Weeks 5 & 6 – Trimester II

Non-European Origins of Mathematics

Originally described as a record of prime numbers and doubling, the Ishango Bone traces its origins to Africa of 20,000 years ago. Further studies of the bone have concluded that it represented a six-month lunar calendar. This has raised the suspicion that it was created by women. Were they our first mathematicians?

Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2 and base 10), algebra, geometry, number theory and trigonometry.

It should come as no surprise that the first recorded use of the number zero happened in India. Mathematics on the Indian subcontinent has a rich history going back over 3,000 years and thrived for centuries before similar advances were made in Europe. Indian mathematicians made seminal contributions to the study of trigonometry, algebra, arithmetic and negative numbers among other areas. Perhaps most significantly, the decimal system that we still employ worldwide today was first seen in India.

Perhaps one of the most significant advances made by Arabic mathematics began in the 9th Century with the work of al-Khwarizmi: The beginnings of algebra, at the “House of Wisdom” in Baghdad. This was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.

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1. Fraction Review : Pattern blocks

This can also be used in the classroom (with blocks).

(Link to Puzzle Point instruction page)

2. Ancient Math – The Ishango Bone

Students investigate the math of the Ishango Bone from Africa- one of the oldest specimens of prehistoric math knowledge.

Here’s a video about fractals in African designs. It’s a little long for this age group, but it’s interesting – you might show part of it.

3. Interesting Number Systems of the World

This worksheet asks students to recognize and interpret number systems of 3 indigenous peoples. All these lessons are based extensively on the book “The Crest of the Peacock, Non-European Roots of Mathematics” by George Gheverghese Joseph.

4. Math from the Babylonians, Mayans, Indians and Arabs

A “Table For Three” game format to this study of 3 Non-European origins of modern math. The PowerPt includes a project suggestion, videos and a magic trick.

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This activity is adapted from a puzzle type found in “Beast Academy” puzzle book Grade 3 from Art of Problem Solving. AOPS is an amazing source of fun yet challenging math.

This is a good time to introduce the vocabulary “Mixed Number” and “Improper Fraction. Make sure the vocabulary is purely descriptive, matched to the pictures of fractions. For example, we can count this fraction as either “Improper” — 7/6 or “Mixed” — 1 and 1/6, depending simply on how we count:

6. Chinese Origins of Pascal’s Triangle

This activity looks at the patterns we can discover in the famous triangle. Named after Pascal, it actually has origins in China, India and Persia.

The activity can be augmented with either of these lesson plans from Boaler’s YouCubed website: “Pascal for Grades 3 – 5” or “Pascal for Grades 6-9 Additionally, the website “Mathigon” has excellent interactive lessons, including one on Pascal’s Triangle.

7. Word Problems

GAME TIME:
Partner Game with Fractions, using Pattern Blocks – free from the DOE in Virginia.

8. The Duplicator Machine

This investigation is adapted from Steve Wyborney

It is a hands-on, visual exploration of pattern development. It is not only fun, it is highly visual and tactile.

9. Building Patterns – Squares Upon Squares

Slide 3 of this set is based heavily on Jo Boaler’s task ” Squares Upon Squares”. The more time spent investigating, the better!

Puzzle points for fast finishers:

This HW continues using pattern blocks to build and visualize fractions.

Quiz #3, Trimester 2 – What about Assessment?