Having good estimating skills is hugely important in mathematics. By extension, 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. Here are some ways we can practice this skill with children.
Estimating Quantities of objects
This one is so simple and so impactful. Just get children to estimate quantities of physical objects they can see. For example, you can show them a plate with blueberries on it and just ask them “roughly how many are on the plate?” You could get them to confirm the amount by counting, particularly with younger children. These exercises lend themselves well to competitive games which children always love. For example, “whoever guesses closest to the actual amount, wins the blueberries.” (You might need to use something a bit more enticing than blueberries!)
Visual Estimation
A number line is exactly that – a line drawn on a page which you can then write numbers on. They’re most often used in classrooms to model arithmetic operations. But they are perfect visual tools to build children’s estimating ability while simultaneously developing their understanding of part-whole relationships, ratios and more.
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 zero,” You can ask them to add other numbers to the line, always encouraging them to talk about their reasoning. If you can get another child to challenge the reasoning, that’s even better. Then you ask that child to explain their reasoning, and hopefully a debate will ensue!
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.
Vary Number Types
You should vary the types of numbers used. These can be done with single digit numbers, double digit, triple digit and higher. Actually, you can alternate through these. So after doing that “where is 70” example, 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 7000 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 ratios, i.e. fractions, decimals and percentages. Switching between whole numbers and ratios, decimals and fractions helps to bring out 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, 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?” Press them for a quick estimate and not to calculate. Then, again, engage them in conversation about their reasoning. It’s good to encourage them to speak in terms of ranges, £50-£60 for example (which is adjacent to rounding numbers).
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