MSAD #55
Mathematics
Benchmarks/Performance
Indicators (adapted)
Math
Skills
6/01/04
Number
Sense
A. Students
will understand and demonstrate a sense of what numbers mean and how they are
used. Students will be able to:
1. Use
numbers in a variety of equivalent and interchangeable forms such as integers,
fractions, decimals and percent, exponential, and scientific notation.
q
a. demonstrate application of integers
(thermometer).
q
b. find a positive power of a whole
number.
q
c.
write a whole number in scientific
number and vice versa (i.e. 323x3.23 x 10 squared)
2. Demonstrate
understanding of the relationships among the basic arithmetic operations on
different types of numbers.
q
a. demonstrate the order of operations
with the four basic operations and a single set of parenthesis.
3. Apply
concept of ratio/proportions, percents, and number theory (e.g. primes,
factors, and multiples) in practical and other mathematical situation.
q
a. understand the concept of ratio.
q
b. express relationships as ratios.
q
c. explain percentages that contain
fractions or decimals.
q
d. apply the concept of factors and
multiples to variable expressions.
q
e. apply factors and multiples of
whole numbers to operations with fractions.
4. Represent
numerical relationships in tables, charts, and graphs.
q
a. interpret multiple line graphs, bar
graphs, pie graphs from collected data
Computation
B. Students
will understand and demonstrate computation skills. Students will be able to:
1. Compute
and model all four operations with whole numbers, fractions, decimals, sets of
numbers and percents, applying the proper order of operations.
q
a. add, subtract, multiply, and divide
fractions and decimals including decimal divisor of 2 non-zero digits.
q
b. demonstrate application of
integers.
q
c. use multiple ways to find the
percentage of a number.
q
d. multiply mixed numbers.
q
e. divide mixed numbers.
q
f. add, subtract, divide, and
multiply positive and negative numbers
g. convert fractions to decimals.
q
h. convert fractions to percentages.
2. Create,
solve, and justify multi-step real life problems with the four basic
operations, including those with percentage, ratio, and proportion.
q
a. solve and justify multi-step real
life problems with percent of a number.
Data
Analysis and Statistics
C. Students
will understand and apply concepts of data analysis. Students will be able to:
1. Organize
and analyze data using mean, median, mode, and range.
q
a. organize, analyze, compute, mean,
median, mode, and range containing integers and fractions using appropriate
technology.
2. Assemble
data and use matrices to formulate and solve problems.
a. create and interpret multiple line graphs and
bar graphs.
3. Construct
inferences and convincing arguments based on data.
q
a. use tables and graphs to develop
ideas, construct inferences and create convincing arguments using multiple sets
of data (whole numbers and decimals, fractions).
Probability
D. Students
will understand and apply concepts of probability. Students will be able to:
1. Find
the probability of simple events and make predictions by applying the theories
of probability.
q
a. find probability of simple events.
2. Explain
that probabilities are represented as fractions between zero (no chance) and
one (always occurring.)
q
a. explain probability as a fraction
with given data, i.e., marbles 1 - green, 3 - blue.
3. Use
simulations to estimate probabilities.
q
a. estimate the number of ...(i.e.,
4x4 posts needed to build a fence 48Õx24Õ).
4. Find
all possible combinations and arrangements involving a limited number of
variables.
q
a. find all possible combinations or
arrangements for up to 3 variables.
Geometry
E. Students
will understand and apply concepts from geometry.
1. Compare
and classify and draw two and three dimensional shapes and figures using
applicable properties.
q
a. identify spaces: parallel,
perpendicular planes.
q
b. identify characteristics of basic
polyhedral (3-d - cubes, spheres)
q
c. use rotational symmetry to describe
geometric figures.
q
d. can classify angles of 3-d figures.
2. Apply geometric properties
to represent and solve real-life problems involving regular and irregular
shapes.
3. Use a
coordinate system to define and locate position.
q
a. use coordinate system to define and
locate a position in first quadrant.
4. Uses
appropriate tools to draw constructions.
q
a. use compass, straightedge and
protractor to construct and
measure circles, triangles, and
other polygons.
.
Measurement
F. Students will understand
and demonstrate measurement skills.
Students will:
1. Demonstrate the
structure and use of systems of measurement
2. Develop
and use concepts that can be measured directly and indirectly (rate).
q
a. compute wage and time problems.
2. Demonstrate
an understanding of length, area, volume, and the corresponding units, square
units, and cubic units of measure.
a. determine
area of a square, triangle, circle using pi.
q
b. determine volume of a cube.
Patterns,
Relationships, Functions
G. Students will understand that
mathematics is the science of pattern, relationships, and functions, Students will be able to:
1. Describe
and represent relationships with tables, graphs, and equations.
q
a. analyze relationships to explain how
a change in one quantity can result as pictured on a line graph.
2. Analyze
relationships to explain how a change in one quantity can result in a change in
another.
a. find solutions to one step linear equations using
integers, fractions, and decimals.
3. Use
patterns and multiple representations to solve problems.
Algebra
Concepts
H. Students
will understand and apply algebraic concepts. Students will be able to:
1. Use the
concepts of variables and expressions.
q
a. interpret a simple word problem and
convert it to an algebraic equation.
2. Solve
linear equations using concrete, informal, and formal methods which apply the
order of operations.
q
a. experiment with and interpret
quadrant graphs through variable equations.
3. Analyze
tables and graphs to identify properties and relationships in a practical
context.
4. Use
graphs to represent two-variable equations.
a. experiment with and interpret quadrant graphs through
variable equations.
5. Demonstrate
an understanding of inequalities and non-linear equations.
q
a. graph integers
q
b. solve algebraic equations with
integers
6. Find solutions for unknown
quantities in linear equations and simple equations and
inequalities.
q
a. solve 1 step inequalities.
Discrete
Mathematics
I. Students
will understand and apply concepts in discrete mathematics. Students will be able to:
1.
Create and use networks to explain practical situations or solve problems.
2.
Identify patterns in the world and express these patterns with rules.
Mathematical
Reasoning
J. The
student will understand and apply concepts of mathematical reasoning.
1. Support
reasoning using models, known facts, properties, and relationships.
q
a. run data samples in an equation and
give reasoning(s) behind or to the solution (simple example - multiplying two
even-numbers will give an even product.
Student will try this type of problem and explain the solution.)
2. Demonstrate
that multiple paths to a conclusion may exist.
q
a. demonstrate different methods used
to solve an equation.
q
b. display multiple problem-solving
solutions to a given situation.
Mathematical
Communication
K. Students will reflect upon and
clarify their understanding of mathematical ideas and relationships.
1.
Translate
relationships into algebraic notation.
2. Use
statistics, tables, and graphs to communicate ideas and information in
convincing presentations and analyze presentations of others for bias or
deceptive presentation.
q
a.
analyze weather patterns for
temperature with integers on a graph to display possible temperature decreases
or increases in degrees over a period of time.
q
b. communicate ideas and processes in
writing.