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STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL
DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND
ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS. |
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A.
Number Sense |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Extend understanding of the number system by constructing
meanings for the following (unless otherwise noted, all indicators for
grade 7 pertain to these sets of numbers as well):
·
Rational numbers
·
Percents
·
Whole numbers with exponents |
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2.
Demonstrate a sense of the relative magnitudes of numbers. |
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3.
Understand
and use ratios, proportions, and percents (including percents greater
than 100 and less than 1) in a variety of situations. |
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4.
Compare and order numbers of all named types. |
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5.
Use whole numbers, fractions, decimals, and percents to
represent equivalent forms of the same number. |
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6.
Understand
that all fractions can be represented as repeating or terminating
decimals. |
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B.
Numerical Operations |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Use and
explain procedures for performing calculations with integers and all
number types named above with:
·
Pencil-and-paper
·
Mental math
·
Calculator |
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2.
Use exponentiation
to find whole number powers of numbers. |
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3.
Understand and apply the standard
algebraic order of operations, including appropriate use of parentheses. |
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C.
Estimation |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Use
equivalent representations of numbers such as fractions, decimals, and
percents to facilitate estimation. |
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STANDARD 4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL
DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES,
RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA. |
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A.
Geometric Properties |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Understand
and apply properties of polygons.
·
Quadrilaterals, including squares, rectangles, parallelograms,
trapezoids, rhombi
·
Regular
polygons |
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2.
Understand
and apply the concept of similarity.
·
Using
proportions to find missing measures
·
Scale
drawings
·
Models of 3D
objects |
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3.
Use logic and reasoning to make and support conjectures
about geometric objects. |
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B.
Transforming Shapes |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Understand
and apply transformations.
·
Finding the
image, given the pre-image, and vice-versa
·
Sequence of
transformations needed to map one figure onto another
·
Reflections,
rotations, and translations result in images congruent to the pre-image
·
Dilations
(stretching/shrinking) result in images similar to the pre-image |
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C.
Coordinate Geometry |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Use
coordinates in four quadrants to represent geometric concepts. |
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2.
Use a
coordinate grid to model and quantify transformations (e.g., translate
right 4 units). |
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D.
Units of Measurement |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Solve
problems requiring calculations that involve different units of
measurement within a measurement system (e.g., 4’3” plus 7’10” equals
12’1”). |
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2.
Select and
use appropriate units and tools to measure quantities to the degree of
precision needed in a particular problem-solving situation. |
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3.
Recognize
that all measurements of continuous quantities are approximations. |
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E.
Measuring Geometric Objects |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Develop and
apply strategies for finding perimeter and area.
·
Geometric
figures made by combining triangles, rectangles and circles or parts of
circles
·
Estimation
of area using grids of various sizes |
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2.
Recognize that the volume of a pyramid or cone is
one-third of the volume of the prism or cylinder with the same base and
height (e.g., use rice to compare volumes of figures with same base and
height). |
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STANDARD
4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL REPRESENT AND
ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE PROBLEMS
INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.
|
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A.
Patterns |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Recognize,
describe, extend, and create patterns involving whole numbers, rational
numbers, and integers.
·
Descriptions
using tables, verbal and symbolic rules, graphs, simple equations or
expressions
·
Finite and
infinite sequences
·
Generating
sequences by using calculators to repeatedly apply a formula |
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B.
Functions and Relationships |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Graph
functions, and understand and describe their general behavior.
·
Equations
involving two variables |
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C.
Modeling |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Analyze functional relationships to explain how a change in one quantity
can result in a change in another, using pictures, graphs, charts, and
equations. |
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2.
Use
patterns, relations, symbolic algebra, and linear functions to model
situations.
·
Using
manipulatives, tables, graphs, verbal rules, algebraic
expressions/equations/inequalities
·
Growth
situations, such as population growth and compound interest, using
recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social
studies standard 6.6) |
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D.
Procedures |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Use graphing
techniques on a number line.
·
Absolute
value
·
Arithmetic
operations represented by vectors (arrows) (e.g., “-3 + 6” is “left 3,
right 6”) |
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2.
Solve simple
linear equations informally and graphically.
·
Multi-step,
integer coefficients only (although answers may not be integers)
·
Using
paper-and-pencil, calculators, graphing calculators, spreadsheets, and
other technology |
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3.
Create, evaluate, and simplify algebraic expressions
involving variables.
·
Order of operations, including appropriate use of
parentheses
·
Substitution of a number for a variable |
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4.
Understand and apply the properties of operations,
numbers, equations, and inequalities.
·
Additive inverse
·
Multiplicative inverse |
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STANDARD 4.4
(DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS) ALL
STUDENTS WILL DEVELOP AN UNDERSTANDING OF THE CONCEPTS AND TECHNIQUES OF
DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL USE THEM
TO MODEL SITUATIONS, SOLVE PROBLEMS, AND ANALYZE AND DRAW APPROPRIATE
INFERENCES FROM DATA. |
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A.
Data Analysis |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Select and
use appropriate representations for sets of data, and measures of
central tendency (mean, median, and mode).
·
Type of
display most appropriate for given data
·
Box-and-whisker plot, upper quartile, lower quartile
·
Scatter plot
·
Calculators
and computer used to record and process information |
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2.
Make
inferences and formulate and evaluate arguments based on displays and
analysis of data. |
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B.
Probability |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Interpret
probabilities as ratios, percents, and decimals. |
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2.
Model situations involving probability with simulations
(using spinners, dice, calculators and computers) and theoretical
models.
·
Frequency, relative frequency |
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3.
Estimate
probabilities and make predictions based on experimental and theoretical
probabilities. |
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4.
Play and analyze probability-based games, and discuss the
concepts of fairness and expected value. |
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C.
Discrete Mathematics—Systematic Listing and Counting |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Apply
the multiplication principle of counting.
·
Permutations: ordered situations with replacement (e.g., number of
possible license plates) vs. ordered situations without replacement
(e.g., number of possible slates of 3 class officers from a 23 student
class) |
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2.
Explore
counting problems involving Venn diagrams with three attributes (e.g.,
there are 15, 20, and 25 students respectively in the chess club, the
debating team, and the engineering society; how many different students
belong to the three clubs if there are 6 students in chess and debating,
7 students in chess and engineering, 8 students in debating and
engineering, and 2 students in all three?). |
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3.
Apply techniques of systematic listing, counting, and
reasoning in a variety of different contexts. |
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D.
Discrete Mathematics—Vertex-Edge Graphs and Algorithms |
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Building upon knowledge and
skills gained in preceding grades, by the end of Grade 7, students will: |
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1.
Use vertex-edge graphs to represent and find solutions to
practical problems.
·
Finding the shortest network connecting specified sites
·
Finding the shortest route on a map from one site to
another
·
Finding the shortest circuit on a map that makes a tour of
specified sites |
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STANDARD
4.5 (MATHEMATICAL PROCESSES) ALL STUDENTS WILL USE MATHEMATICAL
PROCESSES OF PROBLEM SOLVING, COMMUNICATION, CONNECTIONS, REASONING,
REPRESENTATIONS, AND TECHNOLOGY TO SOLVE PROBLEMS AND COMMUNICATE
MATHEMATICAL IDEAS. |
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A.
Problem Solving |
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At each grade level,
with respect to content appropriate for that grade level, students will: |
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1.
Learn
mathematics through problem solving, inquiry, and discovery. |
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2.
Solve
problems that arise in mathematics and in other contexts (cf. workplace
readiness standard 8.3).
·
Open-ended
problems
·
Non-routine
problems
·
Problems
with multiple solutions
·
Problems
that can be solved in several ways |
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3.
Select and
apply a variety of appropriate problem-solving strategies (e.g., “try a
simpler problem” or “make a diagram”) to solve problems. |
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4.
Pose
problems of various types and levels of difficulty. |
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5.
Monitor
their progress and reflect on the process of their problem solving
activity. |
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B.
Communication |
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At each grade level, with respect to content appropriate for that
grade level, students will: |
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1.
Use
communication to organize and clarify their mathematical thinking.
·
Reading and
writing
·
Discussion,
listening, and questioning |
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2.
Communicate
their mathematical thinking coherently and clearly to peers, teachers,
and others, both orally and in writing. |
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3.
Analyze and
evaluate the mathematical thinking and strategies of others. |
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4.
Use the
language of mathematics to express mathematical ideas precisely. |
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C.
Connections |
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At each grade level, with respect to content appropriate for that
grade level, students will: |
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1.
Recognize
recurring themes across mathematical domains (e.g., patterns in number,
algebra, and geometry). |
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2.
Use
connections among mathematical ideas to explain concepts (e.g., two
linear equations have a unique solution because the lines they represent
intersect at a single point). |
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3.
Recognize
that mathematics is used in a variety of contexts outside of
mathematics. |
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4.
Apply
mathematics in practical situations and in other disciplines. |
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5.
Trace the
development of mathematical concepts over time and across cultures (cf.
world languages and social studies standards). |
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6.
Understand
how mathematical ideas interconnect and build on one another to produce
a coherent whole. |
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D.
Reasoning |
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At each grade level, with respect to content appropriate for that
grade level, students will: |
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1.
Recognize
that mathematical facts, procedures, and claims must be justified. |
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2.
Use
reasoning to support their mathematical conclusions and problem
solutions. |
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3.
Select and
use various types of reasoning and methods of proof. |
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4.
Rely on
reasoning, rather than answer keys, teachers, or peers, to check the
correctness of their problem solutions. |
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5.
Make and
investigate mathematical conjectures.
·
Counterexamples as a means of disproving conjectures
·
Verifying
conjectures using informal reasoning or proofs. |
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6.
Evaluate
examples of mathematical reasoning and determine whether they are valid. |
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E.
Representations |
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At each grade level, with respect to content appropriate for that
grade level, students will: |
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1.
Create and
use representations to organize, record, and communicate mathematical
ideas.
·
Concrete
representations (e.g., base-ten blocks or algebra tiles)
·
Pictorial
representations (e.g., diagrams, charts, or tables)
·
Symbolic
representations (e.g., a formula)
·
Graphical
representations (e.g., a line graph) |
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2.
Select,
apply, and translate among mathematical representations to solve
problems. |
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3.
Use
representations to model and interpret physical, social, and
mathematical phenomena. |
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F.
Technology |
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At each grade level, with respect to content appropriate for that
grade level, students will: |
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1.
Use
technology to gather, analyze, and communicate mathematical information. |
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2.
Use
computer spreadsheets, software, and graphing utilities to organize and
display quantitative information. |
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3.
Use graphing calculators and computer software to
investigate properties of functions and their graphs. |
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4.
Use
calculators as problem-solving tools (e.g., to explore patterns, to
validate solutions). |
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5.
Use
computer software to make and verify conjectures about geometric
objects. |
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6.
Use computer-based laboratory technology for mathematical
applications in the sciences. |