Textbooks for the National 5 Content can be downloaded here: https://www.freeapplicationsofmaths.co.uk/n5-apps-textbook-new
Week 1 – Finance
Appreciation, reversing a percentage change, and tax bands (often seen as National Insurance at Nat 5) are essential skills for the finance part of Higher Apps.
Recommended Resources
Understanding percentage change using multipliers: Jo Morgan.
Appreciation and Reverse Percentage: Dr Austin Maths. Loads of content here.
Tax Bands: My advice is to use this site. National Insurance tables are best avoided, as at Higher Applications we will later be finding National Insurance per week rather than annually. Give students the table from the LBTT website, and then give them property prices to work out the tax for. The website can be used to check their answers. You might find this worksheet helpful.
When checking answers for income tax, I’ve found the Which? website useful: Which?
Challenge: Can students create an excel spreadsheet that can calculate tax for them? By the end of the course, they should be able to!
Week 2 – Shape
Volume can appear in the modelling part of the course. Precedence tables will also be expanded upon later in the course.
Recommended Resources
Past Paper Volume Questions – Firrhill High.
Precedence Tables- Free Applications of Maths.
Week 3 – Statistics
Statistics is such a big topic at Higher, it’s worth brushing up on the National 5 content.
Recommended Resources
The Free Applications of Maths website has a nice booklet here.
I recommend motivating the use of computer by having students answer some of the questions using Excel. Find the mean and standard deviation, produce boxplots and 5 figure summaries.
Remember to use the STDEV.S () function for standard deviation, not the STDEV.P function. This is because the formula given at National 5 is the sample formula, not the population one.
Challenge: Have students find the semi-inter-quartile range in Excel. Hint: There is no function for this, but there is a “quartiles” function.
Week 4 – Measures
In the modelling section of the course being able to convert between metric measures is important and worth revisiting here. Especially converting between metric volumes and areas. Tolerance is not assessed in 2023. Students can also be expected to find the gradient given two points.
Recommended Resources
Converting Metric Measures from Jo Morgan.
Converting Metric Units – A worksheet from me that covers more metric conversions.
When recapping gradient, students could be introduced to the idea of rates of change using these Corbett Maths questions: 1 and 2.