||MATHEMATICAL PROCESSES -
Students in Wisconsin will draw on a broad body of mathematical knowledge
and apply a variety of mathematical skills and strategies, including
reasoning, oral and written communication, and the use of appropriate
technology, when solving mathematical, real-world and non-routine
||NUMBER OPERATIONS &
RELATIONSHIPS Students in Wisconsin will use numbers effectively for
various purposes, such as counting, measuring, estimating, and problem
||MEASUREMENT - Students in
Wisconsin will select and use appropriate tools (including technology) and
techniques to measure things to a specified degree of accuracy. They will
use measurements in problem-solving situations.
||ALGEBRAIC RELATIONSHIPS -
Students in Wisconsin will discover, describe, and generalize simple and
complex patterns and relationships. In the context of real-world
problem situations, the student will use algebraic techniques to define
and describe the problem to determine and justify appropriate solutions.
||Use reasoning abilities to:
Formulate questions for further exploration.
Test reasonableness of results.
||Communicate logical arguments clearly
to show why a result makes sense.
||Analyze non routine problems by
modeling illustrating, guessing, simplifying, generalizing, shifting to
another point of view, etc.
||Develop effective oral and written
presentations that include:
The conventions of mathematical discourse (e.g.,
symbols, definitions, labeled drawings).
Understanding of purpose and audience.
Clear organization of ideas and procedures.
||Explain mathematical concepts,
procedures, and ideas to others who may not be familiar with them.
||Read and understand mathematical texts
and other instructional materials and recognize mathematical ideas as they
appear in other contexts
||Read, represent, and interpret various
rational numbers (whole numbers, integers, decimals, fractions, and percents)
with verbal descriptions, geometric models, and mathematical notation
(e.g., expanded, scientific, exponential).
||Perform and explain operations on
rational numbers (add, subtract, multiply, divide, raise to a power, take
opposites and reciprocals).
||Generate and explain equivalences among
fractions, decimals, and percents.
||Express order relationships among
rational numbers using appropriate symbols (>,<,³,²,).
||Apply proportional thinking in a
variety of problem situations that include, but are not limited to:
Percents, including those greater than 100 and
less than one (e.g., discounts, rate of increase or decrease, sales tax)
||Model and solve problems involving
number-theory concepts such as:
Prime and composite numbers
Divisibility and remainders.
Greatest Common factors.
Least common multiples.
||In problem-solving situations, select
and use appropriate computational procedures with rational numbers such
||Demonstrate understanding of basic
measurement facts, principles, and techniques including the following:
Approximate comparisons, between metric and US
Customary units (e.g., a liter and a quart are about the same; a kilometer
is about six-tenths of a mile).
Knowledge that direct measurement produces
approximate, not exact, measures.
The use of smaller units to produce more precise
||Determine measurements indirectly
Ratio and proportion (e.g., similarity, scale
with algebraic expressions in a variety of ways, including:
appropriate symbolism, including exponents and variables.
expressions through numerical substitution.
& subtracting expressions.
with linear & nonlinear patters and relationships in a variety of
them with tables, with graphs, & with algebraic expressions,
equations, & inequalities.
and use generalized properties and relations including:
and multiplicative property of equations and inequalities.
and associatively of addition and multiplication.
and identities for addition and multiplication.
||Writing ratios three different ways in
||Understand the concept of a ratio and
its similarity and difference to a fraction.
||Writing equivalent ratios.
||Using tables to express equivalent
||Understand the difference between a
ratio, rate and proportion.
||Finding unit rates.
||Convert between decimals, and fractions.
||Apply ratio proportion to real world.
||Using proportions to solve similarity.