This unit is about generating number patterns for certain ‘insects’ from the mythical planet of Elsinore. Each ‘Pede’ is made up of square parts and has a number of feet. The patterns range from counting by 2s and 3s to being the number of feet plus three.
 Continue a simple pattern.
 Generalise the pattern.
Pattern is at the basis of much mathematics. There is always a need to find a link between this variable and that variable. This unit provides an introduction to pattern in the context of ‘insects’. The students are given practice in finding the next insect in a sequence. This leads to the main aim, which is for the students to begin to see the link between the number of feet that certain insects have and the number of squares that make them up.
One of the things that is deliberately attempted here is for them to see the link above in both directions. So not only do they get practice in linking squares to feet but they also are asked to try to find the number of feet that an insect with a certain number of squares has.
This unit provides an opportunity to develop number knowledge in the area of Number Sequence and Order, in particular development of knowledge of the Forward Number Word Sequence and skip counting patterns.
As each pede is developed help students focus on the number patterns involved by creating tables as below. Similar tables can be drawn for each type of pede.
Humped Back Pede


Number of Feet

Number of squares

1

2

2

4

3

6

4

8

5

10

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.
The conclusion of each session is an ideal time to focus on the number patterns involved. Questions to develop number knowledge include:
Which number comes next in the number pattern for this pede? How do you know?
Which number will be before 20 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 do you know?
Could a pede with 20 squares be a Spotted Pede? Why / Why not?
Could a pede with 32 squares be a 2pede? Why / Why not?
Are there any numbers that could be Spotted Pedes or Humped Back Pedes? What are they? How did you work that out?
 (Magnetic) tiles
 Squares of coloured paper
Session 1
Here we explore a couple of number patterns related to the mythical insects that live on the planet Elsinore. The patterns involve skip counting by 2s.
On the planet Elsinore there live a strange collection of insects. There is the HumpedBack Pede. The Humped Back 1pede looks like this. Can you see his eye? And the Humped Back 2pede looks like this. He has an eye too. (Show them the pictures below.) Ask the students to work individually or in pairs to make a Humped Back 3pede with the green tiles.
Can you work our how many squares a Humped Back 4pede has?
Gather the students together to talk about the insects that they drew. Explore the number pattern of counting in twos that comes from the HumpedBack Pedes. Also ask them questions like:
Can you tell me how many green squares a Humped Back 5pede will have?
Can you tell me how many green squares a Humped Back 7pede will have?
Can you tell me how many green squares a Humped Back 10pede will have?
How many feet has a HumpedBack Pede with 12 squares?
How many feet has a HumpedBack Pede with 18 squares?
How many feet has a HumpedBack Pede with 20 squares?
Can you tell me how to get the number of squares that a HumpedBack Pede with a particular number of feet has?
Can you tell me how to get the number of feet that a HumpedBack Pede with a particular number of squares has?
Session 2
Here we investigate some more of the mythical insects that live on the planet Elsinore. The patterns here involve skip counting by 3s.
 There are other insects on the planet Elsinore. They look as if they have been made up from squares. The ones with one foot are called 1pedes. The ones with two feet are called 2pedes and the ones with 3 feet are called 3pedes. (Show the students the picture below.)

Did you know that ‘pede’ means ‘foot’?
How many feet would a 4pede have? What about a 5pede?
Can you tell me how many squares a 1pede has?
How many squares does a 2pede have?
What about a 3pede?
(Put the numbers of squares beside the insects as the students answer the questions.)  Can someone tell me what a 4pede looks like?
How many feet will it have?
How many squares will it have?
Can someone make one for me with these square tiles?
Does everyone agree with that?
(Write 11 under the 4pede.)  Let’s have a look at the number of squares that these Pedes have. Count them out. 2, 5, 8, 11.
I wonder what sort of Pede comes next? (A 5pede.)
How many squares does a 5pede have? (14.)
I wonder what sort of Pede comes next? (A 6pede.)
How many squares does a 6pede have? (17)
Is there any pattern in the number of squares that Pedes have? (Add on 3 for each extra foot. Talk about skip counting by threes.)
Session 3
Here we explore patterns further. Here we are particularly interested in linking the number of squares on an insect and the number of feet it has.
 Here we are going to explore the Spotted Pedes. This is what they look like. Talk about the number of squares they have and the number of blue and red squares. Record these beside each of the Spotted Pedes.
 Now ask the students to draw the Spotted 4pedes? As they work ask them the following questions:
How many red squares does a Spotted 4pede have?
How many blue squares does a Spotted 4pede have?
How many squares all together? How did you work that out?
Why are there more blue squares than red squares? How many more?  Repeat with Spotted 5pedes and Spotted 6pedes.
How many red squares does a Spotted 5pede have?
Can you tell me how many blue squares a Spotted 5pede has? Draw it.
How many red squares does a Spotted 6pede have?
How many more blue squares does a Spotted 6pede have? Draw it.  For those students who need challenging ask them about the Spotted 10pede?
How many red squares does a Spotted 10pede have?
How many blue squares does a Spotted 10pede have?  At the end of the session spend time sharing findings as a class. Ask them
What did you find out about the Spotted Pedes?
What patterns did you find?
(Try to get them to see that they have as many red squares as they have feet. This means that it is very easy to find out how many red squares they have.)
Session 4

Here we are going to explore the BigHeaded Pedes. This is what they look like.

Ask the students to work with a partner to draw the next three BigHeaded Pedes (4, 5, 6). As they work ask them the following questions:
How many yellow squares does a BigHeaded Pede 4pede have?
How many yellow squares does a BigHeaded Pede 5pede have?
How many yellow squares does a BigHeaded Pede 6pede have?
Do you need to draw the insects to work out how many squares they have? Why or why not?
Could you work out how many yellow squares a BigHeaded Pede 10pede would have? 
At the end of the session spend time sharing findings as a class. Ask them
What did you find out about the BigHeaded Pedes?
What patterns did you find?
(Try to get them to see that they have three more yellow squares than they have feet. This means that it is very easy to find out how many yellow squares they have.)
I saw a BigHeaded Pede with 16 yellow squares. How many feet did she have?
Session 5

Can you tell me what kinds of Pedes we have been talking about this week?
Discuss the Pedes, the HumpedBack Pedes, the Spotted Pedes and the BigHeaded Pedes. 
Tell them that you want them to work with their partners to invent a Pede of their own. Ask the students to record the first three pedes on one piece of paper and the other three on a second sheet. Ask them to also invent a name for their insect.

Pairs could then swap the first three Pedes to see if they can work out the next three Pedes for each other’s insect. They can then check with each other to see if they arrived at the same Pedes for the 4, 5 and 6 insects.

As time allows get the students to swap pedes with other pairs.

As the pairs work ask them to discuss the various patterns that they have produced. Ask them questions such as:
How many squares does one of your 5pedes have?
Can you tell me the number of squares an X Pede with 10 feet (or some other relatively large number) has?
If I had 15 squares what is the Pede with the largest number of feet that I could draw? 
Collate the classes Pedes into a book of Pede problems that can be worked on by the students during any “free” or “choosing” time.
Dear Parents and Whanau,
In maths this week we have been working on patterns. We have looked at some mythical insects from the planet Elsinore. We have seen the patterns that their numbers of squares have. Here is an animal from Elsinore. Perhaps together you could explore the links between its number of legs and the number of squares that make up its body.
Discuss with your child how many squares does a 2legged animal have?
How many squares does a 3legged animal have?
How many squares does a 4legged animal have?
How many legs does an animal with 20 squares have? Talk together about how you know? What do you have to do to work this out?
We would also like you to help us come up with a name for our animal. Write your ideas here.
We hope that you enjoyed working together on this algebra patterning task.