Sequence Zoo

In preparing for a Year 8 revision lesson for a SATS paper, I came across the following questions:

This is a great example of the requirement for proof and reasoning: any of the nth term expressions would fit the first three terms of 1, 2 and 4, yet depending on the situation it is likely that some of the expressions would be inappropriate.

It is also reminded me of an idea of Lucia Handley, using cubes to investigate sequences.

The Sequence Zoo

The lesson began with an arrangement of animals: giraffes, pigs and cows/zebras. Pupils could then be challenged to work out what the baby of each animal looked like, or to work out whether they could give the number of bricks required to make a species, given its height.

Alternatively, the animals in the image above could be used and pupils had to find out which animal had grown out of sequence.

The cow/zebra is particularly interesting, as you could look either at total number of blocks, or the white / black components.

Thanks Lucia!

Maths is Just Another Language

Inspired by the video of the 10 year old maths teacher, I want to increase my focus on maths as a language.

For example,

Translate these sentences into mathematish

These could be adapted to suit each topic but overall should help students to understand how expressions are formed and therefore also to interpret them. This falls in line with Anne Watson's thinking that students should be taught to read algebraic sentences out loud to give them meaning.

UPDATE: 28/05/2013

For algebra specific translations, translating english to algebrese

http://www.algebra.com/algebra/homework/Human-and-algebraic-language/english-to-algebreze-in-word-problems.lesson

When you take a real-world situation and translate it into math, you are actually 'expressing' it; hence the mathematical term 'expression'.

The Lesson Planning Mountain

A strong focus of the department week has been on lesson planning.

Within our small groups, we analysed our own lesson plans to look for evidence of Learners' Mathematical Development, in terms of the following structure:

see - do - record

see - experience  - master

We were particularly sceptical of the latter of these structures, as experience didn't necessarily imply investigating, doing or analysing, before the pupil was expected to have reached the master phase.

The Lesson Planning Mountain

Instead, we began to consider the lessons using the analogy of a mountain climb of two peaks, as shown below.

• The lesson begins with the class consolidating prior knowledge together, at base camp.
• The climb begins with everyone walking together up the mountain, as new material is introduced. During this stage, pupils will begin to acclimatise to the higher altitude.
• By the time the summit is reached, it is time for the pupils to part ways on their descent and continue as individuals.
• Depending on how comfortable the students feel, they can sled, ski or abseil down (in increasing speed order). This gives the first opportunity for differentiation of activity.
• At the point at which the second mountain comes into view, pupils can make the decision whether to climb higher to explore the subject in more detail or whether to continue practising as they head down the mountain.

Having previously seen the model of the tree where pupils label which person they think they are [insert link here], this mountain analogy could also be used, where pupils label where on the ascent they think they are at any stage in the lesson.

Found in TES ... Technology