The focus of the lesson is developing early algebraic thinking through growing patterns. While doing this children will be showing their facility with number sequences and counting patterns. Ordinal number is also used.
Materials
• Five ice-cream containers or other items which can be imagined as rocks when turned upside down
• About 50 pieces of wool to be the snakes
• A3 Paper and pencils for the students for their work task
The lesson
The children all sat on the floor in a large oval so they could all see what was happening.
The five rocks (in the form of upside down icecream containers) were placed in a row on the floor in the centre of the group. I told them to use their imaginations and imagine that these are rocks and asked them to tell me something about the rocks they were imagining. “They are hard”, “they are brown and black” “One is green” “They are in a line”. I talked about the rocks using ordinal numbers making it clear which was the first rock and asking students to identify the second rock, the fourth rock, etc.
I showed the students my collection of pieces of wool but I called them my collection of snakes. I then read the poem, acting out the movements of the snakes and placing one on the first rock, two together on the second rock, three on the third etc. as the poem was read. I placed the five as a group on the fifth rock so they couldn’t see them easily to count them. After each verse of the poem I asked them about how many were on the first rock, the second etc making sure they know which rock is which and that the numbers building up the pattern are drawn to their attention. At the end of the poem I asked them how many were on the fifth rock (the question in the poem) and how they knew without counting them. We went over the pattern again making sure many students had had a chance to answer a question then I asked them to imagine a sixth rock. How many would be on it?
We repeated the task but this time I started with 4 snakes on the first rock, 5 on the second etc.
For the third reading of the poem, I started with one on the first rock again but had 3 on the second and five on the third etc.
For the fourth one, I started with ten on the first rock, but had nine on the second, eight on the third etc.
I did another where I started with 4 and went 6, 8 , 10
When I judged that the students had the idea that the starting number could be different, the numbers could increase or decrease and the increases could be one, two, three or ... , I told them I wanted them to make up their own pattern. I asked some of them to share what number of snakes they might consider starting with on the first rock. They were told to draw five shapes for rocks and then decide what number of snakes they would put on their rocks for their pattern. They went to the tables to do their drawings and I moved around checking they knew what to do and had started – also telling them the rocks just had to be circles and didn’t need to be coloured in. They were told when they finished they could extend their patterns if they wished by adding a sixth seventh eight and more rocks or that they could make a few different patterns on their paper.
When everyone had at least one pattern of 5 rocks on their sheet I asked them to bring their pictures back to the floor to share what they had done. During the sharing we focused on some of the different patterns noting the different starting points, the different increases (or decreases) and extending the patterns beyond. For each pattern I asked about a rock extending the pattern. For example to extend the ideas, with a simple pattern with 6 rocks I asked how many would be on the eighth rock.
The sharing was what amazed me. Everyone had managed to draw rocks with snakes. All but one had a pattern of some kind. For most of them the number of snakes they had drawn on the rocks corresponded to the number they wrote alongside. There was one child though where there was no relationship. He still managed to draw snakes on rocks and write numbers and proudly counted the snakes on one of the rocks for me.
Click on the following student's work to hear Marj's analysis of the student learning.
| Alejandra | Sam | Avin | Audrey | Ben | Adrian | Annie | Danielle | |Matthew | Jessica |
Another child had drawn 5 snakes on each rock while yet another had used a repeating pattern rather than a growing pattern and had 5, 6, 5, 6, 5 but had the numbers and the number of snakes correct.
The student work here below shows number sequences but is not related at all to the snakes. The student though was very happy writing the numbers
Then there were students with a range of growing patterns, some extended.
Then there were two students who moved outside the box and tried some different patterns – the one shown here was 2, 1, 4, 3, 5 – she wasn’t sure how to keep going. One student though increased the decrease each time and had 10, 9, 7, 4, 0.
Key mathematical content
- Number patterns
- Odd numbers
- Even numbers
- Counting patterns
- Ordinal number
Acknowledgement
This is based on an activity from the Navigator series published by NCTM and the poem with permission of Carole Greenes.
[contributed by Marj Horne, Connect with Maths Community Leader]
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