Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

Appendix on Implementing District Standards

This curriculum unit is aligned with the Virginia Standards of Learning. Virginia did not adopt the Common Core standards; however, the Curriculum Framework clearly states the fraction skills that our students should learn during their school career. Below I have listed relevant standards. As you can see, starting from Grade Three, students should be able to name and write down a fraction represented by a model. They should also be competent in comparing, adding, subtracting, multiplying and dividing fractions. Thus, elementary and middle school teachers will be able to use problems from my unit in their classrooms. Operations with fractions is an essential part of solving problems in Geometry, Trigonometry, Algebra and Calculus. After students master the content within my unit, they will be better prepared for upper level mathematics, biology, chemistry and physics where they have to use fractions on daily basis. In my classroom the unit will help me remediate my students who study Geometry, Math Analysis and AP Calculus.

Implementing Mathematics Standards of Learning for Virginia Public Schools

Grade Three

Number and Number Sense.

3.2 The student will

1. name and write fractions and mixed numbers represented by a model;
2. represent fractions and mixed numbers with models and symbols; and
3. compare fractions having like and unlike denominators, using words and symbols (>, <, =, or ≠), with models.

Computation and Estimation

3.5 The student will solve practical problems that involve addition and subtraction with proper fractions having like denominators of 12 or less.

Measurement and Geometry

3.7 The student will estimate and use U.S. Customary and metric units to measure

1. length to the nearest ¹⁄₂ inch, inch, foot, yard, centimeter, and meter.

Grade Four

Number and Number Sense

4.2 The student will

1. compare and order fractions and mixed numbers, with and without models;
2. represent equivalent fractions; and
3. identify the division statement that represents a fraction, with models and in context.

4.3 The student will

4. given a model, write the decimal and fraction equivalents.

4.4 The student will

2. add and subtract fractions and mixed numbers having like and unlike denominators; and
3. solve single-step practical problems involving addition and subtraction with fractions and mixed numbers.

Grade Five

Number and Number sense

5.2 The student will

1. represent and identify equivalencies among fractions and decimals, with and without models; and
2. compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least.

5.6 The student will

1. solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers; and
2. solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models.

Grade Six

Number and Number sense

6.1 The student will represent relationships between quantities using ratios, and will use appropriate notations, such as ^a⁄_b, a to b, and a:b.

6.2 The student will

1. represent and determine equivalencies among fractions, mixed numbers, decimals, and percents.

Computation and Estimation

6.5 The student will

1. multiply and divide fractions and mixed numbers;
2. solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers

Grade Seven

Computation and Estimation

7.3 The student will solve single-step and multistep practical problems, using proportional reasoning.

1. represent verbal quantitative situations algebraically; and
2. evaluate algebraic expressions for given replacement values of the variables.

Geometry

G.3 The student will solve problems involving symmetry and transformation. This will include

1. investigating and using formulas for determining distance, midpoint, and slope;
2. applying slope to verify and determine whether lines are parallel or perpendicular;

G.14 The student will apply the concepts of similarity to two- or three-dimensional geometric figures.  This will include

1. comparing ratios between lengths, perimeters, areas, and volumes of similar figures;
2. determining how changes in one or more dimensions of a figure affect area and/or volume of the figure; determining how changes in area and/or volume of a figure affect one or more dimensions of the figure.

Trigonometry

Triangular and Circular Trigonometric Functions

T.1  The student, given a point on the terminal side of an angle in standard position, or the value of the trigonometric function of the angle, will determine the sine, cosine, tangent, cotangent, secant, and cosecant of the angle.