Equation model

– An equation

that describes the relationship be-

tween two variables.

Fulcrum

– The balance point of a

teeter-totter or balance.

Graph Model

– A line or curve that

represents a mathematical rela-

tionship. If plotted data show a

trend, a graph model can be drawn

to fit the pattern of change in the

data.

Inverse Relationship

– A nonlin-

ear relationship in which the prod-

uct of two variables is constant. In

an inverse relationship, the values

of one variable decrease as the

values of the other variable in-

crease.

Linear Relationship

– A relation-

ship in which there is a constant

rate of change between two vari-

ables. Y= mx+b

Mathematical Model

– A mathe-

matical representation, such as a

graph or an equation, of the rela-

tionship in a set of data

Relationship

– An association be-

tween two variables, a table, or

with an equation.

Thinking with Mathematical Models

Glossary

Connected Mathematics

Project

Everett Public Schools

Mathematics Program

Proposed Time Frame:

Approximately 6 weeks

Models

Algebra

Unit Goals:

?

mathematical models

?

data

?

interest in a situation

?

variables are related.

Web Resources

WWW.illuminations.nctm.org

Graph Creator

Learning About Rate of Change in

Linear Functions

---

Tips for Helping at Home

Good questions and good listening will

help children make sense of mathemat-

ics and build self-confidence. A good

question opens up a problem and sup-

ports different ways of thinking about it.

Here are some questions you might try,

notice that none of them can be an-

swered with a simple “yes” or “no”.

Getting Started

? What do you need to find out?

? What do you need to know?

?

What terms do you understand or

not understand?

While Working

?

How can you organize the informa-

tion?

?

Do you see any patterns or relation-

ships that will help solve this?

? What would happen if…?

Reflecting about the Solution

?

How do you know your answer is

reasonable?

?

Has the question been answered?

?

Can you explain it another way?

At Home:

1 Talk with your child about

what’s going on in mathematics

class.

2 Look for ways to link mathe-

matical learning to daily activi-

ties. Encourage your child to

figure out the amounts for halv-

ing a recipe, estimating gas

mileage, or figuring a restau-

rant tip.

3 Encourage your child to sched-

ule a regular time for home-

work and provide a comfortable

place for their study, free from

distractions.

4 Monitor your child’s home-

work on a regular basis by

looking at one problem or ask-

ing your child to briefly de-

scribe the focus of the home-

work. When your child asks

for help, work with them in-

stead of doing the problem for

them.

At School

1

Attend Open House, Back to

School Night, and after school

events.

2 Join the parent-teacher organi-

zation

Investigation 1 Linear Models

?

Collect data, record data in tables, and repre-

sent data in coordinate graph

?

Fit a linear model to a graph

?

Make predictions from data tables and graph

models

?

Write an equation given the line of a graph

?

Review the meaning of slope and y-intercept

in relation to a set of data

?

Write an equation of a line given the slope

and the y-intercept, the slope and the coordi-

nates of a point on the line, or the coordi-

nates of two points on the line

Investigation 2: Nonlinear Models

?

Express data in tables and graphs

?

Make predictions from tables and graph mod-

els

?

Distinguish between linear and nonlinear rela-

tionships

?

Identify inverse relationships and describe

their characteristics

Investigation 3: More Nonlinear Models

?

Use knowledge about percents and fractions

to generate data

?

Explore a new type of graph model and com-

pare it to those explored previously

?

Use a graph model to make predictions

?

Continue to develop the idea of using a graph

to model the trend in a data set

Investigation 4: A World of Patterns

?

Use intuitive ideas about rates of change to

sketch and match graphs to given situations

?

Use intuitive ideas about rates of change to

crate stories that fit given graphs

?

Extend understanding of graph models to

include new shapes

Connected Mathematics Project

Mathematics in

Investigations

Phone: 425-385-4062

Fax: 425-385-4092

Email: mstine@everett.wednet.edu