AG rid of Curriculum Topics: Fractions by Tqurg9

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									A Grid of Curriculum Topics: Fractions


                                Strand 1:                            Strand 2:      Strand 3:     Strand 4:
                                Number                              Patterns and   Shape and    Statistics and
                                                                     Relations       Space       Probability
Grade 3    13. Demonstrate an understanding of fractions by:
           • explaining that a fraction represents a part of a
           whole
           • describing situations in which fractions are used
           • comparing fractions of the same whole that have
           like denominators.
           [C, CN, ME, R, V]
Grade 4    8. Demonstrate an understanding of fractions less
           than or equal to one by using concrete, pictorial and
           symbolic representations to:
           • name and record fractions for the parts of a whole
           or a set
           • compare and order fractions
           • model and explain that for different wholes, two
           identical fractions may not represent the same
           quantity
           • provide examples of where fractions are used.
           [C, CN, PS, R, V]

           9. Represent and describe decimals (tenths and
           hundredths), concretely, pictorially and symbolically.
           [C, CN, R, V]

           10. Relate decimals to fractions and fractions to
           decimals (to hundredths).
           [C, CN, R, V]

           11. Demonstrate an understanding of addition and
           subtraction of decimals (limited to hundredths) by:
                               Strand 1:                           Strand 2:      Strand 3:     Strand 4:
                               Number                             Patterns and   Shape and    Statistics and
                                                                   Relations       Space       Probability
          • using personal strategies to determine sums and
          differences
          • estimating sums and differences
          • using mental mathematics strategies to solve
          problems.
          [C, ME, PS, R, V]
Grade 5   7. Demonstrate an understanding of fractions by
          using concrete, pictorial and symbolic
          representations to:
          • create sets of equivalent fractions
          • compare fractions with like and unlike
          denominators.
          [C, CN, PS, R, V]

          8. Describe and represent decimals (tenths,
          hundredths, thousandths), concretely, pictorially and
          symbolically.
          [C, CN, R, V]

          9. Relate decimals to fractions and fractions to
          decimals (to thousandths).
          [CN, R, V]

          10. Compare and order decimals (to thousandths) by
          using:
          • benchmarks
          • place value
          • equivalent decimals.
          [C, CN, R, V]

          11. Demonstrate an understanding of addition and
          subtraction of decimals (limited to thousandths).
          [C, CN, PS, R, V]
Grade 6   4. Relate improper fractions to mixed numbers and
          mixed numbers to improper fractions.
          [CN, ME, R, V]
                               Strand 1:                                Strand 2:                  Strand 3:               Strand 4:
                               Number                                  Patterns and               Shape and              Statistics and
                                                                        Relations                   Space                 Probability

          5. Demonstrate an understanding of ratio, concretely,
          pictorially and symbolically.
          [C, CN, PS, R, V]

          6. Demonstrate an understanding of percent (limited
          to whole numbers), concretely, pictorially and
          symbolically.
          [C, CN, PS, R, V]

          8. Demonstrate an understanding of multiplication
          and division of decimals (1-digit whole number
          multipliers and 1-digit natural number divisors).
          [C, CN, ME, PS, R, V]
Grade 7   2. Demonstrate an understanding of the addition,          7. Model and solve,       1. Demonstrate an        4. Express
          subtraction, multiplication and division of decimals to   concretely, pictorially   understanding of         probabilities as ratios,
          solve problems (for more than 1-digit divisors or 2-      and symbolically,         circles by:              fractions and
          digit multipliers, the use of technology is expected).    problems that can be      • describing the         percents.
          [ME, PS, T]                                               represented by linear     relationships among      [C, CN, R, T, V]
          [ICT: P2–3.4]                                             equations of the form:    radius, diameter and     [ICT: P2–3.4]
                                                                    • ax + b = c              circumference
          3. Solve problems involving percents from 1% to           • ax = b                  • relating
          100%.                                                     • x/a = b, a ≠ 0          circumference to pi
          [C, CN, PS, R, T]                                         where a, b and c are      • constructing circles
          [ICT: P2–3.4]                                             whole numbers.            with a given radius or
                                                                    [CN, PS, R, V]            diameter
          4. Demonstrate an understanding of the relationship                                 • solving problems
          between positive terminating decimals and positive                                  involving the radii,
          fractions and between positive repeating decimals                                   diameters and
          and positive fractions.                                                             circumferences of
          [C, CN, R, T]                                                                       circles.
          [ICT: P2–3.4]                                                                       [C, CN, PS, R, V]

          5. Demonstrate an understanding of adding and                                       2. Develop and apply
          subtracting positive fractions and mixed numbers,                                   a formula for
          with like and unlike denominators, concretely,                                      determining the area
                               Strand 1:                               Strand 2:                  Strand 3:       Strand 4:
                               Number                                 Patterns and               Shape and      Statistics and
                                                                       Relations                   Space         Probability
          pictorially and symbolically (limited to positive sums                             of:
          and differences).                                                                  • triangles
          [C, CN, ME, PS, R, V]                                                              • parallelograms
                                                                                             • circles.
          7. Compare and order positive fractions, positive                                  [CN, PS, R, V]
          decimals (to thousandths) and whole numbers by
          using:
          • benchmarks
          • place value
          • equivalent fractions
          and/or decimals.
          [CN, R, V]
Grade 8   3. Demonstrate an understanding of percents greater      2. Model and solve
          than or equal to 0%, including greater than 100%.        problems concretely,
          [CN, PS, R, V]                                           pictorially and
                                                                   symbolically, using
          4. Demonstrate an understanding of ratio and rate.       linear equations of the
          [C, CN, V]                                               form:
                                                                   • ax = b
          5. Solve problems that involve rates, ratios and         • x/a = b, a ≠ 0
          proportional reasoning.                                  • ax + b = c
          [C, CN, PS, R]                                           • x/a + b = a ≠ 0
                                                                   • a(x + b) = c
          6. Demonstrate an understanding of multiplying and       where a, b and c are
          dividing positive fractions and mixed numbers,           integers.
          concretely, pictorially and symbolically.                [C, CN, PS, V]
          [C, CN, ME, PS]
Grade 9   3. Demonstrate an understanding of rational              3. Model and solve
          numbers by:                                              problems, using linear
          • comparing and ordering rational numbers                equations of the form:
          • solving problems that involve arithmetic operations    • ax = b
          on rational numbers.                                     • x/a = b, a ≠ 0
          [C, CN, PS, R, T, V]                                     • ax + b = c
          [ICT: P2–3.4]                                            • x/a + b = c, a ≠ 0
                                                                   • ax = b + cx
                                                                   • a(x + b) = c
                          Strand 1:                        Strand 2:                Strand 3:           Strand 4:
                          Number                          Patterns and             Shape and          Statistics and
                                                           Relations                 Space             Probability
                                                       • ax + b = cx + d
                                                       • a(bx + c) = d(ex + f)
                                                       • a/x = b, x ≠ 0
                                                       where a, b, c, d, e and f
                                                       are rational numbers.
                                                       [C, CN, PS, V]



                Math Topic                                          Specific Outcome
Math 10-C   Measurement           2. Apply proportional reasoning to problems that involve conversions between SI and
                                  imperial units of measure.
                                  [C, ME, PS]
                                  4. Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve
                                  problems that involve right triangles.
                                  [C, CN, PS, R, T, V]
            Algebra               3. Demonstrate an understanding of powers with integral and rational exponents.
                                  [C, CN, PS, R]
Math 10-3   Measurement           1. Demonstrate an understanding of the Système International (SI) by:
                                  • describing the relationships of the units for length,area, volume, capacity, mass
                                  and temperature
                                  • applying strategies to convert SI units to imperial units.
                                  [C, CN, ME, V]
                                  4. Solve problems that involve SI and imperial area measurements of regular, composite
                                  and irregular 2-D shapes and 3-D objects, including decimal and fractional
                                  measurements, and verify the solutions.
                                  [ME, PS, R, V]
            Geometry              2. Demonstrate an understanding of the Pythagorean theorem by:
                                  • identifying situations that involve right triangles
                                  • verifying the formula
                                  • applying the formula
                                  • solving problems.
                                  [C, CN, PS, V]
            Trigonometry    4. Demonstrate an understanding of primary trigonometric ratios (sine, cosine,
                            tangent) by:
                            • applying similarity to right triangles
                            • generalizing patterns from similar right triangles
                            • applying the primary trigonometric ratios
                            • solving problems.
                            [CN, PS, R, T, V]
                            [ICT: C6–4.1]
            Number          1. Solve problems that involve unit pricing and
                            currency exchange, using proportional reasoning.
                            [CN, ME, PS, R]
                            [ICT: F2–4.7]
                            2. Demonstrate an understanding of income, including:
                            • wages
                            • salary
                            • contracts
                            • commissions
                            • piecework
                            to calculate gross pay and net pay.
                            [C, CN, R, T]
                            [ICT: C6–4.1, C6–4.2, C7–4.2, F2–4.7]
Math 20-1   Trigonometry    2. Solve problems, using the three primary trigonometric ratios for angles from 0° to
                            360° in standard position.
                            [C, ME, PS, R, T,
            Relations and   4. Analyze quadratic functions of the form y = ax^2+ bx + c to identify characteristics
            Functions       of the corresponding graph, including:
                            x
                            • vertex
                            • domain and range
                            • direction of opening
                            • axis of symmetry
                            • x- and y-intercepts
                            and to solve problems.
                            [CN, PS, R, T, V]
                            [ICT: C6–4.1, C6–4.3]
                           11. Graph and analyze reciprocal functions (limited to the reciprocal of linear and
                           quadratic functions).
                           [CN, R, T, V]
                           [ICT: C6–4.1, C6–4.3]
Math 20-2   Measurement    1. Solve problems that involve the application of rates.
                           [CN, PS, R]
                           2. Solve problems that involve scale diagrams, using proportional reasoning.
                           [CN, PS, R, V]
                           3. Demonstrate an understanding of the relationships among scale factors, areas,
                           surface areas and volumes of similar 2-D shapes and 3-D objects.
                           [C, CN, PS, R, V]
Math 20-3   Algebra        1. Solve problems that require the manipulation and application of formulas related
                           to:
                           • volume and capacity
                           • surface area
                           • slope and rate of change
                           • simple interest
                           • finance charges.
                           [CN, PS, R]
                           2. Demonstrate an understanding of slope:
                           • as rise over run
                           • as rate of change
                           • by solving problems.
                           [C, CN, PS, V]
                           3. Solve problems by applying proportional reasoning and unit analysis.
                           [C, CN, PS, R]
Math 30-1   Trigonometry   2. Develop and apply the equation of the unit circle.
                           [CN, R, V]
                           6. Prove trigonometric identities, using:
                           • reciprocal identities
                           • quotient identities
                           • Pythagorean identities
                           • sum or difference identities (restricted to sine, cosine and tangent)
                           • double-angle identities (restricted to sine, cosine and tangent).
                           [R, T, V]
                                         [ICT: C6–4.1, C6–4.4]
Math 30-2     Probability                1. Interpret and assess the validity of odds and probability statements.
Math 30-3     Statistics                 2. Analyze and describe percentiles.
                                         [C, CN, PS, R]
              Probability                1. Analyze and interpret problems that involve probability.
                                         [C, CN, PS, R]



Especially in High School, almost EVERY topic will require a mastery of fractions to do well. I have included those topics
that are a little more explicit in their use of fractions, or those topics where I believe a student without a good
understanding of fractions will have difficulty, so that a teacher might consider a review of fractions.

								
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