MSAD #55
Mathematics
Benchmarks/Performance
Indicators
Math
Skills
1-8-01
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. Work
with numbers in various forms such as integers, fractions, decimals and
percentages.
q
a. recognize
integers.
q
b. demonstrate
an understanding of the relationship of parts to whole as it applies to
decimals and fractions.
2. Work with squaring and cubing
in problem solving.
q
a. square and
cube whole numbers.
3. Demonstrate the relationship
among the basic arithmetic operations.
q
a. apply the
relationship between addition and subtraction as opposites.
q
b. apply the
relationship between multiplication and division as opposites.
q
c. explore the
use of parenthesis in the order of operation.
4. Apply concept of
ratio/proportion.
q
a. explore the
process of writing a ratio as a fraction.
q
b. demonstrate a
practical application of ratio/proportion (scale models, enlargements, projects).
5. Apply concepts of percentages.
q
a. convert
fractions, decimals, and percentages.
q
b. demonstrate
the ability to translate fractions to decimals to percentages.
q
c. explore the
daily use of percentages (scales, grades, etc.)
6. Apply concepts of number theory
with primes, factors, and multiples.
q
a. identify
prime and composite numbers.
q
b. find factors
and multiples of a whole number.
q
c. reduce any
number to its prime factors.
7. Represent numerical relationships
in tables, charts, and graphs.
q
a. apply
negative and positive integers in coordinate graphing.
q
b. construct and
interpret bar graph, scatter plot, and stem plot.
Computation
B. Students
will understand and demonstrate computation skills. Students will be able to:
1. Do
addition, subtraction, multiplication and division of whole numbers and basic
decimals.
q
a. add,
subtract, and multiply fractions with common denominators
q
b. add,
subtract, and multiply decimals.
q
c. square and
cube whole numbers.
2. Do addition and subtraction of
fractions with like denominators.
q
a. convert fractions to a common denominator in a given
problem.
q
b. simplify
improper fractions to a mixed number.
3. Create, solve, and justify multi
step real life problems with the four basic operations.
q
a. create
multi-step real life problems.
q
b. solve multi-
step real life problems.
q
c. justify
multi-step real life problems with 4 basic operation.
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. compute mean,
median, mode, scale and range for sets of data containing whole numbers.
using appropriate technology.
q
b. organize
and analyze a given set of data.
2. Use tables, graphs, and charts to
organize data.
q
a. create and
interpret bar, line, stem plots, scatter graphs, pie graphs, pictographs and
Venn diagrams for whole number data.
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 whole numbers.
Probability
D. Students
will understand and apply concepts of probability. Students will be able to:
1. Determine whether a game is fair
or unfair.
q
a. examine
results and probability of winning a simple game to determine fairness.
2. Explain
that probabilities are represented as fractions between zero (no chance) and
one (always occurring.)
q
a. explain probability as a fraction between 0 and 1.
3. Use simulations to estimate
probabilities.
q
a. compare theoretical problems to experimental
probability (i.e. penny tossing).
4. Find
all possible combinations and arrangements involving a limited number of
variables.
q
a. explore identifying
all possible combinations for 3 variables.
Geometry
E. Students will understand and apply
concepts from geometry.
1. Use
proper geometrical language to describe geometric figures and their components.
q
a. identify
basic polygons : triangles, rectangles, trapezoid, rhombus, parallelogram,
pentagon, hexagon, octagon.
q
a. identify and
measure obtuse, acute, right, straight angles, internal and external angles and
rays.
2a. Apply
geometric properties to represent and solve real-life problems involving
regular and irregular shapes.
q
a. Find the area
and perimeter of a given space within a regular and irregular polygon and
circle. ( See 6 1a. for examples)
2b.
Uses appropriate
tools to draw constructions.
q
a. construct and
measure polygons (see 61a. for examples) and circles. using a straightedge, compass, protractor.
3. Use a coordinate system to define
and locate position.
q
a.
4. Can classify angles according to
their measures.
q
a. measure and
identify interior and exterior angles.
q
b. can classify
right, acute, obtuse and straight angles according to their degree measure.
5. Use rotational symmetry to
describe geometric figures.
q
a. use
rotational geometry to describe geometric figures.
Measurement
F. Students will understand and
demonstrate measurement skills.
Students will:
1. Demonstrate the structure and use
of systems of measurement.
q
a. use
measurements of weights, distance, temperature, and duration of time in practical applications.
2. Demonstrate
an understanding of length, area, volume, and the corresponding units, square
units, and cubic units of measure of simple geometric structures.
q
a. determine the
measurements of base, height, area , and
perimeter of quadrilaterals (square, rectangle, trapezoids, parallelograms).
q
b. define and
identify radius, diameter, circumference of a circle.