# Maths At Home

## in learning to work like a mathematician

Find them in the Learners link.

 Letters & Numbers (3-7) ... Calculations are obviously an important part of a mathematician's work. Equally important though are the related skills of estimating number and being able to calculate an answer in more than one way in order to check it. Estimating, calculating and checking another way are central to this activity. The context is one of giving value to each letter of the alphabet so that the values of words can be estimated, calculated, checked and compared. In the early part of the activity, there are only 2 basic values - \$10 for vowels and \$5 for consonants and the focus is Pets. Later every letter gets its own value, based on its position in the alphabet and the focus becomes first names in the family. The activity rounds off with a game making words from randomly chosen letters (similar to Scrabble or the TV game Letters & Numbers). A print sheet of alphabet tiles with associated values is available in the activity.
 Toss Up (1/2-6) ... A simple game to prepare and play. Print some pages and collect five objects. For instance, caps from bottles of water or milk are easy to find at home. The game is about tossing or dropping the caps on the playing boards, which are all designed the same way but each one uses different numbers. A bit of competitive fun, lots of mental arithmetic (supported by a calculator if chosen) an unspoken comparison between our base 10 place value system and calculation in other bases, and confirmation of how elegant our system is for recording numbers. A few extra challenges are included to extend thinking beyond mere calculation.
 Ainsley and the Planting Problem (3-9) ... This problem is perfect for learning to work like a mathematician. It contains very little 'text book' mathematics - single digit mental arithmetic mostly - but it also contains opportunity after opportunity to display and develop higher order thinking skills, which are the most important part of a mathematician's work. The problem is embedded in a story shell about planting a garden so that each of three children can look after one plant for each year of their age. It encourages drawing a diagram, making a model, looking for the limits in a problem, breaking a problem into parts and trying every possible case. We first learned of the problem through one child's Year 3 remote learning maths class and the activity includes some of that child's reasoning. The problem grows from there to provide plenty of challenge for learners from broad age and experience ranges.
 Cube Nets (2-10) ... A mathematician loves it when there is more than one answer to a problem and that is exactly the case in this activity. Teachers love it too, because it means there are more ways for a learner to be successful. The starting point is a definition of a net in mathematics and identifying collections of six squares that do and don't make the net of a cube. Then, having made their first cube from a net provided, learners are introduced to a mathematical playground on the web called PolyPad. It's freely available and provides tools to aid the search for all the cube nets. Learners can efficiently make nets on screen and use the built in tools to find out if the nets become virtual cubes. Throughout the activity learners are working like a mathematician and being encouraged to imagine, predict and test.
 Princess Catharina's Gold Rings (4-10) ... Princess Catharina has twelve gold rings. She keeps them in a three drawer trinket box with a top drawer, a middle drawer and a bottom drawer. Each ring is made with a different number of grams of gold. The Princess loves maths, so she makes a puzzle for the servant who has to look after the rings. The rules of the puzzle explain which drawer each ring goes in. The servant loves it, because it turns out there is more than one way to use the rules. Life is never boring with this Princess.
 What Can You Do With The Sunday Paper? (K-8) ... Don't throw the Sunday paper in the recycle bin. At least not before you reuse it for maths activities. The whole family can work together on this. The first job is to roll sheets from the paper into tubes and joiners. All you need is a little time and a little masking tape. Some can roll, someone can tear off bits of tape and someone can use the tape to stop the tubes unrolling. You will be amazed at what shapes and objects you can make with just one Sunday paper. But building stuff isn't the end of it, it's only the start. This is really three activities in one. There is also pattern work with shape and number and money calculation? Dive in. A rainy Sunday afternoon is a great time to get started.
 Calculator Walk (K-1/2) ... This activity is for the youngest learners. It combines everything good in learning at home - playing with a 'new machine', learning maths informally with a close older family member, learning what the learner already knows and ... going for a walk. The parent gives the child a calculator, hopefully as a gift they can 'keep forever'. They explore it, discuss it, learn how to write on its screen and take it with them on a number hunt around the house, the yard, the street, ... On return a favourite number is recorded in their journal along with information about where it was found and why it is special. As a bonus to the activity, interest in the calculator as a machine is also harnessed for creative endeavours.
 Times Tables Torture (2-10) ... Let's face it, memorising times tables is torture for some kids! But why should they have all the fun. Now it can be torture for everyone! The activity provides slides of every times table children need to know. They use their technology skills to create their own slide show of 20 slides which challenges them to write each answer against the clock. But they choose the time the slides show. See it ... Write it. The Olympic standard is 2 seconds per slide, but students are encouraged to simply continue reaching for their personal best. You can't do two things at once, so they work with a partner who calls Next and changes each slide at the appointed time. At the end answers are checked with a calculator and conceptual support for how tables derive from multiplication is provided through the linked activity Exploring Times Tables. Learners are encouraged to use the activity for just 10 minutes a day, 4 days a week until they reach a high level of speed and accuracy.
 Colour Spots on a Number Line (3-7) ... Children like colouring and colouring in can be a useful way of illustrating patterns in mathematics. But colouring can also mean more time spent colouring than learning to work like a mathematician. The colouring in this activity is as quick as making a few small spots with a pencil or marker. The act of doing that forces the hand to work in a physical pattern and the mind to ask itself where the next spot will be. The children don't write any numbers on the line, but they are encouraged to imagine which ones are hiding under the colour spots. The mathematics that results produces, firstly, a visual pattern, then a list of related numbers, then a table connecting numbers used for two purposes. The tables beg the question: If I tell you any ..., can you tell me ...?. Any learner who can make such a prediction has generalised the situation and is already involved in algebra. The activity goes on to gently lead from oral, to written, to simple symbolic algebra. The latter part of the activity introduces co-ordinate geometry and a little exploration of straight lines in that context.
 Protons & Anti-Protons (4-10) ... Protons and Anti-Protons are particles with the interesting property that equal numbers of them annihilate each other. Therefore when equal numbers of them are present they have a net zero effect. This is a simplified version of an aspect of particle physics, but sufficiently accurate to be worth exploring further. What happens if we add more particles to a collection? What happens if we subtract some particles from a collection? Investigating these questions, using objects as the particles, leads to a model for 'Proton Arithmetic' which is just one small step away from the arithmetic of positive and negative numbers. At the end of the activity the door to that step is tantalizingly opened.

Maths At Home is a division of Mathematics Centre