The opportunity for discussing mathematical ideas and encouraging mathematical thinking is available in what may seem like the most mundane of opportunities and activities. Today I’ll present two opportunities that you can explore with children aged anywhere from 4 years to 8 years. These two examples illustrate the foundational knowledge of algebraic thinking and the nature of patterns.

### Setting the Table

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The way we set the table for dinner each evening involves an ability to **understand and extend a spatial pattern**. While something so simple might not seem like algebra, or at least not the algebra you remember, it certainly creates the foundation for algebraic thinking.

Setting the table for dinner is a task that the younger members of your family can learn to perform and it involves mathematical thinking. First they must count out how many place mats, forks, knives, spoons, glasses and napkins they will need to give everyone enough to use at the table. This is a necessary step in developing multiplicative thinking.

They then need to set each place at the table in the same manner. The first time they are involved in this activity it will be useful for an older member of the family to show them how to set the first place at the table, perhaps explaining how and why the knife and fork are arranged, where a dessert spoon is placed, where the glass or glasses are placed and so on. As you move to the next table setting, you can then ask your child what goes where and ask them to lay the setting. While it might seem that all they are doing is imitating the first setting, what they are also doing is **noticing the different elements of the pattern and continuing the sequence**. It’s amazing that such a simple activity can offer so much in laying the foundations of algebraic thinking.

### Hanging Out the Clothes

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There’s actually many opportunities to explore algebraic thinking as you go out to hang the washing on the line. Take your child out with you the next time you hang washing and try any of the following.

If you use colourful pegs to hang out the washing you can develop a pattern. Let’s say you have four colours: red, blue, green and yellow. As you hang up a T-shirt you can say “First I’m using a red peg and then I’m using a blue peg.” With the next item of clothing you can continue with the next two colours. With the third item of clothing you can start with a red peg again and then ask your child to tell you which colour should be used next and so on. Depending how your child goes with this activity, you can then ask them which colour pegs to use for the 6th item of clothing or the 10th. **Being able to visualise these groupings of four and to extend the pattern to predict future terms in the sequence is a very advanced skill** and will have your child well on the way to a firm foundation in algebraic thinking!

You could do something similar in the way you hang out your clothes. You might hang a top, then a bottom and then a piece of underwear. Again you can ask your child which piece of clothing to hang next and which might be the 8th piece of clothing and so on.

Another common example to explore when hanging out clothing, or perhaps towels, is how many pegs are used. Often when hanging out towels or pillowcases, two items share one peg. So if you hang out three towels you might use 4 pegs instead of 6. As you are doing this you can ask your child how many pegs are needed to hang 7 towels or 20 towels in this way. **This requires children to see the pattern that is emerging and to form a function** between the independent variable (the number of towels) and the dependent variable (the number of pegs). Children will then use their informal function to find future terms in the sequence.

Each of the above scenarios and opportunities are far from being trivial situations and are in fact **easily accessible situations in which to present and explore mathematical thinking**. Engaging in the world in this way sets your child up for future success with algebraic concepts. And since algebra is the gateway to the **most sophisticated and powerful areas of mathematics**, the sooner you can get started, the better!

*We’d love to hear about any patterns you have explored with your child, please consider leaving a comment below.*

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