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Standards Correlation
Foundational Skills and Concepts
Number
Sense Standards |
Lessons |
(Gr2) NS3.1 |
Use repeated addition, arrays, and counting
by multiples to do multiplication. |
1.1, 4.3, 12.2, 12.3, 14.2 |
(Gr2) NS3.2 |
Use repeated subtraction, equal sharing, and forming equal
groups with remainders to do division. |
2.2, 13.2 |
(Gr2) NS4.1 |
Recognize, name, and compare unit fractions from 1/12 to
1/2. |
6.1, 7.2 |
(Gr3) NS1.3 |
Identify the place value for each digit in numbers to 10,000. |
1.3, 3.3, 7.3, 10.3 |
(Gr3) NS1.5 |
Use expanded notation to represent numbers (e.g., 3,206
= 3,000 +200 + 6). |
1.1, 2.3, 3.3, 7.3, 10.3 |
(Gr3) NS3.1 |
Compare fractions represented by drawings or concrete materials
to show equivalency and to add and subtract simple fractions
in context (e.g., 1/2 of a pizza is the same amount as 2/4
of another pizza that is the same size; show that 3/8 is
larger than 1/4). |
5.1, 6.1, 6.3, 9.2, 9.3 |
(Gr3) NS3.2 |
Add and subtract simple fractions (e.g., determine that
1/8 + 3/8 is the same as 1/2). |
5.1, 8.1 |
(Gr4) NS1.3 |
Round whole numbers through the millions to the nearest
ten, hundred, thousand, ten thousand, or hundred thousand. |
1.2, 1.3, 2.2 |
| (Gr4) NS1.4 |
Decide when a rounded solution is called for and explain
why such a solution may be appropriate. |
1.2, 1.3, 2.2 |
| (Gr4) NS1.5 |
Explain different interpretations of fractions, for example,
parts of a whole, parts of a set, and division of whole numbers
by whole numbers; explain equivalents of fractions. |
6.1, 6.3, 9.3, 17.3 |
| (Gr4) NS1.8 |
Use concepts of negative numbers (e.g., on a number line,
in counting, in temperature, in "owing"). |
2.1 |
| (Gr4) NS2.1 |
Estimate and compute the sum or difference of whole numbers
and positive decimals to two places. |
0.3, 1.3 |
| (Gr4) NS3.1 |
Demonstrate an understanding of, and the ability to use,
standard algorithms for the addition and subtraction of multidigit
numbers. |
0.3, 2.3 |
| (Gr4) NS3.2 |
Demonstrate an understanding of, and the ability to use,
standard algorithms for multiplying a multidigit number by
a two-digit number and for dividing a multidigit number by
a one-digit number; use relationships between them to simplify
computations and to check results. |
1.1, 2.2, 4.3, 5.3, 17.1 |
| (Gr4) NS4.1 |
Understand that many whole numbers break down in different
ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3). |
2.3, 5.3, 12.3 |
| (Gr4) NS4.2 |
Know that numbers such as 2, 3, 5, 7, and 11 do not have
any factors except 1 and themselves and that such numbers
are called prime numbers. |
5.3, 12.3 |
| (Gr5) NS1.1 |
Estimate, round, and manipulate very large (e.g., millions)
and very small (e.g., thousandths) numbers. |
7.3, 10.3, 22.3, 23.3 |
| (Gr5) NS1.2 |
Interpret percents as a part of a hundred; find decimal
and percent equivalents for common fractions and explain
why they represent the same value; compute a given percent
of a whole number. |
7.1, 8.1, 8.2, 17.2, 18.1, 18.3, 19.1, 20.3 |
| (Gr5) NS1.3 |
Understand and compute positive integer powers of nonnegative
integers; compute examples as repeated multiplication. |
21.3, 22.1 |
| (Gr5) NS1.4 |
Determine the prime factors of all numbers through 50 and
write the numbers as the product of their prime factors by
using exponents to show multiples of a factor (e.g., 24 =
2 x 2 x 2 x 3 = 2 x 3 x 3). |
5.3, 12.3 |
| (Gr5) NS1.5 |
Identify and represent on a number line decimals, fractions,
mixed numbers, and positive and negative integers. |
2.1 |
| (Gr5) NS2.0 |
Students perform calculations and solve problems involving
addition, subtraction, and simple multiplication and division
of fractions and decimals. |
10.1, 12.2, 12.3, 13.3, 14.2, 14.3, 15.2, 15.3, 17.1, 18.3 |
| (Gr5) NS2.3 |
Solve simple problems, including ones arising in concrete
situations, involving the addition and subtraction of fractions
and mixed numbers (like and unlike denominators of 20 or
less), and express answers in the simplest form. |
14.3 |
| (Gr6) NS1.1 |
Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line. |
7.2, 8.2, 8.3, 11.3, 13.3, 28.1 |
| (Gr6) NS1.2 |
Interpret and use ratios in different contexts (e.g., batting
averages, miles per hour) to show the relative sizes of two
quantities, using appropriate notations (a/b, a to b, a :
b). |
17.1, 17.3, 20.3, 23.2, 23.3, 27.3 |
| (Gr6) NS1.3 |
Use proportions to solve problems (e.g., determine the
value of N if 4/7 = N/ 21, find the length of a side of a
polygon similar to a known polygon). Use cross-multiplication
as a method for solving such problems, understanding it as
the multiplication of both sides of an equation by a multiplicative
inverse. |
17.3, 19.1, 20.1, 20.3, 23.3 |
| (Gr6) NS1.4 |
Calculate given percentages of quantities and solve problems
involving discounts at sales, interest earned, and tips. |
17.2, 18.1, 18.2, 18.3, 22.3 |
| (Gr6) NS2.1 |
Solve problems involving addition, subtraction, multiplication,
and division of positive fractions and explain why a particular
operation was used for a given situation. |
9.2, 9.3, 10.3, 11.3, 12.2, 12.3, 13.3, 14.2, 14.3 |
| (Gr6) NS2.2 |
Explain the meaning of multiplication and division of positive
fractions and perform the calculations (e.g., 5/8 ÷ 15/16
= 5/8 x 16/15 = 2/3). |
12.2, 12.3, 13.2, 13.3 |
| (Gr6) NS2.3 |
Solve addition, subtraction, multiplication, and division
problems, including those arising in concrete situations,
that use positive and negative integers and combinations
of these operations. |
2.1, 3.1, 3.3, 4.1, 4.3, 6.3, 7.3, 11.2, 15.3, 19.3 |
Algebra
and Fuctions Standards
|
Lessons
|
(Gr2) AF1.1 |
Use the commutative and associative rules to simplify mental
calculations and to check results. |
0.3, 2.3, 14.1 |
(Gr2) AF1.2 |
Relate problem situations to number sentences involving
addition and subtraction. |
2.1, 3.1, 10.2 |
(Gr3) AF1.5 |
Recognize and use the commutative and associative properties
of multiplication
(e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x
3 = 105, then what is 7 x 3 x 5?). |
1.1, 4.3, 14.1 |
(Gr4) AF1.1 |
Use letters, boxes, or other symbols to stand for any number
in simple expressions or equations (e.g., demonstrate an
understanding and the use of the concept of a variable). |
5.2, 9.1, 10.1, 10.2, 11.1, 28.3 |
(Gr4) AF1.2 |
Interpret and evaluate mathematical expressions that now
use parentheses. |
5.2, 9.1, 10.1, 15.3, 25.1, 25.3 |
(Gr4) AF1.3 |
Use parentheses to indicate which operation to perform
first when writing expressions containing more than two terms
and different operations. |
9.1, 25.1, 25.3, 29.3 |
| (Gr4) AF1.5 |
Understand that an equation such as y = 3x + 5 is a prescription
for determining a second number when a first number is given. |
6.2, 12.1, 30.1, 30.2, 31.1, 31.3, 32.3 |
| (Gr4) AF2.1 |
Know and understand that equals added to equals are equal. |
10.2, 11.1, 11.2, 16.3, 26.1 |
| (Gr4) AF2.2 |
Know and understand that equals multiplied by equals are
equal. |
11.1, 11.2, 16.3, 20.1, 26.1 |
| (Gr5) AF1.0 |
Students use variables in simple expressions, compute the
value of the expression for specific values of the variable,
and plot and interpret the results. |
5.2, 13.1, 15.1, 16.1, 25.1, 25.2, 30.1, 32.1 |
| (Gr5) AF1.3 |
Know and use the distributive property in equations and
expressions with variables. |
1.1, 4.3, 10.1, 14.1, 26.1 |
| (Gr5) AF1.4 |
Identify and graph ordered pairs in the four quadrants
of the coordinate plane. |
24.3, 29.1 |
| (Gr5) AF1.5 |
Solve problems involving linear functions with integer
values; write the equation; and graph the resulting ordered
pairs of integers on a grid. |
6.2, 12.1 |
| (Gr6) AF1.0 |
Students write verbal expressions and sentences as algebraic
expressions and equations; they evaluate algebraic expressions,
solve simple linear equations, and graph and interpret their
results. |
10.1, 11.2, 15.3, 21.1, 22.2, 26.2, 26.3, 28.2, 28.3 |
| (Gr6) AF1.3 |
Apply algebraic order of operations and the commutative,
associative, and distributive properties to evaluate expressions;
and justify each step in the process. |
10.1 |
| (Gr6) AF2.0 |
Students analyze and use tables, graphs, and rules to solve
problems involving rates and proportions. |
6.2, 12.1, 21.3, 22.2, 29.2 |
| (Gr6) AF2.1 |
Convert one unit of measurement to another (e.g., from
feet to miles, from centimeters to inches). |
6.2, 19.3, 21.3 |
| (Gr6) AF2.3 |
Solve problems involving rates, average speed, distance,
and time. |
17.1 |
| (Gr6) AF3.0 |
Students investigate geometric patterns and describe them
algebraically. |
4.2, 5.2 |
| (Gr6) AF3.1 |
Use variables in expressions describing geometric quantities
(e.g., P = 2w x 2l, A = 1/2bh, C = pi x
d –the formulas
for the perimeter of a rectangle, the area of a triangle,
and
the circumference of a circle, respectively). |
5.2, 13.1, 15.1, 16.1, 16.2, 21.1 |
Measurement
and Geometry Standards
|
Lessons
|
(Gr4) MG1.0 |
Students understand perimeter and area. |
3.2, 4.2, 5.2, 8.3, 13.1, 32.2 |
| (Gr4) MG2.0 |
Students use two-dimensional coordinate grids to represent
points and graph lines and simple figures. |
3.2, 4.2, 5.2, 8.3, 13.1, 32.2 |
(Gr4) MG2.1 |
Draw the points corresponding to linear
relationships on graph paper (e.g., draw 10 points on the
graph of the equation y = 3x and connect them by using
a straight line). |
3.2, 4.2, 5.2, 6.2, 8.3, 12.1 |
(Gr4) MG2.2 |
Understand that the length of a horizontal
line segment equals the difference of the x-coordinates. |
13.1, 24.3, 29.1 |
(Gr4) MG2.3 |
Understand that the length of a vertical
line segment equals the difference of the y-coordinates. |
13.1, 24.3, 29.1 |
(Gr4) MG3.3 |
Identify congruent figures. |
5.1 |
(Gr5) MG1.0 |
Students understand and compute the volumes
and areas of simple objects. |
14.1 |
(Gr5) MG1.1 |
Derive and use the formula for the area
of a triangle and of a parallelogram by comparing it with
the formula for the area of a rectangle (i.e., two of the
same triangles make a parallelogram with twice the area;
a parallelogram is compared with a rectangle of the same
area by cutting and pasting a right triangle on the parallelogram). |
21.1, 24.2 |
(Gr6) MG1.2 |
Know common estimates of p (3.14; 22/7)
and use these values to estimate and calculate the circumference
and the area of circles; compare with actual measurements. |
15.1, 16.1 |
Probability,
Data, and Statistics Standards
|
Lessons
|
(Gr2) SDP2.1 |
Recognize, describe, and extend patterns and determine
a next term in linear patterns (e.g., 4, 8, 12 ...; the number
of ears on one horse, two horses, three horses, four horses). |
3.2, 4.2 |
(Gr3) SDP1.2 |
Record the possible outcomes for a simple event (e.g.,
tossing a coin) and systematically keep track of the outcomes
when the event is repeated many times. |
00.1, 20.2 |
(Gr6) SDP1.3 |
Understand how the inclusion or exclusion of outliers affects
measures of central tendency. |
00.1 |
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