# Mathematics Standards

## IV. Geometry

**A. Successful students understand and
use both basic plane and solid
geometry. They:**

A.1. know properties of similarity,

congruence and parallel lines

cut by a transversal.

A.2. know how to figure area and

perimeter of basic figures.

A.3. understand the ideas behind

simple geometric proofs and are

able to develop and write simple

geometric proofs (e.g., the

Pythagorean theorem; that there

are 180 degrees in a triangle;

and that the area of a triangle is

half the base times the height ).

A.4. solve problems involving

proofs through the use of

geometric constructions.

A.5. use similar triangles to find

unknown angle measurements

and lengths of sides.

A.6. visualize solids and surfaces in

three-dimensional space (e.g.,

recognize the shape of a box

based on a two-dimensional

representation of its surfaces; and

recognize the shape of a cone

based on a two-dimensional

representation of its surface).

A.7. know basic formulas for

volume and surface area for

three-dimensional objects.

**B. Successful students know analytic
(i.e., coordinate) geometry. They:**

B.1. know geometric properties of

lines (e.g., slope and midpoint

of a line segment).

B.2. know the formula for the

distance between two points .

B.3. solve mathematical and realworld

problems (e.g., ladders,

shadows and poles) that involve

the properties of special right

triangles with the Pythagorean

theorem and its converse.

B.4.* recognize geometric

translations and

transformations algebraically.

**C. Successful students understand basic
relationships between geometry and
algebra. They:**

C.1. know that geometric objects and

figures can also be described

algebraically (e.g., ax + by = c is

the standard form of a line).

C.2. know the algebra and geometry

of circles .

C.3.* know the algebra and geometry

of parabolas and ellipses as a

prerequisite to the study of

calculus.

C.4.* use trigonometry for examples

of the algebraic/geometric

relationship, including Law of

Sines /Cosines.

## V. Mathematical Reasoning

**A. Successful students know important
definitions, why definitions are
necessary and are able to use
mathematical reasoning to solve
problems. They:**

A.1. use inductive reasoning in basic

arguments.

A.2. use deductive reasoning in basic

arguments.

A.3. use geometric and visual

reasoning.

A.4. use multiple representations

(e.g., analytic, numerical and

geometric ) to solve problems.

A.5. learn to solve multi-step

problems.

A.6. use a variety of strategies to

revise solution processes.

A.7. understand the uses of both

proof and counterexample in

problem solutions and are able

to conduct simple proofs.

A.8. are familiar with the process of

abstracting mathematical

models from word problems,

geometric problems and

applications and are able to

interpret solutions in the

context of these source

problems.

**B. Successful students are able to work
with mathematical notation to solve
problems and to communicate
solutions. They:**

B.1. translate simple statements into

equations (e.g., “Bill is twice as

old as John” is expressed by the

equation b =2j).

B.2. understand the role of written

symbols in representing

mathematical ideas and the

precise use of special symbols

of mathematics.

**C. Successful students know a select list
of mathematical facts and know how
to build upon those facts (e.g.,
Pythagorean theorem; formulas for
perimeter, area, volume; and
quadratic formula).**

**D. Successful students know how to
estimate. They:**

D.1. are able to convert between

decimal approximations and

fractions .

D.2. know when to use an

estimation or approximation in

place of an exact answer.

D.3. recognize the accuracy of an

estimation.

D.4. know how to make and use

estimations.

**E. Successful students understand the
appropriate use as well as the
limitation of calculators. They:**

E.1. recognize when the results

produced are unreasonable or

represent misinformation.

E.2.* use calculators for systematic

trial-and-error problem solving.

E.3.* plot useful graphs.

**F. Successful students are able to
generalize and to go from specific to
abstract and back again. They:**

F.1. determine the mathematical

concept from the context of an

external problem, solve the

problem and interpret the

mathematical solution in the

context of the problem.

F.2. know how to use specific

instances of general facts, as well

as how to look for general results

that extend particular results.

**G. Successful students demonstrate
active participation in the process of
learning mathematics. They:**

G.1. are willing to experiment with

problems that have multiple

solution methods.

G.2. demonstrate an understanding

of the mathematical ideas

behind the steps of a solution,

as well as the solution.

G.3. show an understanding of how

to modify patterns to obtain

different results.

G.4. show an understanding of how

to modify solution strategies to

obtain different results.

G.5. recognize when a proposed

solution does not work, analyze

why and use the analysis to

seek a valid solution.

**H. Successful students recognize the
broad range of applications of
mathematical reasoning. They:**

H.1. know that mathematical

applications are used in other

fields (e.g., carbon dating,

exponential growth ,

amortization tables,

predator/prey models, periodic

motion and the interactions of

waves).

H.2. know that mathematics has

played (and continues to

play) an important role in the

evolution of disciplines as

diverse as science,

engineering, music and

philosophy.

## VI. Statistics**

**A. Successful students apply concepts of
statistics and data analysis in the
social sciences and natural sciences.
They:**

A.1. represent data in a variety of

ways (e.g., scatter plot, line

graph and two -way table) and

select the most appropriate.

A.2. understand and use statistical

summaries data (e.g., standard

deviation, range and mode).

A.3.* understand curve-fitting

techniques (e.g., median-fit line

and regression line) for various

applications (e.g., making

predictions).

** The majority of math participants

indicated that knowledge of statistics

is not necessarily a prerequisite for

success in most entry-level university

mathematics courses. However,

participants in other disciplines

identified knowledge of statistics as

important to success in some entrylevel

courses in the social sciences

(e.g., economics) and sciences (e.g.,

biology and ecology). Statistics is

being included within mathematics

for organizational convenience, but

should not be interpreted as

equivalent to the other five areas of

mathematical knowledge and skill for

university success in terms of its

importance in entry-level college

mathematics courses. Statistics

standards also appear in the natural

sciences and social sciences

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