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Grade 7: Pre-Algebra
Seventh graders study, explore, and ultimately master concepts in seven
major
topics of Mathematics which provide the foundation for all other higher-
level
courses. Students begin by learning how to create and interpret different
types of graphs and analyze data. They move to computing with integers
(positive and negative numbers), and then to writing and solving algebraic
equations. Measurements and conversions (decimals, fractions, and percents)
build on their knowledge of graphing and algebraic expressions. In the
geometry unit, students measure and calculate two- and three-dimensional
properties of figures (area, surface area, volume). Linear functions
(points, slope, graphing equations) incorporate many of the above concepts
and readies the students for in-depth study of algebra. The last unit
students encounter is probability, or the predicting of possible outcomes,
given various factors. This culminates in the Probability Fair.
NUMBER SENSE AND OPERATIONS STRAND
Students engage in problem solving, communicating, reasoning, connecting,
and
representing as they:
7.N.1 Compare, order, estimate, and translate among integers, fractions
and
mixed numbers (i.e., rational numbers), decimals, and percents.
This standard is intentionally the same as standard 8.N.1.
7.N.2 Use ratios and proportions in the solution of problems involving
unit
rates, scale drawings, and reading of maps.
7.N.3 Represent numbers in scientific notation (positive powers of ten
only) and use that notation in problem situations.
7.N.4 Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3.
This standard is intentionally the same as standard 8.N.6.
7.N.5 Apply the rules of positive integer exponents to the solution of
problems. Extend the Order of Operations to include positive integer
exponents.
7.N.6 Use the inverse relationships of addition and subtraction, and of
multiplication and division, to simplify computations and solve problems,
e.g., multiplying by 1/2 or 0.5 is the same as dividing by 2.
7.N.7 Estimate and compute with fractions (including simplification of
fractions), integers, decimals, and percents (including those greater than
100 and less than 1).
This standard is intentionally the same as standard 8.N.10.
7.N.8 Determine when an estimate rather than an exact answer is
appropriate
and apply in problem situations.
This standard is intentionally the same as standard 8.N.11.
7.N.9 Select and use appropriate operations—addition, subtraction,
multiplication, division, and positive integer exponents—to solve problems
with rational numbers (including negatives).
This standard is intentionally the same as standard 8.N.12.
PATTERNS, RELATIONS, AND ALGEBRA STRAND
Students engage in problem solving, communicating, reasoning, connecting,
and
representing as they:
7.P.1 Extend, represent, analyze, and generalize a variety of patterns
with
tables, graphs, words, and, when possible, symbolic expressions. Include
arithmetic and geometric progressions, e.g., compounding.
This standard is intentionally the same as standard 8.P.1.
7.P.2 Evaluate simple algebraic expressions for given variable values,
e.g., 3a2 – b for a = 3 and b = 7.
This standard is intentionally the same as standard 8.P.2.
7.P.3 Create and use symbolic expressions for linear relationships and
relate them to verbal, tabular, and graphical representations.
7.P.4 Solve linear equations using tables, graphs, models, and algebraic
methods.
7.P.5 Identify, describe, and analyze linear relationships between two
variables. Compare positive rate of change, e.g., y = 3x + 1, to negative
rate of change, e.g., y = –3x + 1.
7.P.6 Use linear equations to model and analyze problems involving
proportional relationships. Use technology as appropriate.
GEOMETRY STRAND
Students engage in problem solving, communicating, reasoning, connecting,
and
representing as they:
7.G.1 Analyze, apply, and explain the relationship between the number of
sides and the sums of the interior angle measures of polygons.
7.G.2 Classify figures in terms of congruence and similarity, and apply
these relationships to the solution of problems.
This standard is intentionally the same as standard 8.G.2.
7.G.3 Demonstrate an understanding of the relationships of angles formed
by
intersecting lines, including parallel lines cut by a transversal.
This standard is intentionally the same as standard 8.G.3.
7.G.4 Graph points and identify coordinates of points on the Cartesian
coordinate plane (all four quadrants).2
7.G.5 Use a ruler, protractor, and compass to draw polygons and circles.
7.G.6 Predict the results of translations and reflections of figures on
unmarked or coordinate planes and draw the transformed figure.
7.G.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their
physical appearance, distinguishing attributes, and spatial relationships
such as parallel faces.
MEASUREMENT STRAND
Students engage in problem solving, communicating, reasoning, connecting,
and
representing as they:
7.M.1 Select, convert (within the same system of measurement), and use
appropriate units of measurement or scale.
This standard is intentionally the same as standard 8.M.1.
7.M.2 Given the formulas, convert from one system of measurement to
another. Use technology as appropriate.
This standard is intentionally the same as standard 8.M.2.
7.M.3 Demonstrate an understanding of the concepts and apply formulas and
procedures for determining measures, including those of area and
perimeter/circumference of parallelograms, trapezoids, and circles. Given
the
formulas, determine the surface area and volume of rectangular prisms and
cylinders. Use technology as appropriate.
DATA ANALYSIS, STATISTICS, AND PROBABILITY STRAND
Students engage in problem solving, communicating, reasoning, connecting,
and
representing as they:
7.D.1 Select, create, interpret, and utilize the following tabular and
graphical representations of data: circle graphs, Venn diagrams, stem-and-
leaf plots, tables, and charts.
7.D.2 Find, describe, and interpret appropriate measures of central
tendency (mean, median, and mode) and spread (range) that represent a set of
data. Use these notions to compare different sets of data.
This standard is intentionally the same as standard 8.D.3.
7.D.3 Use tree diagrams, tables, organized lists, and area models to
compute probabilities for simple compound events, e.g., multiple coin tosses
or rolls of number cubes.
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