The Power of Manipulatives and Visuals
Throughout the School, the children enjoy using manipulatives (blocks, tiles, counters – anything you can touch and move) and there is valuable research to show how vital this stage is in new learning at any age. It also helps show patterns and generalisations, and how to apply new knowledge to other situations. The Mastery approach to Maths develops new learning through using concrete materials (manipulatives) in order to develop visual representations of number and shape and then leading onto abstract versions. However, these stages are not used discretely, and it is often valuable to move back to the visual stage, and indeed the concrete stage, to discover and investigate misconceptions in all year groups. Here are some ways in which the children across the school are using manipulatives in their classes:
Year 3 have been using Unifix to visualise the 4 times tables and look for patterns and similarities to the 2s and 8s. They have also used Numicon to really understand what division is before moving on to writing division equations.
Year 4 have been using their fraction pieces to investigate equivalent fractions and how to combine fractions. They then moved into the visual and abstract skills in group games to see how well they knew the fractions.
Year 5 have been using place value counters to secure their understanding of multiplication and why we ‘carry’ that extra tens number, giving the abstract concrete, then visual meaning. Similarly in long multiplication, physically creating the multiplied tens and ones ensures a concrete link to the visual grid and onto the abstract numbers. Earlier in the year, Year 5 also used counters to investigate square numbers and how they link to triangle numbers by using their visual representations.
Year 6 have revised their equivalent fractions with strips of paper and also the more edible waffles that are conveniently split into grids and very much reinforced that there were multiple ways to cut them; the children made sure they had the same amount! Later in the unit, by using two layers of plastic, Year 6 were able to visually see a common multiple between two different denominators and why this led to the equivalent fractions that enabled them to add any fractions.
Year 7 have been revising fractions, decimals and percentages by creating a pie chart of 36 skittles and using them to find the angles needed for each colour. Earlier in the year, they also used the tiles to investigate and generalise sequences.
Even the Year 8s, amidst their revision for CE, have benefitted from hands-on practice. Earlier in the year they were using prime factor cards to match common factors and find the HCF and LCM of two numbers.