Hands-on maths!

By Hari Neocleous @the_maths_nuts

Maths manipulatives in the primary classroom

For the summer edition of Cherubs we’re taking a little journey into the classroom to learn about maths manipulatives. These are resources that children use to develop a deeper understanding of concepts and methods.

When you’re doing practical maths you’re touching, exploring and manipulating maths objects. This hands-on approach allows children to have more meaningful learning experiences. Children use ‘maths talk’ to explore ideas and make connections, they’re actively involved and having fun. It’s also important that, as teachers and parents, we allow children to make discoveries themselves, giving them time to think and talk about what they’ve noticed. Silent moments = thinking time.

Conceptual and procedural understanding

I remember being a child in Year 6 and learning methods for adding and subtracting fractions. I memorised procedures but I didn’t really understand the methods or think in pictures. That was procedural learning with no conceptual understanding. In schools today we want both to happen. We’re developing curious minds and literate mathematicians. The emphasis is on discovery learning.

Please note, you don’t have to build a maths cupboard at home! There are some free and excellent websites with virtual manipulatives.

I use mathigon.org/polypad, the teacher tools section at toytheater.com and mathsbot.com

Ten types of maths manipulatives

1.

Numicon shapes are flat colourful shapes with holes in them. Each shape represents a number from 1 to 10. You can use them to build large numbers too. Children quickly learn to recognise numbers by the distinctive shapes and colours. Use them for counting, ordering, odd and even numbers, addition, division, multiplication, area, perimeter and more.

Favourite activity: adding fractions with numicon plates.

You may recognise Cuisenaire rods from your school days. Again, they can represent the numbers 1 to 10 but because these number rods are solid without any holes, children have to think about the sizes and compare. Use them to explore number bonds to 10, 100, bar models, multiplication, division, fractions and decimals.

children understand the magnitude of numbers. You have a tiny cube (these are called ‘ones’), 10 ones create a ten, 10 tens equal one hundred and 10 hundreds equal one thousand. Children build numbers, understanding the value of each digit. They’re also great for column addition and subtraction.

Favourite activity: use them with a number track to learn multiplication facts.

3. Base 10

Base 10 (or Dienes) are blocks that help children understand our number system. Think of a place value chart with the columns: thousands, hundreds, tens and ones. Base ten are different sized blocks that represent each column. They help

Favourite activity: modelling ‘exchanging’ in column subtraction. (We no longer use the term ‘borrowing’ when we go to the next column to take a ten. Instead we ‘exchange’ a ten for ten ones).

4. Place value counters

Children can use place value counters to represent numbers given to them. Alternatively, counters are given and children identify the total. I play a simple game called ‘pincher’. Children ‘pinch’ counters from a pile without looking and arrange their counters in columns. They read and write the number they made. The greatest/lowest number wins.

Favourite activity: Use place value counters to explore short division and remainders.

5. Tens frames

Tens frames are rectangular grids with 10 squares. There are five squares above and five below. You can place counters on them, (double-sided counters are often used). Tens frames are great for subitising (instantly recognising numbers), counting and exploring number bonds.

Favourite activity: exploring different ways to make 10, 20, 100 by changing the value of the counters.

6. Bead manipulatives

In schools we have bead strings with 10 beads, 20, 50 and 100 beads. We also have the Rekenrek (twenty beads on a frame) and the classic abacus. Great for counting, subitising and exploring calculations. I recommend watching the How to use an abacus video on Youtube. It’s fascinating to watch an abacus expert!

Favourite activity: subitising where I slide beads across and children say how many they see.

7. Money

When I introduce money, I’ll place each coin on the corresponding numicon plates to show the value of each coin. For example, 5p will be on the numicon red five, 10p on the blue ten. We live in a society where most money transactions happen by card but these early money experiences are the first step to being financially literate. We add, subtract, step count, solve word problems and learn about change. Pocket money, Monopoly and Pop to the Shops by Orchard Games help children understand money.

Favourite activity: shopping/cafe roleplay with money.

I hope I’ve given you some insight into the wonderful world of manipulatives. I have however left a unique manipulative off the list. Can you guess what it is?

It’s free, easily available to all. Guessed correctly? It’s our fingers. My feature in the autumn issue of Cherubs will be all about fingers aka the ‘human calculator’. So I’ll leave our hands for the next issue and hope that you’ve enjoyed ‘hands on’ maths.

In the meantime, don’t forget to play games, garden games, board games, dominoes and cards. Happy summer everyone!

8. Cubes and counting objects

In class we have cubes and a whole range of objects to count. Shells, gems, plastic fruit, little dinosaurs. Count beans being dropped into a tin, count ten pegs on a clothes hanger. Have 10 teddy bears and hide some of them with a tea towel, ask how many are hiding?

Favourite activity: counting squares on boardgames of course! Play simple number track games with dice.

9. Dice, playing cards and dominos

There are so many great card, dice and domino games, all of which develop number skills. Children perform better when they are motivated and use ‘maths talk’ as they play.

10. Number lines, blank number lines and hundred squares

Last but not least are number lines and hundred squares. We try to have a variety of these in schools. Use for counting, estimating, exploring patterns in multiplication facts and calculations.

Favourite activity: cut up a hundred squares to create a puzzle – how do children put it back together?