A blog about teaching and learning in a maths classroom.

The Land of Algerb

Sunday, 07 March 2010 | 4 Comments

Starting Algebra with Year 8, we spend a couple of lessons on various “algebraic techniques”. I’ve been trying to find some activities which provide a little more engagement. I created “The Land of Algerb“ to explain multiplying pronumerals.

Using a story and a coloured worksheet worked surprisingly well. I don’t know yet if the story has helped my class understand the technique, but they all actively completed the activity keen to ensure their own story way correct.

The activity

  • tell the story, using the PowerPoint as the visual.
  • hand out the template, and get the students to create their own story.

The Story

In the land of Algerb there were two kingdoms, the kingdom of 2x and the kingdom of 3y. The King of 3y and the Queen of 2x both wanted to increase their lands.

The King of 3y and the Queen of 2x took their explorers to the undiscovered land.

Whilst in this new land, the people mingled.

The numbers met the numbers and the letters met the letters.

The two kingdoms became one, the numbers multiplied, but the letters stayed the same.

A new nation had been formed, each nation’s numbers had been made bigger. But the letters of each nation were still distinctive. The xs from the 2x kingdom and the ys from the nation of 3y.

The end.

The Files

In the zip file below there are two files:

  1. the-land-of-algerb.pdf includes the story with visuals, and a colour worksheet with 2 A5 versions of the storyboard.
  1. the-land-of-algerb.pptx is the PowerPoint of the story.
This work is licensed under a Creative Commons License (?).

Posted in • ActivityStoryLesson IdeaAlgebra | Short URL:


Pixeltoy on  07 March 10  at  02:30 AM #
A very powerful way to get the concEpt across. I have created stories for subtration decomposition method and have had ESL students recounting to their ESL teacher with enthusiasm. Using a visual story can only enhance the experience. Hopefully more HS teachers are appreciating this approach.
Heather McMaster on  08 March 10  at  12:17 PM #
Methods like “The Land of Algerb” which are used to teach algebraic technoques are appealing to students because they make the technique easy and there is an element of fun, but when students need to apply the algebraic technique in the longer term, I’ve found that they forget the situation for which the technique is applicable eg. they apply “The Land of Algerb” technique to addition instead of multiplication so they write 2x + 3y = 5 + x + y (add the numbers then add the letters). Also they start to think that in algebra, the numbers are different to the letters so they treat them according to a different set of “rules” (eg. they don’t apply “order of operations” in the same way for the letters as they would if they were all numbers - they “do” the numbers first). What they should be remembering, is that a letter stands for “any number”. I’ve been trying to encourage teachers to use real life contexts with numbers from which students can generalise using algebra. In this way, I’m hoping that students can understand the purpose of algebra and be able to use it to abstract from a context.
malyn on  17 March 10  at  12:50 PM #
Came here because I haven't seen you in Twitter for a while. I'm glad I did as this is an interesting post. You may care to visit [url="htttp://"]my blog[/url] as well because I was exploring the ideas of creativity, contextualised learning and transferability as commented on by Heather McMaster - in fact, would love to hear her advice to my blog question: what's the best way to teach maths. For my year 8 class this year, i had packets of jelly beans. Different packets contained different numbers of jelly beans - hopefully to reinforce the idea that the letters can represent any number. I grew up with the term 'variable' and I mentioned this as being more meaningful than the term we now use, "pronumerals". Anyway, the packets were good to show all operations in Algebra...not quite Order of Ops though. Even division works. I even managed this with expansion, e.g. 2(x + 1) where the 1 is a small piece of chocolate - constant value vs. variable number in packets. I colour-coded my packets so I can use different letters to represent them as well. And yes, the students got to eat some jelly beans as well. Not sure if I'm making sense. Anyway, thanks for this post - I love creativity in the maths classroom.
malyn on  17 March 10  at  12:53 PM #
I just realised how rude I sounded in stating 'i'd love to get HM's comment on my blog' when I'm commenting on your blog. Truly sorry about that - should've previewed first. But please, do visit and comment. I'd love to hear your views as well.

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Simon Job — eleventh year of teaching maths in a public high school in Western Sydney, Australia.
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