5Th Grade Math Estimation Worksheets Scranton School by nky85654

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									                                                    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.

								
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