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# Compiling My Curriculum - Math

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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
Replies (11-20):
by on Jul. 31, 2013 at 1:08 PM

Number Sense

1.0 Students compute with very large and very small numbers, positive integers,

decimals, and fractions and understand the relationship between decimals,

fractions, and percents. They understand the relative magnitudes of numbers:

1.1 Estimate, round, and manipulate very large (e.g., millions) and very small

(e.g., thousandths) numbers.

1.2 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.

1.3 Understand and compute positive integer powers of nonnegative integers; compute

examples as repeated multiplication.

1.4 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 × 2 × 2 × 3 = 23 × 3).

1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and

positive and negative integers.

2.0 Students perform calculations and solve problems involving addition, subtrac­

tion, and simple multiplication and division of fractions and decimals:

2.1 Add, subtract, multiply, and divide with decimals; add with negative integers;

subtract positive integers from negative integers; and verify the reasonableness of

the results.

2.2 Demonstrate proficiency with division, including division with positive decimals

and long division with multidigit divisors.

2.3 Solve simple problems, including ones arising in concrete situations, involving the

addition and subtraction of fractions and mixed numbers (like and unlike denomi­

nators of 20 or less), and express answers in the simplest form.

2.4 Understand the concept of multiplication and division of fractions.

2.5 Compute and perform simple multiplication and division of fractions and apply

these procedures to solving problems.

Algebra and Functions

1.0 Students use variables in simple expressions, compute the value of the expres­

sion for specific values of the variable, and plot and interpret the results:

1.1 Use information taken from a graph or equation to answer questions about a

problem situation.

1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic

expressions in one variable by substitution.

1.3 Know and use the distributive property in equations and expressions with

variables.

1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.

e.

1.5 Solve problems involving linear functions with integer values; write the equation;

and graph the resulting ordered pairs of integers on a grid.

by on Jul. 31, 2013 at 1:09 PM

Measurement and Geometry

1.0 Students understand and compute the volumes and areas of simple objects:

1.1 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).

1.2 Construct a cube and rectangular box from two-dimensional patterns and use

these patterns to compute the surface area for these objects.

1.3 Understand the concept of volume and use the appropriate units in common

measuring systems (i.e., cubic centimeter [cm 3], cubic meter [m3

], cubic inch

[in 3], cubic yard [yd3

]) to compute the volume of rectangular solids.

1.4 Differentiate between, and use appropriate units of measures for, two- and

three-dimensional objects (i.e., find the perimeter, area, volume).

2.0 Students identify, describe, and classify the properties of, and the relation­

ships between, plane and solid geometric figures:

2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles,

and triangles by using appropriate tools (e.g., straightedge, ruler, compass,

protractor, drawing software).

2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles

of any quadrilateral is 360° and use this information to solve problems.

2.3 Visualize and draw two-dimensional views of three-dimensional objects made

from rectangular solids

by on Jul. 31, 2013 at 1:12 PM

Statistics, Data Analysis, and Probability

1.0 Students display, analyze, compare, and interpret different data sets, including

data sets of different sizes:

1.1 Know the concepts of mean, median, and mode; compute and compare simple

examples to show that they may differ.

1.2 Organize and display single-variable data in appropriate graphs and representa­

tions (e.g., histogram, circle graphs) and explain which types of graphs are appro­priate for various data sets.

1.3 Use fractions and percentages to compare data sets of different sizes.

1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data

in terms of the situation depicted by the graph.

1.5 Know how to write ordered pairs correctly; for example, (x, y).

Mathematical Reasoning

1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from

irrelevant information, sequencing and prioritizing information, and observing

patterns.

1.2 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 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.4 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.

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other

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 apply them in other circumstances.

by on Jul. 31, 2013 at 1:15 PM

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 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 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.5 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.

2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.7 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students 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 in new problem situations.

by on Jul. 31, 2013 at 1:18 PM

Measurement and Geometry

1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:

1.1 Understand the concept of a constant such as π; know the formulas for the circum­ference and area of a circle.

1.2 Know common estimates of π (3.14; 22⁄7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.

1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.

2.0 Students identify and describe the properties of two-dimensional figures:

2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).

Statistics, Data Analysis, and Probability

1.0 Students compute and analyze statistical measurements for data sets:

1.1 Compute the range, mean, median, and mode of data sets.

1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.

1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.

1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.

2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:

2.1 Compare different samples of a population with the data from the entire popula­tion and identify a situation in which it makes sense to use a sample.

2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more represen­tative for a population.

2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.

2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.

3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events:

3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.

3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).

3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.

3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

3.5 Understand the difference between independent and dependent events.

by on Jul. 31, 2013 at 1:21 PM

Algebra and Functions

1.0 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:

1.1 Write and solve one-step linear equations in one variable.

1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.

1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.

1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.

2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:

2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centime­ters to inches).

2.2 Demonstrate an understtanding that rate is a measure of one quantity per unit value of another quantity.

2.3 Solve problems involving rates, average speed, distance, and time.

3.0 Students investigate geometric patterns and describe them algebraically:

3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l,

A =⁄2 bh, C = π d—the formulas for the perimeter of a rectangle, the area of a tri­

angle, and the circumference of a circle, respectively).

3.2 Express in symbolic form simple relationships arising from geometry.

by on Jul. 31, 2013 at 1:39 PM

Both my kids have texts books we are using.

by on Jul. 31, 2013 at 1:41 PM

Dang, knew I was forgetting something! LOL, JK

Quoting mem82:

Both my kids have texts books we are using.