Arm Length and Shoe Size
Advanced Algebra
Linear Functions
Chu
Sungchi
Pp
http://www.sungchichu.com
January 20, 2007
January 25, 2007
Copyright 2007. Any2Any Technologies, Ltd.
The objective of this activity is to use the Eval function of the graphics calculator to provide an insight to an age old myth.
Primary 2
Someone claims that there is a strong relationship between the length of forearms of humans and their shoe sizes. You are to investigate
this claim. So that males and females can be considered together, either subtract 1.5 from the women's shoe sizes or add 1.5 to
the men's shoe sizes.<br> <ol> <li>After gathering the data, construct a scatterplot. What domain, range, and
scaling factors work well? Do length of forearm and shoe size appear to be related? What type of relationship seems
appropriate? </li> <li>How linear are the data? Perform linear regression and determine how well the regression
line describe the data. </li> </ol>
You know the area of a triangle can be expressed as $1$
You may know about Herons formula $2$ where a, b, and c are sides of the triangle and $3$ which also gives the area of any triangle.
There is another formula for the area of a triangle.
A = 1/2 bh
x(s-a)
s= a+ b + c
Investigate the residuals of the linear model. Is there a pattern? If so, can you predict using $1$ what type of regression model might be more appropriate?
a-b
Find people outside of your classroom $1$ and dtermine how well the model prdicts their shoe size when you know their arm
length and how well the model predicts their arm length when you know their shoe size.
8 * 9 - 0.9002
This is to set the value of a to 3.45 and explore $1$.
a=a+n/2
If relations from previous work are entered, either delete them (highlight them and press F2 follwed by F1) or turn them
off (highlight them and press F1 so they are no longer selected).
Industry is concerned with profit. Frequently, an industry will use linear programming to determine the maim profit given constraints
that are real factors to the company. Suppose a manufacturer can produce a product one way (Method 1) using 3 hours of unskill labor,
1 hour of machine time, and 2 hours of skilled labor. On the other hand, Method 2 takes 3 hours of unskilled labor, 2 hours of machine
time, and 1 hour of skilled labor. However, constraints have not been considered yet (X - items produced by Method 1 and Y = items
produced by Method 2)<br><br> $1$ ( up to 4200 hours of unskilled labor are available)<br>
$2$ ( up to 2400 hours of machine time are available)<br>
3X + 3Y <= 4200
3X + 3Y <= 2400