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5Th Grade Math Estimation Worksheets document sample
Scranton School District Planned Course Mathematics Unit: 5th Grade Standards Skills/Knowledge Suggested Activities Assessment 2.1 Numbers, Number A. Use expanded notation to 1. Identify and write the place value for Ø Formal assessment and Systems and Number represent whole numbers or each digit in a whole number up to teacher observations Relationships decimals. hundred millions. 2. Write decimals in expanded form using whole numbers, tenths, and hundredths. 3. Place value charts, base ten blocks. 1. Use commutative property, associative B. Apply number theory property and distributive property to Ø Formal assessment and concepts to rename a rename number quantities. on-going teacher number quantity. (e.g. six, 6, 12 observations 3 , 2 x 2, 10 – 4). 2. Worksheets, applicable Practice Book pages (Math Advantage, Harcourt Brace) daily assignments. 1. Solve a variety of story problems using C. Demonstrate that the four operation of Mathematics. Ø On-going teacher mathematical operations can observation and represent a variety of 2. E-Lab Software. assessment problem situations. Standards Skills/Knowledge Suggested Activities Assessment 2.1 Numbers, Number D. Use models to represent 1. Use fraction circles, base ten Ø Teacher observation of Systems and Number fractions and decimals. blocks, decimal number line, and classroom activities Relationships – Con’t. decimal squares to represent involving the use of fractions and decimals (up to manipulatives thousandths). Ø Formal assessment E. Explain the concepts of 1. List the prime numbers to 100. and classroom prime composite numbers. Identify whole numbers as prime or observation composite. 2. Explain in writing the difference between prime and composite numbers. 3. Sieve of Eratosthenes, square tiles F. Use simple concepts of Ø Teacher observation of 1. Use manipulatives such as number negative numbers (e.g., on a classroom activities lines or thermometers to represent number line, in counting, in involving the use of negative numbers. temperature). manipulatives G. Develop and apply number Ø Classroom activities 1. Factor numbers up to 100 using theory concepts (e.g., and formal assessment rules for divisibility by 2, 3, 5, 6, and primes, factors, multiples, 10. composites) to represent numbers in various ways. 2. Use prime factors to find the greatest common factor of two numbers to 50. 3. Use prime factors to find the least common multiple of two numbers up to 50. Standards Skills/Knowledge Suggested Activities Assessment 2.2 Computation and A. Create and solve word problems 1. Story problems Ø Teacher observation and Estimation involving addition, subtraction, 2. Practice book and Mixed formal assessment multiplication and division of whole Applications (Math Advantage, numbers. Harcourt Brace). 3. Student created word problems B. Develop and apply algorithms to 1. Practice book and mixed Ø Teacher observation and solve word problems that involve applications (Math Advantage, formal assessment addition, subtraction, and/or Harcourt Brace). multiplication with decimals with and without regrouping. 2. Student created word problems C. Develop and apply algorithms to Ø Teacher observation and 1. Practice book and mixed solve word problems that involve formal assessment applications (Math Advantage, addition, subtraction, and/or Harcourt Brace). multiplication with fractions and mixed numbers that include like 2. Student created word problems and unlike denominators. 3. Fraction Fireworks software D. Demonstrate the ability to round Ø Teacher observation and 1. Round whole numbers up to the formal assessment numbers. nearest million place and decimals to the nearest tenth, hundredth and thousandth. 2. Classroom place value chart Standards Skills/Knowledge Suggested Activities Assessment 2.2 Computation and E. Determine through estimations 1. Estimate by rounding or use of Ø Teacher observation and Estimation – Con’t. the reasonableness of answers compatible numbers to formal assessment to problems involving addition, determine the reasonableness subtraction, multiplication and of answers in problem solving. division of whole numbers. F. Demonstrate skills for using 1. Fraction calculator Ø Teacher observation and fraction calculators to verify formal assessment conjectures, confirm computations and explore complex problem-solving situations. G. Apply estimation strategies to a 1. Teacher made activities, Ø Teacher observation and variety of problems including workbook pages (Math formal assessment time and money. Advantage, Harcourt Brace). H. Explain multiplication and Ø Teacher observation and 1. Oral and written explanations of division algorithms. formal assessment the involved algorithm. I. Select a method for computation 1. Select paper and pencil, mental Ø Teacher observation and and explain why it is appropriate. formal assessment Math or a calculator to solve a variety of problems and explain the appropriateness of using the selected method. Standards Skills/Knowledge Suggested Activities Assessment 2.3 Measurement and A. Select and use appropriate 1. Metric and English rulers, balance Ø Teacher observation Estimation instruments and units for scales, digital and analog clocks, and formal assessment measuring quantities (e.g., and Fahrenheit and Celsius perimeter, volume, area, weight, thermometers, grid paper and grid time, temperature). transparencies. Ø Teacher observation B. Select and use standard tools to 1. Metric and English rulers, trundle and formal assessment measure the size of figures with wheel, one inch grid paper and one specified accuracy, including centimeter grid paper. length, width, perimeter and area. Ø Teacher observation C. Estimate, refine and verify and formal assessment specified measurements of 1. Metric and English rulers, capacity objects. containers and scales. Ø Teacher observation D. Convert linear measurements and formal assessment within the same system. 1. Metric and English rulers, capacity containers and scales, conversion charts. Ø Teacher observation E. Add and subtract measurements and formal assessment 1. Add and subtract measurements with and without renaming. Standards Skills/Knowledge Suggested Activities Assessment 2.4 Mathematical A. Compare quantities and 1. Less than, greater than and equal to Ø Teacher observation Reasoning and magnitudes of numbers. equations. and formal assessment Connections B. Use models, number facts, 1. Analyze a problem to see how parts Ø Teacher observation properties and relationships to logically relate to each other. and formal assessment check and verify predictions 2. Use synthesis by applying inductive and explain reasoning. reasoning to the facts presented in a problem. Ø Teacher observation C. Draw inductive and deductive and formal assessment conclusions within 1. Draw inductive conclusions within mathematical contexts. mathematical contexts. 2. Draw deductive conclusions within mathematical contexts. 3. Identify relevant and irrelevant information in a word problem. Ø Teacher observation and formal assessment D. Distinguish between relevant and irrelevant information in a 1. Problem solving – Think Along mathematical problem. worksheets (Series Resource Ø Teacher observation book) and formal assessment E. Interpret statements made with precise language of logic (e.g., 1. Solve word problems using key “all”, “or”, “every”, “none”, words “or”, “and”, “but”, etc. Ø Teacher observation “some”, or “many”). and formal assessment F. Use statistics to quantify issues (e.g., in social studies, 1. Cross-curricular activities from the in science). Math Advantage series teacher’s edition. Standards Skills/Knowledge Suggested Activities Assessment 2.5 Mathematical A. Develop a plan to analyze a 1. Demonstrate an understanding of the Ø Formal and informal Problem Solving and problem, identify the information problem. (Retell the problem, list the assessments and Communication needed to solve the problem, pertinent information). teacher observation carry out the plan, check 2. Develop a plan to solve the problem. whether an answer makes (List strategies, predict the answer, sense and explain how the and make an estimate). problem was solved. 3. Solve the problem. Show the solution and write the answer in a complete sentence. 4. Look back and check the answer for accuracy. Explain the steps involved. B. Use appropriate mathematical 1. Same as above. Ø Formal and informal terms, vocabulary, language assessments and symbols and graphs to explain 2. Explain solutions orally and in writing. teacher observation clear and logical solutions to problems. 1. Student created models (drawings, C. Show ideas in a variety of ways, charts, graphs, tables, etc.) to including words, numbers, represent concepts, equations and Ø Formal and informal symbols, diagrams and models. solutions to a variety of math problems. assessments and teacher observation Standards Skills/Knowledge Suggested Activities Assessment 2.6 Mathematical D. Connect, extend and Ø Formal and informal Problem Solving and generalize problem solutions assessments and teacher Communication – to other concepts, problems observation Con’t. and circumstances in mathematics. E. Select, use and justify the methods, materials and 1. Orally explain the reasons for Ø Teacher observation strategies used to solve using specific methods. problems. F. Use appropriate problem- solving strategies (e.g., 1. Given a variety of problems Ø Formal and informal solving a simpler problem, the student will select the assessments and teacher drawing a picture or appropriate strategy and observation diagram). apply that strategy to find the correct solution. Standards Skills/Knowledge Suggested Activities Assessment 2.6 Statistics and Data A. Organize and display data 1. Students will construct charts, line Ø Teacher observation and Analysis using pictures, tallies, graphs, bar graphs and line plots informal assessment tables, charts, bar graphs to describe data. and circle graphs. Ø Formal and informal B. Describe data sets using 1. Given a set of data, the student assessments and mean, median, mode and will supply its mean, median, teacher observation range. mode and range. C. Sort data using Venn 1. Using Venn diagrams, students diagrams. will compare and contrast data. Ø Classroom observation D. Predict the likely number of 1. Number cubes, coins, tree and formal assessment times a condition will occur diagrams, spinners and dice will based on analyzed data. be used to predict probability. E. Construct and defend simple conclusions based on data. F. G. Select and use appropriate Ø Open ended question/ strategies, including 1. Distributive property answer rubric concrete materials, to solve number sentences and 2. Base ten block activity explain the method of solution. 3. Graph paper modeling Standards Skills/Knowledge Suggested Activities Assessment 2.6 Statistics and Data H. Locate and identify points 1. Plant Growth activity, p. 163, Ø Interpreting data on a Analysis – Con’t. on a coordinate system. Principles and Standards graph coordinate grid paper. I. Generate functions from 1. Plant Growth activity, p. 163, Ø Open ended question/ tables of data and relate Principles and Standards, Table answer rubric data to corresponding of Date and Coordinate Grid graphs and functions. Interpretation. Ø Formal assessment Standards Skills/Knowledge Suggested Activities Assessment 2.7 Probability and A. Perform simulations with 1. Coin Toss Activity E62, Harcourt Ø Teacher observation Predictions concrete devices (e.g., Enrichment dice, spinners) to predict Ø Assessment worksheet the chance of an event 2. Dice Activity E63, Harcourt occurring. Enrichment B. Determine the fairness of 1. The probability = Ø Formal assessment the design of the spinner. Number of selections Total number of selections 2. Write each probability as a fraction a/b. C. Express probabilities as 1. Math explorer calculator activities Ø Cooperative group fractions and decimals. using F~D function key. activity Ø Teacher observation 1. Computer software, Number D. Compare predictions Heroes, Probability, Harcourt Ø Teacher Observation based on theoretical probability and experimental results. 1. Enrichment Activity, E64, E65, E. Calculate the probability of Harcourt Ø Formal assessment a simple event. Standards Skills/Knowledge Suggested Activities Assessment 2.7 Probability and F. Determine patterns generated 1. Students create and interpret a Ø Teacher observation Predictions – Con’t. as a result of an experiment. table in which they organize data from an experiment. Ø Worksheet activity G. Determine the probability of an 1. Define terms Ø Worksheet activity event involving “and”, “or”, or “not”. 2. Write sentences using “and”, “or”, and “not” based on student spinner simulation activity. H. Predict and determine why 1. Math journals – define terms and Ø Word search or some outcomes are certain, give examples of each term. crossword puzzle, more likely, less likely puzzlemaker.com equally likely or impossible. 2. Enrichment activity, E66, Harcourt Ø Worksheet activity I. Find all possible combinations 1. Students make an organized list of Ø Teacher observation of and arrangements involving a data (all possible outcomes). students in cooperative limited number of variables. groups J. Develop a tree diagram and list elements. 1. Math journals – define term and Ø Student activity draw illustration. Ø Teacher formal 2. Students develop problems assessment involving multiple combinations and illustrate as a tree diagram. 3. Students list outcomes. Standards Skills/Knowledge Suggested Activities Assessment 2.8 Algebra and Functions A. Recognize, reproduce, 1. Express “growing squares” as Ø Teacher observation extend, create, and describe mathematical sentences. p151, patterns, sequences and Principles and Standards Ø Dot paper sheet relationships verbally, numerically, symbolically, and graphically, using a variety of materials. B. Connect patterns to 1. Use “growing squares” model to Ø Graph paper activity geometric relations and basic predicate area. Extend the number skills. pattern. C. Form rules based on patterns 1. Number patterns – find the next Ø Activity sheet (e.g. an equation that relates three terms. Write the rule. E49, pairs in a sequence). Harcourt Ø Cooperative team activity D. Use concrete objects and combinations of symbols and 1. Rectangular multiplication, base Ø Base ten block activity numbers to create ten blocks. p161, Principles and expressions that model Standards Ø Cooperative team mathematical situations. activity 2. Commutative Property Practice Ø Teacher observation 3. Distributive Property Practice Standards Skills/Knowledge Suggested Activities Assessment 2.8 Algebra and Functions – E. Explain the use of 1. Surface Area Activity p.p.160- Ø Teacher observation Con’t. combinations of symbols 162 Tower of Cubes Principles and numbers in and Standards S = 4 x n + 2 Ø Cooperative team activity expressions, equations and inequalities. Ø Modeling Ø Open-ended question/ 1. Plant Growth Activity p.163, F. Describe realistic situation answer rubric. Samples Principles and Standards using information given in in Performance equations, inequalities, Assessment tables or graphs. Standards Skills/Knowledge Suggested Activities Assessment 2.9 Geometry A. Give formal definition of 1. Glossary Ø Vocabulary word search geometry. 2. Journal Ø Crossword puzzle B. Classify and compare 1. Triangle Land Activity Ø Activity sheets triangles and quadrilaterals 2. Measure Me Activity (E138, Ø Teacher observation according to sides or angles. E139) Harcourt Brace C. Identify and measure circles, 1. Pattern Block activity, Non- Ø Teacher observation their diameters and their radii. standard unit of measure to find Ø Activity sheet patterns in angle, sums of polygons. (tan pattern blocks) D. Describe in words how geometric shapes are 1. Number Heroes Geocomputer Ø Rubric performance constructed. Nest of geometric shapes to be assessment constructed by students. Students describe in written form step by step instructions for shape construction. Harcourt Brace Software 2. Journal E. Construct two and three dimensional shapes and 1. Geocomputer Activities, Harcourt Ø Teacher observation figures using manipulatives, Brace Software geoboards and computer 2. Geoboard and Dot Paper software. Activities. 3. Pattern Block Modeling Standards Skills/Knowledge Suggested Activities Assessment 2.9 Geometry – Con’t. F. Find familiar solids in the 1. Writing activity Ø Rubric environment and describe 2. Glossary them. 3. Journal G. Create an original tessellation. 1. Pattern block activity Ø Teacher observation H. Describe the relationship 1. Discovering area with tangrams. Ø Teacher observation between the perimeter and (Use smallest triangles to area of triangles, quadrilaterals construct squares and and circles. parallelograms). 2. Explore area and perimeter geoboard activities. Mathematics Methods for Elementary and Middle School Teachers 4/e p. 129. Hatfield/Edwards/Bitter/Morrow 3. Journals I. Represent and use concepts of 1. E133, What’s the Point Harcourt Ø Activity sheet line, point and plane. Ø Word search 2. Journals 3. Glossary Ø Crossword puzzle Standards Skills/Knowledge Suggested Activities Assessment 2.9 Geometry – Con’t. J. Define the basic properties of 1. Geocomputer Harcourt software Ø Formal assessment squares, pyramids, 2. Geoboard activities Ø Student/Teacher parallelograms, trapezoids, interview polygons, rectangles, rhombi, 3. Journals – correctly draw and circles, triangles, cubes, prisms, describe spheres and cylinders. 4. Glossary 5. Polygons in Circles Activity, Cuisenaire, Start with Manipulatives. K. Analyze simple transformations Ø Activity sheets 1. How Did I Get Here? Activity, E142, of geometric figures and Harcourt. rotations of line segments. 2. Number Heroes, Geocomputer Software, Harcourt 3. E-Lab Activity 24, Harcourt software. L. Identify properties of geometric Ø Identify geometric 1. Pattern Building Game, Start with figures (e.g., parallel, figures and write a Manipulatives, Cuisenaire perpendicular, similar, congruent definition for each and symmetrical). figure. Standards Skills/Knowledge Suggested Activities Assessment 2.10Trigonometry A. Identify and compare parts of 1. Geoboard Activities, Ø Teacher observation right triangles, including right Pythagorean theorem 2 2 2 angles, acute angles, a +b =c Ø Modeling by student hypotenuses and legs. 2. Make the smallest right triangle Ø Math journal possible. Find the area. A = ½ b x h Construct a square on each side of the triangle. Find the area of each square. A = length x width. What is the relationship between these areas? 1. Geoboard Activity B. Create right triangles on a Ø Identify right triangle geoboard. Standards Skills/Knowledge Suggested Activities Assessment 2.11Concepts of A. Make comparisons of 1. Practice writing sentences comparing Ø Teacher observation Calculus numbers (e.g., more, less, data with the > and <. Ø Dot paper sheet same, least, most, greater than, less than). Ø Graph paper activity B. Identify least and greatest 1. Students write sentences with < and > values represented in bar and comparing least and greatest values on circle graphs. bar graphs and circle graphs. Ø Activity sheet C. Identify maximum and 1. Plot the maximum and minimum values on minimum. a graph. Ø Cooperative team act Ø Base ten block activity D. Describe the relationship 1. Line graph activity; Plot the attendance for between rates of change and 6 months at a baseball stadium. Create a Ø Cooperative team activity time. table displaying the data. Ø Teacher observation Ø Teacher observation E. Estimate areas and volumes 1. Patterns with cubes. Ø Cooperative team as the sums of areas of tiles 2. Share and Share Alike, E77, Harcourt Ø Modeling and volumes of cubes. F. Describe the relationship Ø Open-ended between the size of the unit of 1. Color tiles activity, Students explore and question/answer rubric. measurement and the analyze A = L x W. Samples in Performance estimate of the areas and 2. Students explore and discover V Assessment volumes. = L x W x H. 3. Compare square units and cubic units 4. Estimation skills Tasks 5. Compare cm with cm . Make predictions of areas and volumes of models.