Rich tasks
- These are problem solving open-ended questions that require students to investigate patterns and rules. The tasks can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place, or given as homework or extension.
- Three colour squares
- Can you always win?
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1. Three colour squares
- This task can be extended into number sequences by writing down the numbers of each colour. For example, for the square in the book it could be written as a 1, 4, 4 square because there are 1 green, 4 blue and 4 red counters. When the 5 by 5 square is drawn it might become a 4, 8, 4 square.
- Encourage students to find as many ways to continue their patterns as they can.
2. Can you always win?
- Students could play this game many times and record who started to see if they think that makes a difference. They could also find a way of recording the moves to see if there is any pattern to which moves produce a win.
Repeating patterns
- Use multiplicative strategies to work out what shape in a repeating pattern of shapes the nth shape will be.
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Teacher notes
- Encourage students to use multiplication strategies rather than skip counting or addition to find the answers.
- Students may need to work with materials such as the number line and counters in “What shape?” in the teaching ideas above.
- Students need to know their basic multiplication facts and some revision of these might be necessary. Knowing their doubles is
also useful.
Growing patterns
- Continue a growing pattern and describe in words how to find the number of components in any shape number.
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Teacher notes
- Encourage students to work out the repeating part of the growing pattern first. They could make a sketch showing this.
- A table is a good way to show the number sequence that makes up the growing pattern and see how many are added each time.
- Encourage students to see the multiplicative relationship. For example, if 2 sticks are added each time then part of the the rule will be the shape number times 2.
- Encourage students to see that often there is more than one way of seeing the growing pattern. Get them to discuss their different ways of seeing it.
