## Building a Wheelchair Ramp Model With Slope 1/12

The scenario was the following.

Grandma wanted to come see her grandson play high school football but the bleachers were not wheelchair accessible. The students were asked to build a model wheelchair ramp that was accessible to the top bleacher while also staying within ADAs (Americans With Disabilities) building code—the slope must be exactly 1/12 throughout the ramp.

The students were giving the following model conversion scale

### 5 yards = 1 inch.

Using this, they modeled a 120 x 50 yards football field into a 24’’ x 10’’ football field.

Next, using the bleachers my six year old son built for them, they measured the height at 2’’.

Using the 1/12 slope, they built a 24’’ incline wheelchair ramp.

Then converted these scaled numbers to real life. 5 yards = 1 inch. Meaning a 2’’ height = 10 yards of actual height and 24’’ ramp = 120 yards.

## How Fast is a Toy Car Really Traveling?

To examine this question and teach dimensional analysis we converted feet per second to miles per hour using a toy car.

Step 1: Using a stop watch, yard stick and a windup toy car we calculated the average feet per second to be

22.5ft/6.8sec

Step 2: We set up the problem

Step 3: We used conversion techniques to translate ft/sec to miles/hour.

This little car was traveling approximately 2.26 miles/hour

## Saturday, October 18, 2014

### Proportionality & Grasshoppers

Proportionality & Grasshoppers

What would it mean if students could jump proportionally as far grasshoppers? To find out, I brought in some grasshoppers.

First we measured the length of two grasshoppers to be approximately 1 inch. Next, we measured the distance of three jumps (in inches) from two grasshoppers I found in my backyard and took the average of all three jumps for an average of 43 inches.

Next, we measured the height of two students in inches and took the average for a result of 62 inches.

Finally we formed the proportion

1/43 = 62/x

x = 2,666 inches which is roughly 74 yards.

In essence, if students could jump proportional to grasshoppers we could nearly jump 3/4 of a football field.

## How Matrices Can Help When You’re Dating On A Budget.

The scenario was that each student was treating their partner out on a date for pizza with the only caveat being they were on a tight budget and needed to find the cheapest place to take their date.

I first had my student draw a picture of their dates!

﻿﻿ (Eva didn't talk much) ﻿

The students were asked to skim through three restaurant take-out menus to find the price of a large pizza and placed the prices inside a 1 x 3 matrix (Matrix A).

Next, the students were asked to skim through three restaurant take-out menus to find the price of additional toppings for a large pizza and placed the prices inside another 1 x 3 matrix (Matrix B).

Next, I had each student ask their date how many toppings they wanted on their large pizza (I answered for their dates of course).

The students then multiplied matrix B by the number of toppings they wanted on their pizza and placed the prices inside another 1 x 3 matrix (Matrix C).

Finally, the students were asked to add Matrix A to Matrix C to find the total price at three restaurants for a large pizza with a specified number of toppings and choose the cheapest restaurant.

## Estimating, Error Rates & Plotting

Take your class outside and designate a single starting point. From that point throw 5 or 6 objects at various distances. Next, ask your students to estimate how many feet each object is from the starting point. After they have estimated each object have them measure the length to the nearest foot and record their data in a table such as that below.

Next, have each student calculate their error rate using the formula (actual) – (estimate) / (actual) and change their decimal to a percent.

Finally, have the students plot the points on a coordinate (x,y) plane and form a scatter plot. It’s best to have them graph the equation y = x so that they can see their error rates.

## Friday, September 19, 2014

### Scatter Plots With Ramps

Scatter plots move in two dimensions which allow students to see changes in slope as well as the relationship of the two data sets. The study of scatter plots lends to a lot of fun experiments and can also serve as a great segue to discussions on proportionality or the coordinate system.

Ramp Height & Distance Traveled.

We decided to build ramps and plot the height verses distance traveled. We increased the ramp in (approximately) one inch blocks and rolled a golf ball off the ramp to measure the distance traveled. See Below. To get better results we took the average of three rolls. Lots of FUN!

## Saturday, September 13, 2014

### What To DO With a Handful of Pennies? Measures of Central Tendency

A good icebreaker to use when introducing Measures of Central Tendency (Mean, Median, Mode, etc) is to grab a handful of pennies from your vehicle and lay them out on a table and have your students work in groups to place them in order of date from least to greatest (if you have a large class you may need multiple handfuls of pennies).

Next, start collecting data.

Mode can easily be seen by the largest stack.
Median, Range, Q1, Q3, IQR can also easily be found