Measuring Prisms and Cylinders. Suggested Time: 5 Weeks
|
|
- Barnaby Maxwell
- 7 years ago
- Views:
Transcription
1 Measuring Prisms and Cylinders Suggested Time: 5 Weeks
2 Unit Overview Focus and Context In this unit, students will use two-dimensional nets to create threedimensional solids. They will begin to calculate surface area by drawing nets of 3-D objects before generalizing formulas and using only symbolic representation. They will explore the amount of space enclosed within prisms and cylinders, and then develop and apply formulas for determining the volume of these solids. The volume of any right prism or right cylinder can be calculated using the formula: ( ) Volume= Areaof base height. Throughout the unit, students will be encouraged to draw diagrams and models to help them visualize the 3-D objects that are described. Previous grades haves focused on developing an understanding of two-dimensional measurement. Students have calculated the area of rectangles, triangles and circles, and the volume of right rectangular prisms. In this unit, they will extend that knowledge to calculate the surface area and volume of prisms and cylinders. Math Connects An understanding of areas and volumes is necessary to function in society. Activities that require this knowledge range from day-to-day tasks such as cooking or filling baby bottles, to painting a room or paneling a shed, all the way up to more complex tasks like the scientific investigation of surface area versus volume question that biologists often have to answer. We live in a three-dimensional world. To make sense of size, students need the concepts of surface area and volume. Volume is used in waste management to track how much recycling reduces waste. It is used in engineering and construction to determine the amount of concrete required for a project. Surface area and volume are used when designing packaging to determine the most economical choice. These concepts are used to design buildings and parks, and for city planning. This unit is rich with real-life applications. Students will gain an appreciation of these concepts through relevant problem solving activities. 118 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
3 Process Standards Key [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Curriculum Outcomes STRAND Shape and Space (Measurement) OUTCOME Draw and construct nets for 3-D objects. [8SS] PROCESS STANDARDS C, CN, PS, V Shape and Space (Measurement) Determine the surface area of: right rectangular prisms right triangular prisms right cylinders to solve problems. [8SS3] C, CN, PS, R, V Shape and Space (Measurement) Develop and apply formulas for determining the volume of right prisms and right cylinders. [8SS4] C, CN, PS, R, V GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 119
4 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS Draw and construct nets for 3-D objects. [C, CN, PS, V] Achievement Indicators: 8SS.1 Match a given net to the 3-D object it represents. 8SS. Draw nets for a given right circular cylinder, right rectangular prism and right triangular prism, and verify by constructing the 3-D objects from the nets. Elaborations Strategies for Learning and Teaching In previous grades the focus has been on the study of two-dimensional measurement. Students calculated the area of rectangles and the volume of right rectangular prisms in Grade 6. This was extended in Grade 7 to include the area of triangles and circles. In this unit, students will draw nets, determine correct nets for different objects, and build 3-D objects from nets. They will also connect and extend prior knowledge to determine the surface area and volume of cylinders and prisms. Prior to generalizing formulas and using only symbolic representations to calculate surface area and volume, students will draw nets of 3-D objects. Understanding concrete models allows students to visualize the fi g ures and encourages them to use reasoning rather than merely attempt to follow procedures. This is the students first exposure to the use of nets to investigate and create 3-D solids. A net is a two-dimensional fi g ure that can be cut out and folded up to make a three-dimensional solid. The fi g ure on the left is the net of the solid on the right. Students must first have an understanding of the vocabulary. Representation Example(s) solid shell net pillars, butter milk container, cereal box cardboard box prior to assembly Definition/Explanation 3-D object with a filled interior 3-D object with an empty interior flat diagram that can be folded to create a 3- D solid - shows faces Although the focus is on nets and solids, exposure to the concept of shells could allow for a deeper discussion of the outcome. Continued 10 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
5 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Performance Visit the following websites to explore nets and 3-D objects (8SS.1, 8SS.) Math Makes Sense 8 Lesson 4.1: Exploring Nets ProGuide: pp.4-10, Master 4.6 CD-ROM: Master 4.36 Student Book (SB): pp Practice and HW Book: pp GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 11
6 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS Continued Achievement Indicators: 8SS.1 Continued 8SS. Continued Elaborations Strategies for Learning and Teaching Students must become familiar with, and be able to use with ease, terms such as the following: Net Right Circular Prism Right Prism Area Cube Right Rectangular Prism Right Triangular Prism Surface Area Volume Polyhedron Regular Prism Some samples of 3-D objects and their nets are shown here. When students make nets, their focus should be on the faces, and how the faces fit together to form the shape. They must imagine what the 3-D objects would look like if they were taken apart. Students should be reminded that the pieces must be the correct size to fit together, especially the circles on a cylinder. They must also be reminded to connect the shapes in the net. They may have all the pieces, but still have difficulty drawing the net. Ensure that there are no overlapping pieces or that there is not a hole where there should be a side. Dot paper and grid paper will be useful for this unit. Blackline masters of these can be found in the ProGuide Grade 8 Planning and Assessment Support booklet. 1 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
7 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Math Makes Sense 8 Lesson 4.1: Exploring Nets ProGuide: pp.4-10, Master 4.6 CD-ROM: Master 4.36 SB: pp Practice and HW Book: pp GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 13
8 Strand: Shape and Space (Measurement) Outcomes Elaborations Strategies for Learning and Teaching Students will be expected to 8SS Continued Achievement Indicators: 8SS.3 Predict 3-D objects that can be created from a given net and verify the prediction. It is important to realize that a given 3-D object can be created from more than one net. In this indicator students are asked to predict a solid from an assortment of nets with similar shapes in different arrangements. For example, each of the nets shown below will fold to create a cube. 8SS.4 Construct a 3-D object from a given net. The following strategies can be used to help students recognize whether a net is for a rectangular prism, a triangular prism, or a cylinder. The net of a rectangular prism should have six rectangular sides, four of them congruent and two others congruent to each other. The net of a triangular prism has five sides, two of which are congruent triangles and three of which are congruent rectangles. The net of a cylinder should have two circles and a rectangle. Students should always be encouraged to predict before actually folding the nets to construct the 3-D objects. 14 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
9 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Investigation Refer to the NL government website for Predict 3-D Objects from Nets. The worksheet is displayed below. Dot paper and grid paper would be helpful with this activity. (8SS.3) Math Makes Sense 8 Lesson 4.: Creating Objects from Nets ProGuide: pp CD-ROM: Master 4.37 SB: pp Practice and HW Book: pp Performance Students can construct small gift boxes from greeting cards using Foldable Greeting Card Gift Boxes. Refer to the NL government website for this activity. It is rich with mathematical opportunities. In addition to assessing this current outcome, it can be used to review the Pythagorean Theorem by asking questions about what objects will fit in the box diagonally. It can also reinforce the fractions, decimals and percent outcomes. (8SS.4) GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 15
10 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS3 Determine the surface area of: right rectangular prisms right triangular prisms right cylinders to solve problems. [C, CN, PS, R, V] Elaborations Strategies for Learning and Teaching Students have previously developed and applied formulas for the area of rectangles, triangles and circles. In this unit, they have drawn nets of prisms and cylinders. Now they will make connections between area and nets as they calculate the surface area of rectangular and triangular prisms and cylinders. Achievement Indicators: 8SS3.1 Identify all the faces of a given prism, including right rectangular and right triangular prisms. The concepts of edge, face and vertex have been covered in previous grades. A brief review may be necessary. Triangular Prism A triangular prism has 9 edges, 6 vertices, and 5 faces Cube A rectangular prism has 1 edges, 8 vertices, and 6 faces 8SS3. Explain, using examples, the relationship between the area of -D shapes and the surface area of a given 3-D object. Surface area is the sum of the areas of all faces or surfaces of a solid. Surface area calculations of the solids in this unit should be a direct extension of previous exposure to area formulas and work with nets, and follow smoothly from Achievement Indicator 8SS3.1, which focused on the identification of faces of a solid. A brief review of area of rectangles, triangles and circles may be required. To calculate surface area, students must identify the faces, determine the dimensions of each face, and apply appropriate formulas to calculate area. 16 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
11 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Investigation Select a net of a right rectangular prism from a previous activity. Discuss these questions with the class: (i) How many faces does the prism have? (ii) What shape are the faces? (iii) Are any of the faces congruent? How do you know? (iv) When the net is folded how many edges are there? (v) How many vertices are there? Repeat this exercise for a right triangular prism and a right cylinder. (8SS3.1) Paper and Pencil Identify each figure. Name the faces, edges and vertices. (8SS3.1) Math Makes Sense 8 Lesson 4.3: Surface Area of a Right Rectangular Prism Lesson 4.4: Surface Area of a Right Triangular Prism ProGuide: pp.17-1, -7 SB: pp , Class Discussion How does the notion of area differ for these two objects? (8SS3.) GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 17
12 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS3 Continued Achievement Indicators: 8SS3.3 Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism. Elaborations Strategies for Learning and Teaching Students should be exposed to right rectangular and triangular solids in several shapes so that they can become adept at recognizing the faces and analyzing the corresponding nets. Various shapes are shown here. 8SS3.5 Solve a given problem involving surface area. The surface area of a prism can be determined from its net, as the net shows all faces making up the object. Working from the net also allows for easy identification of congruent faces, which sometimes avoids the necessity of having to find the areas of each face individually. Some students may conclude that the surface area of a rectangular prism can be calculated using the formula SA= lw+ lh+ wh. However, this formula should not be the focus. To ensure students have gained the conceptual understanding of surface area, other strategies should be explored before introducing the formula. The net of a triangular prism shows the two triangular faces and three rectangular faces making up the prism. Students should recognize that the triangular bases of a right triangular prism are always congruent, and the two rectangular faces on the sides are congruent because they are attached to equal sides of the triangular bases. In an equilateral triangular prism, all three rectangular faces are congruent. Students should always be encouraged to include the units as part of the solution. Surface area is measured in units squared. Solving problems involving surface area should be incorporated into work with this achievement indicator, as well as the corresponding indicator for determining the surface area of a right cylinder. 18 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
13 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Class Discussion Consider a rectangular prism and think about how you find its surface area. Is there anything you can do that would shorten the process? Explain. (SS3.3) Take It Further Your parents are renovating your home and have decided to redo the siding. Siding is on sale for $15.00 per square metre. How much will the siding cost to fully cover the outside walls of your house? Note: you will need to ask your parents for an estimation of the dimensions of your home. (SS3.5) Math Makes Sense 8 Lesson 4.3: Surface Area of a Right Rectangular Prism Lesson 4.4: Surface Area of a Right Triangular Prism ProGuide: pp.17-1, -7 CD-ROM: Master 4.38, 4.39 SB: pp , Practice and HW Book: pp.81-8, GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 19
14 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS3 Continued Elaborations Strategies for Learning and Teaching Achievement Indicators: 8SS3.4 Describe and apply strategies for determining the surface area of a given right cylinder. 8SS3.5 Continued Circumference and area of a circle were covered in Grade 7. A review of these formulas, Ccircle = π d and Acircle = πr, may be necessary. Teachers may wish to use objects such as paper towel rolls or Pringles cans to assist with the investigation of the surface area of right cylinders. One possible exploration would involve having students draw a net of a right cylinder. Ask students how to use the net to find the surface area. A sample discussion follows. The faces of a cylinder are two circles (top and bottom) and a rectangle. For the cylinder shown here, first calculate the area of the circles. A A A A circle circle circle circle = πr = π 4 = 16π 50.4m This means the area of two circles is approximately m. It may be easier to recognize that the other face is a rectangle if students use an object that can be unrolled. They should then be able to see that the length of the rectangle is actually the circumference of the circle and the width of the rectangle is the height of the cylinder. So the area becomes A= πr h A= ( π)( 4) A 51.m 10 The surface area is the total area of all faces, or = m. This leads to the development of the formula SA= πr + πrh. 130 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
15 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Journal Use an example to show how the area of the curved surface of a cylinder relates to the area of a rectangle. (8SS3.4) Pencil and Paper Refer to the NL government website for the worksheet Surface Area of Cylinders. (8SS3.4) Take it Further Find the surface area of the composite shapes below. (8SS3.5) Math Makes Sense 8 Lesson 4.7: Surface Area of a Right Cylinder ProGuide: pp CD-ROM: Master 4.4 SB: pp Practice and HW Book: pp mejhm/html/video_interactives/ circles/circlessmall.html This website shows how the circumference unravels to give a straight line. It provides some helpful resources for area and circumference of circles. GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 131
16 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS4 Develop and apply formulas for determining the volume of right prisms and right cylinders. [C, CN, PS, R, V] Elaborations Strategies for Learning and Teaching Volume refers to the amount of space filled by three-dimensional objects. It is measured in cubic units. Students have had previous exposure to the concept of volume, and have developed and applied a formula for determining the volume of right rectangular prisms. This will be extended to include right prisms and right cylinders. Achievement Indicators: 8SS4.1 Determine the volume of a given right prism, given the area of the base. 8SS4.3 Explain the connection between the area of the base of a given right 3-D object and the formula for the volume of the object. The use of base 10 blocks can provide an effective means of developing the relationship between volume and the area of the base. Begin with a flat and discuss with the class the value of a flat (area of one hundred). Stack another flat on top and ask the students the value of this combination. As you stack the flats, count how many units you have altogether and discuss the idea of volume. Continue to stack the fl a ts until you have made a thousandth cube. Discuss the relationship between the stack of flats and a thousandth cube. Students should make the link that the volume of a thousandth cube is equal to the stack of ten flats (10 x 100). Building cube models of prisms should guide students to the realization that rather than counting each cube to calculate the volume, they can multiply the number of cubes in each layer (the area of the base) by the number of layers (the height). Consider this same relationship for a triangular prism. One section of a Toblerone bar is 1 cm thick. The area of one section is 8cm. There are ten sections in a small bar. If we assume that the sections are stacked without spaces in between, what is the volume of the bar? Multiply the area of one Toblerone section by the number of sections, since each section is 1cm thick. Volume = 8cm 10cm = 80cm 3 13 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
17 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Investigation Using 1cm grid paper, draw a right prism that has a base in the shape of your first initial. You will have to draw your first initial as a block letter and extend the vertices to form a 3-D prism. (i) (ii) Count the squares to find the area of your initial. Use a ruler to find the height of the prism, and multiply it by the area of the initial to find the volume. Math Makes Sense 8 Lesson 4.5: Volume of a Right Rectangular Prism Lesson 4.6: Volume of a Right Triangular Prism ProGuide: pp.9-35, 36-4, Master 4.31 (iii) How is the area of your initial and the height of your prism related to the volume? (iv) How does the shape of the base affect the volume of the prism? (8SS4.1) Take it Further Students could also find the volume of other right prisms, such as the ones below. (8SS4.1) SB: pp , 0-08 Practice and HW Book: pp.85-86, GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 133
18 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS4 Continued Achievement Indicators: 8SS4. Generalize and apply a rule for determining the volume of right cylinders. 8SS4.3 Continued. Elaborations Strategies for Learning and Teaching Students should make connections between calculating the volume of a prism and calculating the volume of a cylinder. A sample introductory discussion follows. Anne had a soup can and some unit cubes. She filled the can with unit cubes and counted them all. Do you think the number of cubes in her can is smaller, larger or equal to the actual volume? Explain. Anne then decided to find the volume using a different method. She traced the bottom of the soup can onto cm grid paper and counted the number of squares inside the circle. What information does this give her? What other information does she need in order to find the volume of the soup can? Determine a rule for finding the volume of a cylinder. Once students have determined that calculating the volume involves multiplying the area of the base by the height, they should conclude that since the base is a circle a formula is V cylinder = πr h. Developing formulas in meaningful ways should eliminate the need for students to memorize them as isolated pieces of mathematical facts. Rather, they can derive them from what they already know. Students must be made aware that 1cm = 1ml. It is not necessary to teach basic conversions as students will have this prior knowledge. However, this is the first time that students are exposed to this volume conversion of ml to 3 cm GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
19 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Paper and Pencil The area of one CD is mm. Each CD has a height of 1mm. Sarah has 30 of her CDs on a CD stack. How could you use this information to find the volume? (8SS4., 8SS4.3) Math Makes Sense 8 Lesson 4.8: Volume of a Right Cylinder ProGuide: pp.49-53, Master 4.33 CD-ROM: Master 4.43 Calculate the volume of a cylinder with a radius of 14cm and a height of 1cm. (8SS4.) SB: pp Practice and HW Book: pp What formula could you develop to find the volume of each of these right 3-D objects? (8SS4.1, 8SS4., 8SS4.3) Portfolio The class is having a fundraiser by selling popcorn, and students are making their own containers to save on expenses. (i) If you have sheets of cardboard with dimensions of 7 cm by 43cm, would you have a greater volume if you folded the sheets to make cylindrical containers with a height of 7cm or with a height of 43cm? (You plan on adding a circular base once the cardboard sheet is used for the sides.) (ii) Justify the decision mathematically. (8SS4.) Journal Given any right 3-D object, how can you find its volume? (8SS4.3) GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 135
20 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS4 Continued Achievement Indicators: 8SS4.4 Demonstrate that the orientation of a given 3-D object does not affect its volume. Elaborations Strategies for Learning and Teaching Students may have difficulty understanding the conservation of volume. A good demonstration is to bring in a soup can and ask students to identify the volume, found on the label. Stand the soup can on its end and ask for the volume. Then tip the can on its side and ask the class for the volume. Discuss why the volumes are the same in each case. They should conclude that volume does not change as a result of the cylinder s orientation, since the radius and height stay the same. Similarly, when a prism is placed on a different base, the dimensions do not change. So, the volume, or the space taken up by the prism, does not change. A sample class discussion follows. What is the base of each 3-D shape? How would you find the volume of each shape? Why would the volumes be the same? 8SS4.5 Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism. Throughout this unit, students have developed strategies and formulas for calculating the volume of rectangular prisms, triangular prisms, and cylinders. Students must now apply what they have learned to solve a variety of problems involving volume. They should be encouraged to draw models to help them visualize the shapes described in the problems. Sample problems and solutions are provided here. The solid wooden dowel used to make a paper towel holder has a radius of 1 cm and a height of 37 cm. How much wood is in the dowel? V V = ( Area of Base) V = π r h = π ()( 1 37) V cm 3 height Continued 136 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
21 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Paper and Pencil Refer to the NL government website for Matching Volume of 3-D Objects worksheet. (8SS4.4, 8SS4.5) Math Makes Sense 8 Lesson 4.5: Volume of a Right Rectangular Prism Lesson 4.8: Volume of a Right Cylinder ProGuide: pp.9-34, SB: pp.198, 18 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 137
22 Strand: Shape and Space (Measurement) Outcomes Students will be expected to 8SS4 Continued Elaborations Strategies for Learning and Teaching Achievement Indicator: 8SS4.5 Continued. 3 A triangular prism has a volume of 105cm. It s height is 7 cm. What is the area of its base? V ( Area of Base) = height 3 105cm = A 7cm 3 105cm A 7cm = cm = A An aquarium has the following dimensions: length 80 cm, width 35 cm, and height 50 cm. You must fill the aquarium up to 4 cm from the top. How much water will you put in the aquarium? V ( Area of Base) = height V= l w h V= 80cm 35cm 46cm V= cm 3 Mrs. Hicks is making hot chocolate for her class. The cylindrical hot water urn she is using has a diameter of 5 cm and a height of 50 cm. i) How much hot chocolate can she make in the urn? V V = ( Area of Base) V = πr h = π ( 1.5)( 50) V cm 3 height ii) Mrs. Hicks has 30 students in her class. The cups she is using holds 35 ml of hot chocolate each. Is there enough hot chocolate in the urn for her class? Amount needed: 30 35ml = 7050ml Yes, she will have enough to make hot chocolate for her class. 138 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
23 General Outcome: Use Direct or Indirect Measurement to Solve Problems Suggested Assessment Strategies Resources/Notes Paper and Pencil Refer to the NL government website for Matching Volume of 3-D Objects worksheet. (8SS4.4, 8SS4.5) A certain cube has a surface area of 96 cm. What is the volume of the cube? (8SS4.1, 8SS4.5) Take it Further Comparing Surface Area and Volume: Put students in groups of 3 or 4 and give each group multi-link cubes. Students are to build as many different rectangular prisms as they can, using all their multilink cubes. Students are to record the surface area and volume for each rectangular prism they construct. What happens to the surface area as the prism becomes taller rather than cube like? (8SS4.5, 8SS3.5) Math Makes Sense 8 Lesson 4.5: Volume of a Right Rectangular Prism Lesson 4.6: Volume of a Right Triangular Prism Lesson 4.8: Volume of a Right Cylinder ProGuide: pp.9-34, 36-4, CD-ROM: Master 4.40, 4.41, 4.43 SB: pp , 0-08, Practice and HW Book: pp.85-86, 87-89, GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE 139
24 140 GRADE 8 MATHEMATICS DRAFT CURRICULUM GUIDE
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
More informationSURFACE 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
More information1. 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
More informationGAP 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
More informationActivity 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
More informationGeometry 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
More informationFinding 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.
More informationWhat 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
More information12 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
More informationSurface Area Quick Review: CH 5
I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find
More informationArea 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
More informationVolume 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
More informationEDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 5. Shape and space
Shape and space 5 EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 5 Shape and space SECTION H 1 Perimeter 2 Area 3 Volume 4 2-D Representations of 3-D Objects 5 Remember what you
More informationSolids. 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
More informationArea 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
More informationE XPLORING QUADRILATERALS
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
More informationMD5-26 Stacking Blocks Pages 115 116
MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.
More informationUnit 10 Grade 7 Volume of Right Prisms
Unit 10 Grade 7 Volume of Right Prisms Lesson Outline Big Picture Students will: develop and apply the formula: Volume = area of the base height to calculate volume of right prisms; understand the relationship
More informationDŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet
Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils
More informationVOLUME 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:
More informationPlatonic 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,
More informationMeasurement. Volume It All Stacks Up. Activity:
Measurement Activity: TEKS: Overview: Materials: Grouping: Time: Volume It All Stacks Up (7.9) Measurement. The student solves application problems involving estimation and measurement. The student is
More information16 Circles and Cylinders
16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two
More informationWarning! 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
More informationPizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
More informationCalculating 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
More informationGeometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.
Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find
More informationThe formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE.
Revision - Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B
More information9 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
More informationGeometry 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
More informationArea 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
More informationCALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED
This resource has been produced as a result of a grant awarded by LSIS. The grant was made available through the Skills for Life Support Programme in 2010. The resource has been developed by (managers
More informationGeometry 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
More informationPIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY
PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY The Student Handout is page 11. Give this page to students as a separate sheet. Area of Circles and Squares Circumference and Perimeters Volume of Cylinders
More informationGrade 7 Mathematics. Unit 5. Operations with Fractions. Estimated Time: 24 Hours
Grade 7 Mathematics Operations with Fractions Estimated Time: 24 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization
More informationArea, Perimeter, Volume and Pythagorean Theorem Assessment
Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches
More informationShow 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
More informationThe small increase in x is. and the corresponding increase in y is. Therefore
Differentials For a while now, we have been using the notation dy to mean the derivative of y with respect to. Here is any variable, and y is a variable whose value depends on. One of the reasons that
More informationGAP 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
More informationFilling 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
More informationN Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Performance Assessment Task Swimming Pool Grade 9 The task challenges a student to demonstrate understanding of the concept of quantities. A student must understand the attributes of trapezoids, how to
More informationCylinder Volume Lesson Plan
Cylinder Volume Lesson Plan Concept/principle to be demonstrated: This lesson will demonstrate the relationship between the diameter of a circle and its circumference, and impact on area. The simplest
More informationCalculating the Surface Area of a Cylinder
Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping
More informationThe teacher gives the student a ruler, shows her the shape below and asks the student to calculate the shape s area.
Complex area Georgia is able to calculate the area of a complex shape by mentally separating the shape into familiar shapes. She is able to use her knowledge of the formula for the area of a rectangle
More informationPerimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Overview
Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Overview Summary of Lessons: This set of lessons was designed to develop conceptual understanding of the unique attributes
More informationOverview. 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,
More informationFCAT 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
More informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More informationLateral 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
More informationSTATE GOAL 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable
C 1 Measurement H OW MUCH SPACE DO YOU N EED? STATE GOAL 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy Statement of Purpose:
More informationMENSURATION. 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
More informationUnit 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
More informationVocabulary Cards and Word Walls Revised: June 29, 2011
Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,
More informationShape 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
More informationWhat You ll Learn. Why It s Important
What is a circle? Where do you see circles? What do you know about a circle? What might be useful to know about a circle? What You ll Learn Measure the radius, diameter, and circumference of a circle.
More informationStudent Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)
Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.
More informationAlgebra 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:
More informationArea 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
More informationInv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.
Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE
More informationB = 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
More informationSurfa Surf ce ace Area Area What You Will Learn
Surface Area A skyline is a view of the outline of buildings or mountains shown on the horizon. You can see skylines during the day or at night, all over the world. Many cities have beautiful skylines.
More informationGrade 5 Math Content 1
Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.
More informationG3-33 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:
More informationLesson 4: Surface Area
Lesson 4: Surface Area Selected Content Standards Benchmark Assessed M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures,
More informationThink About This Situation
Think About This Situation A popular game held at fairs or parties is the jelly bean guessing contest. Someone fills a jar or other large transparent container with a known quantity of jelly beans and
More informationME 111: Engineering Drawing
ME 111: Engineering Drawing Lecture # 14 (10/10/2011) Development of Surfaces http://www.iitg.ernet.in/arindam.dey/me111.htm http://www.iitg.ernet.in/rkbc/me111.htm http://shilloi.iitg.ernet.in/~psr/ Indian
More informationCBA 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
More informationChapter 4: Area, Perimeter, and Volume. Geometry Assessments
Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to
More informationLesson 4: Surface Area
Lesson 4: Surface Area Selected Content Standards Benchmarks Addressed: M-1-M Applying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to
More informationNets, Surface Area & Volume: Student Activity Lesson Plan
: Student Activity Lesson Plan Subject/Strand/Topic: Math Measurement & Geometry Measurement and Trigonometry Grade(s) / Course(s): 9: MFM1P, MPM1D 10: MFMP Ontario Expectations: MFM1P: MG.05 MPM1D: MG1.0,
More informationGRADE 10 MATH: A DAY AT THE BEACH
GRADE 0 MATH: A DAY AT THE BEACH UNIT OVERVIEW This packet contains a curriculum-embedded CCLS aligned task and instructional supports. The final task assesses student mastery of the geometry standards
More informationMultiplication and Division of Decimals. Suggested Time: 3
Multiplication and Division of Decimals Suggested Time: 3 1 2 Weeks 225 Unit Overview Focus and Context Math Connects This unit will draw upon students previous knowledge of multiplication and division
More informationGCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.
Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How
More informationPerimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
More informationDeveloping Conceptual Understanding of Number. Set J: Perimeter and Area
Developing Conceptual Understanding of Number Set J: Perimeter and Area Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Perimeter and Area Vocabulary perimeter area centimetres right angle Notes
More informationMATH 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
More informationVolume 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
More informationI. ASSESSSMENT TASK OVERVIEW & PURPOSE:
Performance Based Learning and Assessment Task Surface Area of Boxes I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In the Surface Area of Boxes activity, students will first discuss what surface area is and
More informationALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC
ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC
More informationSA 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.
More informationCHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS
CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change
More informationCHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.
TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has
More informationGAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
More informationACTIVITY: 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
More informationGCSE Revision Notes Mathematics. Volume and Cylinders
GCSE Revision Notes Mathematics Volume and Cylinders irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;
More informationCalculating Perimeter
Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle
More informationMATHEMATICS FOR ENGINEERING BASIC ALGEBRA
MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 4 AREAS AND VOLUMES This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.
More informationDiscovering 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
More informationArea of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above.
Name: Area of Circles Label: Length: Label: Length: A Part 1 1. Label the diameter and radius of Circle A. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and recd
More informationMCB4UW Optimization Problems Handout 4.6
MCB4UW Optimization Problems Handout 4.6 1. A rectangular field along a straight river is to be divided into smaller fields by one fence parallel to the river and 4 fences perpendicular to the river. Find
More informationDear 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
More informationConvert between units of area and determine the scale factor of two similar figures.
CHAPTER 5 Units of Area c GOAL Convert between units of area and determine the scale factor of two. You will need a ruler centimetre grid paper a protractor a calculator Learn about the Math The area of
More informationHow 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)
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationMath. So we would say that the volume of this cube is: cubic units.
Math Volume and Surface Area Two numbers that are useful when we are dealing with 3 dimensional objects are the amount that the object can hold and the amount of material it would take to cover it. For
More informationKindergarten to Grade 3. Geometry and Spatial Sense
Kindergarten to Grade 3 Geometry and Spatial Sense Every effort has been made in this publication to identify mathematics resources and tools (e.g., manipulatives) in generic terms. In cases where a particular
More informationGrade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge:
Grade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge: Standards: Lesson Title and Objective/Description Shape names: square, rectangle, triangle,
More informationBoxed In! Annotated Teaching Guide
Boxed In! Annotated Teaching Guide Date: Period: Name: Area Review Warm-Up TC-1 Area: The space that a two-dimensional shape occupies measured in square units. For a rectangle, the area is found by multiplying
More informationMensuration. The shapes covered are 2-dimensional square circle sector 3-dimensional cube cylinder sphere
Mensuration This a mixed selection of worksheets on a standard mathematical topic. A glance at each will be sufficient to determine its purpose and usefulness in any given situation. These notes are intended
More information