 
Math

Ratio Proportion

Grade 7

A. 
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, realworld and nonroutine
problems. 
B. 
NUMBER OPERATIONS &
RELATIONSHIPS Students in Wisconsin will use numbers effectively for
various purposes, such as counting, measuring, estimating, and problem
solving. 
D. 
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 problemsolving situations. 
F. 
ALGEBRAIC RELATIONSHIPS 
Students in Wisconsin will discover, describe, and generalize simple and
complex patterns and relationships. In the context of realworld
problem situations, the student will use algebraic techniques to define
and describe the problem to determine and justify appropriate solutions. 
Performance Standards 
A.8.1 
Use reasoning abilities to:
Evaluate information.
Perceive patterns.
Identify Relationships
Formulate questions for further exploration.
Evaluate strategies
Justify Statements.
Test reasonableness of results.
Defend work. 
A.8.2 
Communicate logical arguments clearly
to show why a result makes sense. 
A.8.3 
Analyze non routine problems by
modeling illustrating, guessing, simplifying, generalizing, shifting to
another point of view, etc. 
A.8.4 
Develop effective oral and written
presentations that include:
The conventions of mathematical discourse (e.g.,
symbols, definitions, labeled drawings).
Mathematical language.
Understanding of purpose and audience.
Clear organization of ideas and procedures. 
A.8.5 
Explain mathematical concepts,
procedures, and ideas to others who may not be familiar with them. 
A.8.6 
Read and understand mathematical texts
and other instructional materials and recognize mathematical ideas as they
appear in other contexts 
B.8.1 
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). 
B.8.2 
Perform and explain operations on
rational numbers (add, subtract, multiply, divide, raise to a power, take
opposites and reciprocals). 
B.8.3 
Generate and explain equivalences among
fractions, decimals, and percents. 
B.8.4 
Express order relationships among
rational numbers using appropriate symbols (>,<,³,²,). 
B.8.5 
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) 
B.8.6 
Model and solve problems involving
numbertheory concepts such as:
Prime and composite numbers
Divisibility and remainders.
Greatest Common factors.
Least common multiples. 
B.8.7 
In problemsolving situations, select
and use appropriate computational procedures with rational numbers such
as:
Calculating mentally.
Estimating. 
D.8.2 
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 sixtenths of a mile).
Knowledge that direct measurement produces
approximate, not exact, measures.
The use of smaller units to produce more precise
measures.

D.8.4 
Determine measurements indirectly
using:
Ratio and proportion (e.g., similarity, scale
drawings). 
F.8.1 
Work
with algebraic expressions in a variety of ways, including:
Using
appropriate symbolism, including exponents and variables.
Evaluating
expressions through numerical substitution.
Generating
equivalent expressions.
Adding
& subtracting expressions. 
F.8.2 
Work
with linear & nonlinear patters and relationships in a variety of
ways, including:
Representing
them with tables, with graphs, & with algebraic expressions,
equations, & inequalities. 
F.8.5 
Recognize
and use generalized properties and relations including:
Additive
and multiplicative property of equations and inequalities.
Commutatively
and associatively of addition and multiplication.
Inverses
and identities for addition and multiplication. 
Unit
Objectives 
1. 
Writing ratios three different ways in
simplest form 
2. 
Understand the concept of a ratio and
its similarity and difference to a fraction. 
3. 
Writing equivalent ratios. 
4. 
Using tables to express equivalent
ratios. 
5. 
Understand the difference between a
ratio, rate and proportion. 
6. 
Finding unit rates. 
7. 
Convert between decimals, and fractions. 
8. 
Testing proportionality. 
9. 
W4iting proportions. 
10. 
Solving proportions. 
11. 
Scale drawings. 
12. 
Apply ratio proportion to real world. 
13. 
Using proportions to solve similarity. 
