## Hobbit Math: Elementary Problem Solving 5th Grade

[Photo by OliBac. Visit OliBac’s photostream for more.]

The elementary grades 1-4 laid the foundations, the basics of arithmetic: addition, subtraction, multiplication, division, and fractions. In grade 5, students are expected to master most aspects of fraction math and begin working with the rest of the Math Monsters: decimals, ratios, and percents (all of which are specialized fractions).

Word problems grow ever more complex as well, and learning to explain (justify) multi-step solutions becomes a first step toward writing proofs.

This installment of my elementary problem solving series is based on the Singapore Primary Mathematics, Level 5A. For your reading pleasure, I have translated the problems into the world of J.R.R. Tolkien’s classic, The Hobbit.

[Note: No decimals or percents here. Those are in 5B, which will need an article of its own. But first I need to pick a book. I’m thinking maybe Naya Nuki…]

### Printable Worksheet

In case you’d like to try your hand at the problems before reading my solutions, I’ve put together a printable worksheet:

## Can You Read the Flu Map?

[Map as of early afternoon on May 4th, found at the NY Times.]

Compare the dark circles (confirmed cases) for Mexico, New York and Nova Scotia in the top part, or Mexico and the U.S. in the lower part of the map. It’s easy to see which has more cases of the flu — but how many more? Which would you guess is the closest estimate:

Mexico : New York : Nova Scotia

• = 7:3:2 or 20:5:3 or 16:2:1?

U.S. : Mexico

• = 1:2 or 2:5 or 3:7?

## Review: Math Doesn’t Suck

We’ve all heard the saying, Don’t judge a book by its cover, but I did it anyway. Well, not by the cover, exactly — I also flipped through the table of contents and read the short introduction. And I said to myself, “I don’t talk like this. I don’t let my kids talk like this. Why should I want to read a book that talks like this? I’ll leave it to the public school kids, who are surely used to worse.”

Okay, I admit it: I’m a bit of a prude. And it caused me to miss out on a good book. But now Danica McKellar‘s second book is out, and the first one has been released in paperback. A friendly PR lady emailed to offer me a couple of review copies, so I gave Math Doesn’t Suck a second chance.

## An Ancient Mathematical Crisis

[When Alexandria Jones and her family visited an excavation in southern Italy, they learned several tidbits about the ancient school of mathematics and philosophy founded by Pythagoras. Here is Alex’s favorite story.]

It hit the Pythagorean Brotherhood like an earthquake, a crisis of faith which shook the foundations of their universe. Some say Pythagoras himself made the dread discovery, others blame Hippasus of Metapontum.

Something certainly did happen with Hippasus. The Brotherhood sent him into exile for insubordination, or for breaking the rule of secrecy — or was it for proving the unthinkable? According to legend, Hippasus drowned at sea, but was it a mere shipwreck or the wrath of the gods? Some say the irate Pythagoreans threw him overboard…

## The Golden Christmas Tree

Last time, Alexandria Jones and her family were on their way to Uncle William’s tree farm to find the perfect Christmas tree, and Dr. Jones taught us about the Golden Section:

$The \; Golden \; Section \; ratio$

|———————A———————|————B————|

$A \; is \; to \; B \; as \; \left(A + B \right) \; is \; to \; A, \; or . . .$

$\frac{A}{B} = \frac{A + B}{A} = \: ?$

I gave you three algebra puzzles to solve. Did you try them?

• What is the exact value of the Golden Section ratio?

• If a 7-foot tree will fit in the Jones family’s living room, allowing for the tree stand and for a star on top, how wide will the tree be?
• Approximately how much surface area will Alex and Leon have to fill with lights and ornaments?

## Math Adventurer’s Rule: Figure It Out for yourself

Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you have not worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.

## A-Hunting They Will Go

Alexandria Jones and her family piled into the car for a drive in the country. This year, they were determined to find an absolutely perfect Christmas tree at Uncle William Jones’s tree farm.

“I want the tallest tree in Uncle Will’s field,” Alex said.

“Hold it,” said her mother. “I refuse to cut a hole in the roof.”

“But, Mom!” Leon whined. “The Peterkin Papers…”

“Too bad. Our ceiling will stay a comfortable 8 feet high.”