Maths: Tuff problems

Hilary White, teacher, based in Somerset
Thursday, November 1, 2018

For young children, mathematical learning and development is all about the concepts of quantity, space and distance. At this early stage, the hands on exploration of these concepts is of key importance – and a Tuff Tray makes the perfect resource.

Tuff Trays are an important resource at Cypress Primary School Nursery, in Croydon
Tuff Trays are an important resource at Cypress Primary School Nursery, in Croydon

Tuff Trays are just the right height for children to stand at, enabling them to see what they are doing as they manipulate the items they are exploring. The waterproof surface and raised sides are great for containing water and other ‘flowing’ substances (exploring capacity), and the large, flat, single-colour space is useful for heuristic play (counting and sorting). Wheeled toy vehicles offer a fun way of exploring distance and measure – and using vehicles within the Tuff Tray limits both the distances they travel and the lengths to be measured. Try the following activities with your children and make the most of the Tuff Tray to support their mathematical development.         

Playing and exploring

  • Children use water play resources in the Tuff Tray to explore capacity.
  • They investigate the distance vehicles travel within the Tuff Tray space.
  • Children dig up, sort and count items buried in the Tuff Tray.

Capacity: gather a selection of clear plastic receptacles including bottles, bowls, jugs and funnels. Colour quantities of water with food colouring gel and place the Tuff Tray on a waterproof mat. Let the children play with the resources in their own way, and discover and explore the concepts of ‘full’, ‘empty’, ‘holds more than/less than…’ and so on.

Length, distance and measure: provide wooden blocks, wedges and stiff card, and build ramps at the edge of the Tuff Tray for toy vehicles to shoot down. Does a vehicle reach the edge of the tray? If not, mark its stopping place with a sticker and compare how far different vehicles have travelled. With the four-plus age group, measure distances using non-standard measures (longer than/shorter than a ribbon; how many blocks?) and standard measures (rulers, tapes). 

Quantity: put soil in the Tuff Tray and bury groups of small items, plastic or wooden numbers and pebbles with marker pen numerals. If you want to limit the amount of soil or offer a ‘deeper dig’, use boxes. Provide trowels for children to dig up items, and show them how to sort and count their treasures. Put numbers/numeral pebbles in order, and match with corresponding quantities.

Observe how confidently and freely the children explore the Tuff Tray maths resources and activities. How effectively do they use the tray space to extend and develop their play?                                                                                                                                                            

 Active learning

  • Children enjoy open-ended time to explore the Tuff Tray maths activities.
  • They freely develop their exploration of capacity, distance and quantity.
  • Practitioners support children in using accurate approaches to counting.

Exploring the mathematical properties of the resources is a key learning aim of these Tuff Tray activities. Allow children open-ended time periods, and try to ensure that they are not interrupted during their play so they can fully engage with the resources. Encourage them to share new discoveries and work together to solve difficulties. Extend the exploration of capacity for the three-and-a-half plus age group by marking the half-way point on a plastic bottle (half-full, half-empty), and pouring coloured water from one container to another to decide which holds more.

Support children to mix colours and focus on the mathematical process of adding two or more things together to make something different. Set them challenges, such as exploring whether the steepness of the ramp or the size of the vehicle makes a difference to how far it travels. Spark interest in the digging activity by burying unusual items. Help the children to explore the most efficient ways of counting the items they have dug up (touching items as they count, moving items from one group to another, arranging them into pairs).

Observe the children’s motivation as they explore the Tuff Tray maths activities. For how long do they maintain their focus, and to what extent do they develop their exploration? How successfully do they work together and learn from each other?                          

Creating and critical thinking

  • Practitioners support children in finding solutions to difficulties.
  • Children enjoy taking a creative approach to their exploration.
  • Children are encouraged to look out for similarities, differences and patterns.

Encourage children to think critically about the scenarios and obstacles they encounter, and come up with creative responses. For example, investigating problems such as a toy vehicle ramp being unstable, finding solutions and reviewing different construction possibilities. Encourage children to notice patterns, such as large containers taking longer to fill than small containers, and narrow necked containers being harder to pour into than wide necked containers. Help children to decide when it’s handy to use a funnel and be aware of the challenges (because you are not pouring directly into the bottle, it’s easy to overfill). What solutions can they come up with? Explore similar items with different shapes, such as jugs with wide lips and jugs with pointed lips, and encourage children to make critical decisions about which work best. Give children the freedom to ‘spill’ out of the Tuff Tray. For example, by constructing ramps on the floor and choosing their own ramp-building items from around the setting. Encourage them to create a special digging/counting activity for a friend, thinking about what their friend might like to find, how many items to bury and which items are suitable for being buried in soil.

Can children come up with their own, creative ways of exploring the Tuff Tray maths resources? Are they able to identify obstacles and spot patterns in how the different resources and substances behave?                      

Enabling environments
If space and budget allow, have a number of Tuff Trays in your setting. This enables you to offer more than one maths exploration at a time and make an activity available for as long as the children show interest. Display extra plastic receptacles, items for non-standard measurement (ribbons, long thin vegetables, wax crayons) and vehicles on nearby tables for children to use. Make other ‘flowing’ substances available for exploring capacity (sand, smooth gravel, plastic beads). If possible, position the ‘capacity’ and the ‘quantity’ Tuff Trays outdoors so that children can engage freely with messy play. Photograph the children at the Tuff Trays and display the photos as a source of inspiration. Make small counting cards using photos of the buried items and wooden numbers/numeral pebbles, and cards showing different water play actions (filling, pouring, spilling, emptying, scooping, using a funnel). Laminate the cards so children can use them as a reference during Tuff Tray play.         


EYFS Early Learning Goals
Using Tuff Trays to explore mathematical concepts meets the following Mathematics objectives from Early Years Outcomes: Recognises numerals 1 to 5; counts up to three or four objects by saying one number name for each item; counts an irregular arrangement of up to ten objects; enjoys filling and emptying containers; beginning to categorise objects according to properties such as … size; orders two items by … capacity; children use everyday language to talk about size, weight, capacity, position, distance … to compare quantities and objects and to solve problems. You can also link to Communication and Language by introducing appropriate mathematical vocabulary.                            

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