For some children, mathematical concepts can be difficult to master and using physical objects can be a great way to consolidate and reinforce their learning.

The use of manipulatives for maths goes back a long way. Probably the earliest form of manipulatives were fingers but as our concept of number developed, 10 fingers were not sufficient, so other physical objects such as sticks and stones were used instead. This led onto the use of counting boards and the abacus.

In the first years of school, physical objects are used creatively to teach mathematical concepts but as children grow older it is considered to be more important to commit concepts to memory and to be able to recall facts mentally. While this seems a logical move towards academic development, it can be hard and may take longer for some children to achieve success with mental maths. This is where physical objects can be used to reinforce and consolidate learning.

Using natural materials outdoors for maths concepts is helpful on two levels. First of all, the change of environment can be helpful to reduce stress and pressure, especially when a child feels overwhelmed by the classroom environment. And where some children may have internalised the idea that it is wrong to rely on physical objects for support, the change of environment and therefore a change in the learning method makes it seem more acceptable.

Secondly, natural materials are easily available and their neutral colours mean that they are less distracting than brightly coloured counters or cubes. This means that the child's focus is more likely to be on the concepts rather than on the materials themselves. I speak from experience here, having seen how easily children can be derailed from a task by the excitement of building towers out of multilink cubes!

It is easy to make a set of number pebbles using paints or paint pens. I made this set with 0-12 numerals on one side and spots on the other. I also made a set of mathematical signs pebbles to use for number sentences. I keep my set in a cloth bag which can also be used for some of the activities and games.

Starting a session with a treasure hunt or a quiz can be a terrific ice breaker. Pebbles can be quite hard to find though, so don't hide them too well! If you are planning a quiz, scatter the pebbles on the ground and ask the children to find the answers to your questions e.g. How many legs does a spider have? How old are you? How many seasons are there in a year? Adapt your questions according the age of the children you are quizzing!

Here are some more ideas for activities:

__Counting activities__

Either say the number then count the spots to check or count the spots and turn over to check the number.

Match the correct pebble numeral to a collection of other objects such as pine cones.

__Ordering, sorting and place value activities__

Order all the number pebbles from lowest to highest or highest to lowest.

Pick out two pebbles and say which is the highest or lowest number.

Find the next number in a sequence - you could have a sequence that counts in 1's, 2's or 3's.

Pick a pebble and find a number that is 1 more than, 2 more than, 1 less than or 2 less than the first number.

Choose a number and find all the pebbles that have numbers greater or less than the chosen pebble.

Sort the pebbles into piles of odd and even numbers.

Pick two or three pebbles and make the highest or lowest number possible (this may require knowledge of tens and hundreds).

__Addition, subtraction, multiplication and division activities__

Find all the pairs of numbers that add to 10.

Make number sentences using the pebble signs.

Find the missing number in a number sentence e.g. 2 + ? = 5

Find the missing sign in a number sentence e.g. 5 ? 2 = 10

Find all the numbers in the 2, 3 0r 4 times table.

__Shape, space and measure activities__

Make shapes from sticks and find the pebble to match the number of sides or corners.

Use the pebbles to compare the sizes of other objects with each other. e.g. a paving slab might be 10 pebbles long but a seed packet might be 3 pebbles long. Just remember, these are non-standard units as they are not all identical in size or shape.

Arrange the pebbles into a clock face and use sticks for hands to practice telling the time.

As you can see, there are so many possibilities for mathematical activities using natural objects and its so easy to make up a set just like these - its as easy as 1 2 3!!!

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