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Open-ended Investigative Maths
Mathematical Problem-solving

Problem-solving tasks develop mathematical skills and problem-solving tactics. These open-ended investigations for Reception or Early Years settings are designed to take advantage of outdoor learning environments, but many of them can be adapted to run inside.

Session 1 Shape

Objectives

Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.

Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.

Open-Ended Task

Shape Hunt
By looking for and finding shapes, children gain an awareness of similarities of shapes in the environment. They match shapes by recognising similarities and orientation, show curiosity and observation by talking about shapes and begin to use mathematical names for shapes.

Open-Ended Task

More Shapes
By looking for and finding shapes formed by windows, children gain an awareness of shapes, practise matching them, and begin to use mathematical names for them. Use language such as ‘square’ to describe the shape of solids and flat shapes.

Open-Ended Task

Sorting
While playing with and arranging twigs, stones, leaves, etc., children can be encouraged to take an interest in shape and space. They can talk about similarity and difference, while sorting objects. Developing mathematical ideas and methods can be used to solve practical problems.

Session 2 Position and Direction

Objectives

Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.

Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.

Open-Ended Task

Trails
Remember… just about anything you do indoors in maths can be done outside. Some children ‘come alive’ once out of the classroom and may just surprise you with the observations they make or the learning behaviours they show.

Open-Ended Task

Obstacle course
Children use everyday language to talk about position, distance and time when running, or walking, an obstacle course. They compare quantities and objects and solve problems.

Open-Ended Task

Milk the Maths: Wellies
Encourage children to use everyday language to talk about position whatever they are doing! Putting wellies away is a colourful opportunity.

Session 3 Number and Shape

Objectives

Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.

Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.

Open-Ended Task

Holes
When digging holes children can use number names in order in familiar contexts. They can use everyday language to talk about size, capacity, position, distance and time. Holes offer fun opportunities to compare quantities and objects and to solve problems.

Open-Ended Task

Planting and Gardening
While working in a school garden, children can practise using numbers to identify how many objects there are in a set. They say and use number names in order in familiar contexts, and count everyday objects.

Open-Ended Task

Hoist
Playing with a bucket on a hoist, children can use numbers to identify how many objects there are in a set. They can use everyday language to talk about size, capacity, position, distance and time and compare quantities and objects and to solve problems.

Session 4 Number and the Language of Addition/Subtraction

Objectives

Open-ended investigative tasks provide fun, stimulating contexts in which children can connect previous knowledge with new situations, develop mental flexibility, practise mathematical vocabulary and reason mathematically.

Print the sheets and stick them up in suitable play areas. They provide stimulating questions that will enable adults in your classroom to facilitate good mathematical language and learning. Each illustrated activity comes with a list of skills practised that you can use for assessment.

Open-Ended Task

Leaves
When playing with leaves, children have opportunities to see that numbers identify how many objects there are in a set and to say and use number names in order in familiar contexts. They can begin to use the vocabulary involved in adding and subtracting. They can relate addition to combining two and subtraction to ‘taking away’.

Open-Ended Task

Tin Can Alley
Play with cans to explore number names in familiar contexts and to.count up to 10 everyday objects. Children can begin to use the vocabulary involved in adding and subtracting and to relate addition to combining two groups of objects and subtraction to ‘taking away’.

Open-Ended Task

Sand to Sandpit
Children can fill a sandpit (or move sand from one place to another) and count up to 10 everyday objects and begin to use the vocabulary involved in adding and subtracting.

Open-Ended Task

Logs
Put logs onto a trolley and say and use number names in order in familiar contexts. Count and use vocabulary involved in adding and subtracting. Show curiosity and observation by talking about shapes. Begin to use mathematical names for shapes.

Open-Ended Task

More Logs
Playing with logs offers countless opportunities to practise counting! Children can also begin to use the vocabulary involved in adding and subtracting and to relate addition to combining two groups of objects and subtraction to ‘taking away’.