As a school we are focussing on the Mastery approach to Mathematics. This is a method of teaching that promotes learning through clearly embedding and exploring mathematical concepts, allowing children to realise patterns and relationships when working with number to fully embed their knowledge and ability to manipulate numbers.
Maths lessons generally follow very clear stages of skill development where children are able to explore new concepts in a manner that best suits them. Children are given the opportunity to explore through three key methods;
- Concrete: Using manipulative objects and practical representations to solve problems.
- Pictorial: Using visual structures and templates to organise reasoning through visual representations or drawings.
- Abstract: The written form or a number sentence, using symbols and numbers to explore or communicate a problem (e.g. 3+1=4)
An example of Concrete working in Reception:
“Child A is playing with three trains. The adult introduces the language of one more and asks the child how many they would have if they added one more train. The child finds another train. The child then counts the trains to discover they now have four trains. The adult asks the child what happened when they got another train. The child and adult work together to explain that three trains and one more train is the same as four trains.”
To further challenge the child they could explore this concept deeper by continuing to add another one again or could repeat the challenge at another time using a Pictorial method:
“Child A has drawn a picture of three apples. The adult asks the child how many apples he would have if he drew one more. The child then draws another apple and counts the total number, equalling four. Together the adult and child discuss that three apples and one more is the same as having four apples.”
An example of Concrete, Pictorial and Abstract working in Year One:
Children are presented with a real life problem; two classes at Northill are going on a school trip. We need to book a coach to get there. How many seats does the coach need to have? Swans Class has 25 children; Eagles Class has 26.
Other Pictorial methods could include using part whole models:
Through this method the child could draw their three trains in one of the smaller circles, one more in the other then the total number of trains in the largest of the circles.
There are many other Pictorial methods that your child will be introduced to during the reception year however it is likely most children will continue to use Concrete methods.
If the same child were to record their problem solving using the Abstract method, they would simply communicate their problem through the use of an Abstract number sentence:
3 + 1 = 4
Knowing that they began with three objects and added one more to make a total sum of four trains. To reach this stage the child would have been taught to fully understand the symbols used as well as how to read the sentence. As with word reading we usually read a number sentence from left to right, therefore this Abstract method could be verbally read as “Three and one is the same as four.”
Throughout Key Stage One the key focus will be to build upon the skills learnt during the early years, particularly with the Concrete methods of learning, and moving forward to understand and use all three methods of application in our work.
An example of Concrete, Pictorial and Abstract working in Key Stage One:
Children are presented with a real life problem; two classes at Northill are going on a school trip. We need to book a coach to get there. How many seats does the coach need to have? Swans Class has 19 children, Eagles Class has 18.
Children could then make Concrete representations using counters, numicon, deines etc. They could use this to physically add objects together to find the total amount of children. Children could also represent this problem using Pictorial Tens Frames, drawing frames in their book until they have represented all of the children. Both these methods could then support the child to write the Abstract representation of the problem:
Other Pictorial methods could include using part whole models:
Through this method the child could draw representations of one class in one of the smaller circles, one more in the other then the total number of in the largest of the circles.
There are many other Pictorial methods that your child will be introduced to during Key Stage One, however children will always be able to continue to use Concrete methods.
Supporting at home:
At this early stage of Mathematics learning, it is helpful to support your child to reason and solve problems in everyday life. Find examples in your day to day living, for example when asking your child to set the table for dinner ask them to find the correct number of plates. When at the park explore numbers by counting the number of times your child can go down the slide in one minute, repeat and challenge your child to “one more” slide and count how many they have achieved.
There are many resources available to support your child with number, below are some examples:
Board games (for counting and recognising numbers)
Play money is fantastic to use at home (coin recognition and counting in 1’s, 2’s, 5’s and 10’s)
Throughout Key Stage Two children will be exploring all aspects of Mathematics, using all three methods of application (Concrete, Pictorial and Abstract) throughout their maths lessons.
Some great tips for supporting fluency with Times Tables:
1. Hang up a times table sheet
This is an old technique but it’s very effective. Firstly, go through it with your child, filling in each individual box together. Next, hang the completed chart up in a place where your child will see it regularly (e.g. their bedroom door, the fridge door, the cupboard next to the computer). Finally, set a regular time for both you and your child to sit down and have a casual, no pressure run through a particular set of times tables, perhaps just before dinner. Remember, the more often they see and practice their times tables, the more likely they are to learn them.
2. Make sure they can walk before they can run
Teaching times tables should be like building a house – you need to start with the foundations! Teach your children the simplest tables first and save the harder ones (e.g. 7s, 8s, 12s) for the end. Two times tables are a good starting point, they’re pretty straightforward as they just involve doubling each number. 10s are simple too; as they just involve adding a zero to the number you’re multiplying by 10. Once they’ve mastered the basics, your child’s newfound sense confidence will help them conquer the more difficult tables.
3. Teach your kids some tricks
One of the great things about maths is that it’s full of tips and tricks – and times tables are no different. Our favourite trick involves using your fingers to figure out nine times tables. Start by spreading all 10 fingers in front of you. To figure out 9×1, put your left pinky down. What are you left with? 9 fingers! For 9×2 put your left ring-finger down. What are you left with? 1 finger and a gap followed by 8 fingers or 18. This trick works up to 9×9 (8 and 1 or 81). That said, when teaching children these tricks; encourage them to ask why these techniques work and the mathematical reasoning behind them.
4. Listen to some fun songs
What’s a great way to get information stuck in someone’s head? Yep, that’s right! Catchy music! We recommend checking out videos made by Youtuber, Mr.DeMaio, an American elementary school teacher who uses clever parodies of pop songs to teach kids their times tables. Our favourite is definitely his cover of Bruno Mars and Mark Ronson’s song Uptown Funk which aims to teach children their three times tables.
5. Stage a multiplication war
We’ve found a card game that makes learning times tables fun. The game is simple; two players draw a card from a deck. They then flip their cards over and the first person to correctly guess the total of the two cards multiplied together gets to put the cards in their winning pile. For example, if a 3 of hearts and a 7 of diamonds are flipped over, the first person who says 21 gets to keep the two cards. The person with the most cards in their winning pile at the end of the game wins.
6. Draw a Waldorf multiplication flower
One for the creative kids - Children start this activity by drawing the centre of the flower, in which they write a number between 2 and 12. They then draw 12 petals around the centre, with each petal containing the numbers 1 through 12. The last step is to draw another set of 12 petals which contain the centre number multiplied by each petal in the inner circle.
7. Quiz them regularly, but not incessantly
Once you think your child is getting the hang of their times tables, it’s time to put them to the test. It’s best to do this is when there’s nothing else really going on, like while you’re walking them to school or while you’re waiting for a bus. Also, try to normalise these drills by allocating a specific time of the week to quiz them, rather than springing it on them randomly, that way the drills aren’t too stressful.
8. Reward their efforts
When encouraging children to pursue something important, like timetables, there’s no harm in heightening their enthusiasm with a little reward. Remember that you shouldn’t just reward your child for getting answers right, though. Don’t be afraid to give them a treat if you can see they’ve been trying hard but haven’t quite mastered their times tables yet. This encourages persistence. Also, remember not to judge them if they get the answers wrong, learning should always be an enjoyable experience!