Grade 7—Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and re present data sets that have one or more
variables and
identify relationships among variables within a data set by hand and through the
use of an
electronic spreadsheet software program:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot
or box-and-whisker
plot; use the forms to display a single set of data or to compare two sets of
data.
1.2 Represent two numerical variables on a scatterplot and informally describe
how the data points
are distributed and any apparent relationship that exists between the two
variables (e.g., between
time spent on homework and grade level).
1.3 Understand the meaning of, and be able to compute the minimum, the lower
quartile, the
median, the upper quartile, and the maximum of a data set.
Grade 7—Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from
irrelevant information,
identifying missing information, sequencing and prioritizing information, and
observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general
description of the
mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Student use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical
reasoning and
arithmetic and algebraic techniques.
2.4 Make and test conjectures by using both inductive and deductive reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams,
and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using the appropriate
mathematical notation and
terms and clear language; support solutions with evidence in both verbal and
symbolic work .
2.7 Indicate the relative advantages of exact and approximate solutions to
problems and give
answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the
context of the problem.
3.0 Students determine a solution is complete and move beyond a particular
problem by
generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the
original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual
understanding of the
derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and
apply them to new
problem situations.
Algebra I
1.0 Students identify and use the arithmetic properties of subsets of integers
and rational,
irrational, and real numbers, including closure properties for the four basic
arithmetic
operations where applicable:
1.1 Students use properties of numbers to demonstrate whether assertions are
true or false.
2.0 Students understand and use such operations as taking the opposite,
finding the
reciprocal, and taking a root, and raising to a fractional power. They
understand and use the
rules of exponents .
3.0 Students solve equations and inequalities involving absolute values.
4.0 Students simplify expressions before solving linear equations and
inequalities in one
variable, such as 3(2 x-5) + 4( x-2) = 12.
5.0 Students solve multi step problems , including word problems, involving linear
equations
and linear inequalities in one variable and provide justification for each step.
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g.,
graph 2 x + 6y
= 4). They are also able to sketch the region defined by linear inequality
(e.g., they sketch the
region defined by 2 x + 6 y < 4).(1 graphing item; 1 computing item)
7.0 Students verify that a point lies on a line, given an equation of the line.
Students are able
to derive linear equations. by using the point slope formula .
8.0 Students understand the concepts of parallel lines and perpendicular lines
and how their
slopes are related. Students are able to find the equation of a line
perpendicular to a given
line that passes through a given point.
9.0 Students solve a system of two linear equations in two variables
algebraically and are
able to interpret the answer graphically. Students are able to solve a system of
two linear
inequalities in two variables and to sketch the solution sets.
10.0 Students add , subtract, multiply, and divide monomials and polynomials.
Students
solve multistep problems, including word problems, by using these techniques.
11.0 Students apply basic factoring techniques to second- and simple third
degree
polynomials. These techniques include finding a common factor for all terms in a
polynomial, recognizing the difference of two squares , and recognizing perfect
squares of
binomials.
12.0 Students simplify fractions with polynomials in the numerator and
denominator by
factoring both and reducing them to the lowest terms.
13.0 Students add, subtract, multiply, and divide rational expressions and
functions.
Students solve both computationally and conceptually challenging problems by
using these
techniques.
14.0 Students solve a quadratic equation by factoring or completing the square.
15.0 Students apply algebraic techniques to
solve rate problems, work problems, and
percent mixture problems.
16.0 Students understand the concepts of a relation and a function, determine
whether a
given relation defines a function, and give pertinent information about given
relations and
functions.
17.0 Students determine the domain of independent variables and the range of
dependent
variables defined by a graph, a set of ordered pairs, or a symbolic expression.
18.0 Students determine whether a relation defined by a graph, a set of ordered
pairs, or a
symbolic expression is a function and justify the conclusion.
19.0 Students know the quadratic formula and are familiar with its proof by
completing the
square.
20.0 Students use the quadratic formula to find the roots of a second degree
polynomial and
to solve quadratic equations.
21.0 Students graph quadratic functions and know that their roots are the
x-intercepts.
22.0 Students use the quadratic formula or factoring techniques or both to
determine
whether the graph of a quadratic function will intersect the x- axis in zero ,
one, or two points.
23.0 Students apply quadratic equations to physical problems, such as the motion
of an
object under the force of gravity.
24.0 Students use and know simple aspects of a logical argument:
24.1 Students explain the difference between inductive and deductive
reasoning and identify and
provide examples of each.
24.2 Students identify the hypothesis and conclusion in logical deduction.
24.3 Students use counterexamples to show that an assertion is false and
recognize that a single
counterexample is sufficient to refute an assertion.
25.0 Students use properties of the number system to judge the validity of
results, to justify
each step of a procedure, and to prove or disprove statements:
25.1 Students use properties of numbers to construct simple, valid arguments
(direct and indirect)
for, or formulate counterexamples to, claimed assertions.
25.2 Students judge the validity of an argument according to whether the
properties of the real
number system and the order of operations have been applied correctly at each
step.
25.3 Given a specific algebraic statement involving linear, quadratic, or
absolute value expressions
or equations or inequalities, students determine whether the statement is true
sometimes, always,
or never.
