Exploring Different Bases

Math is the beautiful, rich, joyful, playful, surprising, frustrating, humbling and creative art that speaks to something transcendental. It is worthy of much exploration and examination because it is intrinsically beautiful, nothing more to say. Why play the violin? Because it is beautiful! Why engage in math? Because it too is beautiful!

~James Tanton

1. Fraction Review : “Foot Rulers”

Teach this lesson as INQUIRY – give students time to decide on the markings of the ruler. That allows the ruler to cross over from concrete (the folding) to pictorial (the words that describe the folds) to the abstract (the fraction symbols).

(Link to Puzzle Point instruction page)

2. Base 10 – Operations with Powers of 10

In Singapore Math, the decimal point does not “dance” left and right. Instead, the base ten place value blocks shift left (if getting bigger, ie. multiplication) or right (if getting smaller by division) This visualization of the rules for multiplication and division by powers of 10 makes sense and is therefore more easily retained.

3. Base 10 – the Megapenny Project

The MegaPenny Project was originally created by someone identified online as “Kokogiak Media.” Its purpose was to help us visualize large powers of 10. The author took the lowly Lincoln Cent and let it multiply exponentially. Use this presentation as interactively as possible with students.

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4. Base 10 – Day 2

This presentation extends the concept of “Powers of Ten” to decimals. Once the place value concept is understood, this should hopefully present few difficulties.

Powers of Ten Movie by Charles and Ray Eames.

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Made in 1977, but still powerful, visually engaging and fascinating. About 10 minutes long.

5. 3-Act Investigation: How Many Pennies Now?

This activity is adapted from the “3-act” concept by Dan Meyer. Let students work in groups, and simply observe their developing ability to apply knowledge about multiplying by powers of 10.

At this point, it is not about getting right answers to a problem like this, but learning to attack it as systematically as possible for this age group. Praise any answers that reflect thinking and effort.

6. Paper Folding and Powers of Two

Finish the day with this clever video from MythBusters: “Can you REALLY only fold a piece of paper SEVEN times?

7. How to Count Like a Computer

This classwork uses an abacus-like set of sticks and beads to help students figure out numbers in base 2. We let students work in groups with somewhat similar working speeds. It is not necessary to work through all four problem sets – most students finish at least 2, though. The final problem investigates Alice’s telescoping adventures in Wonderland.

PUZZLE TIME – Binary Puzzles. This website does not provide solutions, so students can email you a screenshot of any puzzles they solve correctly. (for puzzle points!)

8. Review Day – Chips Game

Instructions on how to play this game

9. Counting in Base Five

Students use online manipulatives  (see Jamboard link) to carry out operations in base five.

This is not meant to generate rules for base five, but to increase the recognition of the usefulness of a place value chart – in any base.

Because of the manipulative approach, this should be accessible to all students, albeit at different speeds.

10. Exploding Dots!

This activity uses the James Tanton website “Exploding Dots”. Most students (and teachers!) love this website for its playful approach to place value – in multiple bases, no less!

Puzzle points for fast finishers:

Quiz #4, Trimester 2 – What about Assessment?