questions from the homework. 2. Students will work in assigned groups of three students per group. Each team will receive a packet with 6 shapes, rulers, calculators and 3 charts. Each shape will be labeled with a different letter and a unit of measurement indicated on the shape (ex: in, cm, mm). Students will measure the sides of the shapes in the unit indicated on the shape and will fill in the necessary information on the chart, which also includes the formula, substitution and the area written in units squared. 3. After approximately 20 minutes of group work, review a few of the shapes students have found the area of, stress the ideas of square units, using an overhead version of the chart students have. Homework: page 574, #1-3

10 10 DAY 3 - Area of Polygons NYS Standards Performance Indicators: 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebooks, pencils, worksheet #2 on trapezoids, rulers, ETA Alphashapes and Tangram shapes, calculators, TI-73 and viewing screen, worksheets 3 and 4 Warm-Up: -Identify the trapezoids on the given worksheet #2. -Post answers to homework. After checking off completed homework students will check their answers Procedures: 1. To review warm-up students will work with the person they sit next to and will complete the review sheet of trapezoids. We will review this as a group by completing the review sheet on the overhead and calling on students to complete them. Review any questions from the homework. 2. Students will find area of plastic 2-dimensional shapes. They will be given packets of 10 plastic shapes each, rulers, calculators and worksheet #4 to complete. They will complete a chart that directs them to measure the sides of each shape in centimeters or convert the measurement of the side to millimeters, meters or kilometers. 3. Review at least 2 shapes with the entire class to give a summary and be sure students understand all steps. 4. Students will solve word problems that require them to make a sketch of the image, then list the area formula, show substitution and label final answer correctly (students should be able to complete at least 3 of the ten problems on worksheet in class). Homework: complete worksheet on word problems for homework

11 11 DAY 4 - Surface Area of Rectangular Solids NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 3-C - Use grouping symbols to clarify the intended order of operations. 3-D - Apply the associative, commutative and distributive properties. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use measurements in real-world situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebooks, pencils, graphic organized #3, 1-cm graph paper, scissors, small boxes from candy or raisins(each student has the same size box), rulers, clear tape Warm-Up: -Fill in a graphic organizer on geometric solids. -Post answers to homework. After checking off completed homework students will check their answers Procedures: 1. To review the warm-up students will work independently to fill in the graphic organizer on geometric solids. We will review this as a group by completing the review sheet on the overhead and calling on students to give answers. Review any questions from the homework. 2. Discuss 3-dimensional images and review notes that include: -faces, rectangular solids, box, cube, square prism, rectangular prism, dimensions, edges, vertices -review and examples of nets -formulas for the surface area of cubes and boxes -use Relational GeoSolids as examples 3. Each student will receive a piece of 1-cm graph paper, a small box (from candy or raisins) and a ruler. Students will measure the base and height of the top of the box, one side of the box and the front of the box. 4. Through discussion lead students to the idea that: a. there are 2 equal faces that make up the front and back, sides, and top and bottom b. these can all be added together c. these lead to the formula for the surface area of a box

12 12 5. Lead students to the formula and review: a. 2(t X b) + 2(f X b) + 2(s X s) and 2(b X w) + 2(h X b) + 2(w X h) 6.Students will trace the 6 faces of the box onto the 1-cm graph paper, with consecutive sides connected. 7. Students will cut out the net of the box as a 2-dimensional figure. Students will fold the figure along the edges to form a box and will tape the net together creating a 3- dimensional box that is congruent to the original box. 8. Summarize the number of faces, names of the faces, and identify the base, width and height. Steps 3 through 7 of the this lesson will carry over into DAY 5 of the lesson Homework: page 563 # 1-5

13 13 DAY 5 - Surface Area of Rectangular Solids NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 3-C - Use grouping symbols to clarify the intended order of operations. 3-D - Apply the associative, commutative and distributive properties. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use measurements in real-world situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebook, pencils, graphic organizer #4, materials from activity in day 4, ETA Relational GeoSolids, additional 3-dimensional shapes covered in construction paper (various boxes from products), worksheet #5, TI-73 and viewing screen Warm-Up: -Fill in count the edges graphic organizer #4. -Post answers to homework. After checking off completed homework students will check their answers. Procedures: 1. To review the warm-up students will work with the person they sit next to and will complete the graphic organizer. We will review this as a group by completing the review sheet on the overhead and calling on students to complete them. Review any questions from the homework. 2. Students will continue activity from yesterday to complete a net of the candy box. Be sure that their nets are folded along lines that would create the seams of the box. Stress with students that we can find the area of each rectangle that helps form the face of the box. Lead students to the idea that the opposite rectangles are congruent rectangles so that they see the formation of the formula for surface area. 3. Students will begin new activity to measure 3-D solids and find the surface area of each shape. Each group will start with one worksheet per person and one shape. Each shape will be labeled in a capital letter. Charts will be prelabeled with letters A - T. A station will be provided where students can return the solids they have measured and take another one, to cover as many letter as possible within the given time frame. Steps 3 of the this lesson will carry over into DAY 6 of the lesson Homework: page 563 # 8-10

14 14 DAY 6 - Surface Area of Rectangular Solids NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 3-C - Use grouping symbols to clarify the intended order of operations. 3-D - Apply the associative, commutative and distributive properties. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use measurements in real-world situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebook, pencils, graphic organizer #4, materials from activity in day 4, ETA Relational GeoSolids, additional 3-dimensional shapes covered in construction paper (various boxes from products), worksheet #5, TI-73 and viewing screen Warm-Up: -No warm-up, students will go right into groups and continue activity from yesterday. -Post answers to homework. After checking off completed homework students will check their answers. Procedures: 1. Review any questions from homework 2. Students will finish activity from yesterday 3. Summarize concepts of nets, sides and edges of solids. 4. Begin exercise to use word problems to draw and label images Homework: finish worksheet for homework

16 16 DAY 8 - Volume of Rectangular Solids NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use measurements in real-world situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebooks, pencils, Relational GeoSolids, TI-73 and viewing screen Warm-Up: -Copy and answer the following question: Each edge of a wooden cube has a length of 3 inches. What is the least number of cuts needed to cut the cube into 27 one-inch cubes? (answer is 6 cuts) Procedures: 1. To review the warm-up students will work independently. We will review this as a group by completing the review sheet on the overhead and calling on students to complete them. 2. Generate a discussion on the students prior knowledge of volume and complete notes on volume that include the following concepts: -length, width, height, depth -formulas to find volume of rectangular solids (squares, rectangles, others) -finding volume using base of solid -use Relational GeoSolids as examples 3. Complete practice activities on volume using the dimensions of the GeoSolids measured from days 5 and 6 to substitute into the volume formula to find the volume of each solid. Homework: page 479 #3-6

17 17 DAY 9 - Volume of Rectangular Solids NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use measurements in real-world situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebooks, pencils, Relational GeoSolids, 1 aluminum pan per pair (approximately 12 needed), 1 8 oz cup of water per pair (approximately 12 needed), paper towels, worksheet #6 Warm-Up: -Post answers to homework. After checking off completed homework students will check their answers Procedures: 1. After students check the answers to their homework, review any questions they may have. 2.Students will be divided into pairs. Each pair will get 1 aluminum pan, 1 8 oz cup of water, 2 GeoSolids, and 1 worksheet per person. 3. Students will label what solids they have on their worksheet. They will predict which solid will have the greater volume (hold the most water). 4. Students will pour water into the first solid. The extra water in the cup will be dumped into the aluminum pan. Students will pour the water from the first solid into the second solid to demonstrate which has the greater volume. Students will fill in the worksheet accordingly. 5. Students will exchange solids and repeat steps 3 and 4. They will continue until the have compared the volume of all 24 solids in sets of 2. Homework: page 480 #1-4

18 18 DAY 10 - Volume of Rectangular Solids NYS Standards Performance Indicators: 1-C - Derive formulas to find surface area and volume. 4-E - Demonstrate an understanding of algebraic expressions, equations, formulas and properties. 5-A - Estimate, make and use situations. Make appropriate estimates relating to size and capacity. 5-B - Understand the uses of units, square units measurements in real-world and cubic units. 5-C - Know and apply formulas for perimeter and area of polygons. Materials: notebooks, pencils, calculators, TI-73 and viewing screen, worksheet #7 Warm-Up: -Post answers to homework. After checking off completed homework students will check their answers Procedures: 1. Review any questions from the homework. 2. Students will work in pairs to complete diagram review and word problems that distinguish from area, surface area and volume. 3. Students will begin their homework when finished, which is to write 15 test questions 5 on area, -5 on surface area and -5 on volume Homework: to complete the 15 homework test questions

19 19 Worksheet #1 Complete the chart on the area of rectangles, triangles and trapezoids. Letter Area Formula Substitution Final Answer A B C D E F

20 20 Worksheet # 2 Skills: Find the area of a trapezoid In 1-4, tell if each polygon appears to be a trapezoid. Explain why or why not

21 Complete the formula for the area of a trapezoid. b 1 Then, at the right, draw and label a diagram to show what the variables you wrote represent. h A = b 2

22 22 Skills: Find the area of a trapezoid Worksheet #2 Answer Key In 1-4, tell if each polygon appears to be a trapezoid. Explain why or why not Yes; figure has 4 sides; No, figure has no pair of parallel sides. parallel sides Yes; figure has 4 sides, pair of parallel sides. Yes; figure has 4 sides, pair of parallel sides No; figure has 5 sides Yes; figure has 4 sides 7. Complete the formula for the area of a trapezoid. b 1 Then, at the right, draw and label a diagram to show what the variables you wrote represent. h A = _ h(b 1 + b 2 ) b 2

23 Worksheet 3 23

24 24

25 25 Worksheet #4 name dimension of dimension of conversion conversion of shape base in cm height in cm to meters to km

26 26 Worksheet #5 letter formula substitution final answer A B C D E F G H I J K L M N O P Q R S T

27 27 Worksheet #6 name of two solid prediction of greater volume actual greater volume

28 Worksheet #7 28

29 29

30 30 GRAPHIC ORGANIZERS 1-4 Graphic Organizer #1 - To Use Day 1 Name Date Math 8, Area of Polygons HR List at least ten geometric shapes you see around you daily Classify the shapes into the following categories: squares rectangles triangles others

31 31 Graphic Organizer #2 - To Use Day 2 Move into concept of area and perimeter of shapes. Make a concept grid as follows Definition: A parallelogram with 4 Words to know: right angles length width height w Rectangle l Area Formula Perimeter Formula Area = length x width Perimeter = 2 x length + 2 x width A = l x w P = 2l + 2w Definition: A parallelogram with Words to know: 4 right angles and 4 equal sides side right angle Square Area Formula Perimeter Formula Area = side x side Perimeter = 4 x side A = s 2 P = 4s

32 32 Definition Words to know base height obtuse right acute Area Formula triangle Perimeter Formula A = _ b x h h P = s + s + s b Definition: A quadrilateral with Words to know exactly one pair of parallel sides. base height parallel trapezoid Area Formula b 1 Perimeter Formula A = _ (b 1 + b 2 )h P = 2s + b 1 + b 2 h b 2

33 33 Graphic Organizer #3 - To Use Day 3 prism pyramid 3-Dimensional Solids cylinder cone sphere

34 34 Graphic Organizer #4 - To Use Day 5 Count the edges worksheet Figure pentagonal pyramid rectangular pyramid triangular prism rectangular prism pentagonal prism Number of faces Number of Number of Faces + Vertices

35 35 Homework - Day 1 (from textbook page 472, #1 5) HOMEWORK ASSIGNMENTS: Read each problem and complete, show all work including a diagram of shape, area formula, substitution and a labeled answer. 1. What is the area of a rectangle with the dimensions 3 cm and 4 cm? 2. Make an accurate drawing of rectangles to show that the product of 3.2 and 4 is greater than the product of 3 and 4 (use cm as the unit of measurement). 3. If the length and width of a rectangle were measured in centimeters, the area would be given in what unit? 4. Draw a rectangle that is 4 inches by 5 inches and give its area. 5. Draw a rectangular array of dots with 7 rows and 5 columns. How many dots are in the array? Homework - Day 2 (from textbook page 574, #1-3) Read each problem and complete, show all work including a diagram of shape, area formula, substitution and a labeled answer. 1. Find the area of the isosceles triangle DEF that has a base of 38 in and a height of 24 in. 2. Find the area of right triangle ABC, where base AB measures 14 yds and height AC measures 12 yds. 3. A rectangular field ABCD has the following measurements: AB measures 44 m and BC measures 13 m. If you create a diagonal from points A to C, what would be the area of the triangle you create?

36 (homework from day 3 is a continuation of worksheet started in class) 36

37 37 Homework - Day 4 (from textbook page 563 #1-5) Read each problem and complete, show all work including a diagram of shape, area formula, substitution and a labeled answer. 1. A raisin box and all points inside it is an example of a figure called a 2. What is the surface area of a solid? 3. What is a net for 3-dimensional figure? 4. How many faces does a rectangular solid have? 5. Find the surface area of Given a box with the dimensions 9 cm, 12 cm and 7 cm: a. Make a sketch of the box b. Draw a net for the box c. Find the surface area of the box Homework - Day 5 (textbook page 563, #8-10) Read each problem and complete, show all work including a diagram of shape, area formula, substitution and a labeled answer. 8. A box has a length of 2 ft, a height of 18 in and width of 2 in. a. Draw a diagram of the box b. Convert the units of measurement c. Find the surface area in square inches 9. A rectangular solid has a length of L, a width of W, and a height of H. a. Show the surface area of the rectangular solid 10. A shirt is to be given as a gift. It is put into a box. The dimensions of the box are 14, 2.5 and 9. What is the least amount of wrapping paper needed to wrap the gift?

38 38 Homework Day 6 Finish classwork word problems on surface area. (no homework listed for day 7 in lesson) Homework - Day 8 (textbook page 479, #3-6) Read each problem and complete, show all work including a diagram of shape, volume formula, substitution and a labeled answer. 3. Find the volume of the following rectangular solid that has a height of 6 cm, a width of 3 cm and a depth of 4 cm. 4. Find the volume of the following rectangular solid that has a height of 10 meters, a width of W meters and depth of D meters. 5. The area of the base of a rectangular solid is 40 square centimeters and the height is 4 centimeters. Find the volume of the solid. 6. The area of the base of rectangular solid is A and the height is H. Show the volume of the solid. Homework - Day 9 (textbook page 480, #1-4) Read each problem and complete, show all work including a diagram of shape, area formula, substitution and a labeled answer. 1. The floor of a rectangular shaped room is 9 feet by 12 feet and the ceiling is 8 feet high. How much space is there is the room? 2. Give two possible sets of dimensions for a rectangular solid whose volume is 144 cubic inches.

39 39 3. Draw a rectangular solid whose volume is 8 cubic centimeters. What is this rectangular solid called? 4. A portable cassette player is a rectangular solid with the dimensions 12 cm X 9 cm X 4 cm. Another cassette player has the dimensions 18 cm X 55 cm X 19 cm. How many times more volume does the second cassette player occupy? Homework Day 10 Write 15 test questions, 5 on area, 5 on surface area, 5 on volume.

40 40 ANSWERS TO HOMEWORK Day 1 Homework Page 472 (no drawings are attached to answers) cm squared cm vs 12 cm 3. cm squared in squared dots in the array Day 2 Homework Page in squared yds squared m squared Day 3 Homework Answers to worksheet #1 Day 4 Homework Page a rectangular solid 2. the sum of the area of its faces 3. a 2-dimensional flat figure that can be folded into that given shape 4. six faces squared centimeters Day 5 Homework Page b. 24 in, 18 in, 2 in c square inches 9. 2LW + 2LH + 2HW square inches Day 6 Homework (none listed at present time) Day 7 Homework (none listed at present time) Day 8 Homework Page 479

41 cubic centimeters 4. V = 10WD cubic centimeters 6. V = AH Day 9 Homework Page cubic feet in, 12 in and 1 in or 12 in, 3 in and 4 in 3. (this would be a cube whose l,w,h all equal 2 cm each) 4. the second cassette player has 40 times more volume Day 10 Homework (none listed at present time)

42 42 Vocabulary Areas area parallelogram base circle 3-D solid prism cylinder sphere edge, vertex trapezoid rhombus height polyhedron pyramid cone Surface Area net surface area Formulas Area of parallelogram = bh Area of trapezoid = _(b 1 + b 2 ) h Surface area of prism = 2B + Ph Vol of prism is Base x height where base is l x w so... (V= l x w x h ) or (V=1/2 l x w x h) Vol of Cylinder (V= B x h ) where Base equals pi times r squared times h so... (V=ii x r^2 x h ) Vol of a pyramid with a square base (V=1/3 B x h ) where Base is s^2 so... (V=1/3 s^2 x h) Vol of pyramid with different length base (V=1/3 B x h) where Base is _ l x w so... V=1/3(1/2 l x w) x h Maybe make a chart that counts the number of vertices, edges and faces of a polyhedron (Page 495) McDougal Littell and (512) NOTE: EXTREMELY FUN GAME AT under Math

43 43

44 44

45 45

46 46

47 47

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

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

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

Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the

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

Name Date Period. 3D Geometry Project

Name 3D Geometry Project Part I: Exploring Three-Dimensional Shapes In the first part of this WebQuest, you will be exploring what three-dimensional (3D) objects are, how to classify them, and several

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the

Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

Geometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume

Geometry Chapter 12 Volume Surface Area Similar shapes ratio area & volume Date Due Section Topics Assignment Written Exercises 12.1 Prisms Altitude Lateral Faces/Edges Right vs. Oblique Cylinders 12.3

CC Investigation 4: Measurement

Content Standards 6.G., 6.G. CC Investigation : Measurement Mathematical Goals At a Glance PACING 3 days DOMAIN: Geometry Find the volume of a right rectangular prism with fractional edge lengths by packing

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:

2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters

GEOMETRY Vocabulary 1. Adjacent: Next to each other. Side by side. 2. Angle: A figure formed by two straight line sides that have a common end point. A. Acute angle: Angle that is less than 90 degree.

II. Geometry and Measurement

II. Geometry and Measurement The Praxis II Middle School Content Examination emphasizes your ability to apply mathematical procedures and algorithms to solve a variety of problems that span multiple mathematics

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

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

Geometric Concepts. Academic Vocabulary composite

Geometric Concepts 5 Unit Overview In this unit you will extend your study of polygons as you investigate properties of triangles and quadrilaterals. You will study area, surface area, and volume of two-

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

Dear Grade 4 Families,

Dear Grade 4 Families, During the next few weeks, our class will be exploring geometry. Through daily activities, we will explore the relationship between flat, two-dimensional figures and solid, three-dimensional

Grade 3 Math Expressions Vocabulary Words

Grade 3 Math Expressions Vocabulary Words Unit 1, Book 1 Place Value and Multi-Digit Addition and Subtraction OSPI words not used in this unit: add, addition, number, more than, subtract, subtraction,

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

Polygon of the Day Discovering Area Formulas

Polygon of the Day Discovering Area Formulas Utilizing Technology and Manipulatives Cuisenaire pop-cubes Geometry tiles GSP triangles tool Trapezoid magnets Sixth Grade 6-day Unit Plan (40 minute classes)

Geometry and Measurement

Geometry and Measurement (Developmentally Appropriate Lessons for K-5 Students) Amanda Anderson Title I Teacher Lincoln Elementary aanderson@bemidji.k12.mn.us Executive Summary This 10-day unit plan is

Sixth Grade Math Pacing Guide Page County Public Schools MATH 6/7 1st Nine Weeks: Days Unit: Decimals B

Sixth Grade Math Pacing Guide MATH 6/7 1 st Nine Weeks: Unit: Decimals 6.4 Compare and order whole numbers and decimals using concrete materials, drawings, pictures and mathematical symbols. 6.6B Find

E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this

TargetStrategies Aligned Mathematics Strategies Arkansas Student Learning Expectations Geometry

TargetStrategies Aligned Mathematics Strategies Arkansas Student Learning Expectations Geometry ASLE Expectation: Focus Objective: Level: Strand: AR04MGE040408 R.4.G.8 Analyze characteristics and properties

Honors Geometry Final Exam Study Guide

2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

Area, Perimeter, Surface Area and Change Overview

Area, Perimeter, Surface Area and Change Overview Enduring Understanding: (5)ME01: Demonstrate understanding of the concept of area (5)ME02: Demonstrate understanding of the differences between length

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

Course Title: Math Grade Level: Fourth

Course Title: Math Grade Level: Fourth Math - Fourth Page 1 2.1 Numbers, Number Systems and Number Relationships: A. Use expanded notation to represent whole numbers or decimals. B. Apply number theory

Grade 4 Math Expressions Vocabulary Words

Grade 4 Math Expressions Vocabulary Words Link to Math Expression Online Glossary for some definitions: http://wwwk6.thinkcentral.com/content/hsp/math/hspmathmx/na/gr4/se_9780547153131_/eglos sary/eg_popup.html?grade=4

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

Name: Date: Geometry Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

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

Review for Final - Geometry B

Review for Final - Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters

Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7

Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.

Surface Area and Volume Nets to Prisms

Surface Area and Volume Nets to Prisms Michael Fauteux Rosamaria Zapata CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version

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

Lesson 1 2G1 Lesson 2-3 2G1 Lesson 4 2G2 Lesson 5 2.G2 Portions of this lesson are taken from Investigations Unit 2 Session

CMS 2 nd Grade Geometry Unit 1 st Grade Geometry 2 nd Grade Geometry 3 rd Grade Geometry Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a

Volume of Pyramids and Cones

Volume of Pyramids and Cones Objective To provide experiences with investigating the relationships between the volumes of geometric solids. www.everydaymathonline.com epresentations etoolkit Algorithms

MODULE FRAMEWORK EN ASSESSMENT SHEET

MODULE FRAMEWORK EN ASSESSMENT SHEET LEARNING OUTCOMES (LOS) ASSESSMENT STANDARDS (ASS) FORMATIVE ASSESSMENT ASs Pages and (mark out of 4) LOs (ave. out of 4) SUMMATIVE ASSESSMENT Tasks or tests Ave for

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,

Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various

EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan

1 EXPLORING GEOMETRIC FIGURES Grade 10 6-Day Lesson Plan Tangrams Geoboards Equation Grapher Green Globs AlphaShapes Protractor Compass Created by Sandra Metzler 2 OVERALL OBJECTIVES 1- Students will increase

An arrangement that shows objects in rows and columns Example:

1. acute angle : An angle that measures less than a right angle (90 ). 2. addend : Any of the numbers that are added 2 + 3 = 5 The addends are 2 and 3. 3. angle : A figure formed by two rays that meet

ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

5.2. Nets and Solids LESSON. Vocabulary. Explore. Materials

LESSON 5.2 Nets and Solids A net is a flat figure that can be folded to form a closed, three- dimensional object. This type of object is called a geometric solid. Inv 1 Use a Net 229 Inv 2 Use Nets to

Describe as a mixed number where the arrow is pointing to on the number line. Explain how the base 10 system relates to place value.

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

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

Containers come in many different shapes such as cans, bottles and boxes. Which ones are prisms? Look at a selection of prisms and non-prisms.

SUPERMARKET BOXES Containers come in many different shapes such as cans, bottles and boxes. Which ones are prisms? Look at a selection of prisms and non-prisms. 1. What is necessary for a shape to be a

Family Letters. Assessment Management. Playing Fraction Of

Formula for the Area of a Parallelogram Objectives To review the properties of parallelograms; and to guide the development and use of a formula for the area of a parallelogram. www.everydaymathonline.com

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

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3

Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more

Lesson 7: Using Formulas

Lesson 7: Using Formulas Steps for Solving Problems Using a Formula 1. 2. 3. 4. Example 1 Using the formula: Density = mass/volume or D = m/v Find the density of a rock that has a volume of 20 ml with

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

12-8 Congruent and Similar Solids

Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular 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

Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

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

6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY

Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge J.T. is the creative director for a paper products company. The company is introducing a new line of gift boxes, called

CARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM

GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write

Areas of Rectangles and Parallelograms

CONDENSED LESSON 8.1 Areas of Rectangles and Parallelograms In this lesson you will Review the formula for the area of a rectangle Use the area formula for rectangles to find areas of other shapes Discover

Grade 5 supplement. Set C1 Geometry: Triangles & Quadrilaterals. Includes. Skills & Concepts

Grade 5 supplement Set C1 Geometry: Triangles & Quadrilaterals Includes Activity 1: Classifying Triangles C1.1 Activity 2: Sorting & Classifying Quadrilaterals C1.13 Activity 3: Finding the Perimeter &

Volume of Pyramids and Cones. Tape together as shown. Tape together as shown.

7-6 Volume of Pyramids and Cones MAIN IDEA Find the volumes of pyramids and cones. New Vocabulary cone Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz In this Mini Lab, you will investigate

Module: Mathematical Reasoning

Module: Mathematical Reasoning Lesson Title: Using Nets for Finding Surface Area Objectives and Standards Students will: Draw and construct nets for 3-D objects. Determine the surface area of rectangular

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

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

3 rd 5 th Grade Math Core Curriculum Anna McDonald School

3 rd 5 th Grade Math Core Curriculum Anna McDonald School Our core math curriculum is only as strong and reliable as its implementation. Ensuring the goals of our curriculum are met in each classroom,

Texas Assessment of Knowledge and Skills. Exit Level Math Review

Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Perspective TAKS Objective 7 Demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes

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:

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

Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

I Perimeter, Area, Learning Goals 304

U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,

4th Grade Math Vocabulary Resources

4th Grade Math Vocabulary Resources 4th Grade Math Vocabulary Resources contains two resources to promote student independence, develop math vocabulary, and support reading and writing in mathematics.

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

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:

RIT scores between 191 and 200

Measures of Academic Progress for Mathematics RIT scores between 191 and 200 Number Sense and Operations Whole Numbers Solve simple addition word problems Find and extend patterns Demonstrate the associative,

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

Incoming Frederick Douglass HS Geometry Students

Incoming Frederick Douglass HS Geometry Students 2016-2017 Dear FDHS Student, To better prepare you for the upcoming school year, it is the expectation is that all students bring the completed assignment

A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in

7.5 The student will a) describe volume and surface area of cylinders; b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and c) describe how changing

Begin recognition in EYFS Age related expectation at Y1 (secure use of language)

For more information - http://www.mathsisfun.com/geometry Begin recognition in EYFS Age related expectation at Y1 (secure use of language) shape, flat, curved, straight, round, hollow, solid, vertexvertices

MATH 139 FINAL EXAM REVIEW PROBLEMS

MTH 139 FINL EXM REVIEW PROLEMS ring a protractor, compass and ruler. Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice

Fourth Grade. Order the following numbers from smallest to largest: 576, 543, 562, A: 461.5, 543, 562, 576

Standard for Excellence: Number Sense Fourth Grade Mathematics Content Standard Performance Standard SAT 9 Number Sense 1.0 Students understand the place value of whole numbers and decimals to two decimal

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

Overview. Essential Questions. Grade 8 Mathematics, Quarter 4, Unit 4.3 Finding Volume of Cones, Cylinders, and Spheres

Cylinders, and Spheres Number of instruction days: 6 8 Overview Content to Be Learned Evaluate the cube root of small perfect cubes. Simplify problems using the formulas for the volumes of cones, cylinders,

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

12-8 Congruent and Similar Solids

Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. Ratio of radii: Ratio of heights: The ratios of the corresponding measures are

Performance Based Learning and Assessment Task Confetti Task

Performance Based Learning and Assessment Task Confetti Task I. ASSESSMENT TASK OVERVIEW & PURPOSE: In this task, Geometry students will investigate how surface area and volume is used to estimate the

Mensuration Introduction

Mensuration Introduction Mensuration is the process of measuring and calculating with measurements. Mensuration deals with the determination of length, area, or volume Measurement Types The basic measurement

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

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures

Math 6: Unit 7: Geometry Notes -Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons

Lesson 1: Exploring Polygons

Lesson 1: Exploring Polygons Objectives: Students will be able to identify whether a given shape is a polygon using the properties of polygons. Students will be able to identify and name polygons that

Everyday Mathematics. Grade 4 Grade-Level Goals CCSS EDITION. Content Strand: Number and Numeration. Program Goal Content Thread Grade-Level Goal

Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation

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

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby