FM Complex multi-step problem(s)

A complex problem requires requires a multi-step process, typically requiring planning and working through at least two connected steps or processes. Individual problems are based on a combination of the knowledge and/or skills from the mathematical content areas (MCA). At Level 2 it is expected that the student will be able to address individual problems some of which draw upon a combination of all three MCA (number, measures, data) and require students to make connections between those content areas. The context of individual problems at L2 will require interpretation and analysis in order for the student to be able independently to identify and carry out an appropriate mathematical process or processes.

Pancake Day in Exdale is a multi-level graduated Functional Maths workbook for Entry Level 1 to Level 2. A front page overview allows the teacher or learner to decide which levels and topics to work on. All questions are based on one or other of two texts (pancake meals at the local pub and special offers in the Exdale Cook Shop). The emphasis throughout is on problem solving and showing working out.

At Entry Levels the main coverage is time, dates and money. Levels 1 and 2 include questions on time, converting between measures, circumference, percentage discount and mean.

Level
Entry Level 1
Entry Level 2
Entry Level 3
Level 1
Level 2
Maths
FM Simple one step problem(s)
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM E1.6 Read 12 hour digital & analogue clocks in hours
FM E1.7 Know the number of days in a week, months, & seasons in a year. Name & sequence them.
FM E2.5 Add & subtract 2-digit numbers
FM E2.12 Calculate money with pence up to £1 & in whole £s of multiple items, use correct symbols (£ or p)
FM E2.13 Read & record time in common date formats, & read time displayed on analogue clocks in hours, half hours & quarter hours, & understand hours from a 24-hour digital clock
FM E3.10 Calculate with money using decimal notation & express money correctly in writing in pounds and pence
FM E3.13 Read time from analogue & 24 hour digital clocks in hours & minutes
FM E3.14 Use & compare measures of length, capacity, weight & temperature using metric or imperial units to the nearest labelled or unlabelled division
FM L1.12 Approximate by rounding to a whole number or to one or two decimal places
FM L1.14 Calculate percentages of quantities, inc. simple percentage increase / decrease by 5% & multiples of
FM L1.20 Convert between units of length, weight, capacity, money and time, in the same system
FM L1.29 Find the mean & range of a set of quantities
FM L2.14 Convert between metric & imperial units of length, weight & capacity using a) a conversion factor & b) a conversion graph
FM L2.16 Calculate perimeters & areas of 2-D shapes inc. triangles & circles and composite shapes including non-rectangular shapes (formulae given except for triangles & circles)
Context
Retail Hospitality Customer service

NEW 24/2/22  answer sheet now also  available - visit our ANSWER SHEETS page for more information.

A follow-on Valentine's Day resource from the E1-E3 worksheet of the same name. It continues the general problem solving of finding suitable meal deals for various couples and calculating how much they save by purchasing a Valentine's meal deal. For L2 learners it also delves into compound measures with challenging multiple questions on on unit prices (e.g. £/kg, £/litre).

Level
Entry Level 3
Level 1
Level 2
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM E3.10 Calculate with money using decimal notation & express money correctly in writing in pounds and pence
FM E3.21 Extract information from lists, tables, diagrams, charts; create frequency tables
FM E3.23 Organise & represent information in appropriate ways inc. tables, diagrams, simple line graphs & bar charts
FM L1.20 Convert between units of length, weight, capacity, money and time, in the same system
FM L2.15 Calculate using compound measures inc. speed, density & rates of pay
Context
Retail Hospitality Customer service
Catering Food Nutrition

This is a Level 2 based Currency Conversion set of 4 questions with resource sheets and answers.  All exchange rates resources were obtained from web sites such as The Post Office and the Bank of England. 

Editor's note

Also provides useful practice in multiply, dividing with decimals (up to 4 decimal places); sensible rounding of answers; and extracting data from tables.

Level
Level 1
Level 2
GCSE L1-5
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM L2.13 Calculate amounts of money, compound interest, percentage increases, decreases & discounts inc. tax & budgeting
FM L2.14 Convert between metric & imperial units of length, weight & capacity using a) a conversion factor & b) a conversion graph
FM L2.10 Add, subtract, multiply & divide decimals up to 3 decimal places
Context
Business & Money management
Leisure, Hobbies, Travel & Tourism

This resource covers all the Functional Skills content descriptors relating to ratio and proportion. It was written with mixed L1-L2 classes in mind. I wanted to experiment with inverse proportion questions (a new topic in Reformed Functional Maths) but wanted to build up to them gradually. The questions are contextualised and problem based, with no underpinning taught, so learners will need an introduction to ratios (or a refresher) beforehand. Ratios, direct and inverse proportion are covered.

Level
Level 1
Level 2
GCSE L1-5
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM L1.17 Work with simple ratio & direct proportions
FM L2.11 Understand & calculate using ratios, direct proportion & inverse proportion
Context
Catering Food Nutrition

A topical resource that requires students to interpret a news infographic and calculate the difference between two times. There is also a second question for Level 2 learners on Speed, Distance, Time. As well as enabling students to practise time calculations it can lead to discussion about this controversial rail project.

Editor's notes

Really topical and interesting. With curriculum mapping. No answer sheet.

Level
Level 1
Level 2
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM L1.20 Convert between units of length, weight, capacity, money and time, in the same system
FM L2.15 Calculate using compound measures inc. speed, density & rates of pay
Context
Leisure, Hobbies, Travel & Tourism
Motor vehicles & Transport

Challenging set of  questions based on an infographic from a recent TV Licensing annual review.  Aimed at L1-2 but a few questions are Entry 2/3 - there are also  a couple of  "stretch questions" making a bridge to GCSE. Two main topics are covered: working with very large numbers and percentages. Extracting data, equivalents and ordering decimals are also touched upon.

Level
Level 1
Level 2
GCSE L1-5
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM E3.21 Extract information from lists, tables, diagrams, charts; create frequency tables
FM L2.1 Read, write, order & compare positive & negative numbers of any size
FM L2.4 Identify & know the equivalence between fractions, decimals & percentages
FM L2.6 Calculate percentage change (any size increase & decrease), & original value after % change
FM L2.13 Calculate amounts of money, compound interest, percentage increases, decreases & discounts inc. tax & budgeting
GCSE N2 (Apply the four operations)
Context
Art Film Media Music Radio TV

This is a project based on Benford's law. I had this idea after watching the Numberphile series on YouTube. This is a project based activity that involves many skills including working with large numbers, using percentages, representing data and probability.

The investigation is introduced to learners using the PPT (and optional YouTube links). Learners then split into four groups - each is given a random set of  share prices [see Excel file].  Each group investigates the occurrence of numbers starting with each digit from 1 to 9.

Editor's note

Level
Level 1
Level 2
Maths
FM Complex multi-step problem(s)
FM L1.1 Read, write, order & compare large numbers (up to one million)
FM L1.14 Calculate percentages of quantities, inc. simple percentage increase / decrease by 5% & multiples of
FM L1.15 Estimate answers to calculations using fractions and decimals
FM L1.27 Represent discrete data in tables, diagrams & charts inc. pie charts, bar charts, line graphs
FM L1.28 Group discrete data & represent grouped data graphically
FM L1.30 Understand probabilities on a scale from 0 to 1; use to compare the likelihood of events
FM L1.31 Use equally likely outcomes to find probabilities of simple events & express as fractions
Context
Business & Money management

A challenging set of L1-2 maths questions that celebrate 50 years since the first Moon landing. Covers new reformed content such as compound measures and 3 figure bearings. Plus an introductory PPT with background information and pop up answers.

Editor's note

Fully mapped to the new reformed Functional Maths content.  The answer sheet, which includes detailed working out and marking guidance, is only available to site contributors. Please see details within the resource.

 

Level
Level 1
Level 2
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM L1.1 Read, write, order & compare large numbers (up to one million)
FM L2.2 Carry out calculations with numbers up to 1 million inc. strategies to check answers e.g. estimation & approximation
FM E3.14 Use & compare measures of length, capacity, weight & temperature using metric or imperial units to the nearest labelled or unlabelled division
FM L1.20 Convert between units of length, weight, capacity, money and time, in the same system
FM L1.26 Use angles when describing position & direction, & measure angles in degrees
FM L2.15 Calculate using compound measures inc. speed, density & rates of pay
FM L1.29 Find the mean & range of a set of quantities
Context
Science, Nature & Weather
History, culture, museums, libraries

This revision aid for L1/L2 (mainly L2) Pearson Edexcel Functional Skills maths gives a side-by-side comparison of perimeter, area and volume, the sort of units that would be involved with each and a worked Functional Skills example of each with a PAV mnemonic for remembering which is which. I have also looked through the last few years of Pearson Edexcel FS for the sorts of questions that require each one. 
Note: All images from Pixabay, so do not need crediting.

Editor's note

Level
Level 2
GCSE L1-5
Maths
FM Complex multi-step problem(s)
FM L2.3 Evaluate expressions & make substitutions in given formulae in words & symbols
FM L2.16 Calculate perimeters & areas of 2-D shapes inc. triangles & circles and composite shapes including non-rectangular shapes (formulae given except for triangles & circles)
FM L2.17 Use formulae to find volumes & surface areas of 3-D shapes inc. cylinders (formulae given for 3-D shapes except cylinders)
GCSE G14 (use units of measure)
GCSE G16 (area, volume)
GCSE G17 (circles, perimeter)
Area
Circles
Circumference
Perimeter
Volume
Context
Catering Food Nutrition

I wrote this to add to Timings in a Salon by Carrie Bray (see link left) as I needed to encourage my higher level students in the same area.

I started the session by giving students terminology which they had to define, then work out how much it was worth if a=1p b=2p etc. (see PPT).

I used then used tasks to recap on 24 hour and analogue time next then used the attached worksheets alongside Carrie's worksheet.

I then provided a Tarsia puzzle at the end to recap on time.

Editor's notes

Level
Entry Level 3
Level 1
Level 2
Maths
FM Straightforward problem(s) with more than 1 step
FM Complex multi-step problem(s)
FM E3.13 Read time from analogue & 24 hour digital clocks in hours & minutes
FM E3.12 Read, measure & record time using am & pm
Context
Hairdressing & Beauty therapy