Maths in the Mantle of the Expert
Children establish ‘agency’ in mathematics through applying their knowledge in different contexts. The experiential opportunities offered by the Mantle of the Expert, allow children to work collaboratively to use maths in different tensions and commissions. This allows them to gain confidence, make connections within mathematical knowledge and allow children to fully exercise the wider application of maths skills. Below are examples of how each Mantle topic to be delivered in 2022-23 links with maths and provides opportunities for a variety of investigations to enrich the mathematics that children learn in discrete maths lessons.
Time can often be a challenging, abstract concept to children, but is vital in terms of developing an understanding of the world around them.
As time-travellers, children will start to use the language of time with more confidence, telling the time throughout the day, first using o’clock and then half past.
Their experiential learning will encourage children to tell the time on analogue clocks and recording it, sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] and relate time to historical knowledge; recognising and using language relating to dates, including days of the week, weeks, months and years and comparing sequence intervals of time;
· Family Timeline; look at some old family photographs; create a personalised timeline for family showing important events such as births, marriages or house moves.
· Watchmaker; Find photographs of as many different types of watches as you can find and create a collage, design a watch incorporating some exciting new functions
· Representing time; create a pie chart to show the proportion of time each day on tasks/activities, like brushing your teeth or doing your hair? Are there any activities you would like to do more or less? What would the pie chart of your perfect day look like?
· Constructing a historical time line
· Constructing a geological time line
The Animal rescuers will have to think carefully about the animals they are trying to understand, choosing and using appropriate standard units to estimate and measure length/height and mass; the temperature (°C) of their habitats and the distance/ position of their locations. The rescuers will get involved in a range of fund raising activities; recognising and using symbols for pounds (£) and pence (p); combine amounts to make a particular value, while using money and calculations to solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change.
Pupils will handle and name a wide variety of common 2-D and 3-D shapes including: quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape while preparing and constructing animal shelters. They will also use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts and mathematical vocabulary to describe position, direction and movement, when navigating their way through difficult terrain and transporting materials and resources to their conservation site.
During their studies of bees, their biology, habitats and conservation, children will learn about a wide variety of common 2-D and 3-D shapes including: quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape and use vocabulary precisely, such as sides, edges, vertices and faces.
Children will also record, interpret, collate, organise and compare information about bees, the plants that they feed on and pollinate by;
· interpreting and construct simple pictograms, tally charts, block diagrams and simple tables
· examining simple questions by counting the number of objects in each category and sorting the categories by quantity
· examining questions about totalling and comparing categorical data including time
· Investigating questions like; what flowers are visited by bees? When did you see your first bee of Spring? What sort of bees did you see? What plants/food would disappear if it weren’t for bees?
Children will also use a variety of maths skills to construct a ‘Bee-tastic’ board game- learning about number, counting and calculating.
They will also take part in investigations such as the mathematics of bees eyes, how scientists have proven that bees are amazing mathematicians, how patterns and sequences in nature help bees and a variety of measuring/ geometric skills to ‘build’ a bee.
As tour guides, children will measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units and simple equivalents of mixed units. They will also compare measures and develop simple scaling by integers connecting with newly acquired knowledge in multiplication connects to multiplication.
While designing basic and bespoke tour itineraries, they will extend knowledge of the properties of shapes to symmetrical and non-symmetrical polygons and polyhedra using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.
Geographical skills and map-work will require children to understand and use simple scales with increasing accuracy, and continue to interpret data presented in many contexts. Planning for tours and visits invites children to think creatively about multi-step problems and reasoning; choosing the appropriate operation and working with increasingly harder numbers. This include correspondence questions such as the numbers of choices of a meal on a menu, transport required for trips and the management of distances and routes to optimise accessibility for visitors.
The tensions and skills associated with their conservation roles will allow children to both develop their understanding apply their mathematical knowledge of the properties of shapes and symmetrical /non-symmetrical polygons and polyhedra. They will be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.
As part of outdoor maths and environmental tensions children will (for example):
· observe and name angles around them
· Use their knowledge of, and vocabulary associated with 2D and 3D work to describe and construct frames in greenhouses, hides and environmental monitoring structures
· Use knowledge and vocabulary associated with position, angles and measures to construct visitor routes, orienteering programmes and the use of/ understanding of forms of topographical representation
While coordinating teams of environmental consultants, children will increasingly consider how to measure with accuracy and make connections between measure and number in terms of place value, estimation and representation- applying this knowledge to problem solving in a real life context. They will also be faced with ‘scaling’ problems to connect with mental and written multiplication and division strategies and will become increasingly fluent in recognising the value of money, metric measures, conversion and analogue/digital 12-hour clocks
As an environmental group, they will be responsible for recording, monitoring and describing biodiversity, to present plans and reasoned arguments to the commissioning body. Through this they will exercise their ability to understand and use simple scales and use graphical representations in order to solve one-step and two-step questions, often looking at changes over time.
This commission allows children to engage in a variety of aspects of number and calculation for example, estimation (how many sacks in the barrow? how many litres per bucket?) and calculation of physical and human resources for a task. Children will also apply spatial knowledge and skills when developing routes and orienteering tasks i.e.; Directional language (over, under or through), Positional language (forwards or backwards), time taken to complete (stop-watch, sand timer)
While experiencing Roman life, the children will engage with Roman numerals building an understanding that there have been different ways to write whole numbers in different historical contexts. The will have the opportunity to use their experiences to engage with many different aspects of Number, recognising that the important concepts of zero and place value were introduced over a period of time. They will solve number and practical problems and engage with increasingly large positive numbers to; solve problems involving multiplying and adding, use the distributive law, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.
This MoE commission will also encourage them to measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres and find the area of rectilinear shapes by counting squares.
Children will engage with more investigations this term, applying what they have learnt within foundation subjects, for example:
· Count like the ancients; reading Roman numerals to 100 (I to C)
· Figure out Roman road routes around school using only straight lines and right angles
· Experience a Roman shopping challenge
· Investigate the areas of different Roman villas
· Weigh out ingredients to make Roman bread and scale up the ingredients for a class feast
· Look at numerical and symbolic sequences, examining the work of ancient scholars (such as Fibonacci)
· Work collaboratively within NRICH maths investigations
Health Spa developers
In their role as Ancient Egyptians, children will develop their use of large numbers (5-7-digits), understanding of fractions, decimals multiples and factors. The commission involves valuable opportunities to investigate abstract concepts such as ratio, proportion and formulae as well as consolidating and extending children’s understanding of 2 and 3D shapes.
Children will fully exercise their understanding of mathematics by contextual mathematics, investigating such things as:
· Maths problems linked to time zones
· The mathematics of a holiday to Egypt:
o Luggage allowances
o Travel costs
· Ancient Egyptian number problems
· Designing a tomb
· Data logging to interpret best places to exhibit important artefacts
· Fitting out a museum, geometry, cost calculations, use of display cabinets
· Mathematics of pyramid building; measurement, conversion, ratio and proportion, formulae and statistics
This commission encourages pupils to extend their understanding of the number system and place value to include larger integers, developing the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.
They will be faced with a number of challenges which will test their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation.
More able children will lead collaborators in the application of increasingly abstract ideas, such as equations and formulae, to illustrate how these ideas are applied in real life contexts; calculating costs, amount of resources, consumer footfall…
Pupils will work together to develop scale plans of the Health Spa, and consider it’s dimensions- and associated problems associated with ratio and proportion, in designing and resourcing their attraction/ facility.
In addition to enhancing and applying geographic and scientific knowledge, in the final term’s commission, children will consolidate and apply mathematics through a sequence of investigations associated with:
· the properties of 3-D shapes
· accurate measurement of length and angles
· Topographic indices such as position, coordinates, translations and transformations
· ‘scaling’ problems and mental and written multiplication and division conversions and measures of quantities, time and space
The findings and recommendations of their projects will be supported by statistics and a variety of data handling techniques, helping them to record, monitor and describe biodiversity, and to utilise data as they present plans and reasoned arguments to the commissioning body.
This term will also allow children to use a variety of computing packages, such as spreadsheets, modelling programs and logic-based software to test mathematical predictions, patterns and formula.