| STANDARDS MAP for a Basic Grade-Level
Program |
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| Grade Eight –
Mathematics (Algebra I) |
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Publisher Citations |
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| Standard
No. |
Standard Language |
Primary Citations |
Supporting Citations |
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ALGEBRA I |
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| 1 |
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: |
2.03 to 2.05 |
1.07 |
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| 2.10
to 2.12 |
1.08 |
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| 2.21
to 2.25 |
1.11 |
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| 2.43 |
2.07 |
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| 12.09 |
2.13 to 2.20 |
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| 12.18 |
2.26 to 2.30 |
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| 12.25 |
2.51 |
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| A1.02
to A1.08 |
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| A2.05
to A2.21 |
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| 1.1 |
Students use properties of numbers to
demonstrate whether assertions are true or false. |
1.07 |
2.03 |
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| 1.08 |
2.07 |
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| 1.11 |
2.53 |
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| 2.43 |
2.54 |
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| 2.44 |
3.17 |
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| 2.49 |
3.20 |
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| 2.51 |
3.29 |
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| 2 |
Students understand and use such operations as
taking the opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents. |
2.08 |
2.09 |
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| 2.43 |
2.12 |
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| A2.07 |
9.24 to
9.38 |
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| 12.00
to 12.08 |
10.20 |
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| 12.59
to 12.66 |
10.35 |
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| 2.31 to 2.37 |
12.67 |
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| 9.00
to 9.23 |
12.68 |
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| 3 |
Students solve equations and inequalities
involving absolute values. |
3.26 |
3.28 |
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| 3.27 |
3.29 |
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| 8.23 |
3.61 |
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| 8.24 |
8.25 |
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8.26 |
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8.40 |
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| 4 |
Students simplify expressions before solving
linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) =
12. |
2.43 to 2.46 |
1.04 to
1.06 |
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| 3.13 to 3.17 |
2.34 to 2.42 |
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| 8.06 |
2.47 |
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| 8.07 |
2.48 |
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2.50 |
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2.51 |
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3.19 |
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3.20 |
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3.23 to 3.25 |
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| 5 |
Students solve multistep problems, including
word problems, involving linear equations and linear inequalities in one
variable and provide justification for each step. |
1.12 to
1.14 |
1.15 to
1.24 |
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| 1.26 |
1.27 to 1.29 |
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| 3.14
to 3.17 |
3.01 to 3.12 |
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| 3.30
to 3.32 |
3.19 |
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| 3.34 |
3.20 |
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| 3.35 |
3.33 |
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| 3.45 to 3.48 |
3.36
to 3.44 |
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| 3.51
to 3.53 |
3.49 |
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| 3.56 |
3.50 |
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| 8.01
to 8.10 |
3.54 |
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| 8.13
to 8.16 |
3.55 |
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3.58 |
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3.59 |
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3.61 |
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3.62 |
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8.11 |
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8.12 |
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8.21 |
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8.22 |
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| 6 |
Students graph a linear equation and compute the
x- and y- intercepts (e.g., graph 2x
+ 6y = 4). They are also able to sketch the region defined by linear
inequality (e.g., they sketch the region defined by 2x + 6y < 4). |
5.13 to 5.17 |
5.18 |
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| 5.23 |
5.19 |
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| 5.24 |
5.21 |
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| 5.27 to 5.37 |
5.22 |
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| 5.41 |
5.25 |
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| 8.27 |
5.26 |
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| 8.28 |
5.38 to 5.40 |
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5.65 |
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8.32 to 8.34 |
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8.40 |
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| 7 |
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. |
5.13 |
5.21 |
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| 5.33 |
5.22 |
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| 5.55 |
5.39 |
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| 5.56 |
5.40 |
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5.65 |
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| 8 |
Students understand the concepts of parallel
lines and perpendicular lines and how those slopes are related. Students are
able to find the equation of a line perpendicular to a given line that passes
through a given point. |
5.42 to 5.46 |
5.47 |
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5.48 |
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5.65 |
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| 9 |
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. |
7.05 |
7.01 |
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| 7.11
to 7.15 |
7.06 to 7.10 |
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| 7.22
to 7.28 |
7.16 to 7.21 |
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| 8.29 |
7.47 |
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| 8.30 |
8.31 to 8.34 |
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8.40 |
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8.41 |
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| 10 |
Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep problems, including word
problems, by using these techniques. |
10.05 to 10.07 |
10.18 |
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| 10.14
to 10.17 |
10.19 |
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| 10.20
to 10.26 |
10.27 |
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| 10.29
to 10.32 |
10.28 |
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| 10.35
to 10.40 |
10.33 |
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| 10.43
to 10.48 |
10.34 |
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10.41 |
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10.42 |
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10.49 |
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10.50 |
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11.30 to 11.33 |
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| 11 |
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. |
10.51 to 10.59 |
10.60 to 10.63 |
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| 10.64
to 10.67 |
10.68 to 10.70 |
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| 10.71 |
10.73 to 10.78 |
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| 10.72 |
10.85 |
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10.86 |
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| 12 |
Students simplify fractions with polynomials in
the numerator and denominator by factoring both and reducing them to the
lowest terms. |
11.02 |
11.06 to 11.09 |
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| 11.03 |
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| 11.04 |
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| 11.05 |
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| 13 |
Students add, subtract, multiply, and divide
rational expressions and functions. Students solve both computationally and
conceptually challenging problems by using these techniques. |
11.10 |
11.12 |
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| 11.11 |
11.16 to 11.18 |
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| 11.13
to 11.15 |
11.23 to 11.25 |
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| 11.19
to 11.22 |
11.28 |
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| 11.26 |
11.29 |
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| 11.27 |
11.32 |
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| 11.30 |
11.33 |
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| 11.31 |
11.37 |
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| 11.34
to 11.36 |
11.38 |
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| 11.39
to 11.45 |
11.51 |
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| 14 |
Students solve a quadratic equation by factoring
or completing the square. |
10.79 |
10.83 |
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| 10.80 |
10.84 |
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| 13.03
to 13.06 |
11.39 |
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| 13.21
to 13.24 |
12.47 |
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12.56 |
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13.07 to 13.12 |
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13.25 |
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13.26 |
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13.63 |
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| 15 |
Students apply algebraic techniques to solve
rate problems, work problems, and percent mixture problems. |
6.15 to 6.19 |
3.38 |
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| 7.23
to 7.26 |
3.39 |
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| 11.42 |
3.55 |
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| 11.44 |
5.50 to 5.57 |
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| 11.45 |
7.27 |
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7.28 |
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11.43 |
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11.46 |
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11.47 |
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11.49 to 11.51 |
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| 16 |
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. |
6.00 to 6.02 |
6.03 |
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| 6.04 |
6.05 |
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| 6.06
to 6.12 |
6.13 |
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6.14 |
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| 17 |
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. |
6.01 |
6.13 |
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| 6.02 |
6.14 |
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| 6.06 |
6.33 |
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| 6.10 |
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| 18 |
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. |
6.02 |
6.13 |
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| 6.06 |
6.14 |
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| 6.11 |
6.33 |
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| 19 |
Students know the quadratic formula and are
familiar with its proof by completing the square. |
13.27 |
13.28 |
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| 13.30 |
13.29 |
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13.31 |
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13.33 to 13.38 |
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13.51 to 13.54 |
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13.63 |
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| 20 |
Students use the quadratic formula to find the
roots of a second-degree polynomial and to solve quadratic equations. |
13.27 |
13.28 |
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| 13.31
to 13.35 |
13.29 |
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13.36 to 13.38 |
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13.63 |
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| 21 |
Students graph quadratic functions and know that
their roots are the x-intercepts. |
13.46 |
13.53 |
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| 13.47 |
13.54 |
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| 13.48 |
13.63 |
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| 13.51 |
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| 22 |
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. |
13.49 |
13.53 |
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| 13.50 |
13.54 |
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| 13.51 |
13.63 |
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| 13.52 |
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| 23 |
Students apply quadratic equations to physical
problems, such as the motion of an object under the force of gravity. |
10.81 |
12.41 |
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| 10.82 |
13.10 |
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| 10.84 |
13.12 |
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| 12.45 |
13.34 |
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| 13.16 |
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| 13.20 |
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| 13.38 |
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| 24 |
Students use and know simple aspects of a
logical argument: |
1.26 |
2.55 |
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| 2.52 |
9.11 |
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| 2.53 |
9.17 |
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| 2.54 |
10.34 |
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| 5.37 |
12.08 |
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| 9.05 |
13.38 |
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| 9.17 |
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| 10.30 |
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| 10.31 |
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| 12.05 |
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| 12.40 |
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| 12.62 |
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| 13.30 |
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| 24.1 |
Students explain the difference between
inductive and deductive reasoning and identify and provide examples of each. |
2.52 |
2.55 |
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| 2.53 |
5.37 |
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| 2.54 |
9.05 |
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9.11 |
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9.17 |
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12.05 |
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12.08 |
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12.62 |
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13.3 |
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13.38 |
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| 24.2 |
Students
identify the hypothesis and conclusion in logical deduction. |
2.53 |
2.55 |
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| 2.54 |
5.37 |
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9.05 |
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9.11 |
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9.17 |
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12.05 |
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12.08 |
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12.62 |
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13.30 |
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13.38 |
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| 24.3 |
Students use counterexamples to show that an
assertion is false and recognize that a single counterexample is sufficient
to refute an assertion. |
2.52 |
1.11 |
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| 2.54 |
2.03 |
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| 12.05 |
2.07 |
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2.51 |
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2.55 |
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9.11 |
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9.23 |
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12.08 |
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| 25 |
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: |
2.03 |
1.07 |
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| 2.44 |
1.08 |
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| 2.49 |
1.11 |
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| 2.51 |
2.07 |
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| 2.52
to 2.54 |
2.43 |
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| 3.09 |
2.44 |
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| 3.17 |
2.55 |
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| 3.56 |
3.20 |
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| 5.37 |
10.30 |
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| 9.05 |
10.31 |
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| 9.11 |
10.34 |
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| 9.17 |
10.74 |
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| 12.05 |
10.78 |
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| 12.40 |
12.08 |
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| 12.53 |
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| 12.62 |
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| 13.30 |
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| 13.38 |
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| 25.1 |
Students use properties of numbers to construct
simple, valid arguments (direct and indirect) for, or formulate
counterexamples to, claimed assertions. |
2.03 |
2.07 |
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| 2.51 |
2.43 |
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| 9.05 |
2.44 |
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| 9.11 |
2.55 |
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| 9.17 |
3.20 |
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| 9.23 |
10.30 |
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| 10.74 |
10.31 |
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| 10.78 |
10.34 |
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| 12.05 |
12.40 |
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| 12.08 |
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| 13.30 |
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| 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. |
1.05 |
3.20 |
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| 1.08 |
11.09 |
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| 1.11 |
12.53 |
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| 1.25 |
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| 2.44 |
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| 2.49 |
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| 2.51 |
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| 2.53 |
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| 2.54 |
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| 3.09 |
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| 3.17 |
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| 3.56 |
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| 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. |
1.29 |
1.05 |
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| 3.20 |
1.07 |
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| 3.29 |
1.08 |
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| 8.12 |
2.20 |
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| 12.53 |
2.49 |
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| 13.54 |
9.11 |
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9.23 |
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11.09 |
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| Appendix |
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| All
citations state chapter number and section number (#.#). |
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| A1 refers to Appendix 1 and A2 refers to Appendix 2. |
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