This presentation is a collection of 15 short (1-6 slides) fun facts or mini enrichment activities, along with a slide of suggestions on where to look for more. Topics range from geometry and set theory (to make Venn diagrams more exciting) to data and graphs. The idea is they can easily be copied and pasted into another presentation as a short add-on to each lesson. Bite-size introduction to 4D geometry anyone? They would make good starters or conclusions to lessons on related subjects, with the goal of firing the imagination of the students and hopefully getting them doing their own research! Or when it comes to the fun facts, it may just make them smile. Some of these topics are covered more extensively as part of my full-length lessons on fractals and infinity.

This is primarily an enrichment topic, but also an extremely useful concept for students to encounter before integration/differentiation/calculus in general! The powerpoint is essentially a script that can just be read out loud, with the goal that no additional explanation or research is needed. It’s a short trip through various thought experiments on the weird and wonderful world of infinity - physics teachers may wish to discuss the short prompts on slide 22 about whether we ever actually encounter infinity in real life. Primarily it supports an intuition around infinite series that add up to a finite number, how basic arithmetic differs with infinities and hopefully makes integrating between infinity and -infinity seem like a less daunting prospect! Some of the presentation may be more engaging when narrated by the teacher without the slides visible to students. It captured the interest of many of my students, from GCSE down to a group of particularly advanced primary school students I shared it with!

This pack contains three ways to approach fractions and a worksheet on fractions walls. The first is a basic approach suited to students seeing the topic for the first time or recapping after a first lesson (Pathway 1). It does not introduce the concept by splitting a single object into parts and emphasises sharing collections between people, after some of my primary school students struggled to transition from visualising cakes/pizzas to tackling fractions of numbers. The second is a refresher for older students, using the traditional depiction with circles/pizzas and fraction walls (Pathway 2). The third is an alternative approach to solving more complex fraction problems by visualising it with blocks. This was a massive help for some of my GCSE learners who were struggling with percentages - the lesson begins by introducing the blocks for use with fractions and can then be continued to make fractions and percentages identical.

This lesson demonstrates the surprising fact that a chaotic and unpredictable process can lead to an ordered, predictable outcome, throwing in concepts and calculations from probabilities and geometry. It can be a great contrast to sequences and series, where they use a repetitive nth term rule to get an ordered list. The resource contains a word document that will lead students through the Chaos Game (consider keeping page 2 for yourself and talking through it!). It has simple rules but plenty of interesting discussion points around probability. Having seen this unique fractal arising from an unpredictable process, they can explore how and why it happens before moving onto the powerpoint about fractals in nature. The slides also lead them through the surprisingly simple proof that a Koch snowflake (another fractal!) has infinite perimeter and yet finite area - all they need is knowledge of fractions. It’s an enrichment lesson designed to engage the students and give them pride in the amazing things they can prove! This lesson is suitable for most secondary school classes.

It can be challenging for students to understand decimals, and they may try to memorise a set of rules to deal with them rather than developing a deeper understanding. These slides walk them through a (fictional) historical story that motivates the invention of decimals and prompts them to invent the rules for adding and multiplying decimals, with the secondary goal of explaining why the number 10 has the magical property of moving the decimal point around. I put the lesson together for a class with some deep misconceptions about place value and decimals, e.g. thinking that multiplying by 10 always adds a zero and therefore 3.2 x 10 = 30.2, which these slides cleared up. The standard form and bounds topics right at the end are a great test of understanding for older students, but the other slides should be fine soon after introducing decimals for the first time!