# Maths Investigations

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I am a Deputy Head in an Edinburgh Primary School, and I am passionate about Maths! So as well as my full time day job, I spend some of my weekends and holidays creating Maths resources. My particular mission is to get children to THINK about Maths, not just be able to do it. Hence 'Maths Investigations'. I find the question 'Why?' is a great one for pushing the boundaries!

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I am a Deputy Head in an Edinburgh Primary School, and I am passionate about Maths! So as well as my full time day job, I spend some of my weekends and holidays creating Maths resources. My particular mission is to get children to THINK about Maths, not just be able to do it. Hence 'Maths Investigations'. I find the question 'Why?' is a great one for pushing the boundaries!

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#### Quadrilaterals Investigation: Angles, Sides and Symmetry

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A wide ranging investigation for upper primary or early secondary pupils into the different kinds of quadrilaterals and their properties. The materials will cover several lessons. Includes: - group discussion cards to stimulate pupils thinking around the topic - three open-ended challenges looking at angles, sides and reflective &amp; rotational symmetry - full teachers notes (and answers!) to guide what will likely be a wide-ranging discussion. Covers square, rectangle, several trapeziums, rhombus, parallelogram and various kinds of kite. By the end of the investigation, your pupils (and you!) should be quadrilateral experts!

#### Chopping up a Metre Stick - Fractions, Decimals and Division

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A wide-ranging PRACTICAL investigation for Upper Primary pupils. Full notes for teachers, plus a variety of copymasters for pupils which can be used selectively depending on how the investigation develops: Learning Intentions: - to make intelligent estimates and improve on them through trial and improvement - to understand the inverse relationship of multiplication and division - to interpret remainders in division - to round calculator answers to an appropriate degree of accuracy - to find fractions of a quantity. Great fun! Be prepared for lots of enthusiasm!

#### Train Journey Investigation: Maps, Scale, Time, Timetables, Distance and Speed

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A wide-ranging investigation for 10-12 year olds into a real or imaginary train journey. We do this with our Primary 7 pupils before they go off to London for the week in November. During the investigation we cover: - how train timetables work - working out time intervals between stops - finding the route on an atlas - learning about scale - measuring with string - taking averages - using conversion tables to calculate distances in real life and (for the ambitious) - calculating speeds by first converting times in minutes to times in decimal hours! I've written comprehensive notes for teachers and included lots of pupil copymasters, which our staff use flexibly depending on the level of their pupils. There is enough to keep the children engaged for a week or more. Have fun! And if you use it, do let me know how it went. I always appreciate feedback. :-)

#### Measurement and Multiplication Investigation: How Many Hula Hoops?

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A highly engaging practical and thinking investigation for pupils aged 7-9, exploring ideas in measurement and how to solve a big problem by beginning with a smaller one. Best used with a whole class working in groups. One metre stick per group, and individual whiteboards required. The idea for this investigation came from a pupil who had seen an advert where hula hoops (the small, crunchy, eating variety) were stacked in a pile beside Big Ben (the clock on the Houses of Parliament in London) from top to bottom to see how many there would be. One of our pupils thought it would be much more interesting to find out how many would stretch from the school to Big Ben – it turned out to be quite a lot, since we were in Edinburgh in Scotland! You will have GREAT fun investigating this! The children drive the investigation with their ideas. The first step is to work out how many hula hoops fit into one metre. There aren't enough in one packet to fill a whole metre, so the children have to come up with all sorts of different strategies. After that you are likely to be onto one of the mapping websites to find out the distance from your place to Big Ben. And then the work with Big Numbers begins!

#### Counting in Tens Beyond 100: How Many Fingers do we have here?

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An engaging whole-class dialogue for pupils aged 6-7, exploring what happens when you start counting in 10s and keep going! The (apparently simple!) objective is to work out how many fingers there are in the class altogether but it provides fabulous opportunities for discussion about different ways of counting, and what happens if you try to count in tens beyond 100. Just gather the children round in a circle and then pose the question: How many fingers do we have here? Then they are off! Someone will no doubt say 'ten' not realising that the question refers to the whole group. But when you point out that you have 10 and Sarah has 10 and Jamie has 10... then it gets exciting! Using teacher-led dialogue, you can lead them to counting in 10s, explore what happens when you get to 100, and explore patterns using a table. If they are really going strong you can investigate toes as well! Great fun!

#### Understanding Fractions & Decimals - Practical Activities & Games - Part 1

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A comprehensive guide for parents and teachers to PRACTICAL activities, conversations, chants and games to help young children (ages 5-9) master the early concepts in fractions and decimals. Children often have difficulty understanding fractions and decimals. The approach I have developed, using counters and metre sticks, is great for making it all make sense! I've divided the guide up by age and stage with an A4 page on each concept which you can print for reference in the classroom and also send home for parents to refer to. There are also links to my tablet materials in Wise Owl Maths which can be used for extra consolidation. I haven't found a way of putting these on TES yet, but you can find them on my web site at www.mathsinvestigations.com The guide is in two parts. This is Part 1. Part 2 is still being written! Part 1 covers Step 1: - Halves - Halving and Doubling - Splitting into Equal Groups Step 2 (includes 4 pupil sheets): - Count, Speak, Write &amp; Draw Halves - Quarters and Quartering - Count, Speak, Write and Draw Quarters - Count, Speak and Write other Fractions - Counting Caterpillar and Tap Say Turn Step 3: - Halves of Metres and Mixed Numbers - Numerator and Denominator - Quarters of Metres and Improper Fractions - Quadruple and Quarter Numbers; Factors Step 4; - Single Place Decimals - Tenths and Halves - Decimals &amp; Equivalences - Tenths and Fifths - Fractions of 12 and 20 - Unit Fractions using Tables - Fifths and Tenths using Tables - Something out of Something as a Fraction - Halves and Quarters with Remainders Let me know if you find this guide useful and it will motivate me to press on with writing Part 2! Enjoy! Rob

#### The Algebra of Throwing - Equations of Motion

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A challenging guided investigation for Lower Secondary pupils into the height reached and flight time of a thrown object Gives a real and engaging context for helping pupils to understand WHY algebra is useful, There is enough material here for at least a week's work, possibly more, depending on pupils' level. Contains full notes for teachers and a carefully structured set of worksheets, which lead pupils step by step through the thinking process. g (the acceleration due to gravity) is taken to be -10 throughout, rather than -9.8, so an appealingly simple set of numbers results. Encourages children to explore patterns and to make predictions, some of which, interestingly, turn out to be false. Numerous opportunities are given for consolidating skills in evaluating expressions and solving equations, including those where negative numbers are involved. Graphing of the equations of motion is also thoroughly explored.

#### TapSayTurn - Multiplication Tables game that helps children actually LEARN the facts.

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We use this game across our whole school of 1000 pupils from Primary 2 to Primary 7 because it really works. It is a simple card game, with a very particular set of rules, which help the children build their learning step by step. We are even adapting it for French and Spanish vocabulary! We use it along with the Counting Caterpillar (also on TES). The Caterpillar helps children to master the stations of each table so when they come to the memorising stage, half the learning is already secure. Each child has a record card where they can keep track of their learning - first self assessment, then peer, then teacher! I encourage my colleagues to teach both games to the whole class to start with so they can be sure all the children have fully understood the rules of the game, which need to follow EXACTLY if it is to work properly! Once the pupils are clear on the rules, they can be let loose on different tables according to their own level and work on them both in school at home. Full differentiation! We find that little and often is the key. It is also a great quiet lesson starter if you want to get all the children settled before you start the teaching part. PS If you use these, please let me know. I always welcome feedback. :-)

#### Multiplication Rectangles and Factor Rainbows

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A whole class investigation for 7-10 year olds best used with children working in groups. Covers: Use of arrays to represent multiplication; links to multiplication triangles, factor rainbows; with possible extensions to square numbers and prime numbers. Problem solving strategies: Work systematically, Use a table Children love the idea of creating factor rainbows and will get totally carried away with this. And there is lots of potential for a wide-ranging mathematical discussion: which numbers have few factors? which have many? and why!? Enjoy!

#### Counting Caterpillar - Multiplcation Tables game for actually LEARNING the Facts!

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This is my most-used resource. We have it going across our school of 1000 pupils from Primary 2 to Primary 7 because it really works! It doesn't just get the children to PRACTISE their tables, it actually helps them LEARN them! Our parents love it too. Simple, but VERY effective. It's a practical activity which the children do independently, each working at their own level. All they need is a printed caterpillar sheet and a set of 11 counters, which we get them to keep in a plastic wallet. When they master a table they first assess themselves, then get a friend to assess them and finally ask the teacher to test them. There is an individual record card where they can keep track of their progress. We use this game together with Tap, Say, Turn (which I have also put on TES resources). The Caterpillar teaches the pupils to count the stations. Tap Say Turn helps them to memorise the facts. I've included detailed notes for teachers and a short explanation for parents. Do read them carefully. You have to teach the children to follow the rules EXACTLY or the game will not be properly effective. When we introduce it to a new class, we get everyone doing it together to begin with so we can make sure they have all learned it correctly. Once everyone has got it, we get them doing it at home too!