Having good estimating skills is hugely important in mathematics and everyday life. The ability to quickly and accurately estimate prices, quantities, rates and percentages (and more) does wonders for our ability to make good decisions in our lives. Good estimation skills also help with making predictions and planning. These skills have always been crucial to humans. And as more and more of us are outsourcing cognitive work to algorithms and so-called AI, it’s essential to help our children to develop their estimations skills. Here are a few ways we can do this.
Estimating Quantities of objects
This one is so simple. Just get children to estimate quantities of physical objects they can see. For example, show them a plate with blueberries on it and just ask them “roughly how many blueberries are on the plate?” You could get them to check how close they got by physically counting the blueberries. This is great to help the younger children practice their foundational counting skills. These exercises lend themselves well to competitive games which children always love. For example, “whoever guesses closest to the actual amount, wins the blueberries.” (Depending on your child, you might need to use something a bit more enticing than blueberries to really motivate them!)
Visual Estimation
A number line is a key tool in maths learning. It’s simply line drawn on a page which you can then write numbers on. They’re most often used in classrooms to model things like counting strategies and arithmetic operations. They are also perfect visual tools to build children’s estimating ability, while simultaneously developing their knowledge of proportions and part-whole strictures.
For example: Write 0 on the far left of the lines and 100 at the other end. Ask the child “Where is 70, roughly?” They make a mark at their chosen spot, then you ask them to explain their reasoning, “Why do you think 70 goes there? Why not all the way down the other end?” You’ll hear things like “70 is closer to 100 than to 0,” You can ask them to add other numbers to the line, always encouraging them to talk about their reasoning.
Child Ownership of their Learning
A quick aside on why it’s important to encourage children to explain their reasoning. The more we can get children owning the learning experience the better. Encouraging children to think about and explain their reasoning is super-powerful in maths because it deepens their understanding of the concepts they’re working with. It also gives you the opportunity to spot any areas of their reasoning that need a bit of fine-tuning.
If you can get another child to comment on the reasoning of their peer, that’s even better. Then you ask that child to explain their reasoning, and hopefully a debate will ensue! It also opens the door to children working together which creates a rich learning experience for them.
As with everything when it comes to learning, it’s best to get the children doing the drawing and writing themselves. As well as paper and whiteboards, why not give them some chalk and let them draw the number lines on the ground. Anything that gets the children using their whole bodies leads to deep, embodied learning. Maths is so much more than writing numbers on a sheet of paper.
Vary Number Types
You should vary the types of numbers used. These number lines can be done with single digit numbers, double digit, triple digit and higher. Actually, you can alternate between these. So after doing “where is 70” you can replace the 100 with 1000 and then ask “where is 700?” This will help show some important structural ideas. The child will see the connections between 70 and 700 and the similarities between tens and thousands. I like to go to a range that’s way outside of the child’s normal range, so they see how these patterns help to make those huge numbers understandable. E.g. 700,000 is to 1,000,000 what 7 is to 10, 70 is to 100, etc).
As well as whole numbers, you should get children estimating fractions, decimals and percentages. Switching between whole numbers and proportions reveals the structural similarities between them. They can see how 70% is to 100% what 7/10 is to a whole, 0.7 is to 1.0, etc.
Verbal Estimation
The possibilities for verbal estimation exercises are endless. You can do something like asking a child for rough answers to arithmetic operations. “Without working it out, roughly what is 23 * 9?” They’ll want to calculate it but tell them you want an estimate, not an exact answer.
Word problems are good for this too. You can give simple ones like “this T-shirt costs £5 for one, roughly how much would 13 of them cost?” This is how we use maths in everyday life, so let’s get children practicing this. Press them for a quick estimate and not to calculate. It’s good to encourage them to speak in terms of ranges, £50-£60 for example (which is adjacent to rounding numbers). And always engage them in conversation about their reasoning.
Conclusion
Estimation is of those foundational maths skills that we use all the time. We need it to estimate prices, change, journey times, resources needed and more. I hope you find these simple exercises useful and that your children enjoy themselves as they develop this vital maths and life skill.
Peace, Ely