Once upon a maths story…

    Published: 16 June 2020

    For World Book Day in March, our team of Herts for Learning maths advisers scurried off to our bookshelves to bring you a blog called ‘Love that MATHS in books!’, which allowed us to share with you some of our favourite books that include maths! In this blog, we will look further at how stories can be a tool for encouraging and inspiring mathematical concepts to be discussed and investigated.  

    Favourite stories and tales can be lovely ways to encourage talk around mathematical concepts and lead to further exploration. Detailed in ‘Big Ideas of Early Mathematics’ is an example of where a Reception class had enjoyed a book so much – the book in question was ‘Dear Peter Rabbit’ by Alma Flor Ada – that it lead to a mathematical exploration.

    In the book, a variety of characters from different traditional tales are invited to a party and so the children were asked to plan which characters they would invite to their party. The children were allowed to invite 10 characters and had to present a poster showing the name of the story and how many from that story were to be invited. At the party, you could have Goldilocks and the three bears – this would be 4 of the invitees, then Hansel and Gretel, leaving 4 more to invite - perhaps the three little pigs and the big bad wolf (who would of course be on his best behaviour!).

    Here, the idea that within the number 10 live other numbers – so 10 being constructed of 4 + 2 + 4 – was the mathematical concept being explored. The children could then find different ways of regrouping 10 – maybe the three blind mice and the seven dwarves – or if they wanted to invite Shrek, Princess Fiona and Donkey, how many more characters would they be able to invite?

    Year 1 children could also consider what this would look like in a part whole diagram as shown below:

     

    Number graphic

     

    Now let’s take the well-loved book ‘The Gruffalo’ by Julia Donaldson.

    Discussing the order of events in any story will help to support children’s use of ordinal language as well as supporting their use of sequencing. First, second, third etc. could be used discuss the order in which the mouse comes across different characters. Adults could model this by saying, “First the mouse met the fox. Then the mouse met the owl. The owl was the second animal that the mouse met.” Also, no matter what order the mouse meets the characters in, by the end of the story, he has met 4 animals.

    A lot of the images in the book could be used to encourage discussion around positional language such as ‘on top of’, ‘above’, ‘close and far’ and (the potentially less well rehearsed) ‘between’.

    In ‘The Gruffalo’, and lots of stories, a journey is described - the mouse walks through the woods meeting different characters as he goes. These journeys could inspire children to design maps of an area or place. Younger children could again use positional language to describe where they would plot things such as the owl’s house and how they would get to where the snake lives.

     

    Chalk drawings on pavement

     

    These photographs were taken by an old teacher colleague while on a walk in her local area. A talented neighbour had mapped out the story outside their house. Thank you Katherine for allowing me to share these – what a wonderful idea!

    Older children could do similar but use grid lines and coordinates to describe position. Upper Key Stage 2 children could draw maps using a scale and consider appropriate measurements to use – how much land area is the wood likely to take up? Can they use their multiplicative reasoning to position places accurately? For example, if on their plan or map their chosen scale is 1cm:100m, how many centimetres would they need to leave in-between 2 places which were 300m apart? What about 550 metres apart?

    This idea of mapping could be used with any story that involves a journey and I am sure that you will think of many stories that involve journeys for older children to be inspired by such as Kensuke’s Kingdom by Michael Morpurgo and The Girl of Ink and Stars by Kiran Millwood. The Girl of Ink and Stars tells the story of a cartographer’s daughter so there is much to explore in terms of mapping.

    In ‘The Gruffalo’, we meet a snake who invites the mouse to have lunch in his log pile house. Constructing and building models encourages mathematical thinking. How will I make the house tall enough or strong enough? Can I draw a plan for my model before building and then adapt this if needed? Again, there are many stories where children could be inspired to imitate and build structures.

    The use of characters, either from read and well known stories or an invented character, can also be engaging. Children are often keen to explain or respond to questions posed by puppets or characters – I’ve taught Year 5 and 6 classes who were always ready to help our class puppet Charlie out with his misconceptions!

    As mentioned, in ‘The Gruffalo’ we meet the snake and J. Robertson describes on her website Creative Star Learning, a character called Sammy the 1 metre Rope Snake. Sammy could accompany a walk and be used to help measure things – the fact that the snake is flexible means objects don’t need to be straight to be measured. Older children could use the 1 metre length to estimate the measurement of objects. This is also a good way in when exploring the parts of a circle and the circumference in Year 6. The ideas on her blog are mainly aimed at Early Years but there are many ways that the concepts could be extended. For example, Sammy the Snake can be folded to represent halves and quarters but could also be folded to fifths and tenths. 

    In Rachel Rayner’s recent blog, she considers activities that have ‘hidden’ maths within them. One such activity, inspired by completing a drawing of a beloved characters’ face, has many concepts to discuss – are the features symmetrical? What is the distance between the nose and the chin? What pressure will I need to put on the paper to create different tones? What direction will I move the pencil in to create the pattern/texture?

     

    Fox drawings

     

    These examples are from Year 6 pupils work from Nash Mills School based on the book Pax by Sara Pennypacker.

    There are lots of stories which feature food and could inspire investigation with recipes. In ‘The Gruffalo’, the mouse is offered lunch at the different characters’ houses. I wonder what they would be having (if mouse wasn’t on the menu of course!)? Perhaps a nice fruit salad?

     

    Recipe list

     

    In this Year 1 handout from ESSENTIALmaths, pupils are told that this is enough for one person. But what if we need to make a salad for two people?

    A year 3 child might explore how many would be needed for 3 people and use their knowledge of the 3 times tables to help them.

     

     

    Many characters spring to mind when thinking about interesting diets – Frobscottle from the BFG and a whole world of sweet things from Charlie and the Chocolate Factory. In fact, you can take your pick from characters in Roald Dahl books to create recipes for!

    I have really enjoyed watching episodes of this year’s ‘Great British Menu’ on BBC2 as the theme for this series is children’s literature. There is so much maths to be discussed when cooking – measurement, temperature, timings and as with mapping, children can practise and explore the multiplicative relationships.

    Upper Key Stage 2 children could investigate more complex changes as exemplified in this ESSENTIALmaths destination question. One in which they need to work out what the amounts needed for 1 smoothie are so that they can explore the recipe for 7 people and the other where a bar model is used as a representation of a more complex ratio problem.

     

    Recipe graphic

     

    As detailed in our ‘Love that MATHS in books!’ blog, there are many books where the book and story are based on mathematical concepts and so make the links more explicit. One book which I have recently discovered is called ‘The Tangram Cat’ and Rachel Rayner references this book in her blog mentioned earlier. In this book, a cat is created out of a tangram and then we join the cat’s creator while they design different objects and animals. Children could copy the tangrams in the book before exploring making more characters of their own. I spent an enjoyable Sunday morning exploring how I could build an elephant character for the story and this lead me to thinking about how different shaped pieces might be helpful to create my elephant. Children could design variations on a tangram but splitting up a square into other shapes. Might it be useful perhaps to have 2 square pieces as well as the two triangles which can make a square? 

    Further Professional Development Opportunities:

    For more ideas on using stories to inspire maths discussions and activities, have a look at the following websites:

    www.nzmaths.co.nz/picture-books-mathematical-content

    www.mathsthroughstories.org

    See also this guest blog written in 2016:

    www.hertsforlearning.co.uk/blog/finding-maths-storybooks-tale-turning-training-good-practice

    Happy reading and exploring!


    References:

    Erikson Institute ‘Big Ideas of Early Mathematics’ (2014)

    Donaldson J ‘The Gruffalo’ (1999)

    Morpurgo M ‘Kensuke’s Kingdom’ (1998)

    Millwood Hargrave K ‘The Girl of Ink and Stars’ (2016)

    Pennypacker S ‘Pax’ (2012)

    Dahl R ‘The BFG’ (1982)

    Dahl R ‘Charlie and the Chocolate Factory’ (1964)

    Robertson J www.creativestarlearning.co.uk ‘Introducing Sammy the 1-metre Rope Snake’ (2016)

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