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§111.23. Mathematics, Grade 7.
(a) Introduction.
(1) Within a well-balanced mathematics curriculum, the primary focal points
at Grade 7 are using proportional relationships in number, geometry,
measurement, and probability; applying addition, subtraction,
multiplication, and division of decimals, fractions, and integers; and using
statistical measures to describe data.
(2) Throughout mathematics in Grades 6-8, students build a foundation of
basic understandings in number, operation, and quantitative reasoning;
patterns, relationships, and algebraic thinking; geometry and spatial
reasoning; measurement; and probability and statistics. Students use
concepts, algorithms, and properties of rational numbers to explore
mathematical relationships and to describe increasingly complex situations.
Students use algebraic thinking to describe how a change in one quantity in
a relationship results in a change in the other; and they connect verbal,
numeric, graphic, and symbolic representations of relationships. Students
use geometric properties and relationships, as well as spatial reasoning, to
model and analyze situations and solve problems. Students communicate
information about objects or situations by quantifying attributes,
generalize procedures from measurement experiences, and use the procedures
to solve problems. Students use appropriate statistics, representations of
data, reasoning, and concepts of probability to draw conclusions, evaluate
arguments, and make recommendations.
(3) Problem solving, language and communication, connections within and
outside mathematics, and formal and informal reasoning underlie all content
areas in mathematics. Throughout mathematics in Grades 6-8, students use
these processes together with technology (at least four-function calculators
for whole numbers, decimals, and fractions) and other mathematical tools
such as manipulative materials to develop conceptual understanding and solve
problems as they do mathematics.
(b) Knowledge and skills.
(1) Number, operation, and quantitative reasoning. The student represents
and uses numbers in a variety of equivalent forms. The student is expected
to:
(A) compare and order integers and positive rational numbers;
(B) convert between fractions, decimals, whole numbers, and percents
mentally, on paper, or with a calculator; and
(C) represent squares and square roots using geometric models.
(2) Number, operation, and quantitative reasoning. The student adds,
subtracts, multiplies, or divides to solve problems and justify solutions.
The student is expected to:
(A) represent multiplication and division situations involving fractions
and decimals with concrete models, pictures, words, and numbers;
(B) use addition, subtraction, multiplication, and division to solve
problems involving fractions and decimals;
(C) use models to add, subtract, multiply, and divide integers and connect
the actions to algorithms;
(D) use division to find unit rates and ratios in proportional
relationships such as speed, density, price, recipes, and student-teacher
ratio;
(E) simplify numerical expressions involving order of operations and
exponents;
(F) select and use appropriate operations to solve problems and justify the
selections; and
(G) determine the reasonableness of a solution to a problem.
(3) Patterns, relationships, and algebraic thinking. The student solves
problems involving proportional relationships. The student is expected to:
(A) estimate and find solutions to application problems involving percent;
and
(B) estimate and find solutions to application problems involving
proportional relationships such as similarity, scaling, unit costs, and
related measurement units.
(4) Patterns, relationships, and algebraic thinking. The student represents
a relationship in numerical, geometric, verbal, and symbolic form. The
student is expected to:
(A) generate formulas involving conversions, perimeter, area,
circumference, volume, and scaling;
(B) graph data to demonstrate relationships in familiar concepts such as
conversions, perimeter, area, circumference, volume, and scaling; and
(C) describe the relationship between the terms in a sequence and their
positions in the sequence.
(5) Patterns, relationships, and algebraic thinking. The student uses
equations to solve problems. The student is expected to:
(A) use concrete models to solve equations and use symbols to record the
actions; and
(B) formulate a possible problem situation when given a simple equation.
(6) Geometry and spatial reasoning. The student compares and classifies
shapes and solids using geometric vocabulary and properties. The student is
expected to:
(A) use angle measurements to classify pairs of angles as complementary or
supplementary;
(B) use properties to classify shapes including triangles, quadrilaterals,
pentagons, and circles;
(C) use properties to classify solids, including pyramids, cones, prisms,
and cylinders; and
(D) use critical attributes to define similarity.
(7) Geometry and spatial reasoning. The student uses coordinate geometry to
describe location on a plane. The student is expected to:
(A) locate and name points on a coordinate plane using ordered pairs of
integers; and
(B) graph translations on a coordinate plane.
(8) Geometry and spatial reasoning. The student uses geometry to model and
describe the physical world. The student is expected to:
(A) sketch a solid when given the top, side, and front views;
(B) make a net (two-dimensional model) of the surface area of a solid; and
(C) use geometric concepts and properties to solve problems in fields such
as art and architecture.
(9) Measurement. The student solves application problems involving
estimation and measurement. The student is expected to estimate measurements
and solve application problems involving length (including perimeter and
circumference), area, and volume.
(10) Probability and statistics. The student recognizes that a physical or
mathematical model can be used to describe the probability of real-life
events. The student is expected to:
(A) construct sample spaces for compound events (dependent and
independent); and
(B) find the approximate probability of a compound event through
experimentation.
(11) Probability and statistics. The student understands that the way a set
of data is displayed influences its interpretation. The student is expected
to:
(A) select and use an appropriate representation for presenting collected
data and justify the selection; and
(B) make inferences and convincing arguments based on an analysis of given
or collected data.
(12) Probability and statistics. The student uses measures of central
tendency and range to describe a set of data. The student is expected to:
(A) describe a set of data using mean, median, mode, and range; and
(B) choose among mean, median, mode, or range to describe a set of data and
justify the choice for a particular situation.
(13) Underlying processes and mathematical tools. The student applies Grade
7 mathematics to solve problems connected to everyday experiences,
investigations in other disciplines, and activities in and outside of
school. The student is expected to:
(A) identify and apply mathematics to everyday experiences, to activities
in and outside of school, with other disciplines, and with other
mathematical topics;
(B) use a problem-solving model that incorporates understanding the
problem, making a plan, carrying out the plan, and evaluating the solution
for reasonableness;
(C) select or develop an appropriate problem-solving strategy from a
variety of different types, including drawing a picture, looking for a
pattern, systematic guessing and checking, acting it out, making a table,
working a simpler problem, or working backwards to solve a problem; and
(D) select tools such as real objects, manipulatives, paper/pencil, and
technology or techniques such as mental math, estimation, and number sense
to solve problems.
(14) Underlying processes and mathematical tools. The student communicates
about Grade 7 mathematics through informal and mathematical language,
representations, and models. The student is expected to:
(A) communicate mathematical ideas using language, efficient tools,
appropriate units, and graphical, numerical, physical, or algebraic
mathematical models; and
(B) evaluate the effectiveness of different representations to communicate
ideas.
(15) Underlying processes and mathematical tools. The student uses logical
reasoning to make conjectures and verify conclusions. The student is
expected to:
(A) make conjectures from patterns or sets of examples and nonexamples; and
(B) validate his/her conclusions using mathematical properties and
relationships.
Source: The provisions of this §111.23 adopted to be effective September 1,
1998, 22 TexReg 7623.
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