MSAD #55
Mathematics
Benchmarks/Performance
Indicators
Math
Skills
3-21-06
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( i.e. integer,
fraction, decimal, percent, exponential, and scientific notation) in problem
solving.
q
a. write and speak standard and word
form up to the thousandths place and billions place.
q
b.
show an understanding that
fractions are a part of a whole.
q
c.
show an understanding of fractions
with denominators of 100.
q
d. explain that a number can be made
into squares called square numbers (root).
2.
Demonstrate
understanding of the relationships among the basic arithmetic operations
on different types of numbers..
q
a. show understanding of addition,
subtraction, multiplication, division.
q
b. show understanding that addition is
the opposite of subtraction.
q
c. show understanding that multiplication is the opposite
of division.
q
d. show understanding of factor pairs
1-25.
q
e. show understanding of prime number
under 100.
q
f. show understanding of skip
counting (multiples).
3.
Apply
concepts of ratios, proportions, percents, and number theory (e.g., primes,
factors, and multiples) in practical and other mathematical
situations. .
q
a. write a percent as a decimal and
fraction.
q
b. show an understanding that ratio
compares a number to 100 by using the symbol %.
q
c. multiply to find the percent of a
number. (also in computation)
q
d. show understanding that ratio is
the comparison of two numbers or sets of data.
q
e. show understanding that a ratio can
be written as different fractions.
q
f. show understanding that ratio
is the comparison of two numbers or sets of data.
q
g. show understanding that a ratio can
be written as different fractions.
q
h. show understanding of factor pairs
1-25.
q
i. show understanding of prime
number under 100.
q
j. show understanding of skip
counting (multiples).
4. Represent
numerical relationships in tables, charts, and graphs.
q
a. interpret data from graph.
q
b. graph ordered pairs.
q
c. take information to create a table,
chart, or graph (line graph, bar graph).
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
whole numbers.(double digit multiplication, division with 2 digit divisors.
q
b. add and subtract decimals up to
thousandths place.
q
c. multiply decimals up to hundredths
place.
q
d. recognize fractions with like
denominators.
q
e. add fractions with like
denominators.
q
f. subtract fractions with like
denominators.
2. Create, solve,
and justify multi step real life problems including those with ratio and
proportion.
q
a. create 1-2 step real-life problems.
q
b. solve 1-2 step real-life problems.
q
c. justify 1-2 step real-life
problems.
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. demonstrate an understanding of
mean, median and mode.
2. Assemble
data and use matrices to formulate and solve problems.
q
a. organize data using tables.
q
b. organize data using charts.
q
c. organize data using graphs.
3. Construct
inferences and convincing arguments based on data.
q
a. come to conclusions based on given
data.
q
b. use data to convince others that a conclusion is reasonable
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. understand the term probability.
q
b. understand that a game is fair if
each player has the same chance of
winning.
q
c. understand that if one person has a
better chance to win the game, the game is unfair.
2. Explain
the idea that probability can be represented as a fraction between and
including zero) and one .
q
a. explore the representation of a
fraction between 0 and 1.
3. Use
simulations to estimate probabilities.
q
a.N/A
4. Find
all possible combinations and arrangements involving a limited number of
variables.
Geometry
E. Students
will understand and apply concepts from geometry.
1. Compare,
classify, and draw two-dimensional shapes and three-dimensional figures.
q
a. identify solid figures (cone,
sphere, pyramid)
q
b. define polygon
q
c. identify obtuse, acute, right
angles
q
d. identify perpendicular and parallel
lines.
2 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 regular polygon and circle. (Ex: square or rectangular lawn that needs
seeding.)
3. Use a
coordinate system to define and locate position.
q
a. read a coordinate system and locate
specified positions.
q
b. create a coordinate system and
place a marker on a specified position.
4.
Uses
the appropriate geometric tools and measurements to draw and construct two and
Three-dimensional figures.
q
a. identify right acute obtuse angles.
q
b. measure angles using a turtle
turner.
q
c. use compass and straightedge to
construct circles and triangles
Measurement
F. Students will understand
and demonstrate measurement skills.
Students will:
1. Demonstrate
the structure and use of systems of measurement.
q
a. identify units as metric or U.S.
standard.
q
b. use tools to measure length,
weight, liquid quantities and duration of time.
q
c. find benchmarks for foot, meter,
minute, pound, kilogram, liter, cup.
2. Develop and use
concepts that can be measured directly, or indirectly (e.g. the concept of
rate).
q
a. measure the length and width to
determine area of a rectangle and square.
q
b. explore value relationships among
different containers and among solids.
3.
Demonstrate an understanding of length,
area, volume, and the corresponding units,
square units, and cubic
units of measure. .
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. use tables to create graphs; uses
graphs to create tables.
q
b. draw conclusions from tables and
graphs.
q
c. practice using equations to find
unknowns.
q
d. approximate the closest number in
the base ten system, (to the tens, hundreds, thousands...)
q
e. use the pattern on the 10,000 chart
to locate a specific square.
2. Analyze relationships
to explain how a change in one quantity can result in a change in another.
q
a. determine a number pattern by
analyzing a sequence of numbers.
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, expressions.
q
a. understand that a variable
represents a specific number within a given equation.
q
b. use guess and check strategy to
determine the value of a variable
2. Solve
linear equations using concrete and informal and formal methods, which apply to
the order of operations.
q
a. use critical thinking skills and
knowledge about the order of operations
(
+,-.x,/) to solve basic equations.
q
b. determine the best method to solve
a problem( mental math, paper and pencil, or calculator).
q
c. use manipulatives to solve basic
equations.
3. Analyze
tables, graphs, and rules to identify properties and relationships in a
practical context.
q
a. collect and represent data through
the use of graphs and tables.
2.
Use
graphs to represent two variable equations.
3.
Demonstrate
an understanding of inequalities and non-linear equations.
4.
Find
solutions for unknown quantities in linear equations and in simple equations
and 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. demonstrate reasoning in solving a
given problem through the use of appropriate models.
2. Demonstrate that multiple paths to a conclusion may
exist.
q
a. demonstrate a minimum of two ways
to solve a problem.
Mathematical
Communication
K. Students will reflect upon and
clarify their understanding of mathematical ideas and relationships.
1. Translate relationships into algebraic notation.
q
a. use a variable and a mathematical symbol to write one or
more number sentences.
2. Use statistics, tables, and graphs to
communicate ideas and information in convincing
presentations and analyze presentations of other for bias or
deceptive presentation.