#### A Math Forum Project

 ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary

Student Version

### Mosaic - posted April 16, 2001

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Mosaic

In Mosaic, you can use different colors and lengths of blocks to fill a canvas. Your first job will be to try to fill in the map of the USA and approximate its area.

To add a block, first select the row to which you want to add your block by clicking on the circle next to the corresponding row. Then enter the value of the block by changing the values of the numerator and the denominator of the fraction (for example, to change the denominator, click on the number in the denominator; this will highlight the number and you can replace it with the one you want). Then select the color of your block by clicking on one of the color swatches. You will see a preview of your block above the swatches. When you are ready, click the "Add Block" button.

Each row has an area of 1 square unit. This means that if you add a fraction block of 1/3, you are filling 1/3 square units of space.

### Questions

1. What is the approximate area of the map of the USA?

2. How could you get a better estimate of the area of the map of the USA?

3. Design your own image, and use Mosaic to create it. Describe it here, briefly explaining how you made it.

Teacher Support Page

We didn't get many submissions this week, and we're not sure why. One of the few students who did submit a solution described her answers clearly, and is highlighted below.

It seems some students didn't understand how to count up the blocks to estimate the area of the map in the mosaic. They were fractions of the line, so the total number couldn't be more than the number of lines.

Others didn't understand how to make a mosaic to find the area of the underlying map. Maybe this part was a little unclear on our part. The reason different colors were allowed was so you could use one or more colors for the U.S. area and another color for the area not in the U.S.

In response to question 2, students didn't think of the best ways (that is, ways we thought of :^]) to improve the estimate on the map area. The idea of changing block size and shape -- for example, the height -- either didn't occur to them or they thought they should have changed the way they did the problem, for example, use more blocks or only add some of the area.

The third question, design your own mosaic, was actually the next toughest question after question 2. I guess they just didn't believe they were allowed to do anything they wanted.

### Highlighted solutions:

 From: Nina H., age 14 School: Taipei American School, Taipei, Taiwan

```QUESTIONS

1. What is the approximate area of the USA map?
~ 4 5/18 sq. units

2. How could you get a better estimate of the area of the USA map?
~ I could probably get a better estimate of the area if I could just
leave the smaller bits of the USA map blank, and just fill in with
blocks for the bigger areas of the map. For example, if the top edge
of the country would only fill up one cm of space, I would just leave
that piece and continue to fill in the other larger areas of the map.

3. Design your own image and use Mosaic to create it. Describe it
here, briefly explaining how you made it.
~ I designed a butterfly and I used the different rows and colors to
show the wings and the butterfly's body. For the first 1/3 of the row
I used a light blue color and then for the little head of the
butterfly I used the yellow, then I switched colors to a pink. So the
top left wing is blue and the body will stay yellow, and the top
right wing is pink. For the rest of the butterfly, I just changed the
colors around so that the bottom left wing is pink and the body will
stay yellow and the bottom right wing is light blue.
```

### 1 students received credit this week.

Nina H., age 14 - Taipei American School, Taipei, Taiwan