Welcome to our brand new maths blog!
Each blog will feature a snapshot of learning that has taken place in school, explanations of calculation strategies we teach, top tips for helping your child at home, a look at famous mathematicians, book recommendations and maths challenges.
May has been a busy month with lots of great maths going on in every class, as you can see in the pictures below.
Hummingbirds have continued learning about money,
Emperors have been exploring fractions of shapes and quantities. The children found equal parts of a whole, focusing on halves, quarters and thirds. They have made super progression from practically finding fractions using concrete resources to formal recording involving shapes and amounts! Super understanding Emperors, well done!
Cardinals had visitors from KPMG, a global accounting organisation, who explained their roles and how they use maths in their everyday lives; maths is everywhere after all! The children had chance to ask their visitors lots of questions and found out that even though their jobs involve using numbers now, not everyone at the organisation always enjoyed maths or felt that they were good at it. The children also learned how mathematics can be important in a wide range of jobs other than accounting too - this linked well with a display we have in school showing how everyone from hairdressers to fighter pilots uses maths! I wonder what jobs Cardinals would like to have in the future and how they’ll be using maths!
have mastered translation and reflection this month. They finished their learning by playing Flip and Slide: a two player game which requires secure translaation skills! They love a maths game - what a fun way to learn!
Monarchs finished revising everything they have learned this year and then showed off all of their knowledge during their SATs tests. We are very proud of each child and how they approached the three, tricky maths tests with positivity and determination to succeed. Monarchs then had chance to apply maths skills on their residential trip - they probably didn't even think about how angles were involved when firing arrows in archery, for example!
Following last month's blog about the extremely useful rebalancing strategy 'equal sum', this month I am highlighting a similar tool to help us with subtraction: 'equal difference'.
Let's explore this strategy with single digits to begin with. The calculation 8 - 5 is represented by the image below. The arrow shows the difference between the number 8 and 5. What is the difference? It's 3.
What would happen if we add another cube to each of the numbers? We would have a new calculation, 9 - 6, but the answer (or the difference between the cubes) would remain 3.
This would also be the case if we subtracted 1 from 8 and 5, creating a new calculation 7 - 4. The answer would still be 3. Changing a calculation in this way, keeping the difference between the numbers the same, is known as equal difference.
What is the point in using the equal difference strategy though? It allows us to manipulate the calculation in order to make it simpler for us to complete. So long as we manipulate both numbers in the same way - by adding or subtracting the same amount - we can easily create a simpler calculation that uses friendlier numbers. Let's look at it again with slightly more challenging numbers:
28 - 13 could be rebalanced by adding 2 to both numbers. This would give me a new calculation of 30 - 15. These numbers are much friendlier and therefore the calculation is easier for me to now perform with a reduced possibility of making errors. Similarly, I could have subtracted 3 from both numbers to give a new calculation of 25 - 10. Again, this is much easier than the original calculation and means I do not need to use any kind of formal, written method.
So how would you use equal difference to rebalance 96 - 48? Would you add 4 to both numbers and make a new calculation of 100 - 52? Would you add 2 to both number to change the calculation to 98 - 50? Or would you subtract 6 from both sides to create 90 - 42? Whichever way you would choose, the answer would be the same as in the original question; this is the beauty of equal difference!
The use of mathematics vocabulary is a strong indicator of student success. Language skills and comfort with mathematics vocabulary can have great impact on pupils' achievement. Quite simply, one has to understand what the question is asking in order to answer it correctly! In addition, many everyday words have different meanings when presented in a mathematical context, and understanding and having meaningful mathematics discussion is key to deepening understanding.
With this in mind, we have developed a document that outlines the progression in vocabulary acquired and used in each year group. It is important that we work together and make sure that we are all using the same vocabulary when talking to children about mathematics. You can find it linked here:
We are aware that there will be some changes since many of you were at school. Borrowing or purchasing a maths illustrated dictionary, such as the one pictured, may be of use. Hopefully this monthly blog helps to unpick some terminology too. Of course, our doors are always open to helping you to support your children at home as well!
Albert Einstein - Physicist and Mathematician
Albert Einstein was a scientist and mathematician whose work changed our understanding of time, space, gravity and the universe. Einstein grew up in Germany, where it took him four years to formulate his first word. When he was young, his father gave him a compass. The compass inspired him to try to find scientific explanations for what happened in the world around him. He was fascinated by how objects worked and, although he didn’t love school, he loved physics and maths books. One teacher said, “He will never amount to anything.” However, as time went on it became clear that Albert Einstein was no ordinary student. He excelled at maths and physics
At the age of 16, Albert moved to Switzerland. Eventually, he was allowed to study at the institution now known as the Swiss Federal Institute of Technology. His brilliant mind contemplated space and time, and he eventually came up with the theory of relativity. He shared his knowledge with the rest of the world, becoming the most original mind of the twentieth century.
He also invented the equation E=mc². This equation explained that energy and mass (matter) are different forms of the same thing. They are interchangeable and can be converted from one to another. This is thought to be the most famous equation in the world. In 1921, Einstein received the Nobel Prize for physics.
This book, which celebrates diversity, maths and storytelling, is about three young sisters who are looking at the same seven stars from different perspectives. While lying on the ground, they can see different things: Aarti sees a dipper, Usha sees a digger, and Gloria a kite. They are arguing about what they can see until they realise that by changing their perspective, they can now see the objects the other siblings have described. At the most basic level, the story provides an opportunity for very young children to notice shapes. However, the storyline also provides a nice introduction to the mathematical concept of transformation, particularly rotation. If purchasing the story online, don't forget to support the Friends of Margaret Wix by buying using Amazon Smile.
Despite only being in school for 10 days in April due to the Easter Holidays, the children at Margaret Wix have continued to wow us with their determination to succeed and willingness to give new learning a try. Here’s a snapshot of the great work that has taken place this month:
Hummingbirds investigated the value of different coins and tried grouping them according to their size, colour and shape. They enjoyed playing a ‘guess the coin’ game. Also, they tried matching Cuisenaire rods to the coins and using them to work out the total value of different groups of coins. Some of the children cut out different coins and put them in order of ascending value.
Emperors have mainly been working on halving and doubling in April. They used arrow cards to make 2 digit numbers, represented them with the dienes and then halved them. They thought about whether even/odd numbers could both be halved and some of them even had to regroup a ten when they couldn't halve the number of tens exactly.
Admirals have worked hard on percentages this month. They began by learning about where we would see and use percentages in real life such as the battery level on our phones, on labels when a sale is on in a shop, and on food packaging showing the amount of salt in a certain food. They then studied how to convert percentages to fractions and decimals before learning how to scale fractions up or down to make them accurate percentages. The children can now can find 10%, 25%, 50%, and 75% of numbers too! Finally, they successfully applied this knowledge to real life problems too.
Monarchs have been beavering away this month preparing for their SATs tests. After completing mock tests, Mrs Gibbs and Mrs Walters used the results to target and recap a few key areas of learning to ensure that all children are feeling more confident before the real ones next month. Nearly there, Monarchs!
Below are pictures from some of our classes showing maths in school this month.
This month I am putting a strategy in the spotlight that, once mastered, enables the children to become much more efficient. The strategy in question is used for addition and is known as equal sum.
Equal sum focuses on the closeness of landmark or ‘friendly’ numbers and utilises the skill of rounding. It ensures pupils think about what a reasonable response to a question is and develops number sense.
Children must first have a secure understanding of the concept of sum as well as the fact that numbers can be partitioned in many ways yet will remain the same number (look back at February’s blog that shows how we can use the part-whole model to demonstrate this).
To demonstrate the equal sum strategy I will be using numbers that we can all easily manipulate, but this strategy works with larger numbers and decimal numbers too.
When we add two amounts together, the answer is called the sum. In the calculations below, we can see that the sum remains the same even when the addends (parts being added) change.
25 + 13 = 38
30 + 8 = 38
28 + 10 = 38
It is clear that the first calculation is more challenging than the other two and that is because the other two use ‘friendlier’ numbers. These are numbers that we are confident in using. Multiples of ten are a treat as when we add to them or add them to something else, there is rarely any need to exchange anything.
In order to solve 25 + 13, many pupils would have to perform calculations involving a number of steps or even carry out a formal, written method. We can use equal sum to change the calculation and make it simple and efficient to perform mentally.
Firstly, we must think about which addend is closest to a friendly number. In class, this is often shown using a beadstring:
This also means that the children can physically move the beads from one side of the calculation to the other. In this case, we could move 3 beads from the right side of the calculation to the left. We have not added any new beads or taken any away so our sum will remain the same. The new calculation will be 28 + 10 though, which is much easier for me to perform quickly and accurately in my head than 25 + 13. Some of you may have looked at the calculation and wanted to move 5 beads from the left to the right, creating a new calculation of 20 + 18. You’ve also used a friendly number, I just had to move a few more beads! Once again though, the sum remains 38.
Alongside the physical resource, we encourage children to draw what they are doing. Representing the calculations pictorially will prove to the children that the sum doesn’t change when they move an amount from one side of the calculation to the other and, if it does, something has gone wrong! After mastering this strategy and becoming confident in sliding beads from one side of the calculation to the other, the children will begin to be able to do it mentally, thus developing an efficient strategy for calculation.
Below is an example of how an older child has used equal sum with larger numbers to change the calculation. They have needed to use a formal written method, but in finding friendlier numbers first, they have drastically reduced the likelihood of errors being made when exchanging in the formal method.
As teachers, there is nothing we love more than seeing children enjoying learning, but unfortunately some children face feelings of worry, panic, anxiety and frustration during maths lessons. The signs and symptoms vary from flushed faces and heads in hands, to making excuses to go to the toilet and avoid tasks. Some children try to mask it by copying others, whilst others are vocal about feeling “not good at maths” and saying that they “hate it”. These negative feelings impede on working memory and stop children from being able to think clearly and understand maths. This response is known as maths anxiety.
This is a fantastic video from the team at Childline that explains what anxiety is in a child-friendly way:
Before we can help children with their maths anxiety, we need to know the cause. This isn’t always obvious, but it may stem from a fear of failure (maths involves answers being right or wrong and that can be tricky for some children) or they might have overheard adults speaking negatively about maths (if you are someone who talks openly about how much you disliked maths at school you might want to try to keep that from the children around you as they soak everything up, like sponges).
2018 Ipsos MORI poll
There are a number of things that we do in our classrooms to try to reduce maths anxiety, such as ensuring that children work in mixed ability groups and with different learning partners. This is so that children of different abilities, with different strengths, weaknesses and learning styles, can also help each other overcome obstacles and see new ways of tackling number problems. We also try to instil growth mindsets in our pupils, that is believing that mistakes are learning opportunities and understanding the power of the word ‘yet’.
My top tips for you to help reduce maths anxiety at home are:
Alan Turing - War Hero
Born in London, in 1912, Alan Turing’s mathematical skills were noticed early on in his life, whilst at school. From equations to tough concepts, he managed to understand things which even adults found challenging.
After finishing school, he attended Cambridge University to study Maths, before inventing the Universal Machine. This can be understood as one of the world’s earliest computers, which managed to read simple codes.
During the Second World War, Turing then worked at Bletchley Park. This was the home of the Government Code and Cipher School (GC&CS). Thanks to Alan’s understanding of code and his Universal Machine, he was able to decipher secret messages of enemy forces, such as Germany. With his team, Alan could work out where and when the enemy was planning to attack. He shared this information with the government and British army, so they could prepare.
Without Turing’s amazing discoveries and understanding of code, the Second World War could have lasted much longer, and many more people could have died. In this sense, he can be seen as an inspiring figure who used Maths and Science to save lives.
Sir Cumference and Lady Di of Ameter discover fractions while purchasing cloth and cheese at the fraction faire. While two-fourths may seem the same as one-half, in truth it denotes both two parts of one-half or two quarters of the whole. But the real mystery is the fact that items at the fair keep disappearing, and Sir C, Lady Di, and the Earl of Fraction must set a numeric trap for the thief, teaching an important lesson along the way about the comparative size of fractions. There are puns, both literal and visual, abound in this fun adventure story with beloved characters and a solid mathematical foundation. If buying this book online, do not forget to support the Friends of Margaret Wix by using Amazon Smile.
March has seen our littlest learners immersed in mathematics! Firetips have been making patterns, baking, playing maths games with their parents and carers, and choosing their own mathematical activities in child initiated learning. Foundations for counting are so important so it is brilliant to see so many of our youngest children enjoying mathematics.
Hummingbirds have also been working hard - they have been representing numbers in different ways, using numicon, tens frames and multi-link. They selected 2 digit numbers and then, with a partner, tried to make that number using the different concrete resources. They found out that there were many ways to make each number!
Emperors have been enjoying a variety of maths games including 'Race to Zero' to help them learn how to exchange one ten for ten ones. This will help them to understand how to do this when they move onto the formal, written method. As well as number, the children have also explored 2D-shapes, grouping them according to the number of vertices and sides, and according to whether they are regular or irregular. They also looked at how they could sort shapes using a Carroll diagram.
At the other end of the school, Monarchs have seen how lots of their prior learning has been helpful when tackling algebra. As well as learning about the order of operations, variables and formulae, they played a fun loop game in order to practise calculating unknown values. You can see images of this, and learning from other classes in the photo slideshow below.
Bar modelling is a strategy used to pictorially represent a problem in which there are some known and some unknown values. Bar models in themselves do not solve problems but they do help children to visualise and decide which operations to use. They are especially useful when solving worded problems. Let’s look at a few examples.
This question might be seen in year one and involves subtraction or finding the difference:
Tom has five sweets and James has three sweets. How many more sweets does Tom have than James?
You can see that this bar model has been built using cubes to represent the sweets. Arranging them in bars helps children to clearly see the difference. They can then discuss what they notice and then think about which operation to use to solve the problem. Writing the abstract calculation is the final step.
In this year two example we can see that building the model with cubes would not be efficient as we would need so many. Drawing the model is still helpful though in order to visualise this problem:
Amber has 27 gel pens. She buys 30 more. How many gel pens does she now have?
Once drawn, the children can derive a number of facts from the model as shown. They can think about which is the correct calculation to solve the problem.
This year three example shows how multiplication and division problems can be represented using bar modelling too:
Leigh is helping in the school library. She is packing books into two boxes. The first box has 5 books in it. The second box has five times as many books in it as the first box has. How many more books does the second box hold than the first?
Once the children have drawn the bar model and have seen that they need to multiply five by five to work out how many books are in the second box, they can then choose an efficient strategy to calculate the difference between the two totals.
This model could be adapted to solve further, related problems such as:
How many books have been packed into the two boxes in total?
And, how many books need to be taken from box 2 and placed in box 1 to make them equal?
Bar modelling is an excellent strategy to use to visualise fraction problems, such as this year four problem:
Sally buys four fifths of the shop’s apples. If the shop had 30 apples, how many apples did she buy?
Here we can see how building the problem with concrete resources can then be transferred into a pictorial representation. Children can then see that they need to divide 30 by 5 to work out what each smaller piece (fifth) is worth, before multiplying that answer by 4.
Problems continue to increase in complexity as we move into year five. The bar model is still an excellent tool for visualising problems however, as demonstrated with this percentages problem:
Twelve is 40% of a number. What is the number?
Representing the problem in this way means that children can clearly see that to work out 10% they must divide 12 by 4. Once they know what 10% is worth, they can then see they just need to multiply this answer by 10 to calculate 100%.
Finally, in this year six example, we can see how bar modelling can be used to solve complex ratio problems:
In a survey, the ratio of the number of people who preferred ‘ready-salted’ to ‘cheese and onion’ crisps was 5:3. Forty-six more people preferred ready-salted. How many people took part in the survey?
Modelling the ratio problem in this way means that children can clearly see that two squares on the model are worth 46. From this, they can work out what a single square is worth. Then they are able to solve the problem quite simply.
Bar modelling is important as children often find it challenging to interpret worded problems in particular. Building or drawing the models in this way enables children to break the problems down and think logically about each individual step. The fact it can be used to help solve problems throughout primary school shows what an excellent tool it is.
Challenge: Send Miss Abbott a photo of how you have used a bar model in your home learning, or to help you solve one of her following challenges, and see your maths featured on our maths blog!
In a football match, the red team scored two goals and the blue team scored three goals. How many goals were scored altogether?
Use this form to send Miss Abbott photos of your completed maths challenge. She will add them to our maths blog!
Use technology to support the development of mental fluency at home. You don’t have to do all the work yourself; there are a number of excellent online resources that you can utilise to make your child’s screen time really worthwhile!
White Rose Maths have brought out a new one-minute maths app. It's free to download the app and it helps children build greater number fluency and confidence. It's all about targeted practise in engaging one-minute chunks! We would recommend starting with the subitising section (the skill of instantly recognising the number of items in a group without counting) in early years and building from there.
Times Table Rockstars is a carefully sequenced programme of daily times tables practice. Children can log in using the username and password provided by their class teacher and successfully use the app to help boost their times tables recall speed and accuracy. This app is suitable for pupils in year two upwards.
NumBots is a highly engaging platform for learning to add and subtract. The app can be used to help children improve understanding, recall and fluency in mental addition and subtraction so that they can move from counting to calculating. This app is aimed at pupils in year one upwards.
Twinkl Mental Maths App offers an engaging way for children to practice mental maths across a range of key maths topics. There are over 100 game modes of varying difficulties covering six key topics: times tables, addition, number bonds, division, doubling and halving. You can try parts of this app for free but to access them all requires a subscription.
Katherine Johnson - space pioneer!
After falling in love with maths at a young age, Katherine studied the subject at university and graduated at just 18. She was one of the first three black women to attend West Virginia University and she challenged the stereotypes that surrounded her, becoming an inspiration to women and people of colour. Katherine joined NASA in 1953 and used her knowledge and mathematical skills to calculate the trajectory for Project Mercury and the Apollo 11 flight to the moon, which means she helped the first spaceship and the first Americans reach the moon! Believing that “everything is physics and math(s)”, she encouraged girls to pursue careers in science, technology, engineering and maths (STEM) and often gave talks on the subject.
This is an excellent picture book to help children understand the concept of big numbers. Pipkin, the smallest penguin, is always asking questions, but what he wants to know most of all is how big is a million? So he sets off to find out, and along the way meets a hundred penguins, sees a thousand snowflakes and meets one new friend before being amazed to finally find out how big a million really is. A special fold-out poster at the end of the book shows Pipkin looking at the sky, which is printed with exactly one million stars. It is beautifully illustrated by Serena Riglietti. If buying this book online, do not forget to support the Friends of Margaret Wix by using Amazon Smile.
In February, we worked with a local artist to explore the use of shape and lines in art. We used the famous artwork below, by Kandinsky and Mondrian, in addition to work by our local artist, as inspiration when creating our own whole-school artwork.
EYFS and KS1 talked about shapes and sizes using key vocabulary such as straight, curved, bigger and smaller. KS2 discussed parallel, perpendicular, horizontal and vertical lines as well as naming a range of polygons and angles.
Isn’t our finished artwork brilliant? You can see our amazing, collaborative project on display on the wall opposite The Hub. Take a look at some of the images below of the work in progress too.
The part-whole (or cherry) model, shows how a whole number can be reduced to smaller parts, or how smaller parts can be combined to make a whole. This model can be used for single or multi-digit numbers, including decimals and fractions, and is an excellent calculation strategy used throughout primary school.
The pictorial representations above help children to visualise multiple calculations. For example, the first model shows:
6 + 4 = 10
4 + 6 = 10
10 - 4 = 6
10 - 6 = 4
It is important that children see these calculations written the other way around too, for example:
10 = 6 + 4
10 = 4 + 6
6 = 10 - 4
4 = 10 - 6
From the second example we can see that:
2 + 3 + 1 = 6
2 + 1 + 3 = 6
3 + 1 + 2 = 6
3 + 2 + 1 = 6
1 + 2 + 3 = 6
1 + 3 + 2 = 6
6 - 2 - 1 = 3
6 - 1 - 2 = 3
6 - 3 - 1 = 2
6 - 1 - 3 = 2
6 - 3 - 2 = 1
6 - 2 - 3 = 1
You could use the second model to begin to write more complex balanced equations too, such as:
6 - 3 = 2 + 1
6 - 2 = 3 + 1
6 - 1 = 3 + 2
Children may use objects (such as counters) or pictures (such as dots) in their part-whole models rather than writing digits. At home you could easily create part-whole models using conkers, pine cones, buttons or anything else you can find! The models can also be made larger, and do not need to be confined to paper!
Finally, it is important that children see part-whole models in a variety of orientations and with multiple parts as shown in the examples above too.
Challenge: Send Miss Abbott a photo of how you have used a part-whole model in your home learning, or one that you have just created for fun! How many calculations can you write from your part-whole model?
Use this form to send Miss Abbott photos of your completed maths challenge. She will add them to our maths blog!
Times tables are essential and the aim is for children to have mastered those up to 12 x 12 by the end of year four. Much of this learning happens before year four, however.
When children are first learning times tables they benefit from seeing the multiplication table build up from the beginning, looking first at one group of the amount then building up by adding another group each time and seeing what the total becomes. This can be done physically using objects you have at home. In the images below we can see one group of three is worth three (1 x 3 = 3), four groups of three are worth 12 (4 x 3 = 12) and seven groups of three are worth 21 (7 x 3 = 21). It would also be important to point out no groups of three before beginning this process of adding another row or group of objects each time.
Children can move on from counting every object in the groups to skip counting. This can begin by whispering some of the numbers and saying the multiples of three more loudly e.g. 1, 2, 3, 4, 5, 6, 7, 8, 9…
Eventually, the children can move on to simple counting in threes.
After this, games are a fantastic way to begin to help the children memorise the facts rather than have to count up each time. An easy game to create would include cards with a question on one side and the answer on the other - involve the children in the process of making them too! Once made, mix them up and the children must choose a question to answer; if they get the answer correct, they can keep the card. They could play against you to make the game more competitive!
There is a logical order which usually works when learning times tables:
- 2s, 5s and 10s come first (usually around Year 2)
- 3s, 4s and 8s are taught next (usually around Year 3)
- 11s, 6s, 9s, 12s and then 7s come later (usually around Year 4)
The importance of developing understanding before memory cannot be underestimated. Recall comes last so take time in the early stages and even once you think your child has mastered one, remember to return to it to keep the facts fresh. Using Times Table Rockstars is a good way to do this; ask your child’s teacher if you are struggling with login information for this. Another way that might help is to practice chanting or singing times table songs - they don't need to be boring though, you can use well known songs that have been turned into times tabl versions. Want to practise the 8 times table to the tune of Adele's 'Rolling in the Deep' or the 6 times table to the tune of 'Shake it Off' by Taylor Swift? If so, take a look at this YouTube Playlist.
Ada Lovelace - the mother of computers!
Born in 1815, Ada was taught maths from a young age, which was very unusual for women at the time. In 1833, she met Charles Babbage who had begun designs for a machine that answered very difficult maths problems. Unfortunately, his ideas were ahead of their time and it was hard to get money to build this machine because most people didn’t understand what it could do. Luckily Ada did! She developed plans and described how codes could be created to handle letters and symbols. She also came up with a method for the engine to repeat instructions - something that Charles hadn’t thought of and something that computer programmes still use today. Ada Lovelace is now celebrated every year; she is recognised as the very first computer programmer who made excellent contributions to the fields of maths, science, technology and engineering. How inspiring!
What do one hundred sunbathing snails have in common with ten crabs? This joyful, award-winning counting book has a funny focus on feet! Children will love this hilariously illustrated introduction to simple counting and multiplication with big feet and small – on people and spiders, dogs and insects, snails and crabs – from one to one hundred! You can buy the book here - make sure you are contributing to the Friends of Margaret Wix by using Amazon Smile.