The unit investigates patterns made using matches and tiles. The relation between the number of the term of a pattern and the number of matches that that term has, is explored with a view to finding a general rule that can be expressed in several ways.
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. AO elaboration and other teaching resources
Specific Learning Outcomes
Description of Mathematics This unit builds the concept of a relation using growing patterns made with matches. A relation is a connection between the value of one variable (changeable quantity) and another. In the case of matchstick patterns, the first variable is the term, that is the step number of the figure, e.g. Term 5 is the fifth figure in the growing pattern. The second variable is the number of matches needed to create the figure. Relations can be represented in many ways. The purpose of representations is to enable prediction of further terms, and the corresponding value of the other variable, in a growing pattern. For example, representations might be used to find the number of matches needed to build the tenth term in the pattern. Important representations include:
Further detail about the development of representations for growth patterns can be found on pages 34-38 of Book 9: Teaching Number through Measurement, Geometry, Algebra and Statistics. Links to NumeracyThis unit provides an opportunity to focus on the strategies students use to solve number problems.The matchstick patterns are all based on linear relations. This means that the increase in number of matches needed for the ‘next’ term is a constant number added to the previous term. Encourage students to think about linear patterns by focusing on the different strategies that can be used to calculate successive numbers in the pattern. For example, the pattern for the triangle path made from 9 matches can be seen as in a variety of ways: 3 + 2 + 2 + 2 1 + 2 + 2 + 2 + 2 3 + 3 X 2 1 + 4 X 2 Questions to develop strategic thinking:
Strategies for representation and prediction will support students to engage in the more traditional forms of algebra at higher levels.
Opportunities for Adaptation and Differentiation The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
Tasks can be varied in many ways including:
The context for this unit can be adapted to suit the interests and cultural backgrounds of your students. Matches are a cheap and accessible resource but may not be of interest to your students. They might be more interested in other thin objects such as leaves or lines on tapa (kapa) cloth. You might find growth patterns in friezes on buildings in the community. Be aware of opportunities to learn that connect to the everyday experiences of your students.
Required Resource Materials
Note: All of the patterns used in this unit are available in PowerPoint 1 to allow easy sharing with data projector or similar. Session 1: Triangle PathsIn this session we look at a simple pattern created by putting matches together to form a connected path of triangles.
Extension idea: Vey-un has another way to work out the number of matches for a 10-triangle pattern. He writes 10 x 3 – 9 and gets the same number of matches as Kiri and Jamie, 21. Ask students to explain how Vey-un’s strategy works. What do the numbers in his calculation refer to? [Vey-un imagines ten complete triangles that require 10 x 3 = 30 matches to build. He imagines that the ten triangles join and that creates nine overlaps. He subtracts nine from 30 to allow for the overlapping matches.] Session 2: Square PathsHere we look at a simple pattern created by putting matches together to form a connected path of squares.
Session 3: House PathsThe ideas learnt in the last two sessions are reinforced here using ‘house paths’.
Session 4: What’s My Path?The ideas of the first three sessions are extended and reinforced in another context. This time the problem gives a rule and the students find the pattern.
Session 5: Other Ways of Seeing ThingsIn this session, the concept of a relation is explored with a more complicated spatial pattern.
Dear parents and whānau, This week in maths we have been looking at patterns made with matches. We looked at the first term, the second term, … the tenth term, … and so on and tried to find a relation between the number of matches and the number of the term. For example, we explored this pattern with matches: Ask your students to explain how they could predict the numbers of matches in a ten-house path. What else can they share with you about the pattern? Enjoy your exploration of this algebra problem!
matchstick-patterns.pptx105.08 KB |