  # Maths At Home

## Supporting learners, parents, teachers and schools  Find them in the Learners link. Fill The Board (K-6) ... A playing board with five rows of five circles is supplied. A dice is rolled and circles are covered or crossed off. Investigate the most likely number of rolls to cover them all. A simple game which becomes an investigation into probability and purposeful collection and interpretation of data. It can be played by early years learners for informal learning and older learners as a more documented experience. Cambridge University NRICH project has designed software to support the investigation. Networks (Y4-8) ... The starting point for a mathematician is an interesting problem. Something they don't know the answer to, but find interesting enough to explore. It doesn't matter what the problem is. It does matter that it is interesting. In the beginning this activity is a game of placing square tiles to make a pathway. The problem is, how do I win the game. Then, when I've got that figured, what happens if I ...? One of those 'what happens if...' questions leads to changing the way lines are drawn on the tile and from there to heaps of ways of creating tiling patterns and mathematical art. Number Tiles (Y4-10) ... You have the digits 1 to 9 on cards. You put three down to make a three digit number. Then another three under that to make another three digit number. Now add those two 3-digit numbers. It is possible to make the answer with the three cards left in your hand. Not always of course, but sometimes. Can you find one way to do it? How about another? How about five more? How many solutions are there? How do you know when you have found them all? The focus throughout is on putting learners in a position where they know that they have worked like a mathematician. Rectangle Fractions (Y4-8) ... Fractions are introduced through the familiar model of a whole rectangle and its main parts - rows, columns and cells. The language used supports the gentle development of the concept and a gradual, understandable growth towards symbolic representation. As the physical model and its links to language expand, operations and equations involving fractions flow naturally. Pythagoras 1 (Y6-10) ... A puzzle with four congruent pieces becomes the basis for demonstrating Pythagoras' Theorem. The investigation is based on a dissection proof discovered by amateur mathematician Henry Perigal in the 19th century. Learners use pieces supplied to do the first demonstration, then have to design and construct their own pieces based on a different right angle triangle. The activity finishes as it began, with the four congruent quadrilaterals used as to construct two squares, but this time using rotation and/or translation only. Cars In A Garage (Y2-10) ... We supply the garages. You supply the cars. How many ways can three cars be parked in three garages? Four cars in four garages? Five cars in five garages? Mmm, looks like there might be a pattern developing here. But how do we explain it so that someone else could learn from us? And how do we do the calculations when it gets to be say 100 cars and 100 garages? The activity includes sample student videos and journal reports. Steps (Y2-10) ... Nine digits have to be arranged in a step shape so that the two horizontal and the two vertical lines all add to the same number. Success is finding one solution. More success is finding more than one. Greater success is the four possible line totals. An even larger measure of success is finding all 12 unique solutions and knowing why there are no more. Year 2 arithmetic through to Year 10 logic and reasoning. Red To Blue (Y4-10) ... Easy to state and easy to start, this activity only needs reasoning to solve. It's seems easy, and is when you know how, but it can be a bit tricky to crack. Once solved, the challenge is to explain to someone else and there are several ways to do this. An example of Year 6 students using a video to do this is included. The problem goes deeper when we ask the mathematician's question, "What happens if...?" Guess what? A pattern and even algebra. Six Plus (K-6) ... Don't let the title fool you. This is not just a game for little kids. Yes the game is explained using the simple example of starting with 6 and adding a single digit number. However, by keeping the structure of the game and asking the mathematician's question 'What happens if...? challenges develop for students at every level at least as far as Year 6. The game is simple in structure. One player hides a number in the calculator and the other has to find it in as few guesses as possible. It's ironic, but using this game, children in the first years of primary school, solve equations that appear in text books for the first years of secondary school. Tricube Constructions A (Y4-8) ... With the help of easily made Tricubes (just 3 cubes joined together as the name implies) the challenge is to use isometric drawing to show solutions to puzzles. Each puzzle is made from 4 Tricubes and the looking down view of the completed object is shown. The extra challenge is to create front and side views from each isometric solution. (Isometric drawing is a way of representing a 3D object on 2D paper.) Garden Beds (Y4-10) ... Plants are sown in a row and a path of tiles is built to enclose them. If you are told any number of plants, can you calculate the number of tiles needed? Sounds pretty forward - almost like text book question - but the joy of it is that different people see the solution in different ways. That's what opens the door from this one problem to almost all of the algebra curriculum. How?? There's only one way to find out. Wallpaper Patterns (Y4-8) ... It's amazing how many really cool designs can come from simple starting points. This activity explores one way to design wallpaper starting with a design in one square and repeating it on a grid by following rules. There is lots of opportunity for learners to create their own wallpaper. Mathematically it builds experience in transformation geometry, with an emphasis on sliding (also called translation), reflection and rotation. Exploring Times Tables (Y2-8) ... Of course kids have to learn their times tables, but they don't have to learn them dumbly. This activity involves exploring a times tables chart you have never seen before. Learning times tables becomes part of a growing understanding of multiplication as an array of equal rows. It encourages swiftness, accuracy, flexibility and creativity and, most of all, helps learners build a brain picture around rectangles that will be applicable in many other areas of mathematics. Doug's Tablecloth (Y4-8) ... Doug bought a new tablecloth and it exactly fitted into the depth of the drawer. We know the dimensions of the tablecloth and the dimensions of the drawer, but how on earth did he fold it to get it in there? As one student said, It's hard until you get it and then it's easy. Once you figure how it was folded to fit the depth, you wonder what the measurements would be if also had to exactly fit the width. There's fractions formed by folding the whole cloth too and number patterns when you investigate the folds and creases. Maths At Home is a division of Mathematics Centre