As part of my work in Sheffield with other teachers I have shown them the many different and varied ways of using cards as a basis for learning. Some of which are shown below. Cards are so simple to use and can be picked up for next to nothing, but can be used in so many different ways. So what are you waiting for, how can cards be used in your class today?
Game 1 – Can you sort it? Yes you can!
Players – 2 to 4
Materials – Cards with numbers cut off corners.
Early maths – recognising numbers from cards (corners cut off) Number sense develops first before number names. Can they sort them into piles (by colour, by shape, by number of items. Can be started with numbers up to 3 and then developed further.
Game 2 – Pairs
Players – 2 to 4
Materials – Cards (ace to 10 – remove picture cards) Numicon, digit cards, multilink, photos of numicon, photos of numbers in real life.
Chn have to match the digit card with the picture that matches it – alternatives to this include cards and then chn matching it to the numicon, or multilink or whatever you want to use!
Game 3 – Target Number
Players 2 to 4
Materials – Cards Ace through 10. or a set of dominoes
Pairs that total _____. Cards face down, chn take turns to reveal 2 cards and count to see if they total the target number. Leave them turned over if they don’t so the next player can use if they want to. If they get a target number they get to keep the cards, or get a multilink, or build the numicon.
Game 4 – Highest Card wins
Players – 2 to 4
Materials – Cards Ace through 10 face down on table. (Or dominoes as an alternative)
Highest card wins – chn turn over a card each and count the symbols. Winner is person with highest card. Can be adapted to number closest to____ or the person with the number that is the same as this numicon shape(need to show picture for this)
Game 5 – The Secret Card
Players: Groups of two
Materials: Cards Ace through 10 for each player, face cards removed
Each child gets a set of cards Ace through 10 (for the numbers 1-10).
The first player then tells whether the secret card is greater than or less than the face-up card. The second player continues to make guesses by selecting and showing different cards until he/she has discovered the value of the secret card.
Players then switch roles.
Game 6 – Who can make…Players: - As many as you would like.
Materials: - Pack of cards or set of dominoes
Pick 3 (or 4 or 5) cards – Who can make the biggest number? Who can make the number closest to ________.
Progression: - Can you multiply the numbers to try and make a number close to 50? 60? Etc
Game 7 – 10’s go fish
Players: - Up to 5
Materials – Pack of cards (face cards removed) or set of dominoes (or can be done with numicon pieces or pictures)
Number bonds to 10 game. Players are dealt the pack of cards between them and have to find the bonds to 10 as pairs. These are put to one side. They then have to go fish to try and lose all their cards as pairs that total 10. They say, “Go Fish” to ask for a card from the person who is next.
Game 8 – What do I have?
Players: - Small group work
Materials: - Pack of cards (faces removed)
Teacher or child chooses 2 cards and tells the children that they add up to _____ - what could the cards be?
Game 9 – Factors of ??
Players: - Can be a whole class or small group activity
Materials: - Dominoes or pack of cards
Teacher chooses 2 cards and tells the children that they are factors of ______. What numbers might I have in my hand?
Game 10 – Maths I-Spy
Players – as many as you’d like
Materials: - A pack of cards (face cards removed but leave Jokers in) or dominoes
The aim of this game is to be the person with the most cards at the end of the game.
A whole set of cards (face cards missing) are placed face up on a table.
Teacher (or game leader) says, “I spy with my maths eye, 2 numbers that add up to 7”
Children have to look at the table to find two numbers which are adjacent to each other either horizontally, or vertically and point to them as quick as they can.
Once they have found the two numbers they are removed and cards moved closer to each other. That person then becomes the Spy.
Can be extended to multiplication for Y2 (just use number cards 2,5,10 for instance). Extended further to all multiplication facts for Y4 onwards.
Not a card game.
Game 11 – Make a difference
Players – 2 (y1-y2)
Materials – 3 x 4 grid (numbered 1-12), two dice, coloured counters.
The aim of this game is to cover the most numbers when using simple addition or subtraction involving numbers less than 6.
The chn throw the dice. If they get a 3 and a 5 they can either do 3+5 (8) or 5-3 (2) they would then place their counter on their chosen number on the games board. Once their counter is their it cannot be replaced.
Children repeat this until all numbers are covered.
Winner is player who has most counters on at the end of the game.
This game can be easily extended by using bigger grids, using three dice, using multiplication instead of addition and subtraction.
Useful Websites with many more ideas on how to use cards!
Today, I spent the day with some brilliant teachers in Sheffield helping them to discover the brilliance of teaching maths outdoors. I do have to say at this point that I got most of my ideas from CreativeStar Juliet Robertson is at the forefront of outdoor education. By looking at her blog you can see how enthusiastic she is about getting children and teachers working outside and the benefits it has for everybody. The blog has a link to many videos as well, take your time to read them. Her book is also coming out soon - that will be worth it's weight in gold!
So why work outside?
We all work in a variety of different schools and settings. Some have vast outdoor spaces, some do not. That doesn't mean we all shouldn't be using the outside to learn. Outdoor learning is a source of a different kind of learning experience. It can be described in a many number of ways. Exciting, powerful, inspirational and developmental are some I'd use. Scary, worrying, and frightful are the words some teachers might use. How do we get the children engaged in learning and not just throwing sticks or stones at each other? That's up to the teacher to make the learning meaningful and engaging. Juliet's blog has millions of ideas, I've only used the maths ones so far. It's about training the children to also see the outside environment as a learning area as well.
Outdoors develops social skills, brain development and creativity and it develops emotional resilience, confidence and physical development and learning. Need I say more than that!
We spent a good chunk of the day looking at how we can use a readily available material (sticks) for anything maths related. What if I don't have any sticks? Go to the nearest wood and get some! Or alternatively go to www.muddyfaces.co.uk (they have a whole range of outdoor equipment to use!) You can even buy a bag of measured sticks!
Ideas we looked at
- Identifying parallel and perpendicular lines
- identifying acute, obtuse and reflex angles
- building the tallest tower (thinking skills needed for this one!)
- Identifying fractions, decimals and percentages (if the picture doesn't show how to do this please ask me to explain on twitter)
Scale and Enlargement
This one really lends itself to outdoor learning. How often do we get kids to look at scales and draw something bigger than it is/was. We took this and changed it around, they had to build a house from the sticks provided (www.muddyfaces.co.uk) and then use squared paper to scale it down. This proved a challenge, but worthwhile. A really fun maths activity that all can access. Learning in an outdoor environment with maths in an active manner.
We also looked at who could create a shape with a surface area of ???cm squared? A perimeter of ?cm Another great activity which will get children to see the difference between perimeter and area in a real context - not just drawn on paper.
Following all this work with sticks it was time for the chalk to do the talking. Every school has rubbish, stones, sticks, leaves etc. Why not get the children to make their own data handling chart outside? We began with a simple tally chart to record what we had found in 2 minutes (thus tidying the school grounds!)
We then went onto trying to use our collected materials to make a caroll diagram or a Venn diagram. It all became very scientific after that, but data handling is taught through science in my school so I thought this proved my point about this strand of maths. In that it should be taught through science and we should not expect children to produce data based on what their favourite colour/ food is. Data handling can be and should be a lot more exciting than that!
After a quick lunch stop of meat and tatty pie from the school dinners (which was very nice!) We looked into other elements of the outside that we can use. Now all schools have a sand tray in FDN, some stretch into KS1 but some schools do even better and have fabulous sand trays in the playground for all to use (but beware of the cats!) We didn't have one to use today, but I wish we did. Using the sand pit can be great for maths. Measuring and weighing particularly come to mind. Creating areas / perimeters in the sand. Can you measure out a volume of ??? Sand can be used in so many ways, and it is not just for early years children. Would the children in your class know what 1kg of sand felt like?
The water tray is another traditional piece of equipment that is rarely seen beyond Y1. Why? Water is great for making learning fun, especially in the summer months when the children can get wet and not worry about it! After all, they can g changed in school afterwards! Recently in SATs the children were asked questions regarding how much liquid would a teacup hold, would your kids know? Get them outside with a huge VaT of water and lots of measuring equipment and let them investigate. Our favourite today was the water race (this is linked to Sciene) How many sponges would it take to fill the bowl? This links to absorption etc but was a real fun activity that I am sure all your children would enjoy. How much water can a sponge hold? How much water is lost on the journey? What is the best way to complete the challenge of transferring the water? Lots of possible ideas with this one.
Our last activity was my favourite. I'm an outdoors teacher master chef. Each child is given a recipe to make something outdoors. This lends itself brilliantly to weighing and measuring and can be easily differentiated to suit any age group. We stayed simple today with simple recipes of sticks, stones and leaves. But it is easy to make mud pie recipes, it's not just for FDn and KS1 you know!! You can use a range of measuring equipment and the recipe cards themselves can be made as easy or as hard as you like. E.g. A recipe for a mud pie could be. 1/5 water, 1/2 mud 30%stones. Using decimals, percentages and fractions like this would really stretch the children mathematically in KS2.
We finished on this brilliant activity, everyone went away happy. We shared as many ideas as we could in one day. We are lucky in the fact we have the Internet to use. It is a fabulous resource full of excellent ideas from brilliant people like Juliet. It's just about finding those brilliant people and learning from them.
The outdoors is a special place that children deserve to use as part of everyday school. Can you take learning outside everyday? It's possible, but it would be very hard to justify it everyday, but you could plan one outside activity per week. Literacy, art, PE, science, everything can be done outside. The questions is - are you a brave enough teacher to do it? Or are you a teacher who knows that you must do it, because you know it will be a memorable learning experience for the children involved?
I hope you enjoyed reading this entry. Please share these ideas and get your children outside!
Games Based Learning in Mathematics
Numeracy is a core subject of the national curriculum and a subject which has no boundaries in which it could be taught. Creativity in mathematics is not new. Teachers have been trying to teach this subject and make it interesting for all children since schools began but with a multitude of failings along the way. Making the resources to teach creatively can be time consuming and it is inevitable that teachers will turn to ready made worksheets for the children to complete.
“It is all too easy to fall into the lessons-by-rote trap when teaching maths, simply because there are so many required elements to be covered throughout the year. A steady diet of worksheets can be the quickest way to boredom on everyone’s part.”
The problem with worksheets is that they do not work. Their use has been extensive but has failed to help children better understand abstract written mathematics.
(Worthington and Carruthers, 2003)
Indeed the guidance produced by QCA (2000) for the foundation stage states that:
“for children to become young mathematicians requires creative thinking, an element of risk-taking, imagination and invention - dispositions that are impossible to develop within the confines of a work-sheet or teacher-led written mathematics”.
The argument against the overuse of worksheets continues further with Davis and Briggs (2008) devoting a whole chapter to the end of death by worksheet. They claim that worksheets tend to focus on practice rather than allowing the children the opportunity to explore mathematics further and that they are not always clear for learners. You may ask why I have devoted so much space to the question of worksheets and their involvement in maths learning. Although they do have their advantages for the teacher in that they are already made, easy to store and easy to reproduce, teaching is about expanding and involving the childs mind. Allowing them to delve into the deepest caves to discover things that they did not think possible in maths.
Getting children involved in maths and enjoying the subject is essential if we want to create young and interested mathematical learners. As Kendall (2010) states: “there is a real need to find a way of making the process of learning maths more enjoyable and meaningful for all concerned”. Being able to locate this enjoyable and meaningful learning is why I have chosen to teach maths through games with specific emphasis on playing board games in Key Stage One.
Briggs, M and Davis S (2008) highlight this...
•Games can encourage successful learning and increase self esteem.
•Games can encourage mathematical discussion between children and with adults.
•Games can be fun.
•Games can support different learning styles by providing a different format for similar activities.
•Games can help reinforce knowledge in different ways.
•Games can help support the introduction of new areas and ideas.
I have a real passion for talk for learning in all my lessons in school and believe that children learn best when given the opportunity to work with other children and discuss their learning. Liverpool mathematics team (2007) discuss the use of talking in maths.
“Research indicates that speaking and listening skills are crucial to the development of children’s thinking strategies when solving mathematical problems. In achieving this, language is a vital element.”
Without knowing the vocabulary and the context in which it should be applied; knowledge of mathematics and in particular using and applying the skills they have learnt will be a very weak area.
Playing board games with children is a prime opportunity for the teacher to stand back and watch the children in action, the activity is student led and just slightly guided by the teacher. This is to ensure that the children have “the time to explore mathematics without adult intervention which allows time to pose the questions themselves and to ‘have a go’ at activities without being told there is a specific way to approach an activity” (Briggs, M and Davis, S. 2008) The game will have an objective attached to it, but the learning itself will have no pre-determined outcome. I am hoping sincerely for a whole host of incidental learning to take place. Talk for learning will be a key part of this incidental learning and will be guided by the teacher when necessary.
Board games are ‘entertaining and guaranteed to appeal to everyone; they provide invaluable ways of practising basic calculations and mental arithmetic’ (Yougman, 2010). If the children enjoy playing the games they will participate with confidence and take pleasure from the experience. They will be learning the basic arithmetic needed to progress further in mathematics as well as being introduced to vocabulary, practicing their vocabulary already in place and having fun at the same time. The perfect mix for learning to take place.
This is a brief part of my analysis into the importance of why talk is important in maths and formed part of a PG cert assignment into the collaboration between teachers.
Child: Child Communication as a learning tool and communication skills review.
The main basis of this is that children do learn best when given the opportunity to discuss mathematical thinking and their learning, but they must be taught how to act in group situations. Don't just expect them to know how to act in a group.
“Children need to be helped to learn how to use language to work effectively together; to enquire, reason, and consider information, to share and negotiate their ideas, and to make joint decisions”. (MERCER AND SAMS 2006)
Barwell (2005), Sfard and Kieron (2001), Forman and Van Oers (1998) and Yackel et al (1991) have all proclaimed the use of group learning and child: child discussion as essential for the development of learning through discussion in maths. The study by Yackel, et al. (1991) advocates in particular the use of group activities in maths because they “offered the children valuable learning opportunities….through talk; something that would not have been possible through a traditional teacher guided lesson”. Mercer and Sams (2006) further the argument for group/partner discussions in maths with the statement that, “talk based group activities can help the development of individuals mathematical reasoning, understanding and problem solving skills”. Or as Vygotsky (1978) states: “Intermental (social) activity – typically mediated through language can promote intramental (individual) intellectual development”. In other words, the more we can work as groups and discuss our mathematics, the more we will learn independently.
That does not mean however that teacher guided lessons should be dismissed or that group learning is always successful. Bennet and Cass (1989), Galton (2007), and Mercer (1995) provide the research for this. The belief that group work always means learning is proven to not always be the case. The main points of this being, “talk is often un-cooperative and off task” (Bennet and Cass, 1989), or as we see regularly in class, “when pupils do talk to each other… the conversations tend to revolve around their social lives rather than their learning”. (Galton, 2007) In addition to this Mercer (1995) and Mercer and Sams (2006) show that for the children to be effective communicators many other influences or ideas need to be involved in the process.
It is clear to see that a combination of pupil and teacher discussion, teacher-led talk, pupil led dialogue and giving children a clear understanding of the focus and rules for discussions are essential for pupil to pupil mathematical discussions to be successful and a learning experience for all involved.
An excellent article from nrich can be found here...
Talk in maths and other lessons is obviously common place, but it is how you structure the talk and ensure it is essential for the learning that is vital. Many activities allow children to talk about maths, but no more so than learning through games. (more on that to follow soon.
Don't forget to comment if you have enjoyed reading.
Barwell et.al (2005) Ambiguity in the Language Classroom. Language and Education; 19 (2) 118-126
Bennet and Cass. (1989) The effects of group composition in group interactive processes and pupil understanding. British Educational Research Journal. 15 p119-132.
Forman and Van Oers (1998) Mathematical Learning in Socio-Cultural Contexts. Learning and Instruction; 8 (6) p469-472
Galton, M. (2007) Learning and Teaching in the Primary Classroom. Sage. London.
Mercer, N. (1995) The Guided Construction of Talk amongst teachers and learners. Clevedon. Multilingual matters.
Mercer, N and Sams, C. (2006) Teaching Children How to Use Language to Solve Maths Problems. Language and Education; 20. (6) 506-528
Sfard and Kieron (2001) Cognition as communication: Rethinking learning by talking through multi-faceted analysis of students mathematical interactions. Mind, Culture and Activity; 8 (1) p42-76
Vygotsky, L. (1978) Mind and Society: The development of Higher psychological processes. Cambridge, M.A. Harvard University Press
Yackel et al (1991) Small group interactions as a source of learning opportunities in 2nd grade maths. Journal for Research in Mathematics Education. (22) p390-408
So how do you teach area and perimeter? I'm hoping that it isn't by measuring tables, etc. BORING!!! This is truly one of the easiest maths topics to make the kids get excited about. So many different ways to approach this that I could go on and on so will just share my favourite few. Once the children have mastered the steps needed to calculate the area and perimeter of shapes it is important to use these skills in many different ways.
Make your door like this! They will see it everyday and hopefully will never forget it!
Teach the steps needed to find the area then play this game to practice it. Work in pairs to roll a pair of dice, draw the rectangle to match the measurements given. Write out the perimeter and area of the shape. The winner is the first person to fill their entire block. Not only using area and perimeter skills but also using their thinking and problem solving skills.
BIG CHALK!! Get it and get drawing outside - get the kids measuring or simply calculating the area or perimeter of shapes you have drawn on the floor (or that they have drawn on the floor for each other). An alternative to this is to make shapes on the floor throughout the school using masking tape. Either way, they are not just sat at their desk looking at examples of shapes with measurements on (although this is also necessary to ensure they can read a diagram carefully). I usually get the children to work in pairs or trios to do this. I usually try to have at least 15 different shapes drawn on the floor ranging from simple squares to right angled triangles as well as composite shapes for the children who have a thorough grasp of the topic.
STICKS!! Can the children use the sticks available in your playground (if you don't have any you could always go to the local park and get some) to measure out a given perimeter using their estimation skills? This will test their knowledge of measures and is an excellent chance to get the kids outside and enjoying themselves. (For more ideas on getting them outside visit the blog of Juliet Robertson www.creativestarlearning.blogspot.com)
Once children seem to have grasped the concepts of area and perimeter it is important that they engage with it through different investigations. There are many of these on the internet, many of which you will find with a simple search on google.
Plus my favourite activity that I have ever come across that I am going to give a try this week. Something I found on www.pinterest.com
For now that is it. There are so many area and perimeter videos on youtube (a few of which I have linked to on my maths videos shape, space and measures page).
So if you are teaching area and perimeter soon, get creative, get outside, get them challenged and get them enjoying maths.
Use this in class as part of your topic on 2d and 3d shapes. Children should work in groups of 4
1 person choose the shape
The other three could ask yes/no questions and marked on the sheet which shape it could be.
A point for the person who correctly worked out which shape it was.
To stop them guessing they had to narrow it down on their sheet until they only had one shape remaining. They also wrote down all the questions that were asked and the responses.
They enjoyed it thoroughly and it made them think very carefully about the properties of 2d shapes. It develops their visualisation skills, thinking skills, questioning skills and they had fun learning about 2d shapes!!!
Below you will find what we use in school as the maths curriculum document. Split into different sections this has really helped develop the skills of the student. They are able to see what the next steps in the learning are and has enabled better differentiation (especially for pushing the higher ability children). Implemented 3 years ago teachers are finding maths easier to plan and the children can see how each step develops into the next. More understanding is now evident and maths has become a subject in school which all children look forward to doing in class.
This approach was used in my previous school, but is now out of date. However, the approach to planning and the progress of an objective still stands. Teachers should know the next step for every child. Using an approach like this worked to extend all learners. Whether it developed a 'mastery' level is unknown but results at L4, L5 and L6 improved year on year for the years since it was introduced.
I'm a deputy head in Scarborough, England and love using media and tech to develop writing. I'm also a keen advocate of Learning Without Limits and believe in a games based approach to developing mathematicians.