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									                               2011-2012 5th Grade Mathematics Pacing Guide




                                                                                                                               module and on any
                                             First Nine Weeks




                                                                                                                                module after that
                                                                                                                                 Can be on TLI

                                                                                                                                 starting at this
                                                                                                                                  Assessment
 Enduring Understanding - Successful problem solvers know how to use a variety of strategies
                          and know if their answers are reasonable.
  Essential Question - What are the specific strategies that have wide application in attacking
                         problems and can help in problem solving?
                           Solve, with and without appropriate technology , two -step problems using a variety of methods
        NO.3.5.3           and tools                                                                                                   1
                           Example: objects, mental computation, paper and pencil
                           Develop and use strategies to estimate the results of whole number computations and to judge
        NO.3.5.4                                                                                                                       1
                           the reasonableness of such results
1. Enduring Understanding - Operation strategies and mathematical properties are used to solve a
                                     variety of problems.
       1. Essential Question - How do operation strategies and number properties assist in
                                         computation?
                           Develop and use a variety of algorithms with computational fluency to perform whole number
       NO.3.5.1a           operations using addition and subtraction (up to 5 digit numbers), including real world                     1
                           problems
                           Apply rules (conventions) for order of operations to whole numbers where the left to right
        NO.2.5.4                                                                                                                       1
                           computations are modified only by the use of parentheses
        NO.2.5.2           Identify commutative and associative properties                                                             1
                           Identify the distributive property by using physical models to solve computation and real world
                           problems
        NO.2.5.3           Sample strategies may include using manipulatives or array multiplication to illustrate:                    1
                           3 x 42 = (3 x 40) + (3 x 2) = 3(40) + 3(2)
                           7 x 259 = (7 x 200) + (7 x 50) + (7 x 9) = 7(200) + 7(50) + 7(9)
                           Develop and use a variety of algorithms with computational fluency to perform whole number
       NO.3.5.1b                                                                                                                       1
                           operations using multiplication (up to 3-digit x 2 digit), including real world problems
        NO.2.5.1           Use divisibility rules to determine if a number is a factor of another number (2, 3, 5, 10)                 1
                           Develop and use a variety of algorithms with computational fluency to perform whole number
       NO.3.5.1c           operations using division (up to 2-digit divisor) interpreting remainder, including real world              1
                           problems
    2. Enduring Understanding - The base-ten place-value system extends infinitely far in two
        directions. Between any two place values, the ten-to-one ratio remains the same.
2. Essential Question - How is the ordering of decimals the same as ordering whole numbers and
                                       how is it different?
        NO.1.5.2           Develop understanding of decimal place value using models                                                   1
       NO.1.5.4a           Round decimals to a given place value: whole number , tenths, and hundredths                                1
       NO.1.5.4b           Compare decimals to a given place value: whole number , tenths, and hundredths                              1
 3. Enduring Understanding - Operations strategies with decimals are similar to those used with
                                       whole numbers.
 3. Essential Question - What strategies can be developed to show computation with decimals?
                           Model addition and subtraction of decimals
       NO.2.5.5a                                                                                                                       2
                           Sample manipulatives may include base-ten blocks, money, decimal squares, etc.
                           Model multiplication of decimals
       NO.2.5.5b                                                                                                                       2
                           Sample manipulatives may include base-ten blocks, money, decimal squares, etc.
                           Develop and use algorithms to add and subtract numbers containing decimals (up to
       NO.3.5.2a.                                                                                                                      2
                           thousandths place)
       NO.3.5.2b           Develop and use algorithms to multiply decimals (hundredths x tenths)                                       2
       NO.3.5.2c           Develop and use algorithms to divide decimals by whole number divisors                                      2


   5th Grade Mathematics                                                                                             Cabot Public Schools
   2010-2011                                                         1                                                         May, 2010
                                                                                                                             module and on any
                                   First Nine Weeks (cont.)




                                                                                                                              module after that
                                                                                                                               Can be on TLI

                                                                                                                               starting at this
                                                                                                                                Assessment
   4. Enduring Understanding - Patterns and relationships can be represented graphically,
                         numerically, symbolically, and verbally.

                     4a. Essential Question - How can a pattern be identified?
                         Solve problems by finding the next term or missing term in a pattern or function table using real
      A.4.5.1                                                                                                                        2
                         world situations
                         Model and describe quantities that change using real world situations
      A.7.5.1                                                                                                                        2
                         Example: age & height

4b. Essential Question - How are graphs, tables, and symbols used to represent relationships?

                         Interpret and write a rule for a one-operatio n function table
      A.4.5.2                                                                                                                        2
                         Example: adding 3




 5th Grade Mathematics                                                                                           Cabot Public Schools
 2010-2011                                                          2                                                      May, 2010
                                                                                                                           at this module and on
                                                                                                                           any module after that
                                                                                                                           Assessment starting
                                        Second Nine Weeks




                                                                                                                               Can be on TLI
Enduring Understanding - Successful problem solvers know how to use a variety of strategies
                        and know if their answers are reasonable.
  Essential Question - What are the specific strategies that have wide application in attacking
                         problems and can help in problem solving?
                          Solve, with and without appropriate technology , two -step problems using a variety of methods
       NO.3.5.3           and tools                                                                                                 1
                          Example: objects, mental computation, paper and pencil
                          Develop and use strategies to estimate the results of whole number computations and to judge
       NO.3.5.4                                                                                                                     1
                          the reasonableness of such results
5. Enduring Understanding - Algebraic representations represent quantities and can be used to
                                 solve real world problems.
5. Essential Question - How do mathematical rules and algebraic representations help you solve
                                    real world problems?
                          Model and solve simple equations by informal methods using manipulatives and appropriate
       A.5.5.1                                                                                                                      3
                          technology
                          Write expressions containing one variable (a letter representing an unknown quantity) using
       A.5.5.2                                                                                                                      3
                          rules for addition and subtraction
       A.5.5.3a           Select and write algebraic expressions with one variable by substitution.                                 3
                          Evaluate algebraic expressions with one variable by substitution
       A.5.5.3b                                                                                                                     3
                          Example: evaluate x + 4 if x=7
6. Enduring Understanding - Fractions, decimals, and percents express a relationship between
                                        two numbers.
   6a. Essential Question - What relationships are represented with fractions, decimals, and
                                           percents?
                          Use models and visual representations to develop the concepts of the following:
                          Fractions:
      NO.1.5.1a                                                                                                                     4
                          • parts of unit wholes
                          • parts of a collection
                          Use models and visual representations to develop the concepts of the following:
                          Fractions:
      NO.1.5.1b           • locations on number lines                                                                               4
                          • locations on ruler (benchmark fractions )
                          Example: benchmark fractions such as 1/4, 1/2, and 3/4 for location and estimation purposes
                          Use models and visual representations to develop the concepts of the following:
                          Fractions:
      NO.1.5.1c                                                                                                                     4
                          • divisions of whole numbers
                          Example: 8/20 is the same as 8÷20
      NO.3.5.5b           Use factors of numbers to find common factors of two numbers                                              4
      NO.3.5.5c           Use factors of numbers to simplify fractions to the lowest terms                                          4

                          Use models of benchmark fractions and their equivalent forms to analyze the size of fractions
      NO.1.5.5a                                                                                                                     4
                          Example: Benchmark fractions are 1/4, 1/2, and 3/4.

                          Use models of benchmark fractions and their equivalent forms to determine that simplification
      NO.1.5.5b           does not change the value of the fraction                                                                 4
                          Example: Benchmark fractions are 1/4, 1/2, and 3/4.
                          Use models of benchmark fractions and their equivalent forms to convert between mixed
      NO.1.5.5c           numbers and improper fractions                                                                            4
                          Example: Benchmark fractions are 1/4, 1/2, and 3/4.
                          Use models and visual representations to develop the concepts of the following:
                          Ratios:
      NO.1.5.1d                                                                                                                     4
                          • part-to-part (2 boys to 3 girls)
                          • part-to-whole (2 boys to 5 people)
                          Use models and visual representations to develop the concepts of the following:
      NO.1.5.1e           Percents:                                                                                                 4
                          • part-to-100
  5th Grade Mathematics                                                                                        Cabot Public Schools
  2010-2011                                                       3                                                      May, 2010
                                                                                                                             module and on any
                                                                                                                              module after that
                                Second Nine Weeks (cont.)




                                                                                                                               Can be on TLI

                                                                                                                               starting at this
                                                                                                                                Assessment
6. Enduring Understanding - Fractions, decimals, and percents express a relationship between
                                    two numbers. (cont.)
 6b. Essential Question - How are equivalent fractions, decimals, and percents determined?
                         Identify decimal and percent equivalent s for benchmark fractions
      NO.1.5.3                                                                                                                       4
                         Example: Benchmark fractions are 1/4, 1/2, and 3/4.
7. Enduring Understanding - Operation strategies with fractions are similar to those used with
                                      whole numbers.

7. Essential Question - What strategies can be developed to show computation with fractions?
                         Model addition and subtraction of fractions with like and unlike denominators
     NO.2.5.5c           Sample manipulatives may include fraction models, pattern blocks, number cubes, egg cartons,                4
                         Cuisenaire Rods, etc.
     NO.3.5.2d           Develop and use algorithms to add and subtract fractions with like denominators                             4
                         Model multiplication of fractions with like and unlike denominators
     NO.2.5.5d           Sample manipulatives may include fraction models, pattern blocks, number cubes, egg cartons,                4
                         Cuisenaire Rods, etc.
  8. Enduring Understanding - Locations and distances can be shown on a coordinate grid.

  8. Essential Question - How can you show locations and distances on a coordinate grid?
                         Use geometric vocabulary (horizontal/x-axis, vertical/ y-axis, ordered pairs ) to describe the
      G.10.5.1                                                                                                                       4
                         location and plot points in Quadrant I
                         Count the distance between two points on a horizontal or vertical line and compare the lengths of
      M.13.5.5           the paths on a grid                                                                                         4
                         Example: shortest path, paths of equal length, etc.




 5th Grade Mathematics                                                                                             Cabot Public Schools
 2010-2011                                                         4                                                         May, 2010
                                                                                                                              this module and on any
                                                                                                                              Assessment starting at
                                           Third Nine Weeks




                                                                                                                                  module after that
                                                                                                                                   Can be on TLI
 Enduring Understanding - Successful problem solvers know how to use a variety of strategies
                         and know if their answers are reasonable.

  Essential Question - What are the specific strategies that have wide application in attacking
                         problems and can help in problem solving?
                          Solve, with and without appropriate technology , two -step problems using a variety of methods
       NO.3.5.3           and tools                                                                                                    1
                          Example: objects, mental computation, paper and pencil
                          Develop and use strategies to estimate the results of whole number computations and to judge
       NO.3.5.4                                                                                                                        1
                          the reasonableness of such results
9. Enduring Understanding - Selection and use of standard measurement tools and units depends
                                   on the real world situation.

 9a. Essential Question - How are specific tools and units used to measure different attributes?
                          Identify and select appropriate units and tools to measure
       M.12.5.1                                                                                                                        5
                          Example: angles with degrees, distance with feet
                          Determine which unit of measure or measurement tool matches the context for a problem
       M.13.5.2                                                                                                                        5
                          situation
      M.13.5.3a           Draw and measure distance to the nearest cm accurately                                                       5
      M.13.5.3b           Draw and measure distance to the nearest ¼ inch accurately                                                   5
                          Solve real world problems involving one elapsed time , counting forward
       M.13.5.1                                                                                                                        5
                          Example: calendar and clock

             9b. Essential Question - How are problems involving perimeter solved?
      M.13.5.4a           Develop and use strategies to solve real world problems involving perimeter of rectangles                    5

         9c. Essential Question - How do different units of measure relate to each other?
                          Make conversions within the customary measurement system in real world problems
       M.12.5.2                                                                                                                        5
                          Example: hours to minutes, feet to inches, quarts to gallons, etc.
       M.12.5.3           Establish through experience benchmark prefixes of mili-, centi-, and kilo-                                  5

                    10. Enduring Understanding - Powers and roots are related.

 10a. Essential Question - How are powers and roots related to each other and to measurement?
                          Use factors of numbers to introduce exponents
      NO.3.5.5a                                                                                                                        5
                          Example: 36= 6 x 6 or 6²
       NO.1.5.6           Use models to differentiate between perfect squares up to 100 and other numbers                              5
      M.13.5.4b           Develop and use strategies to solve real world problems involving area of rectangles                         5

    10b. Essential Question - What is the relationship between perimeter, area, and volume?

      M.12.5.4a           Understand when to use linear units to describe perimeter , in real world situations                         5

      M.12.5.4b           Understand when to use square units to describe area or surface area , in real world situations              5

      M.12.5.4c           Understand when to use cubic units to describe volume , in real world situations                             5
                          Model the differences between covering the faces (surface area /nets ) and filling the interior
       M.12.5.5                                                                                                                        5
                          (volume of cubes )

11. Enduring Understanding - Geometric relationships exist between two- dimensional and three-
                                    dimensional figures.

   11. Essential Question - How are two- dimensional and three- dimensional figures related?
       G.11.5.1           Using grid paper, draw and identify two-dimensional patterns (nets) for cubes                                6




  5th Grade Mathematics                                                                                           Cabot Public Schools
  2010-2011                                                        5                                                        May, 2010
                                                                                                                                     module and on any
                                                                                                                                      module after that
                                  Third Nine Weeks (cont.)




                                                                                                                                       Can be on TLI

                                                                                                                                       starting at this
                                                                                                                                        Assessment
12. Enduring Understanding - Geometric figures can change position and maintain the same
                             attributes on a coordinate plane.
12. Essential Question - How does the movement of a geometric figure affect its attributes?
     G.8.5.4            Model and identify the properties of congruent figures                                                               6
                        Predict and describe the results of translation (slide), reflection (flip), rotation (turn) , showing that
     G.9.5.1                                                                                                                                 6
                        the transformed shape remains unchanged

 13. Enduring Understanding - Points, lines, and planes are the foundations of geometry.
      13a. Essential Question - How are properties used to classify geometric figures?
     G.8.5.1            Identify and model regular and irregular polygons including decagon                                                  6
                        Identify and draw congruent and adjacent angles
     G.8.5.2a                                                                                                                                6
                        Label parts of an angle: vertex, rays, interior and exterior
                        Identify and draw obtuse, acute, right and straight angles
     G.8.5.2b                                                                                                                                6
                        Label parts of an angle: vertex, rays, interior and exterior
     G.8.5.3            Model and identify circle, radius, diameter, center, circumference, and chord                                        6

                        13b. Essential Question - How are angles measured?
                        Use benchmark angles to estimate the measure of angles
     M.13.5.6                                                                                                                                6
                        Example: Benchmark angles are 45 degrees, 90 degrees, 120 degrees, 180 degrees.




5th Grade Mathematics                                                                                                  Cabot Public Schools
2010-2011                                                           6                                                            May, 2010
                                                                                                                             this module and on any
                                                                                                                             Assessment starting at
                                           Fourth Nine Weeks




                                                                                                                                 module after that
                                                                                                                                  Can be on TLI
 Enduring Understanding - Successful problem solvers know how to use a variety of strategies
                         and know if their answers are reasonable.
  Essential Question - What are the specific strategies that have wide application in attacking
                         problems and can help in problem solving?
                           Solve, with and without appropriate technology , two -step problems using a variety of methods
        NO.3.5.3           and tools                                                                                                       1
                           Example: objects, mental computation, paper and pencil
                           Develop and use strategies to estimate the results of whole number computations and to judge
        NO.3.5.4                                                                                                                           1
                           the reasonableness of such results

     14. Enduring Understanding - Choices in data collection and representation affect their
                                   interpretation and use.
          14. Essential Question - What data display is appropriate for a given set of data?
       DAP.14.5.1          Develop appropriate questions for surveys
                           Collect numerical and categorical data using surveys, observations and experiments that would
       DAP.14.5.2
                           result in bar graphs, line graphs, line plots, and stem-and-leaf plots
      DAP.14.5.3a          Construct and interpret frequency tables , charts, line plots and bar graphs
      DAP 14.5.3b          Construct and interpret stem-and-leaf plots
      DAP.15.5.1a          Interpret line graphs
      DAP.15.5.1b          Interpret double bar graphs




                                                                                                                                     Taught after the last TLI assessment
      DAP.15.5.1c          Interpret circle graphs
       DAP.16.5.1          Make predictions and justify conclusions based on data
                           Draw conclusions and make predictions, with and without appropriate technology , from models,
         A.6.5.1
                           tables, and line graphs

15. Enduring Understanding - Statistical measures provide a numeric picture of the shape of data.
15. Essential Question - How can the mean, median, mode, and range be used to describe a set of
                                            data?
                           Determine, with and without appropriate technology , the range, median and mode (whole
      DAP.15.5.2a
                           number data sets) and explain what each indicates about the set of data
                           Determine, with and without appropriate technology , the mean (whole number data sets) and
      DAP.15.5.2b
                           explain what it indicates about the set of data
 16. Enduring Understanding - The expected outcome of an event is a prediction of what might
                               actually happen in the long run.
      16. Essential Question - How is the probability of an event determined and described?
       DAP.17.5.1          Identify and predict the probability of events within a simple experiment
       DAP.17.5.2          List and explain all possible outcomes in a given situation


       Sixth grade teachers have asked fifth grade teachers to review at the end of the year divisibility rules
   (NO.2.5.1 and NO.2.6.1) and factorization (NO.3.5.5 and NO.3.6.5), so they will be less likely to regress over the
                       summer and be ready to start the new year being successful in math.




  5th Grade Mathematics                                                                                          Cabot Public Schools
  2010-2011                                                         7                                                      May, 2010

								
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