Beetle Wheels
In this unit of work we link the development of skipcounting patterns to bars on a relationship graph. We also plot our skipcounting patterns on a hundreds board.
AO elaboration and other teaching resources
AO elaboration and other teaching resources
 continue a skipcounting pattern
 describe skipcounting patterns
 use graphs to illustrate skipcounting patterns
In this unit we look at skipcounting patterns. These are patterns obtained by adding the same, constant, number to make the next number every time. So the difference between any two terms in a skipcounting pattern is the same. This is a good exercise to help reinforce the various concepts relating to pattern. In particular, it helps us to understand the idea of a recurrence relation between consecutive terms.
But this exercise has two other links. First it links Algebra and Statistics by using a bar chart to represent the skipcounting pattern. It is worth remembering that there are many links in mathematics. Being able to see and use such links is a powerful tool to have.
And second, skipcounting patterns are also called Arithmetic Progressions. In secondary school these are considered again and expressions for both the general term of the progression and the sum of all of the numbers in the progression are found. These are both reasonably simple algebraic expressions.
Links to Numeracy
This unit provides an opportunity to develop number knowledge in the area of Number Sequence and Order, in particular development of knowledge of skip counting patterns. It can also be used to focus on the development of strategies to solve multiplication problems.
Once students have created bar graphs of the relationships, help them to focus on the number patterns involved by creating tables. For example:
Number of Beetle Wheels  
Number of Beetles 
Number of Wheels

1

4

2

8

3

12

4

16

5

20

As students create tables focus their attention on the patterns that are emerging and pose questions about the continuation of the patterns. Use of a hundreds chart will help students visualise the number patterns more easily and help them to predict which numbers will be part of the patterns. Patterns of 2, 5 and 10 are a good place to start but for students that are coping well you can make it more difficult by using larger numbers. For example, if there were 7 friends in each beetle how many people would there be in 2 beetles? 3 beetles? What about 10 beetles?
Working with larger numbers of beetles (or other items) will help students develop strategies to solve multiplication and division problems. Encourage students to talk about the way they are solving these problems. Are they using materials, repeated addition or can they derive some of the answers from known multiplication facts?
Questions to develop knowledge / strategy use:
Which number comes next in this pattern?
How do you know?
Which number will be before 24 in this pattern? (or another number as appropriate)
How do you know?
What is the largest number you can think of in this pattern? How did you work it out?
How many wheels will there be in 5 beetles? 10 beetles? How did you work it out?
If there were 48 wheels in a car park how many beetles would there be? How did you work it out?
patterns, next, before, largest, how many? table, graph
Getting Started
Today we explore the pattern of 4’s by counting the number of wheels on cars. We then use this information to build a relationship graph.
 Ask: How many wheels does a beetle have?
 Share ideas. Hopefully someone will link the beetle to the Volkswagen car rather than the insect or you may have to give a few more hints.
 Using counters begin to develop a chart of the number of wheels to the number of cars.
1 car  Ask: How many wheels are there on 2 beetles?
How did you work that out?  It is useful for the students to listen to the strategies that others use. More advanced Level 1 students will be be to count on from 4 to find the answer and many would have 4 + 4 as a known fact.
 Repeat the process with 3 and 4 VW beetles. Each time continue to add the information to the chart.
 Ask the students to work out how many wheels there would be on 6 beetles. If some of the students find the answer quickly, ask them to find the answer using another strategy.
 Share solutions. These may include:
 skipcounting with or without the calculator;
 counting on using a number line or hundred’s board;
 using counters to find 6 groups of 4.
 As the class to complete the chart up to 6 cars.
 Ask: What can you tell me about this chart?
Share ideas. Encourage the students to focus on the relationship between the number of cars and the number of wheels.  Ask the students how they could record this information using grid paper.
Exploring
Over the next 23 days the students work in pairs to explore the number patterns of other skipcounts. At the end of each session the students share their charts with the rest of the class.
 Place pictures of items that the students are to investigate in a “hat”. Ask each pair to draw one out and then investigate the pattern up to at least 6. Encourage the more able to students to extend the pattern beyond 6.
 Pictures could include:
 tricycles (3 wheels)
 bicycles (2 wheels)
 hands (5 fingers)
 spiders ( 8 legs)
 glasses (2 lenses)
 frog (4 limbs)
 stool (3 legs)
 Remind the students that they are to record their explorations on a chart.
 At the end of each session share and discuss charts and number patterns. Ask the students to identify the patterns that are the same.
Reflecting
In today’s session we use calculators to extend our skipcounting into the hundreds. We record our patterns on a hundred’s chart.
 As a class look at the chart to show hands (5 fingers). Skip count together in 5’s shading the counts on a hundred’s chart.
 As the chart is shaded ask questions which encourage the students to look for patterns in the numbers as they make their predictions.
Which number will be next?
How do you know?
 Give the students (in pairs) a hundred’s chart and ask them to shade in one of the skip counting patterns that they had charted on the previous days.
 Display, share and discuss at the end of the session.
Dear Parents and Whanau,
This week in maths we have been looking at skipcounting patterns and the charts that can be made from them.
Your child will be able to explain to you exactly what we did in class. Here is a chart made from a skipcounting pattern. Talk with your child about what the next number in the pattern will be. Put that number onto the chart. Discuss with your child how the pattern would continue.
Try to think of how that pattern might describe something in your family. Could you make a similar chart of another number pattern that you can both think of.
This is an important part of maths. Thank you for your help.