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# Compiling My Curriculum - Math

Posted by on Jul. 31, 2013 at 12:47 PM
• 26 Replies

This is probably my second favorite subject to teach (right behind science of course.lol) My boys are just as comfortable with math as with science, so again they are kinda all over the map when it comes to grade levels. But my eldest (who just turned 12) is pretty much in 7th grade and my youngest (at 9) is pretty much in 5th grade..lol.

Enjoy!

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Albert Einstein --
"Everybody is a Genius. But if you judge a fish by its ability to climb a tree, it will spend its whole life believing it is stupid."

by on Jul. 31, 2013 at 12:47 PM
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Replies (1-10):
by on Jul. 31, 2013 at 12:51 PM

Number Sense

1.0 Students know the properties of, and compute with, rational numbers ex­

pressed in a variety of forms:

1.1 Read, write, and compare rational numbers in scientific notation (positive and

negative powers of 10) with approximate numbers using scientific notation.

1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and

terminating decimals) and take positive rational numbers to whole-number

powers.

1.3 Convert fractions to decimals and percents and use these representations in estima­

tions, computations, and applications.

1.4 Differentiate between rational and irrational numbers.

1.5 Know that every rational number is either a terminating or repeating decimal and

be able to convert terminating decimals into reduced fractions.

1.6 Calculate the percentage of increases and decreases of a quantity.

1.7 Solve problems that involve discounts, markups, commissions, and profit and

compute simple and compound interest.

by on Jul. 31, 2013 at 12:52 PM

2.0 Students use exponents, powers, and roots and use exponents in working with

fractions:

2.1 Understand negative whole-number exponents. Multiply and divide expressions

involving exponents with a common base.

2.2 Add and subtract fractions by using factoring to find common denominators.

2.3 Multiply, divide, and simplify rational numbers by using exponent rules.

2.4 Use the inverse relationship between raising to a power and extracting the root of a

perfect square integer; for an integer that is not square, determine without a calcu­

lator the two integers between which its square root lies and explain why.

2.5 Understand the meaning of the absolute value of a number; interpret the absolute

value as the distance of the number from zero on a number line; and determine the

absolute value of real numbers.

Algebra and Functions

1.0 Students express quantitative relationships by using algebraic terminology,

expressions, equations, inequalities, and graphs:

1.1 Use variables and appropriate operations to write an expression, an equation, an

inequality, or a system of equations or inequalities that represents a verbal descrip­

tion (e.g., three less than a number, half as large as area A).

1.2 Use the correct order of operations to evaluate algebraic expressions such as

3(2x +

2

.5)

1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the

process used.

1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality,

expression, constant) correctly.

1.5 Represent quantitative relationships graphically and interpret the meaning of a

specific part of a graph in the situation represented by the graph.

by on Jul. 31, 2013 at 12:53 PM

2.0 Students interpret and evaluate expressions involving integer powers and

simple roots:

2.1 Interpret positive whole-number powers as repeated multiplication and negative

whole-number powers as repeated division or multiplication by the multiplicative

inverse. Simplify and evaluate expressions that include exponents.

2.2 Multiply and divide monomials; extend the process of taking powers and extract­

ing roots to monomials when the latter results in a monomial with an integer

exponent.

3.0 Students graph and interpret linear and some nonlinear functions:

3.1 Graph functions of the form y = nx2

and y = nx3

and use in solving problems.

3.2 Plot the values from the volumes of three-dimensional shapes for various values of

the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a

fixed height and an equilateral triangle base of varying lengths).

3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit

of horizontal change (change in x-value) is always the same and know that the ratio

(“rise over run”) is called the slope of a graph.

3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the

number of an item, feet to inches, circumference to diameter of a circle). Fit a line to

the plot and understand that the slope of the line equals the quantities.

4.0 Students solve simple linear equations and inequalities over the rational

numbers:

4.1 Solve two-step linear equations and inequalities in one variable over the rational

numbers, interpret the solution or solutions in the context from which they arose,

and verify the reasonableness of the results.

4.2 Solve multistep problems involving rate, average speed, distance, and time or a

direct variation.

by on Jul. 31, 2013 at 12:54 PM

Measurement and Geometry

1.0 Students choose appropriate units of measure and use ratios to convert within

and between measurement systems to solve problems:

1.1 Compare weights, capacities, geometric measures, times, and temperatures within

and between measurement systems (e.g., miles per hour and feet per second, cubic

inches to cubic centimeters).

1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as

products (e.g., person-days) to solve problems; check the units of the solutions; and

use dimensional analysis to check the reasonableness of the answer.

2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They

know how perimeter, area, and volume are affected by changes of scale:

2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional

figures and the surface area and volume of basic three-dimensional figures, includ­

ing rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and

cylinders.

2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.

2.3 Compute the length of the perimeter, the surface area of the faces, and the volume

of a three-dimensional object built from rectangular solids. Understand that when

the lengths of all dimensions are multiplied by a scale factor, the surface area is

multiplied by the square of the scale factor and the volume is multiplied by the

cube of the scale factor.

2.4 Relate the changes in measurement with a change of scale to the units used (e.g.,

square inches, cubic feet) and to conversions between units (1 square foot = 144

square inches or [1 ft2

] = [144 in2

], 1 cubic inch is approximately 16.38 cubic centi­

meters or [1 in3

] = [16.38 cm3

]).

3.0 Students know the Pythagorean theorem and deepen their understanding of

plane and solid geometric shapes by constructing figures that meet given

conditions and by identifying attributes of figures:

3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, mid­

points, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii,

diameters, and chords of circles) by using a compass and straightedge.

by on Jul. 31, 2013 at 12:55 PM

3.2 Understand and use coordinate graphs to plot simple figures, determine lengths

and areas related to them, and determine their image under translations and reflec­

tions.

3.3 Know and understand the Pythagorean theorem and its converse and use it to find

the length of the missing side of a right triangle and the lengths of other line seg­

ments and, in some situations, empirically verify the Pythagorean theorem by

direct measurement.

3.4 Demonstrate an understanding of conditions that indicate two geometrical figures

are congruent and what congruence means about the relationships between the

sides and angles of the two figures.

3.5 Construct two-dimensional patterns for three-dimensional models, such as cylin­

ders, prisms, and cones.

3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectan­

gular solids) and describe how two or more objects are related in space (e.g., skew

lines, the possible ways three planes might intersect).

Statistics, Data Analysis, and Probability

1.0 Students collect, organize, and represent data sets that have one or more vari­

ables 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 boxand-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.

by on Jul. 31, 2013 at 12:56 PM

Mathematical Reasoning

1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrel­

evant 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 Students 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 under­

standing 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.

by on Jul. 31, 2013 at 12:57 PM

Algebra I

Symbolic reasoning and calculations with symbols are central in algebra. Through

the study of algebra, a student develops an understanding of the symbolic language

of mathematics and the sciences. In addition, algebraic skills and concepts are devel­

oped and used in a wide variety of problem-solving situations.

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, 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(2x-5) + 4(x-2) = 12.

5.0 Students solve multistep 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

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).

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.

by on Jul. 31, 2013 at 12:57 PM

8.0 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.

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.

by on Jul. 31, 2013 at 12:58 PM

17.0 Students determine the domain of independent variables and the range of de­

pendent variables defined by a graph, a set of ordered pairs, or a symbolic ex­

pression.

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.

by on Jul. 31, 2013 at 12:58 PM

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 cor­

rectly 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 state­

ment is true sometimes, always, or never.