Rich tasks for this chapter - page 181
- 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.
- Odds and evens
- What fraction?
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1. Odds and evens
- Students could explore this in groups and share the arrays they drew.
- Encourage students to explain their answers using arrays rather than doing a lot of calculations and arriving at answers without understanding why.
- Point out the link to probability for the second part of this Rich Task.
2. What fraction?
- This is a challenging task because students need to have an understanding of fractions.
- Students will need to know how to find a fraction of a region, make equivalent fractions and how to change between mixed fractions and improper fractions.
- Encourage students to problem solve the ways they might be able to work out the fractions required by breaking up the shape.
Finding the rule for a growing pattern - page 182
- Explain in words the rule for how to continue a pattern or how to form the pattern from the shape number.
- Begin to use multiplicative strategies to find any number in a pattern.
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Teacher notes
- This section supports students understanding that using multiplicative strategies to find later terms is more efficient than adding a constant value over and over again.
- Encourage students to verbalise and write down using equations how they been able to continue a pattern.
- Working with materials is a good way for students to gain an understanding of how patterns continue and also how to work out their rules.
Using graphs and tables to describe a growing pattern - page 188
- Use a spreadsheet package or draw a graph to describe a pattern and find later terms in the pattern.
- Know that when a graph that describes a pattern is a straight line, the pattern is linear.
- Know that a linear pattern is one which increases or decreases by a constant value.
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Teacher notes
- Encourage students to understand what the spreadsheet is telling them, rather than simply learning an algorithmic way of using it.
- Emphasise that linear patterns have a constant difference between terms and check that students understand why this gives a straight-line graph.
Number patterns - page 192
- Begin to understand multiples and primes and explore the patterns in multiples.
- Explore odd and even patterns in multiples.
- Be able to continue an equation pattern and explain how it was formed.
- Be able to find the rule that gave rise to the output numbers of a number machine if the input and output numbers are given.
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Teacher notes
- Introduce students to multiples and primes. More work is done on this in level 4.
- Students only need to understand that factors of a number are any numbers that divide evenly into that number. More practice in finding factors is given in level 4.
- The main point students need to know at this level about prime numbers is that they can only be shown as an array of one line. This is because they have only two factors, themselves and 1.
- Encourage students to continue the equation patterns by looking for the patterns and relationships rather than doing any calculations.
