Download 7th Grade Math Advanced Course Objectives File - Parsippany

Parsippany-Troy Hills School District
PARSIPPANY-TROY HILLS TOWNSHIP SCHOOLS
COURSE PROFICIENCIES
Course:
MTH 775
Title:
GRADE 7 ADVANCED MATH
In accordance with district policy as mandated by the New Jersey Administrative Code and the Common Core State Standards (CCCS), the following
are proficiencies required for the successful completion of the above named course.
EXPRESSIONS & REAL NUMBERS
The student will:
1. Recognize the sets of whole numbers, integers, rational, irrational, and real numbers.
2. Determine the classification of all real numbers and demonstrate the interrelationships between its subsets.
3. Identify the commutative, associative, distributive, identity and inverse properties and apply them to facilitate mental arithmetic.
4. Apply properties of operations as strategies to add, subtract, multiply, divide, and exponentiate rational numbers.
5. Apply and extend previous understandings of addition, subtraction, and absolute value to evaluate algebraic expressions involving addition and
subtraction of integers.
6. Apply and extend previous understandings of multiplication and division to evaluate algebraic expressions involving multiplication and division
of integers.
7. Apply and extend previous understandings of addition and subtraction of decimals and fractions to evaluate algebraic expressions involving
addition and subtraction of rational numbers.
8. Apply and extend previous understandings of multiplication and division of decimals and fractions to evaluate algebraic expressions involving
multiplication and division of rational numbers.
9. Simplify algebraic expressions by application of the distributive property and/or combining like terms.
10. Create, evaluate, and simplify algebraic expressions, rewriting such expressions as needed to help analyze a problem.
11. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how quantities in it are
related.
12. Convert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in zeroes or eventually repeats.
13. Solve real world and mathematical problems involving the four operations with rational numbers.
14. Determine the Greatest Common Factor (GCF) and/or Least Common Multiple (LCM) for a set of numbers using prime factorization.
15. Interpret the representation of very large or very small numbers on a calculator; translate between scientific and standard notation; perform
arithmetic operations on numbers in scientific notation.
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Evaluate expressions with positive and negative exponents.
Estimate and determine square and cube roots of rational numbers.
EQUATIONS & FUNCTIONS
The student will:
18. Write and solve one step equations through application of inverse operations.
19. Write and solve one step inequalities, graphing the solution set on a number line.
20. Write and solve two step equations of the form px + q = r or p(x + q) = r where p, q, and r are specific rational numbers.
21. Interpret and solve word problems leading to equations of the form px + q = r or p(x + q) = r where p, q, and r are specific rational numbers.
22. Write and solve inequalities of the form px + q > r or p(x + q) < r where p, q, and r are specific rational numbers.
23. Interpret and solve word problems leading to inequalities of the form px + q > r or p(x + q) < r where p, q, and r are specific rational numbers.
24. Write and solve equations and inequalities with multiple variable terms on the same side.
25. Write and solve equations and inequalities with variable terms on both sides.
26. Write and solve a literal equation for a given variable.
27. Convert a repeating decimal to a fraction through use of algebraic equations.
28. Use variables to represent quantities in a real world or mathematical problem, construct equations and inequalities to solve problems by
reasoning about the quantities.
29. Understand that a function is a rule that assigns to each input exactly one output, and that the graph of a function is the set of ordered pairs
consisting of an input and its corresponding output.
30. Compare properties of two functions each represented in a different way (algebraically, numerically in tables, or by verbal descriptions) and
determine which would have a greater rate of change.
31. Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; be able to give examples of functions that are not
linear.
32. Construct a function to model a linear relationship between two quantities given a table, equation, or graph.
33. Determine the rate of change and initial value of the function from description of a relationship or two (x, y) values; interpret the rate of change
and initial value in terms of the situation it models and its graph or table of values.
34. Describe qualitatively the functional relationship between two quantities by analyzing a graph, or sketch a graph that would exhibit the
qualitative features of a function that has been described verbally.
RATIO & PROPORTION
The student will:
35. Identify, write and compare ratios and rates.
36. Find equivalent ratios and identify proportions.
37. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
38. Represent proportional relationships by equations; solve proportions by using cross products.
39. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and
reproducing a scale drawing at a different scale.
40. Define the fundamental relationship of similarity between geometric figures; use proportions to find missing measures of similar polygons.
41. Draw (freehand, with ruler/protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from
three measures of angles and sides, noticing when the conditions define a unique triangle, more than one type of triangle, or no triangle.
42. Understand the relationship between percents, fractions, and decimals and perform conversions between them.
43. Solve problems by estimating with percents.
44. Find either the percent, percentage (part) or base (whole) using the proportion or equation method; include percents greater than 100 and less
than 1.
45. Solve problems involving percent increase or decrease.
46. Solve problems involving discount, tax, tip, commission, interest, and other real-life applications.
47. Solve problems involving simple interest and future growth, compare compound interest to simple interest for a given situation.
STATISTICS & PROBABILITY
The student will:
48. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a
population from a sample space are valid only if the sample is representative of that population; random sampling tends to produce
representative samples and support valid inferences.
49. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples
(or simulated samples) of the same size to gauge the variation in estimates or predictions.
50. Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the
centers by expressing it as a multiple of a measure of variability.
51. Determine the mean, median, mode and range of a set of data.
52. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about
two populations.
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Select, construct and use appropriate graphical representations (line plot, stem-and-leaf plot, and frequency table) for a set of data.
Understand and apply the ratio definition of probability (success/total outcomes); understand that a probability near 0 indicates an unlikely
event and a probability near 1 indicates a likely event.
Interpret probabilities as ratios, percents, and decimals.
Model situations involving probabilities using simulations (using spinners, dice, calculators, and computers) and theoretical models.
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-term frequency;
predict/estimate the approximate relative frequency given the probability.
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Compare
probabilities from a model to observed frequencies; if the agreement is not good, explain possible discrepancies.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the
compound event occurs.
Represent sample spaces for compound events using methods such as organized lists, tables, tree diagrams, and simulation.
Design and use simulation to generate frequencies for compound events.
GEOMETRY
The student will:
63. Verify experimentally the properties of rotations, reflections, and translations.
64. Understand that a plane figure will be congruent to another if the second can be obtained from the first by a sequence of rotations, reflections,
and translations; given two congruent figures describe a sequence of rotations, reflections, and translations that exhibits the congruence
between them.
65. Describe the effect of dilations, translations, reflections, and rotations on two dimensional figures in the coordinate plane.
66. Understand that a plane figure will be similar to another if the second can be obtained from the first by a sequence of dilations, rotations,
reflections, and translations; given two similar figures describe a sequence of rotations, reflections, and translations that exhibits the similarity
between them.
67. Identify supplementary, complementary, vertical, and adjacent angles, and use facts about them in a multi-step problem to write and solve
simple equations for an unknown angle in a figure.
68. Use informal arguments to establish facts about the angle sum, exterior angle sums of triangles, angle-angle criterion for similarity of triangles,
and the angles created when parallel lines are cut by a transversal.
69. Explain a proof of the Pythagorean Theorem, and its converse.
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Apply the Pythagorean Theorem to determine unknown side lengths of right triangles in real-world and mathematical problems in two and
three dimensions.
Apply the Pythagorean Theorem to determine the distance (in units) between two points on the coordinate plane.
Develop and apply a variety of strategies for determining the area of parallelograms, triangles, trapezoids and composite figures.
Discover and understand the concept of π (pi) as the ratio of circumference to perimeter; know the formulas for area and circumference and
use them to solve real-world and mathematical problems.
Identify and classify three-dimensional figures.
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right
rectangular pyramids.
Develop and apply strategies and formulas for finding the surface area of prisms, cylinders and spheres; use them to solve real-world and
mathematical problems.
Develop strategies and formulas for finding the volume of prisms; use them to solve real-world and mathematical problems.
Know the formulas for volume of cones, cylinders, and spheres; use them to solve real-world and mathematical problems.