Mayan Adventure

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Purpose

This is a level 3 geometry and algebra activity from the Figure It Out theme series.

A PDF of the student activity is included.

Achievement Objectives
GM3-4: Represent objects with drawings and models.
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Student Activity

    

Click on the image to enlarge it. Click again to close. Download PDF (479 KB)

Specific Learning Outcomes

make a three dimensional model with multilink cubes from a two dimensional drawing

describe and continue a sequential pattern

explore the Mayan number system

 

Required Resource Materials

Counters, string, multilink cubes

 

FIO, Level 3, Theme: Time Travel, Mayan Adventure, pages 12-13

 

Ice block sticks or Cuisenaire rods

Activity

Activity One
The Mayan number system is built up using only three symbols: a stylised shell for 0 (shell. ), a dot for 1 (•), and a horizontal line for 5 (—). Point out to the students that this is a base 20 system with 5 being a significant number.
These exercises are very good for whole-part thinking because the numbers are expressed in terms of ones, fives, twenties, and so on, with these terms being added together to arrive at the total.
The students will probably do Mayan addition and subtraction in one of two ways: either all in “Mayan” without converting, or else they will convert to base 10, perform the operation, then convert the answer back into Mayan. Both ways are fine.

Activity Two

In this activity, the students investigate patterns in the number of blocks used to build Mayan pyramids.
Page 11 of Geometry, Figure It Out, Levels 2–3 and pages 8–9 of Geometry, Figure It Out, Level 3 give students experience in interpreting views of buildings from the top and the side and in using this experience to make multilink cube models. You may also find the teachers’ notes for these activities useful in preparing the students for this Time Travel activity.
If the students are having difficulty identifying the number patterns, encourage them to draw diagrams. They can then add to their diagram the number of blocks along the base of the pyramid, the total number of blocks, and the mass of the pyramid.

pyramid.
The students could also use a table for question 4 and look for patterns in the numbers, for example,

table.

When a new layer is added to a pyramid, the base is made larger. This is done by adding a row of single blocks to each side of the old base. This makes each side of the new base two blocks longer than each side of the old base. So for each successive pyramid, the total number of blocks added is given by the number of blocks in the new base. The easiest way of calculating this is to take the number of blocks along one side of the new base and then multiply this number by itself.
Note that this activity and its answers are based upon the assumption that the pyramids are solid structures with no interiors. In reality, the pyramids are very intricately constructed with a maze of rooms and passages running through them.
The Mayans invented a calendar and used a type of matrix multiplication system. Some interesting Mayan structures still exist (mainly in Mexico), and some students may like to copy these structures and build models of them. There are a large number of interesting websites available on the Internet that look more fully into Mayan mathematics and culture, for example:
www.civilization.ca/civil/maya/mmc05eng.html
www.saxakali.com/historymam2.htm
http://mathforum.org/alejandre/numerals.html
The students could also investigate (using the websites above) how to represent numbers greater than 99 in Mayan numbers. For example, 100 is represented by a line at the same level as the dots that represent 20s.

Answers to Activities

Activity One
1.

answers.
2.

answers.
3.

answers.
Activity Two
1. Practical activity. Teacher to check
2. a. 35
b. 17.5 tonnes
3. a. Practical activity
b.

answer.
4. a. (9 x 9) + (7 x 7) + (5 x 5) + (3 x 3) + (1 x 1) = 165
b. Multiply the length of a side of the bottom layer by itself. Then subtract two from the length, and multiply that number by itself. Continue to do that until you reach 1.
Then add the numbers.

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Level Three