Content Goal

The student will:

Content Knowledge and Skills:

Benchmarks

1.1 Understand and perform computations accurately

1.  Apply properties of the real number system.

i. Identify and apply properties: associative, commutative, distributive, identity, inverse, multiplicative property of negative one, reflexive, substitution, symmetric, transitive, and zero property of multiplication

ii. Analyze real number relationships based on the position of numbers on a number line (e.g., using relative magnitude, absolute value).

iii. Classify real numbers as whole, integer, rational, or irrational numbers and support the grouping

Compare and order real numbers.

2.  Understand and use positive and negative numbers, absolute value, fractions, decimals, percentages, and scientific notation, including reall world situations.

i. Use integers in reality-based situations

ii. Use and apply fractions.

iii. Use and apply decimals.

iv. Use percents to solve problems such as sales tax, commission, simple interest, discount, percent of change, total pay, time-and-a-half, sales price, mixtures, and tips.

v. Use scientific notation to express large and small numbers in the context of real science situations.

2. vi.  Manipulate problems with time and a half and overtime wages.

3. Apply properties of  exponents and logarithms.

i. Perform operations on numerical expressions containing integral and fractional exponents.

4.  Identify exact and approximate roots without simplification.

  i. Perform operations on number sentences containing radicals.

5. Solve problems using number theory concepts (factors, multiples, primes).

6.   Use appropriate vocabulary.

 See attached list

1.2. Perform

computations accurately.

1. Use the proper order of operations. Perform operations with real  numbers.

i. Use order of operations to simplify numerical expressions which include integers, rational numbers exponents, radicals, etc..

2. Use graphs, matrices, and sequences to represent and solve problems.

i. Compute compound interest from the number of compounding periods, principal, and annual interest rate.

ii. Add, subtract, and multiply matrices.

1.3. Estimate and judge reasonableness of results.

1.  Apply number sense to every day situations.

i. Determine the reasonableness solutions to computation and word problems, choosing an appropriate method.

ii. Estimate driving time to a given destination.

2.  Understand that error accumulates in a computation when there is rounding at intermediate steps.

1.4 Understand and use

a variety of problem- solving skills.

1.  Use a variety of methods, including common mathematical

formulas, to solve problems drawn from daily life.

i. Apply various methods, including common mathematical formulas, working backwards, drawing diagrams, guess and check, make a systematic list, make a model, make a table, solve a simpler problem, write an equation, use logical deduction, etc., to obtain problem solutions drawn from everyday life.

ii. Analyze a problem to determine the purpose or goal and identify the unknowns.

1.5. Use reasoning skills to recognize problems and express them mathematically.

a. Use inductive and deductive reasoning to set up a problem.

i. Write a paragraph explaining a solution to a problem.

ii.  Use logic to predict outcomes.

b. Use logic to make mathematical proofs.

  i. Solve if-then logic problems.

c.Make and evaluate logical arguments.

i. Use logic to make a mathematical proof (i.e. explain why it is not possible to divide by zero).

Content Goal-

 The student will:

Content Knowledge and Skills:

Benchmarks:

2.1. Understand and use U.S. customary and metric measurements.

1. Determine length, perimeter, circumference, area, surface area, volume, capacity, weight, time, and temperature.

2. Solve problems involving circumference, perimeter, or area of triangles, circles, and rectangles.

i. Calculate the area of a rectangle using algebra tiles.  Relate algebra tiles to area and write an algebraic expression to represent the area represented by the tiles.

ii.  Given algebraic expressions as the dimensions for 2- or 3- dimensional figures, write an expression to represent perimeter, area, volume, etc...

iii.  Calculate the length, perimeter, circumference, area, surface area, and volume of an object.

2.2 Apply the concepts of rates, ratios, and proportions.

1.  Use rates, ratios, proportions, and map scales in problem-solving situations.

i. Use proportional relationships to determine lengths of sides of a figure that are represented by algebaic relationships .

ii.  Use map scales to solve problems.

2.  Apply concepts of rates and direct and indirect measurements.

i. Solve direct and inverse variation problems

.

3. Construct equivalent units, comparable units, and conversions.

 i. Convert between units in a given measurement system.

ii.  Solve unit rate problems.

2.3. Apply dimensional analysis.

1. Understand units and their relationship to one another and to real world applications involving length, area, capacity, weight, time, temperature, and rate.

i. Check reasonableness of a calculation based on the resulting units.

ii.  Apply dimensional analysis to solve indirect measurement problems such as convert miles per hour to feet per second

2.4 Apply appropriate techniques and tools to determine measurements.

1. Determine and use appropriate units.

i. Make measurements using appropriate units.

ii. Solve distance-rate-time problems where the units have to be converted before solving.

2.5 Perform error analysis.

a. Understand tolerance, precision, and their applications.

iii. Use absolute value inequalities to determine the tolerance or acceptable variation for a given situation.

b. Understand that error accumulates in a computation when there is rounding at intermediate steps.

2.6. Understand and use

a variety of problem- solving skills.

1.  Use a variety of methods, including common mathematical

formulas, to solve problems drawn from daily life.

iii. Apply various methods, including common mathematical formulas, working backwards, drawing diagrams, guess and check, make a systematic list, make a model, make a table, solve a simpler problem, write an equation, use logical deduction, etc., to obtain problem solutions drawn from everyday life.

iv. Analyze a problem to determine the purpose or goal and identify the unknowns.