# Let the Modeling Begin!

### Math Models for Thinking

## Wendy Curtner

Fort Worth, TX

## Nancy Trent

Fort Worth, TX

Students put their own ideas in the top three boxes. Then, on teacher’s cue, they move about the room asking the other students for one of their ideas. At the same time they give one of theirs. This is done until all boxes are filled.

## Mastery Connect

## What is Mathematical Modeling?

A model *for* thinking about a mathematical concept refers to any object, picture, or drawing that represents the concept.

- To see a concept in a model you must have some relationship in your mind to impose on the model.
- Models give children something to think about, explore with, talk about, and reason with.

## What are the advantages and disadvantages of using virtual models versus physical models?

## Strip Diagrams / Tape Diagrams / Percent Bars

## Ratio tables

## Algebra Tiles

## Number Lines

Do taller Olympic sprinters have an unfair advantage?

A relay team consisting of four runners – Anne, Bryn, Carmen and Dahlia – completed a race in 72 minutes. Anne’s leg of the race took 1/5 of the total time; Bryn’s took 1/3 of the total time; and Carmen’s took 3/10 of the total time. How many minutes did Dahlia take to run her leg of the race? | The official ratio of the Fly(length) to Hoist(width) of the rectangular flag of the United States of America is 1.90 to 1.00 as set by Executive Order 10834. There is a list of eleven permissible specific flag sizes (specified by length and width) for flags displayed over government agencies: 38.00 × 20.00; 19.00 × 10.00; 17.00 × 8.95; 11.00 × 7.00; 9.50 × 5.00; 5.50 × 4.33; 6.65× 3.50; 4.00 × 3.00; 5.70 × 3.00; 4.50 × 2.37; and 2.50 × 1.32. How many of these 11 flag dimensions are in the official 1.90:1.00 ratio? | The Edge Tickets, Inc. is offering 5% off the price of tickets to diving events. A Category A ticket to the men's 3-meter springboard finals is $420. How much would 4 tickets to that event cost after the discount? |

The official ratio of the Fly(length) to Hoist(width) of the rectangular flag of the United States of America is 1.90 to 1.00 as set by Executive Order 10834. There is a list of eleven permissible specific flag sizes (specified by length and width) for flags displayed over government agencies: 38.00 × 20.00; 19.00 × 10.00; 17.00 × 8.95; 11.00 × 7.00; 9.50 × 5.00; 5.50 × 4.33; 6.65× 3.50; 4.00 × 3.00; 5.70 × 3.00; 4.50 × 2.37; and 2.50 × 1.32.

How many of these 11 flag dimensions are in the official 1.90:1.00 ratio?