Here is the
Match sticks
pattern of houses with matchstick
write the general rule for this pattern in explain please
Answers
Answer:
48 match sticks are used for making 8 houses
if 6 matchstick are used for making one House.
Step-by-step explanation:
Matchstick Patterns
Purpose
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.
Achievement Objectives
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
Predict the next term of a spatial pattern.
Find a rule to give the number of matches in a given term of the pattern.
Find the member of the pattern that has a given number of matches.
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:
Tables of values
Word rules for the nth term
Equations that symbolise word rules
Graphs on a number plane
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 Numeracy
This 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:
What numbers could you use to describe the way the pattern is made and how it grows?
What do the numbers and operations tell you about the pattern?
In what order do we perform the calculations like 3 + 3 x 2? (Note order of operations)
Are the expressions the same in some way? For example, How is 3 + 2 + 2 + 2 the same as 3 + 3 x 2?
Which expressions are the most efficient ways to calculate the number of matches?
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:
providing matchsticks so students can build the growth patterns
using colour to highlight repeating elements in diagrams of the growth patterns
easing the calculation demands by providing calculators
modelling creating tables and other ways for students to record their working and ease demands on their working memory.
Tasks can be varied in many ways including:
reducing the ‘distance’ of the terms involved, particularly predicting the number of matches for terms that are easy to build and check
reducing the complexity of the patterns, e.g. increasing in twos, threes, and fives rather than sixes, twelves, etc
collaborative grouping so students can support others
reducing the demands for a product, e.g. oral presentation rather than a lot of calculations and words.
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
Matches with the heads burnt, or toothpicks, iceblock sticks, nursery sticks, trimmed bamboo skewers, etc.
Dot paper as an alternative to using matches
PowerPoint One