# Dragon Races

The 479th Annual Dragon Race is today on the Island of Barnacle. The race is out to Otter Island and back. The three fastest dragons, Manic, Crater, and Comet, have been invited to compete.

After `sf text(1)/sf text(3)` of an hour Manic is seen `sf text(1)/sf text(4)` of the way to Otter Island. Crater is seen turning around at Otter Island after 45 minutes. Comet is seen returning from Otter Island halfway back to the Island of Barnacle after 1`sf text(1)/sf text(3)` hours.

Based on the different sightings of the dragons, who do you predict will return to the finish line first? Provide mathematical evidence to support your prediction.

### More Accessible Version

The 479th Annual Dragon Race is today on the Island of Barnacle. The three fastest dragons have been invited to compete. The race is out to Otter Island and back.

- After `sf text(1)/sf text(3)` of an hour Manic is seen `sf text (1)/sf text(4)` of the way to Otter Island.

- After `sf text(3)/sf text(4)` of an hour Crater is seen turning around at Otter Island.

- After 1`sf text(1)/sf text(2)` hours Comet is seen returning from Otter Island halfway back to the Island of Barnacle.

Based on the different sightings of the dragons, who do you predict will return home first? Provide mathematical evidence to support your prediction.

### More Challenging Version

The 479th Annual Dragon Race is today on the Island of Barnacle. The race is out to Otter Island and back. The three fastest dragons have been invited to compete. Based on the dragons measurements, provided below, which would you predict to be the fastest? Why?

Manic is 20 feet tall, with a wingspan of 40 feet and weighs 720 pounds. Crater is 45 feet tall, with a wingspan of 90 feet and weighs 3,780 pounds. Comet is 8 feet tall, with a wingspan of 16 feet and weighs 352 pounds.

Once the race is underway, officials report out the following information.

After `sf text (1)/sf text(3)` of an hour Manic is seen `sf text (3)/sf text (7)` of the way to Otter Island. Crater is seen turning around at Otter Island after 45 minutes. Comet is finally seen halfway back to the Island of Barnacle after 1`sf text (1)/sf text (9)` hours.

Based on the different sightings of the dragons, who do you predict will return home first? How does this compare to your original prediction? Provide mathematical evidence to support your thinking.

## Plan

#### Underlying Mathematical Concepts

#### Possible Problem-Solving Strategies

#### Formal Mathematical Language and Symbolic Notation

**Teacher Notes**:

Possible questions to pose when launching this task:

- What units can be used to represent speed?
- How can you simplify a complex fraction where a fraction is in the numerator and in the denominator?
- What does the dragon race look like? Is there a model you can use to show what’s happening during the race?

Possible misconceptions that students may encounter with this task:

- Students may misinterpret the meaning of fractional quantities in relation to the whole they decide to use i.e., `sf text(1)/sf text(2)` way to Otter Island is `sf text (1)/sf text(4)` of the race.

### Suggested materials

Engagement Image:

Teachers may project the image below to launch this task for their students, define nouns, promote discussion, access prior knowledge, and inspire engagement and problem solving.