Project: Connect 4 Counters

Algebra connect 4 counters project for exploring and analyzing number patterns.

Print instructions: Connect-Four-Pattern-Project

Patterns

Create one of the following patterns using connect four counters. Build shapes 3, 4 and 5 of your pattern.

Pattern 1

Pattern 2

Pattern 3

Pattern 4

Project outline:

Choose one pattern from patterns 1 – 4. Decide how the pattern continues – there may be more than one approach.

Draw the first five shapes on paper with red and yellow pencils (or any other two colours).

Predict how many total, how many red, how many yellow counters will be in your 10th shape!

Generalise to the n^{\text{th}} shape. Define the letters you use as variables. Create a formula for each of: the number of red counters in the n^{\text{th}} shape, yellow counters and total counters.

Explain how your formula arise from the shape pattern. Video example of shape pattern to formula.

Finally, create and investigate your own connect-4 counter pattern.

 

Graphing applet

(or graph directly on geogebra.org)

Grading Criteria

These are the descriptors for a project that will be graded as proficient in each category:

Communication
  1. I have completed all parts of this project.
  2. My project can be read independently of the instructions.
  3. My project has a title page with my name, a title for the project, a sentence desribing the objective of the project and perhaps a relevant image.
  4. I have used text, diagrams and space to effectively communicate the calculations
  5. It is evident that have thought of the reader when structuring each page. That is, the elements (text, diagrams) of each page are placed in an order that makes sense to the reader.
  6. I have used correct math notation.
  7. I have used correct math vocabulary.
  8. My math is written clearly. When there is more than one line in a single calculation, my ‘=’ signs are lined up.
  9. I have written my math by hand or I have used a math-type tool on MS word/Equatio etc.
Reasoning
  1. I have demonstrated understanding of each part of the project.
  2. My lines of work record each step in the calculations clearly, one step at a time.
  3. My writing (including text/diagrams) is sufficient to demonstrate my understanding.

 

Project work can also be graded as extending. In which case, the elements in the table below may be present in your work. Alternatively, you may have advanced your learning significantly in another way that represents the curricular competencies, in which case your grade will reflect that learning.

Communication Creative, insightful use of colour/text/diagrams to explain results/ generalisations.
Reasoning Sophisticated understanding of patterns/relations present in the project. Sufficiently complex shapes (as per the patterns #1-4 given) are used. Formula are explained using a system or diagrams that demonstrate the continuation of the pattern and the relationship between the shapes and each term in the formula.