VIEWS: 2 PAGES: 8 POSTED ON: 9/16/2012
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.