PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY


 Geoffrey Walker
 5 years ago
 Views:
Transcription
1 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 and Rectangular Prisms Comparing Cost Teaching Suggestions begin on page 12. Lesson One: Area and Cost A. Area of Pizza (TC1) Triplets Jim, Joe, and Jeff want to order pizza for their upcoming triple birthday party. Since their money is limited, they decide to compare costs of pizzas to make sure they get the best value for their money. The brothers want a variety of pizzas and think having both round and square pizzas would be a good idea. So they first decide to compare sizes and surface areas of pizzas. Joe thinks he and his brothers need to get organized in their comparisons by making a table of their findings. So Joe creates tables that include sizes, shapes, and areas of common pizzas sold at their favorite restaurants along with price comparisons for supreme pizzas. On the next page, calculate the area of each size pizza. Round the areas to the nearest whole square inch. On your handout titled, PIZZA SIZE AND PRICE COMPARISONS, record your data in column 2, Area of Pizza. The following formulas may be helpful: Area of a circle = π r 2 Use 3.14 as the value of π If not using a scientific calculator. Area of a square = length x width Pizza! Pizza! Teacher Materials Page 1 of 13
2 Personal Pan Pizzas 6 inches 6 inches A = in 2 A = 36 in 2 Small Pizzas 9 inches 9 inches A = in 2 A = 81 in 2 Medium Pizzas 12 inches 12 inches A = in 2 A = 144 in 2 Large Pizzas 15inch 15 inches A = in 2 A = 225 in 2 Pizza! Pizza! Teacher Materials Page 2 of 13
3 B. Interpreting Data (TC2) Jim, Joe, and Jeff are surprised when they find out the areas and prices of the pizzas at their two favorite pizza restaurants. One restaurant specializes in the square pizzas listed on your handout, while the other restaurant bakes round pizzas. Write three observations they make regarding sizes, shapes, and/or prices of pizzas from the data on your handout. (Sample answers.) Observation 1: A 6inch round pizza is smaller than a 6inch square pizza but costs a dollar more. Observation 2: The area of each round pizza is always smaller than the area of the square pizza of the same dimension. The round pizza also costs more. Observation 3: Four 6inch square pizzas have the same area as one 12inch square pizza. C. Comparisons (TC2) Jeff, the oldest of the triplets, notices some relationships in the areas of a few of the pizzas. He thinks this will help the brothers decide which pizzas will be the best value. First, Jeff sees that two 12inch round pizzas are about equal in area to one 15inch square pizza. How do they compare in cost? The price of 2 12inch pizzas is almost double the cost of one 15inch pizza. Next, Jeff notices that the area of a 6inch square personal pan pizza goes into the area of a 12inch square pizza an exact number of times. How many 6inch square pizzas equal one 12inch square pizza? 4 How much would you pay for the 6inch pizzas? $31.96 Which is the better value if you compare the equivalent areas? Since a 12inch square pizza is $11.99 compared to the $31.95 price of the same amount of pizza in 4 6inch pizzas, the 12inch pizza is a much better value! Finally, Jeff gets carried away with his mental math expertise and notices that if he buys four 12inch square pizzas he will have the same amount of pizza as a certain number of 9inch round pizzas. He decides to let his brothers have a little mental exercise and figure out how many 9inch round pizzas equal four 12inch square pizzas. What do they get for an answer? It takes nine 9inch round pizzas to equal the same amount of pizza as four 12inch square pizzas Pizza! Pizza! Teacher Materials Page 3 of 13
4 Cost of the 12inch square pizzas? $47.96 Cost of the 9inch round pizzas? $ How do the prices compare? The four 12inch pizzas cost less than half the cost of nine 9inch pizzas even though they have the same area. D. $80.00 Budget (TC3) The brothers now must decide how much pizza they can buy on their budget of $ Since they are triplets born on the third day of the third month, they decide to get three slices of pizza for each guest. They plan to feed 15 guests plus themselves at the birthday party. How many slices of pizza do they need to purchase? 18 x 3 = 54 slices Since Jim, Joe, and Jeff want to have both round and square pizzas, find three combinations of pizzas within their $80.00 budget that could give them enough pizza for the party with only a few or no slices left over. You may or may not need all the rows on the tables. Order Combination 1 # of Pizzas Total # of Slices Size, Shape, and Cost per Pizza inch each inch each Total Cost per Size $31.98 $47.96 Total Slices: 56 Total Cost: $79.94 Order Combination 2 # of Total # of Slices Size, Shape, and Cost per Total Cost per Size Pizzas Pizza inch each $ inch $ inch 9.99 $ 9.99 Total Slices: 54 Total Cost: $77.94 Pizza! Pizza! Teacher Materials Page 4 of 13
5 Order Combination 3 # of Total # of Slices Size, Shape, and Cost Total Cost per Size Pizzas per Pizza inch each inch inch 9.99 $31.98 $29.98 $ 9.99 Total Slices: 54 Total Cost: $71.95 E. Calculating Area of Pizza Orders and Cost per Square Inch TC4 Calculate the area of pizza purchased by each order and the cost per square inch of pizza for each order. Show your work. Order Combination inch round: 177 x 2 = 354 in inch square: 113 x 4 = 452 in = 806 in 2 $ =.099 $.10 per square inch Order Combination inch round: 177 x 2 = 354 in inch square: 113 x 3 = 339 in inch square: 81 x 1 = 81 in = 774 in 2 $ = $.10 per square inch Order Combination inch round: 177 x 2 = 354 in inch square: 225 x 2 = 450 in inch square: 81 x 1 = 81 in = 885 $ = $.08 per square inch Which order is the best value? Order Combination 3 Pizza! Pizza! Teacher Materials Page 5 of 13
6 Lesson Two: Volume (TC5) A. The local pizza restaurants sell frozen pizzas to supermarkets throughout Washington. To ship the frozen pizzas, the pizzas are packed twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical and rectangular shipping cartons for the different size pizzas? Volume of a Rectangular Prism = length x width x height or Volume = (area of square pizza) x (height of carton) Volume of a Right Cylinder = πr 2 h or Volume = (area of round pizza) x (height of the carton) Volume of Shipping Cartons for 12 Frozen Pizzas Round to the nearest hundredth of an in 3. Square Pizzas Volume of Carton Round Pizzas Volume of Cylinder 6inch Square 432 in 3 6inch Round in 3 9inch Square 972 in 3 9inch Round in 3 12inch Square 1728 in 3 12inch Round in 3 15inch Square 2700 in 3 15inch Round in 3 Show work on the next page and record the data above. Pizza! Pizza! Teacher Materials Page 6 of 13
7 Computing Volumes for Pizza Cartons 12 Pizzas per Carton Hint: Height of all cartons will be 12 inches. 6inch Square 6 x 6 x 12 = 432 in 3 6nch Round 9 x 12 x π = in 3 9inch Square 9inch Round 9 x 9 x 12 = 972 in x 12 x π = in 3 12inch Square 12 x 12 x 12 = 1728 in 12inch Round 36 x 12 x π = in 3 15inch Square 15inch Round 15 x 15 x 12 = 2700 in x 12 x π = in 3 B. Compare the volume of a shipping carton for four 6inch square personal pan pizzas with the carton for one 12inch square pizza. The amount of pizza is the same for both, and all the pizzas are one inch thick. Show your work here. Four 6inch square: V = 6 x 6 x 4 = 144 in 3 $7.99 x 4 = $31.96 One 12inch square: V = 12 x 12 x 1 = 144 in 3 $11.99 Volume for four 6inch square pizzas?144 in 3 Volume for one 12inch square pizza? 144 in 3 How do the prices compare for the two orders? (Refer back to handout.) (Sample answer.) The cost of the four 6inch square pizzas is $4.00 less than three times the cost of one 12inch square pizza. Pizza! Pizza! Teacher Materials Page 7 of 13
8 Lesson Three: Circumference and Perimeter (TC6 ) Jeff was surprised when he noticed that the area of the square and round pizzas with the same width and diameter were so different. He wondered if there would be a relationship between the perimeter of the square pizzas and the circumference of the round pizzas. Find the circumference of the round pizzas and the perimeter of the square pizzas. Show your work in the boxes. Perimeter of a Square = Side + Side + Side + Side or Perimeter of a Square = 4S Circumference of a Circle = 2π r or Circumference of a Circle = dπ 6inch Square 6inch Round P = 4 x 6 = 24 inches C = 6π C = inches 9inch Square 9inch Round P = 4 x 9 = 36 inches C = 9π C = inches 12inch Square 12inch Round P = 4 x 12 = 48 inches C = 12π C = inches 15inch Square 15inch Round P = 4 x 15 = 60 inches C = 15π C = inches Which two pizzas measure about the same around the outside edge? The 12inch square pizza and the 15inch round pizza both measure 48 inches around the outside edge. Looking back on the handout, how do their areas compare? The area of the 15inch round pizza is 33 square inches greater than the area of the 12inch square pizza. Pizza! Pizza! Teacher Materials Page 8 of 13
9 A 6inch square pizza is half the perimeter of a 12inch square pizza, but their areas are quite different. Compare the areas of two 6inch square pizzas to one 12inch square pizza. The area of one 12inch square pizza is double the area of two 6inch square pizzas. The circumference of five 6inch round pizzas is about the same measurement as the two perimeters of which size pizza? five 6inch round: 19 x 5 = 95 inches two 12inch square: 2 x 48 = 96 inches What is the area of five 6inch round pizzas? 28 x 5 = 140 square inches What is the difference between the areas of these pizzas? The five 6inch round pizzas have about the same area as only one 12inch square pizza. Pizza! Pizza! Teacher Materials Page 9 of 13
10 Name: Date: Period: PIZZA SIZE AND PRICE COMPARISONS Personal Pan Pizzas (4 slices per pizza) Size & Shape Area of Pizza Price of Pizza 6inch round 28 in 2 $ inch square 36 in 2 $7.99 Small Pizzas (6 slices per pizza) Size & Shape Area of Pizza Price of Pizza 9inch round 64 in 2 $ inch square 81 in 2 $9.99 Medium Pizzas (8 slices per pizza) Size & Shape Area of One Slice Price of Pizza 12inch round 113 in 2 $ inch square 144 in 2 $11.99 Large Pizzas (12 slices per pizza) Size & Shape Area of Pizza Price of Pizza 15inch round 177 in 2 $ inch square 225 in 2 $14.99 Pizza! Pizza! Teacher Materials Page 10 of 13
11 TEACHING SUGGESTIONS Lesson One: Area and Cost Lesson One may take two class periods to complete. A suggested split in the lesson would be to complete sections AC on day one, then DE on day two. TC1 A. Area of Pizza 1. Concepts of diameter and radius. Using a circle diagram, draw a radius off the diameter to show the difference. 2. Area of a circle: Area = π r 2 3. Area of a rectangle: Area = length x width Some students may benefit by using graph paper to visualize the concept of area with the grid lines. Cutting out pizzas using graph paper with given diameters or side lengths and placing the round pizza over the square pizza will enable the student to compare the areas. 4. Concept of square inches (in 2.) Using the squares the graph paper and circles on or cut from graph paper, discuss the concept of area as square inches. 5. Calculator keys: x 2 and π Help students locate these important keys on their scientific calculators. Practice a few calculations to familiarize students with use of these keys. 6. Rounding decimals to nearest whole number. Rounding is used throughout the lesson. Students may need to review. Students need to use the approximation symbol to represent their answers. Example: A = in 2 TC2 B. Interpreting Data C. Comparisons 7. Students will be making observations and comparisons about area and cost data. Observations will vary in complexity. Lead a class discussion around observations guiding them into a more complex observation prior to letting them write three of their own. To practice comparisons, have students write comparisons three ways: difference between values, percents, and how many times one is greater/less than the other. Extension activities: Students may write comparisons using both area and cost. Students may write several comparisons using the data and challenge the class with guiding questions. As an additional pizza option, a pizza with an 18inch diameter could be added, though this is not a common pizza size. Pizza! Pizza! Teacher Materials Page 11 of 13
12 TC3 D. $80.00 Budget 8. Lead a sample pizza purchase discussion. Begin the example with a combination you know will cost more than $ Discuss strategies for the pizza combinations. Should you consider price, number of slices per pizza, or cost when choosing pizzas to order? 10. Extensions activities: How much pizza could you get for $80.00 if there is no limit to the area or number of slices purchased? What is the most expensive combination of pizzas to get 54 slices? If the restaurant gives a 10% discount if you purchase one pizza of each size, what combination would you buy and what would be the cost? TC4 E. Calculating Area of Pizza Orders and Cost per Square Inch 11. To calculate the cost per square inch of pizza, areas of each quantity and size of pizza must first be determined, and then totaled. Next, the total cost of the order must be divided by the total area of the order. Students will need to refer back to the tables on the handout. 12. Rounding practice will again enter into the final approximate answer for the cost per square inch. This time, the final cost will be below one dollar. Students may confuse the correct format for writing values less than one dollar. 13. Using your sample purchase over $80.00, model the steps for determining area of the order and cost per square inch. TC5 Lesson Two: Volume 14. To let students visualize volume of a box, construct a box with graph paper. Have students draw a net of a box, cut it out, and tape the sides together. Then fill the box with oneinch cubes. You will need to construct a box in advance to make sure that your dimensions will work for filling with cubes. 15. For the volume of a cylinder, fill a can with dry beans or rice. You could then fill the box with the volume of the cylinder if you want to also determine how many square inches filled the cylindrical can. 16. The concept of inches 3 may be introduced using the wooden blocks and/or drawings of cubes. Emphasize that now you are using three dimensions to determine volume, thus the use of inches 3. The 3 as the exponent represents the three dimensions: length, width, height. 17. For right cylinders, help students understand the idea of stacked round pizzas by stacking round objects. You may use quarters as the pizzas and fill a coin wrapper that represents the cylinder. 18. Model the calculations of volume of a rectangular prism and cylinder by walking students through the volume for the 6inch square and round pizzas. Pizza! Pizza! Teacher Materials Page 12 of 13
13 TC6 Lesson Three: Circumference and Perimeter 19. To visualize the concepts of circumference and perimeter, use string to measure the outer edge of round objects commonly found in a classroom. Then take the length and shape it into a square. 20. Planning in advance, shapes equivalent to the sizes of the pizzas in the problem could be cut out from sturdy cardboard or poster board. Students could use string to measure the outer edges of each. Next, students can compare their string measurements with the actual calculations of perimeter and circumference on page 9. How accurate were their string measurements? What factors affected the accuracy of the string measurements? 21. After completing the comparisons provided on page 9, have students write their own comparisons. Include data from the tables as well as the perimeter and circumference data on page 9. Pizza! Pizza! Teacher Materials Page 13 of 13
Name: Date: Period: PIZZA! PIZZA! Area of Circles and Squares Circumference and Perimeters Volume of Cylinders and Rectangular Prisms Comparing Cost
Name: Date: Period: PIZZA! PIZZA! Area of Circles and Squares Circumference and Perimeters Volume of Cylinders and Rectangular Prisms Comparing Cost Lesson One Day One: Area and Cost A. Area of Pizza Triplets
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 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 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 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 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 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 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 informationDATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation
A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal
More informationLesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
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 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 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 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 informationArea of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
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 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 threedimensional composite shapes.
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 informationGeometry 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 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 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 twodimensional 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 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 informationFinding Areas of Shapes
Baking Math Learning Centre Finding Areas of Shapes Bakers often need to know the area of a shape in order to plan their work. A few formulas are required to find area. First, some vocabulary: Diameter
More informationThe GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
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 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 information9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2D Shapes The following table gives the names of some 2D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
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 informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 91.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
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 informationKeystone National High School Placement Exam Math Level 1. Find the seventh term in the following sequence: 2, 6, 18, 54
1. Find the seventh term in the following sequence: 2, 6, 18, 54 2. Write a numerical expression for the verbal phrase. sixteen minus twelve divided by six Answer: b) 1458 Answer: d) 16 12 6 3. Evaluate
More informationEMAT 6450  Mathematics in Context
Melissa Wilson EMAT 6450  Mathematics in Context Course/Unit: Accelerated Coordinate Algebra/Analytic Geometry A for Unit 9, Circles and Volume (This unit corresponds to Unit 3 in Analytic Geometry. The
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 informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS  SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
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 informationArea and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
More informationCircumference of a Circle
Circumference of a Circle A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If
More informationRevision Notes Adult Numeracy Level 2
Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands
More informationMeasuring Irregular Shapes and Circles
5 Measuring Irregular Shapes and Circles It is not hard to find the area and perimeter of shapes made from straight lines. These shapes include rectangles, triangles, and parallelograms. But measuring
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 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 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 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 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 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 informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More informationLESSON 7 Don t Be A Square by Michael Torres
CONCEPT AREA GRADE LEVEL Measurement 56 TIME ALLOTMENT Two 60minute sessions LESSON OVERVIEW LESSON ACTIVITIES OVERVIEW LEARNING OBJECTIVES STANDARDS (TEKS) Students will learn the relationship between
More informationCircles: Circumference and Area Lesson Plans
Circles: Circumference and Area Lesson Plans A set of lessons for year 7. Lesson 1: Circumference of the circle and Pi Lesson 2: Area of the circle Lesson 3: Consolidation and Practice Lesson 1: Circumference
More informationJulie Rotthoff Brian Ruffles. No Pi Allowed
Julie Rotthoff Brian Ruffles rott9768@fredonia.edu ruff0498@fredonia.edu No Pi Allowed Introduction: Students often confuse or forget the area and circumference formulas for circles. In addition, students
More informationWarmUp 1. 1. What is the least common multiple of 6, 8 and 10?
WarmUp 1 1. What is the least common multiple of 6, 8 and 10? 2. A 16page booklet is made from a stack of four sheets of paper that is folded in half and then joined along the common fold. The 16 pages
More informationLesson 11: Volume with Fractional Edge Lengths and Unit Cubes
Lesson : Volume with Fractional Edge Lengths and Unit Cubes Student Outcomes Students extend their understanding of the volume of a right rectangular prism with integer side lengths to right rectangular
More informationGAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
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 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 informationKristen Kachurek. Circumference, Perimeter, and Area Grades 710 5 Day lesson plan. Technology and Manipulatives used:
Kristen Kachurek Circumference, Perimeter, and Area Grades 710 5 Day lesson plan Technology and Manipulatives used: TI83 Plus calculator Area Form application (for TI83 Plus calculator) Login application
More informationTask: Representing the National Debt 7 th grade
Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was $16,743,576,637,802.93.
More informationSection 7.2 Area. The Area of Rectangles and Triangles
Section 7. Area The Area of Rectangles and Triangles We encounter two dimensional objects all the time. We see objects that take on the shapes similar to squares, rectangle, trapezoids, triangles, and
More informationMath Common Core Sampler Test
Math Common Core Sampler Test This sample test reviews the top 20 questions we have seen on the 37 assessment directly written for the Common Core Curriculum. This test will be updated as we see new questions
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 informationPerimeter. 14ft. 5ft. 11ft.
Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine
More informationMinimize the Surface Area of a SquareBased Prism
9.3 Minimize the Surface Area of a SquareBased Prism The boxes used in packaging come in many shapes and sizes. A package must be suitable for the product, visually appealing, and cost efficient. Many
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 informationCircumference and Area of a Circle
Overview Math Concepts Materials Students explore how to derive pi (π) as a ratio. Students also study the circumference and area of a circle using formulas. numbers and operations TI30XS MultiView twodimensional
More informationReal World Performance Tasks
Real World Performance Tasks Real World Real Life, Real Data, Real Time  These activities put students into real life scenarios where they use real time, real data to solve problems. In the Seriously
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 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 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 informationCourse 2 Summer Packet For students entering 8th grade in the fall
Course 2 Summer Packet For students entering 8th grade in the fall The summer packet is comprised of important topics upcoming eighth graders should know upon entering math in the fall. Please use your
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 informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More information8 th Grade Task 2 Rugs
8 th Grade Task 2 Rugs Student Task Core Idea 4 Geometry and Measurement Find perimeters of shapes. Use Pythagorean theorem to find side lengths. Apply appropriate techniques, tools and formulas to determine
More informationExercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of
More informationWEDNESDAY, 4 MAY 10.40 AM 11.15 AM. Date of birth Day Month Year Scottish candidate number
FOR OFFICIAL USE G KU RE Paper 1 Paper 2 2500/403 Total NATIONAL QUALIFICATIONS 2011 WEDNESDAY, 4 MAY 10.40 AM 11.15 AM MATHEMATICS STANDARD GRADE General Level Paper 1 Noncalculator Fill in these boxes
More informationGeometry  Calculating Area and Perimeter
Geometry  Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry
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 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 informationLesson 22. Circumference and Area of a Circle. Circumference. Chapter 2: Perimeter, Area & Volume. Radius and Diameter. Name of Lecturer: Mr. J.
Lesson 22 Chapter 2: Perimeter, Area & Volume Circumference and Area of a Circle Circumference The distance around the edge of a circle (or any curvy shape). It is a kind of perimeter. Radius and Diameter
More informationNumeracy and mathematics Experiences and outcomes
Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different
More informationThe relationship between the volume of a cylinder and its height and radius
The relationship between the volume of a cylinder and its height and radius Problem solving lesson for Volume 3 rd Year Higher Level Teacher: Cara Shanahan Lesson plan developed by: Stephanie Hassett,
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 informationMath 2201 Chapter 8 Review
Olga Math 2201 Chapter 8 Review Multiple Choice 1. A 2 L carton of milk costs $3.26. What is the unit rate? a. $0.83/500 ml b. $3.27/2 L c. $0.61/L d. $1.63/L 2.. drove 346 km and used up 28.7 L of gas.
More informationTallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
More informationApplied. Grade 9 Assessment of Mathematics LARGE PRINT RELEASED ASSESSMENT QUESTIONS
Applied Grade 9 Assessment of Mathematics 2014 RELEASED ASSESSMENT QUESTIONS Record your answers to multiplechoice questions on the Student Answer Sheet (2014, Applied). LARGE PRINT Please note: The format
More informationArea and Perimeter: The Mysterious Connection TEACHER EDITION
Area and Perimeter: The Mysterious Connection TEACHER EDITION (TC0) In these problems you will be working on understanding the relationship between area and perimeter. Pay special attention to any patterns
More informationMATHEMATICAL LITERACY LESSON PLANS.
MATHEMATICAL LITERACY LESSON PLANS. GRADE 10. LESSON PLAN 1. Lesson Plan: Number and operations in context. Number f Activities : 3 Duration : +/ 9H00 Week 1 2 Date: Context : Mathematics in everyday
More informationMD526 Stacking Blocks Pages 115 116
MD526 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 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 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 informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationWEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet  36 inches. 1 Rod 5 1/2 yards  16 1/2 feet
WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet  36 inches 1 Rod 5 1/2 yards  16 1/2 feet 1 Furlong 40 rods  220 yards  660 feet 1 Mile 8 furlongs  320 rods  1,760 yards 5,280 feet
More informationMultistep Word Problems
Solutions are at the end of this file. Use after Delta Lesson 15 Multistep Word Problems The Student Text includes some fairly simple two step word problems. Some students may be ready for more challenging
More informationAll I Ever Wanted to Know About Circles
Parts of the Circle: All I Ever Wanted to Know About Circles 1. 2. 3. Important Circle Vocabulary: CIRCLE the set off all points that are the distance from a given point called the CENTER the given from
More information2. A painted 2 x 2 x 2 cube is cut into 8 unit cubes. What fraction of the total surface area of the 8 small cubes is painted?
Black Surface Area and Volume (Note: when converting between length, volume, and mass, 1 cm 3 equals 1 ml 3, and 1 ml 3 equals 1 gram) 1. A rectangular container, 25 cm long, 18 cm wide, and 10 cm high,
More informationChapter 4: The Concept of Area
Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding
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 informationPrimary Curriculum 2014
Primary Curriculum 2014 Suggested Key Objectives for Mathematics at Key Stages 1 and 2 Year 1 Maths Key Objectives Taken from the National Curriculum 1 Count to and across 100, forwards and backwards,
More informationMathematical Modeling and Optimization Problems Answers
MATH& 141 Mathematical Modeling and Optimization Problems Answers 1. You are designing a rectangular poster which is to have 150 square inches of tet with inch margins at the top and bottom of the poster
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 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 information