Minimum Set

In this document we have listed things students should be able to explain and tasks students should be able to perform.  True mathematical literacy includes the capacity to perform simple computations in the mind, more complex computations with traditional algorithms, and computations with large numbers or complex arithmetic with a computing device and have sense of whether or not the result is correct.  Students will be expected to give sound mathematics reasons for the decisions they make in computations and in problem solving.   The goal is to have the students think above the knowledge and skill level and be able to do higher order or critical thinking.  To accomplish this, we urge that teachers be trained in how to let students do critical thinking and not make the mistake of doing it for the students under the assumption that the students cannot do it.

The instruction should require the student to know how to do these things:

1. Use mathematics to solve “real life” problems.
2. Have a strategy to solve problems that requires the student to select data that is essential to solve the problem, have a plan of attack to find the solution to the problem, perform any necessary calculations or operations to find the solution, determine if the solution is reasonable and correct, and be requires the student to be able to justify the steps taken in the solution process.
3. Develop a way to use mathematics to express relationships by using such approaches as symbols, diagrams, graphs, mathematical language, manipulatives, technology, text, or real objects.
4. Use the skills learned in number three to justify and defend a solution to a problem.

Numbers--The student should be able to:

1. Identify a number as a whole number, integer or rational number and explain why the number fits in the specified set.
2. For any number in the selected sets, identity its opposite (additive inverse), its reciprocal (multiplicative inverse), and its absolute value.  This will include being able to explain why a number is an additive inverse or multiplicative inverse for another number.
3. Locate positions for a number or a set of numbers on the number line and be able to compare and order the numbers.
4. Be able to read numbers in their various forms and use place value names to trillions and hundred thousandths.

Operations—The student will be able to:

1. Do each of the basic number for facts for addition, subtraction, multiplication, and division with 100% accuracy in 3 minutes or less.
2. Perform addition, subtraction, multiplication, and division on integers, common fractions and mixed numbers, and decimal numbers.
3. Show that multiplication is a shortcut for addition and that division is a shortcut for multiple subtractions.
4. Recognize and use the various notations for expressing multiplication and division.
5. Show that dividing by a number or multiplying by its reciprocal will result in equivalent values. Show that subtracting a number or adding its opposite will result in equivalent values.
6. Be able to state the Order of Operations and successfully compute the result for expressions having
7. Develop number sense to recognize unreasonable answers and be able to determine if a quantity is increased or decreased when multiplied by a fraction whether proper or improper.

Proportionality—The student will be able to:

1. Define and describe ratios and percent and give equivalent forms of a number as a fraction, ratio and a percent.
2. Convert measurements from one unit to another using proportions and unit rates.
3. Use equations of the form y = ax to describe the constant of proportionality and to solve problems where two of the three values in the equation are known.
4. Use ratios and percent to show comparisons between two quantities by division...
5. Show relationships in real world problems using ratios, rates, percent, scale factors and proportions.
6. Solve real world problems to find a missing value in situations involving a percent, a ratio, a proportion, a scale factor.
7. Solve for a missing value in a proportion using the ratios as equivalent fractions and by the cross multiply approach.

Expressions, Equations, and Relationships—The student will be able to:

1. Recognize independent and dependent quantities from word descriptions, table and graphs.
2. Write an equation that represents a given situation shown using a verbal descriptions, tables, charts, and graphs.
3. Generate equivalent expressions using the order of operations, exponents, factorization, and such axioms as inverses, identities, commutative, associative, and distributive properties.
4. Write and solve one variable, one step equations and inequalities including real world circumstances and represent the solution on a number line.

Geometric Shapes and Properties:  The student will be able to:

1. State and use properties of triangles including the sum of the angles of a triangle, the relationship between lengths of sides and measures of angles, and determine when three segment lengths will for a triangle.
2. Show how area formulas for parallelograms, trapezoids, and triangles are derived and uses the formulas appropriately.
3. Write equations and solve problems related to perimeters and areas of rectangles, parallelograms, trapezoids, triangles, circles and the volumes of right rectangular prisms, cubes, pyramids, cylinders and cones using equations when the dimensions for these figures are positive rational numbers.
4. Determine if triangles are congruent, similar or neither and justify the conclusion.

Measurement and Data:  The student will be able to:

1. Graph data points on a coordinate plain in all four quadrants using ordered pairs of rational numbers.
2. Analyze and solve problems representing and interpreting data summarized in various graphical forms.
3. Summarize data with information including the mean and median, the interquartile range, relative frequency, and percent for data categories.