Download 7th Grade Math Course Objectives File - Parsippany

Parsippany-Troy Hills School District
MTH773 – Math Grade 7
A Course Outline for Grade 7 Mathematics
Approved by the Board of Education
____________
Developed:
Revised:
Approved:
MTH773: Math – Grade 7
PARSIPPANY-TROY HILLS TOWNSHIP SCHOOLS
COURSE PROFICIENCIES
Course:
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MTH 773
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.
THE NUMBER SYSTEM
The student will:
1. Recognize the sets of whole numbers, integers and rational numbers.
2. Compare and order integers and rational numbers.
3. Apply and extend previous understandings of addition and subtraction to add and subtract
rational numbers; represent addition and subtraction on a horizontal or vertical line.
4. Describe situations in which opposite quantities combine to make zero (for example, a hydrogen
atom has 0 charge because its two constituents are oppositely charged).
5. Interpret absolute value as the distance from zero on a number line and determine the absolute
value for a specified number.
6. Understand p + q as the number located a distance |q| from p, in the positive or negative
direction depending on whether q is positive or negative. Show that a number and its opposite
(additive inverse) have a sum of zero. Interpret sums of rational numbers by describing real
world contexts
7. Understand subtraction of rational numbers as addition of the additive inverse; p + q = p + (-q).
Show that the distance |q| between two rational numbers on a number line is the absolute value
of their difference, and apply this principle in real world contexts.
8. Apply properties of operations as strategies to add and subtract rational numbers.
9. Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
10. Understand that multiplication is extended from fractions to rational numbers by requiring that
operations continue to satisfy the properties of operations, particularly distributive property,
leading to products such as (-1)(-1) = 1 and rules for multiplying signed numbers. Interpret
products of rational numbers by describing real world contexts.
11. Understand that integers can be divided, provided the divisor is not zero, and every quotient of
integers (with non-zero divisor) is a rational number. If p and q are integers, then (-p/q) = (-p)/q =
p/(-q). Interpret quotients of rational numbers by describing real world contexts.
12. Apply properties of operations as strategies to multiply and divide rational numbers.
13. Convert a rational number to a decimal using long division; know that the decimal form of a
rational number terminates in zeroes or eventually repeats.
14. Solve real world and mathematical problems involving the four operations with rational numbers.
EXPRESSIONS & EQUATIONS
The student will:
15. Identify the commutative, associative, distributive, identity and inverse properties and apply
them to facilitate mental arithmetic.
16. 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.
MTH773: Math – Grade 7
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17. Create, evaluate, and simplify algebraic expressions, rewriting such expressions as needed to help
analyze a problem.
18. Use variables to represent quantities in a real world or mathematical problem, construct simple
equations and inequalities to solve problems by reasoning about the quantities.
19. Solve equations of the form px + q = r or p(x + q) = r where p, q, and r are specific rational
numbers.
20. 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.
21. Read, write and graph inequalities on a number line.
22. 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. Apply algebraic expressions and equations to model and solve a variety of word and real life
problems.
RATIO & PROPORTION
The student will:
25. Identify, write and compare ratios and rates.
26. Find equivalent ratios and identify proportions.
27. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
28. Represent proportional relationships by equations; solve proportions by using cross products.
29. 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.
30. Define the fundamental relationship of similarity between geometric figures; use proportions to find
missing measures of similar polygons.
31. Draw (freehand, with ruler/protractor, and with technology) geometric shapes with given conditions.
32.
33.
34.
35.
36.
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
Understand the relationship between percents, fractions, and decimals.
Solve problems by estimating with percents.
Find either the percent, percentage (part) or base (whole) using the proportion or equation method;
include percents greater than 100 and less than 1.
Solve problems involving percent increase or decrease.
Solve problems involving discount, tax, tip, interest, percent increase and decrease and other real-life
applications.
STATISTICS & PROBABILITY
The student will:
37. 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.
38. 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.
MTH773: Math – Grade 7
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39. 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.
40. Determine the mean, median, mode and range of a set of data.
41. Use measures of center and measures of variability for numerical data from random samples to
draw informal comparative inferences about two populations.
42. Select, construct and use appropriate graphical representations (line plot, stem-and-leaf plot, and
frequency table) for a set of data.
43. 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.
44. Interpret probabilities as ratios, percents, and decimals.
45. Model situations involving probabilities using simulations (using spinners, dice, calculators, and
computers) and theoretical models.
46. 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.
47. 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.
48. 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.
49. Understand that, just as with simple events, the probability of a compound event us the fraction
of outcomes in the sample space for which the compound event occurs.
50. Represent sample spaces for compound events using methods such as organized lists, tables, tree
diagrams, and simulation.
51. Design and use simulation to generate frequencies for compound events.
GEOMETRY
The student will:
52. Select appropriate units that will measure quantities to a desired level. Include conversion of
units from one form to another within a given system.
53. Solve problems requiring calculations that involve different units of measure within a measurement
system.
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.
55. 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 problems.
54.
56. Develop and apply a variety of strategies for determining circumference and perimeter.
57. Develop and apply a variety of strategies for determining the area of circles, parallelograms, triangles,
trapezoids and composite figures.
58. Identify and classify three-dimensional figures.
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59. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in
plane sections of right rectangular prisms and right rectangular
60. Develop strategies and formulas for finding the volume of prisms.
61. Develop and apply strategies and formulas for finding the surface area of prisms, cylinders and spheres.
62. Solve real world and mathematical problems involving volume and surface area of two and three
dimensional figures composed of triangles, quadrilaterals, polygons, cubes, and right prisms