Across the school, we aim to make maths as practical as possible. We use a range of resources to help us picture our problems and work out the answers by physically handling objects where we can. In Class 1, children have access to maths resources at all times and are able to explore these resources independently during play. In Class 2, we aim to make most elements in maths practical. Children have access to maths resources at all times and are encouraged with certain equipment to best help them. In Class 3, practical elements of maths are still included in every lesson. Children have access to maths resources at all times and are able to select the equipment to best help them.
Concrete resources, also known as manipulatives, are physical objects that children can pick up and manipulate. They enhance the understanding of different maths concepts. Concrete materials allow children to visualise and understand the maths. Concrete materials also help students learn new concepts and relate them to what they have already learnt. One of the main reasons why concrete maths resources play a key role in learning is because they support the mastery style approach.
Essential resources you will find in our classrooms:
Numicon are a system of flat plastic shapes with holes in them. Each shape represents a number from one to 10 and each number has its own colour. It is used to investigate numbers to help children see connections. Numicon helps children make important connections between numbers. Each Numicon shape provides children with both a physical and a visual image of a number. It introduces the idea of counting, particularly for EYFS children. Numicon appeals to children’s sense of pattern and helps them to understand how numbers fit together.
Coloured counters with a range of values printed on them. Broadens children’s depth of place value knowledge. Secures their learning at 3 digits, then expand to include up to millions and down to three decimal points. Supports maths curriculum coverage of counting, comparing and ordering numbers, understanding place value, counting in fractional steps and recognising fractions and decimals. KS1 focus on ones, tens and hundreds. KS2 focus on thousands to millions and decimals to 3 places.
Cubes link together on all sides so that pupils can build and explore spatial relationships. Great for counting, sorting and measuring.
Helps look at the relationships between ones, tens, hundreds and thousands. Linking directly to the decimal system. Base ten helps to develop children’s knowledge of multiplication and division by 10. Each unit measure is represented by a different colour, making it easier for children to distinguish the difference in value. Base 10 blocks are used to experiment with basic addition and subtraction. Base 10 describes how much numerical value each digit has in a whole number. Each number = 10x (times) the value to its right.
Helps children explore concepts of number. An easy way to teach addition and subtraction, multiplication and division, fractions, place value and algebra. Making numerical values easier to understand through physical representations. Improve the depth of understanding.
A great manipulative to aid the learning of number concepts. Can be used to teach addition and subtraction, multiplication and division, fractions, place value and algebra.
A maths resource that usually consists of 10, 20 or 100 beads on a string, grouped by colour. They allow children to move the beads whilst counting and visualising groups of ten. The beads usually alternate between blue/red every five beads. They encourage problem solving, number exploration and familiarity with multiples of ten. Most pupils find bead strings an easier way of explaining their thought processes and show their workings out.
Other resources frequently used:
They support children to explore number relationships. It’s the perfect concrete material to support learning on addition, counting, sorting and matching
Playing cards are great for maths games as they show the digits as well as the value of each number.
Pupils can sort and count using colours, size and weight with these versatile teddy bears.
Enable a deeper understanding of number. Lots of different types of dice to explore a range of maths concepts from random number generation, probability and statistics.
This helps children to explore the patterns and relationships between numbers, e.g. times tables.
When using resources like the above, we use a variety of models. These are taught to give children a bank of strategies to use when solving questions and encourage independence and confidence in own abilities. These methods are a stepping stone that are built upon as they progress through their school journey. These methods become more complex as the children progress in their learning.
The main models we use include:
Part-whole helps children understand the links and relationships between a whole number and its component parts. It helps children understand the connections between addition and subtraction (inverse calculations) and helps them interpret, visualise and solve a range of problems. For example, children use the two smaller circles when adding two numbers together, with the bigger circle being used to work out the answer. When subtracting, children work backwards. They use the bigger circle with their starting amount, subtract the given amount away into one of the smaller circles and see what number is left over.
Number lines are used as a visual aid with a range of calculations and across a range of mathematical concepts. Children can find it easier to compare and look at the relationship between numbers when they are written on a number line. Children need to understand whether they are making their number bigger (count up) or smaller (count back). They can use number lines to add and subtract, multiply and divide or to estimate and round.
Five/ten frames help children to delivery number sense and early Numeracy skills. Five frames are one-by-five rectangular frames that form a base for which objects lime counters can be placed. Ten frames are two-by-five and help children develop number sense in a visual and physical way. As tens frames are so visual, they are a great tool for helping children to subitise. This is where a child can instantly recognise ‘how many’ of something there is without having to count.
Bar models are a maths strategy that aims to make abstract questions slightly more concrete. The bar model is a visual strategy to help solve number problems using different sized bars to represent numbers. It does not provide the answer but it gives the use an understanding of what calculation is needed to find the answer. Bar models are visual representation of problems or ideas that can be used for any of the four operations. In word problems, bar models have the big benefit of helping children to decide which operations they can use or how to visualise problems.
Place value grids help children to understand the value of each digit shown in any number depending on its position. For example, the digit 5 has a different value in the number 75 compared to the number 502. Using a grid allows children to clearly visualise the different values of a number when separated. This acts as a great pictorial representation to make the concept clearer to children. Place value counters and Base 10 are used alongside this to physically represent the numbers.
The column method is where the numbers to be added or subtracted are set out above one another in columns. The calculation is done by ‘carrying’ and ‘borrowing’ numbers from column to column. This is the quickest method for a child to add and subtract increasingly large numbers, but only if they have a good understanding of place value. This is introduced in Year 2 with two-digit numbers and used throughout Years 3 and 4 with three and four-digit numbers.
SUAT supports and leads in the set-up of new academies joining the partnership. The services provided by the central support function cover both educational and non-educational support. In terms of educational support, SUAT is linked to the School of Education of Staffordshire University, which is an outstanding ITT provider.
