Surface Area. Assessment Management
|
|
- Emerald Johnston
- 7 years ago
- Views:
Transcription
1 Surface Area Objective To introduce finding the surface area of prisms, cylinders, and pyramids. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Measure the dimensions of a cylinder in inches and centimeters. [Measurement and Reference Frames Goal ] Use rectangle and triangle area formulas to find the surface area of prisms and cylinders. Apply a formula to calculate the area of a circle. [Measurement and Reference Frames Goal 2] Identify and use the properties of prisms, pyramids, and cylinders in calculations. [Geometry Goal 2] Key Activities Students find the surface areas of prisms, cylinders, and pyramids by calculating the area of each surface of a solid and then finding the sum. Ongoing Assessment: Informing Instruction See page 892. Ongoing Assessment: Recognizing Student Achievement Use journal pages 389 and 390. [Measurement and Reference Frames Goals and 2] Key Vocabulary surface area Materials Math Journal 2, pp. 389 and 390 Study Link 6 slate calculator cardboard box per workstation: 2 cans, tape measure, ruler, triangular prism, square pyramid Plotting and Analyzing Insect Data Math Journal 2, pp. 390A and 390B Students plot insect lengths in fractional units on a line plot. They use the line plot to analyze the data. Math Boxes Math Journal 2, p. 39 Students practice and maintain skills through Math Box problems. Study Link Math Masters, p. 34 Students practice and maintain skills through Study Link activities. ENRICHMENT Finding the Smallest Surface Area for a Given Volume Math Masters, p. 342 per partnership: 2 cubes Students find the rectangular prism with the smallest surface area for a given volume. ETRA PRACTICE Finding Area, Surface Area, and Volume Math Masters, p. 343 Student Reference Book, pp. 96 and 97 Students practice calculating area, surface area, and volume. Advance Preparation For Part, organize workstations for groups of 4 students (2 partnerships each). Each group will need 2 cans (see Lesson -3) and each of the triangular prism and square pyramid models (Math Masters, pages 324 and 326) constructed in Lesson -. Place a cardboard box with the top taped shut near the Math Message. Teacher s Reference Manual, Grades 4 6 pp Unit Volume
2 Getting Started Mental Math and Reflexes Have students write numbers from dictation and mark the indicated digits. Suggestions:,024,039 Circle the digit in the thousands place, and put an through the digit in the hundred-thousands place. 28,794,02 Circle the digit in the ten-thousands place, and put an through the digit in the hundreds place Circle the digit in the thousandths place, and put an through the digit in the hundredths place. 0, Circle the digit in the thousandths place, and put an through the digit in the thousands place Circle the digit in the tens place, and put an through the digit in the hundredths place. 94,679,424 Circle each digit in the millions period, and put an through each digit in the ones period. Math Message If you were to wrap this box as a gift, how would you calculate the least amount of wrapping paper needed? Study Link 6 Follow-Up Briefly review the answers. Ask: How would you explain the difference between capacity and volume? Volume is the measure of how much space a solid object occupies. Capacity is the measure of how much a container can hold. Teaching the Lesson Math Message Follow-Up (Math Journal 2, p. 389) WHOLE-CLASS Ask volunteers to use geometry vocabulary to describe the box. The box is a rectangular prism that has six rectangular faces. Then have students explain their solution strategies. If wrapping paper covers each face of the box exactly, the least amount of wrapping paper needed is the sum of the area of each of the six faces. Tell students that the sum of the areas of the faces or the curved surface of a geometric solid is called surface area. If wrapping paper covers each face of the box exactly, the area of paper required is the surface area of the box. If the area of the available wrapping paper is less than the surface area of the box, the paper will not completely cover the box. Ask a pair of students to measure the length, width, and height of the box to the nearest inch. Have students record these dimensions on the figure in Problem on journal page 389, find and record the areas of the six sides of the box, and add these to find the total surface area. Remind students that opposite sides (top and bottom, left and right, front and back) of the box have the same area. This means that students need to calculate only three different areas. Finding the Surface Area of a Can (Math Journal 2, p. 389) PARTNER PROBLEM SOLVING Algebraic Thinking Distribute one can to each partnership. Ask students to imagine that the top lids of their cans have not been removed. Ask: How would you find the surface area of your can? 7 Surface Area The surface area of a box is the sum of the areas of all 6 sides (faces) of the box.. Your class will find the dimensions of a cardboard box. a. Fill in the dimensions on the figure below. b. Find the area of each side of the box. Then find the total surface area. Area of front 3 in Area of back in 2 Area of right side in 2 Area of left side in 2 Area of top in 2 Area of bottom in Total surface area in 2 2. Think: How would you find the area of the metal used to manufacture a can? a. How would you find the area of the top or bottom of the can? b. How would you find the area of the curved surface between the top and bottom of the can? c. Choose a can. Find the total area of the metal used to manufacture the can. Remember to include a unit for each area. Area of top Area of bottom Area of curved side surface Total surface area Sample answers: First measure the diameter of the can, and divide by 2 to find the radius. Then calculate the area (A π º r 2 ). Calculate the circumference of the base (c π º d ), and multiply that by the height of the can Math Journal 2, p in. front 7 top right side Sample answers for a can with a diameter and 3 cm height: in. in. Lesson 89
3 3. Use your model of a triangular prism. a. Find the dimensions of the triangular and rectangular faces. Then find the areas of these faces. Measure lengths to the nearest _ 4 inch. base = 2 in. length = 4 _ 2 in. height = 3_ 4 in. width = 2 in. Area = 3_ 4 in 2 Area = 9 in 2 b. Add the areas of the faces to find the total surface area. Area of 2 triangular bases = 3 _ 2 in 2 Analyzing Fraction Data Kerry measured life-size photos of common insects to the nearest _ 8 of an inch. His measurements are given in the table below. Insect Length Length (nearest _ 8 in.) Insect (nearest _ 8 in.) American Cockroach 3_ 8 Heelfly _ 3 8 Ant _ 4 Honeybee 3_ 4 Aphid _ 8 House Centipede 3_ 8 Bumblebee _ 2 Housefly _ 4 Cabbage Butterfly _ 4 June Bug Cutworm _ 2 Ladybug _ 8 Deerfly 3_ 8 Silverfish 3_ 8 Field Cricket 7_ 8. Make a line plot of the insect lengths on the number line below. Be sure to label the axes and provide a title for the graph. Number of Insects Surface Area continued Area of 3 rectangular sides = in 2 Total surface area = 30 _ 2 in 2 4. Use your model of a square pyramid. a. Find the dimensions of the square and triangular faces. Then find the areas of these faces. Measure lengths to the nearest tenth of a centimeter. length = 6.3 cm base = 6.3 cm width = 6.3 cm height =. Area = cm 2 Area = 7.32cm 2 b. Add the areas of the faces to find the total surface area. Area of square base = cm 2 Area of 4 triangular sides = cm 2 Total surface area = cm _EMCS_S_MJ2_U_76434.indd 390 Formula for the Area of a Triangle A = _ 2 º b º h where A is the area of the triangle, b is the length of its base, and h is its height Math Journal 2, p. 390 Insect Lengths Length (inches) /4/ 7:04 PM Remind students that in this problem they are finding the area of the surface of their can, not the volume. Give students plenty of time to explore solution strategies among themselves, without your help. Add the areas of the top, bottom, and curved surface to find the total surface area. Ask a volunteer to explain how to find the area of the circular top and bottom. Use the formula A = π r 2. Ask another volunteer to explain how to find the area of the curved surface between the top and bottom of the can. Calculate the circumference of the base using the formula c = π d, and then multiply the circumference by the height of the can. If students are unable to suggest an approach for finding this area, remind or show them that the label on a food can is shaped like a rectangle if it is cut off and unrolled. Draw a rectangle on the board: If you cut a can label in a straight line perpendicular to the bottom, it will have a rectangular shape when it is unrolled and flattened. How would you measure the can to find the length of the base of the rectangle? Guide students to recognize the following two possibilities:. Measure the circumference of the base of the can with a tape measure. 2. Measure the diameter of the base of the can. Calculate the circumference of the base, using the formula c = π d. How would you find the other dimension (the width) of the rectangle? Measure the height of the can. Have partners measure the dimensions of their cans and complete Part 2 on journal page 389. Circulate and assist. Ongoing Assessment: Informing Instruction Watch for students who seem to have difficulty with visualizing the cutting and unrolling of the can label. Have them use the following procedure to cut a sheet of paper to use as a label for the side of the can:. Mark the top and bottom rims of the can at the can s seam. 2. Lay the can on the sheet of paper with the marks touching the paper. Mark these points on the paper. 3. Roll the can one complete revolution, until the marks touch the paper again. Mark these points on the paper. 4. Connect the four marks on the paper to form a rectangle. Cut out the rectangle. Math Journal 2, p. 390A _EMCS_S_MJ2_U_76434.indd 390A 3/3/ 9:23 AM 892 Unit Volume
4 Finding the Surface Area of a Prism and a Pyramid (Math Journal 2, p. 390) PARTNER Algebraic Thinking Have partners measure each solid constructed in Lesson - from Math Masters, pages 324 and 326 and record the dimensions on journal page 390. Then have them calculate and record the face areas and total surface area for each solid. Circulate and assist. Ongoing Assessment: Recognizing Student Achievement Journal pages 389 and 390 Use journal pages 389 and 390 to assess students ability to measure to the nearest _ 4 inch and 0. cm and to find the area of circles, triangles, and rectangles. Students are making adequate progress if they correctly answer Problems 2 and 3 and use rectangle, circle, and triangle area formulas to find the surface area of prisms and cylinders. [Measurement and Reference Frames Goals and 2] Analyzing Fraction Data continued Use the data and the line plot you made on journal page 390A to solve these problems. Give all answers in simplest form. 2. What is the maximum length of the insects measured? 3. What is the minimum length? 4. What is the range of insect lengths? _ 8 in.. What is (are) the mode length(s) of the insects? 6. What is the median length of the insects? 7. How much longer is the American cockroach that Kerry measured than the field cricket? 3_ 8 in. 3_ 8 in. 3_ 4 in. _ 2 in. _ 2 in. 8. Suppose ladybugs were placed end to end. How long would they be? 3 _ 8 in. 9. How many times as long is the bumblebee than the housefly? 6 times as long 0. a. Suppose all of the insects less than 3_ 4 inch long were placed end-to-end. How long would they be? 2 3_ 8 in. b. Suppose all of the insects greater than _ 8 inch long were placed end-to-end. How long would they be? 9 _ 8 in. c. What is the total length of all insects placed end to end? 2 in.. What is the mean length of the insects that were measured? Math Journal 2, p. 390B 4_ in _EMCS_S_MJ2_G_U_76434.indd 390B 4/7/ 3:8 PM 2 Ongoing Learning & Practice Plotting and Analyzing Insect Data (Math Journal 2, pp. 390A and 390B) INDEPENDENT Students plot insect lengths in fractional units on a line plot. They use the line plot to analyze data and solve problems involving addition, subtraction, multiplication, and division with fractions. As needed, review how to make a line plot based on fractional units and how to perform operations with fractions. Math Boxes Math Boxes (Math Journal 2, p. 39) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews Unit 2 content.. Write each number in simplest form. a. b. 80_ = 6 3_ 6 8 _ = 6 8 _ 2 c. 8 24_ 48 = 9_ d. 38_ 4 = Find the volume of the rectangular prism. Volume of rectangular prism V = B * h 2. How are cylinders and cones alike? Both have a circular base and one curved surface Find the area and perimeter of the rectangle. 3 2 cm Study Link (Math Masters, p. 34) INDEPENDENT Home Connection Students practice using formulas to calculate volume and surface area. If students use calculators, remind them to enter 3.4 for π if necessary. V = 2 cm 3. Solve the pan-balance problems below. a. b. 3 cm cm Area = Perimeter = (unit) 2 cm (unit) One weighs as much as 3 s. One weighs as much as 6 s. One weighs as much as One weighs as much as paper clips. paper clips Math Journal 2, p _EMCS_S_MJ2_U_76434.indd 39 3/4/ 7:04 PM Lesson 893
5 Name STUDY LINK Volume and Surface Area Area of rectangle: A = l º w Volume of rectangular prism: V = l º w º h. Kesia wants to give her best friend a box of chocolates. Figure out the least number of square inches of wrapping paper Kesia needs to wrap the box. (To simplify the problem, assume that she will cover the box completely with no overlaps.) Amount of paper needed: 88 in 2 Explain how you found the answer. Sample answer: I found the area of each of the 6 sides and then added them together. Yes Explain. A 4 in. 4 in. 3 _ 2 in. box has a volume of 6 in 3 and a surface area of 88 in Could Kesia use the same amount of wrapping paper to cover a box with a larger volume than the box in Problem? Find the volume and the surface area of the two figures in Problems 3 and Volume: 4. Volume: Surface area: 3. 2 Study Link Master 0 cm Circumference of circle: c = π º d Area of circle: A = π º r 2 Volume of cylinder: V = π º r 2 º h 26 in 3 Surface area: 26 in 2 2 in. 6 in. 6 in. cube in. 3 Differentiation Options ENRICHMENT PARTNER Finding the Smallest Surface Area for a Given Volume (Math Masters, p. 342) 30 Min Algebraic Thinking To apply students understanding of volume and surface area, have them use given volumes to find the dimensions of rectangular prisms. Partners use the patterns in the dimensions to identify the dimensions of a prism that would have the smallest surface area. When students have finished, discuss any difficulties or curiosities they encountered _EMCS_B_MM_G_U_76973.indd 34 Math Masters, p. 34 3/9/ 8:44 AM ETRA PRACTICE INDEPENDENT Finding Area, Surface Area, and Volume (Math Masters, p. 343; Student Reference Book, pp. 96 and 97) Min Students practice calculating area, surface area, and volume of various geometric figures. Name Teaching Master A Surface-Area Investigation Name Teaching Master Area, Surface Area, and Volume In each problem below, the volume of a rectangular prism is given. Your task is to find the dimensions of the rectangular prism (with the given volume) that has the smallest surface area. To help you, use centimeter cubes to build as many different prisms as possible having the given volume. Record the dimensions and surface area of each prism you build in the table. Do not record different prisms with the same surface area. Put a star next to the prism with the smallest surface area.. 2. Dimensions (cm) Surface Area (cm 2 ) Volume (cm 3 ) Dimensions (cm) Surface Area (cm 2 ) Volume (cm 3 ) If the volume of a prism is 36 cm 3, predict the dimensions that will result in the smallest surface area. Explain. 3 º 3 º 4; I used the smallest 3 dimensions that would result in the given volume. 4. Describe a general rule for finding the surface area of a rectangular prism in words or with a number sentence. Find the area of each face. Then find the sum of these areas. Math Masters, p. 342 Area of rectangle: A = l w Volume of rectangular prism: V = B h or V = l w h. Record the dimensions and find the area. Length = Width = _ 2 ft 2 _ 8 ft Area = 4 7_ 6 ft2 How many square tiles, each ft long on a side, would be needed to fill the rectangle? 4 7_ 6 Circumference of circle: c = π d Area of circle: A = π r 2 Volume of cylinder: V = π r 2 h Record the dimensions, and find the volume and surface area for each figure below. Round results to the nearest hundredth. 3. Rectangular prism 2 ft Volume = 280 cm ft Surface area = 262 cm 2 Math Masters, p Record the dimensions and find the volume. Area of base = 20 cm 2 2 cm Number of -centimeter unit cubes needed to fill the box: 40 Volume = 40 cm 3 4. Cylinder Diameter = Height = 9 ft 7 ft 7 ft 9 ft Volume = ft 3 2 cm Surface area = ft _EMCS_B_MM_G_U_76973.indd 342 3/9/ 8:44 AM _EMCS_B_MM_G_U_76973.indd 343 4/7/ 9:43 AM 894 Unit Volume
6 Name Area, Surface Area, and Volume Area of rectangle: A = l w Volume of rectangular prism: V = B h or V = l w h Circumference of circle: c = π d Area of circle: A = π r 2 Volume of cylinder: V = π r 2 h. Record the dimensions and find the area. 2. Record the dimensions and find the volume. 2 8 ft 2 cm 2 ft Length = Width = Area = How many square tiles, each ft long on a side, would be needed to fill the rectangle? Area of base = Number of -centimeter unit cubes needed to fill the box: Volume = Copyright Wright Group/McGraw-Hill Record the dimensions, and find the volume and surface area for each figure below. Round results to the nearest hundredth. 3. Rectangular prism 4. Cylinder Diameter = Height = 9 ft 7 ft Volume = Volume = Surface area = Surface area = 343
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
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 informationSubtracting Mixed Numbers
Subtracting Mixed Numbers Objective To develop subtraction concepts related to mixed numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters
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 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 informationThe Distributive Property
The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com
More informationComparing Fractions Objective To provide practice ordering sets of fractions.
Comparing Fractions Objective To provide practice ordering sets of fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management
More informationObjective To introduce a formula to calculate the area. Family Letters. Assessment Management
Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationLine Plots. Objective To provide experience creating and interpreting line plots with fractional units. Assessment Management
Line Plots Objective To provide experience creating and interpreting line plots with fractional units. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family
More informationObjective To guide exploration of the connection between reflections and line symmetry. Assessment Management
Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family
More informationObjective To introduce the concept of square roots and the use of the square-root key on a calculator. Assessment Management
Unsquaring Numbers Objective To introduce the concept of square roots and the use of the square-root key on a calculator. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
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 informationReview: Comparing Fractions Objectives To review the use of equivalent fractions
Review: Comparing Fractions Objectives To review the use of equivalent fractions in comparisons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters
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 informationFactor Trees. Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers.
Factor Trees Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice
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 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 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 informationMiddle Value (Median) of a Set of Data
Middle Value (Median) of a Set of Data Objectives To guide children as they sort numerical data and arrange data in ascending or descending order, and as they find the middle value (median) for a set of
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 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 informationParentheses in Number Sentences
Parentheses in Number Sentences Objective To review the use of parentheses. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management
More informationObjective To guide the development and use of a rule for generating equivalent fractions. Family Letters. Assessment Management
Equivalent Fractions Objective To guide the development and use of a rule for generating equivalent fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More informationCapacity. Assessment Management
Capacity Objective To review units of capacity. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards
More informationThe Lattice Method of Multiplication
The Lattice Method of Multiplication Objective To review and provide practice with the lattice method for multiplication of whole numbers and decimals. www.everydaymathonline.com epresentations etoolkit
More informationComparing and Ordering Fractions
Comparing and Ordering Fractions Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. www.everydaymathonline.com epresentations etoolkit Algorithms
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 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 informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
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 informationSunrise-Sunset Line Graphs
Sunrise-Sunset Line Graphs Objectives To guide children as they analyze data from the sunrise-sunset routine; and to demonstrate how to make and read a line graph. www.everydaymathonline.com epresentations
More informationMeasuring with a Ruler
Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. www.everydaymathonline.com epresentations
More informationBaseball Multiplication Objective To practice multiplication facts.
Baseball Multiplication Objective To practice multiplication facts. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common
More informationChange Number Stories Objective To guide children as they use change diagrams to help solve change number stories.
Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
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 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 informationReading and Writing Large Numbers
Reading and Writing Large Numbers Objective To read and write large numbers in standard, expanded, and number-and-word notations. www.everydaymathonline.com epresentations etoolkit Algorithms Practice
More informationEveryday Mathematics GOALS
Copyright Wright Group/McGraw-Hill GOALS The following tables list the Grade-Level Goals organized by Content Strand and Program Goal. Content Strand: NUMBER AND NUMERATION Program Goal: Understand the
More informationHidden Treasure: A Coordinate Game. Assessment Management. Matching Number Stories to Graphs
Hidden Treasure: A Coordinate Game Objective To reinforce students understanding of coordinate grid structures and vocabulary. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM
More informationReading and Writing Small Numbers
Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationBox Plots. Objectives To create, read, and interpret box plots; and to find the interquartile range of a data set. Family Letters
Bo Plots Objectives To create, read, and interpret bo plots; and to find the interquartile range of a data set. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
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 informationCalculator Practice: Computation with Fractions
Calculator Practice: Computation with Fractions Objectives To provide practice adding fractions with unlike denominators and using a calculator to solve fraction problems. www.everydaymathonline.com epresentations
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 informationBuying at the Stock-Up Sale
Buying at the Stock-Up Sale Objective To guide children as they multiply using mental math and the partial-products algorithm. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM
More informationMultiplying Fractions by Whole Numbers
Multiplying Fractions by Whole Numbers Objective To apply and extend previous understandings of multiplication to multiply a fraction by a whole number. www.everydaymathonline.com epresentations etoolkit
More informationThe Half-Circle Protractor
The Half-ircle Protractor Objectives To guide students as they classify angles as acute, right, obtuse, straight, and reflex; and to provide practice using a half-circle protractor to measure and draw
More informationAssessment Management
Facts Using Doubles Objective To provide opportunities for children to explore and practice doubles-plus-1 and doubles-plus-2 facts, as well as review strategies for solving other addition facts. www.everydaymathonline.com
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 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 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 informationMath 0306 Final Exam Review
Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire
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 informationReview of Basic Fraction Concepts
Review of asic Fraction Concepts Objective To review fractions as parts of a whole (ONE), fractions on number lines, and uses of fractions. www.everydaymathonline.com epresentations etoolkit lgorithms
More informationAddition of Multidigit Numbers
Addition of Multidigit Numbers Objectives To review the partial-sums algorithm used to solve multidigit addition problems; and to introduce a column-addition method similar to the traditional addition
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 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 informationOpen-Ended Problem-Solving Projections
MATHEMATICS Open-Ended Problem-Solving Projections Organized by TEKS Categories TEKSING TOWARD STAAR 2014 GRADE 7 PROJECTION MASTERS for PROBLEM-SOLVING OVERVIEW The Projection Masters for Problem-Solving
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 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 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 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 informationEveryday Mathematics. Grade 4 Grade-Level Goals CCSS EDITION. Content Strand: Number and Numeration. Program Goal Content Thread Grade-Level Goal
Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation
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 informationEveryday Mathematics CCSS EDITION CCSS EDITION. Content Strand: Number and Numeration
CCSS EDITION Overview of -6 Grade-Level Goals CCSS EDITION Content Strand: Number and Numeration Program Goal: Understand the Meanings, Uses, and Representations of Numbers Content Thread: Rote Counting
More informationNCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5
NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students
More informationEveryday Mathematics. Grade 4 Grade-Level Goals. 3rd Edition. Content Strand: Number and Numeration. Program Goal Content Thread Grade-Level Goals
Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation
More informationMultiplication and Division of Positive and Negative Numbers
Multiplication and Division of Positive Objective o develop and apply rules for multiplying and dividing positive and www.everydaymathonline.com epresentations eoolkit Algorithms Practice EM Facts Workshop
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 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 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 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 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 informationnumerical place value additional topics rounding off numbers power of numbers negative numbers addition with materials fundamentals
Math Scope & Sequence fundamentals number sense and numeration of the decimal system Count to 10 by units Associate number to numeral (1-10) KN 1 KN 1 KN 2 KN 2 Identify odd and even numbers/numerals and
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 informationKristen Kachurek. Circumference, Perimeter, and Area Grades 7-10 5 Day lesson plan. Technology and Manipulatives used:
Kristen Kachurek Circumference, Perimeter, and Area Grades 7-10 5 Day lesson plan Technology and Manipulatives used: TI-83 Plus calculator Area Form application (for TI-83 Plus calculator) Login application
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 informationEVERY DAY COUNTS CALENDAR MATH 2005 correlated to
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
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 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 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 informationAssessment Management
Weight Objectives To review grams and ounces as units of mass and weight; and to guide the estimation and measurement of weight in grams and ounces. www.everydaymathonline.com epresentations etoolkit Algorithms
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 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 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 TI-30XS MultiView two-dimensional
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 informationMATH 100 PRACTICE FINAL EXAM
MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number
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 informationCAMI Education linked to CAPS: Mathematics
- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
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 informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
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 informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
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 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 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 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 informationSandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.
Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.
More information