Our maths lessons always began with drill. Counting practice, number facts and speed drills, depending on the age of the child. If there was one thing I learned about teaching maths, it was practice, practice, practice. Here are the things we did that I believe are non-negotiables and helped make learning maths easier on both the children and me.
1. 100 chart for counting
Recognising numbers and counting are the first maths skills your young child will learn. A 100 chart is really helpful for training in this skill. Counting numbers visually, and not just verbally, helps him see the groups of ten and other number patterns. It gives him a mental picture he can refer to when doing other maths problems.
You can teach skip counting and number patterns by colouring the number squares. I made paper copies of the 100 chart and placed a transparent wipe clean sheet over the top for the children to mark the numbers for skip counting as a speed drill. You can also use a wipe clean 100 chart with a whiteboard marker.
2. Drill number facts and multiplication facts
Rote learning number facts is the single most important skill that advances a child in learning maths. Some children learn this quickly and some take a few years, but don’t give up. One reason children struggle with maths in highschool is because they never learned their times tables. Instant recall of multiplication facts is important for algebra and is an everyday life skill that no child should be without.
You can drill multiplication facts using flash cards or listing the facts on a chart. Singing the facts is also helpful for some children (make sure they use headphones!).
Using flash cards: Start with the whole equation showing and as the child learns the fact, hide the answer and sometimes one of the factors. If your child does well at memorising, you can even do the division facts.
Using a chart: Type and print out the facts listed with one group to a page. As with flash cards, memorise with the answers showing first, then cover the answer as they learn them.
When your child is confident, have them recite the facts to you.
Should you learn the facts in order? Well, we didn’t. We started with the 1s and 2s, then 3s, 6s and 9s. The 9s are one of the easiest, as the digits in each answer will add up to 9, eg 2 x 9 = 18 (1+8=9). Recognising the patterns is a great help in learning the facts.
3. Use manipulatives
Most learning is at its best when it is multi-sensory. Seeing, hearing and touching are all important for children to grasp the concept of quantities. There are so many ways children can learn through using manipulatives, from shapes and fractions with their sandwich or fruit, to place value with a base 10 set. Whatever and however you use them, manipulatives are fun and highly useful in learning maths concepts and help extend the theory into everyday life. For ideas on what you can use, have a look at our maths manipulatives kit.
4. Reinforce concepts in daily life
Learning how to apply maths in everyday living is essential for children to see its relevance. Here are a few ideas of some practical ways children can practice maths skills:
Measurement: have your children measure their height and weight, or the area you want to turn into a veggie patch, the space you need to fit a new oven into, etc. The list is endless.
Money: I’m sure many of you take your children shopping with you often, but how often do you use cash? Make an effort to use cash on a regular basis or use play money at home. Spending, saving, budgeting, and for older students, inflation, paying bills, investments, compound interest. Include your kids in your discussions and decision making regarding expenses and spending as well as mortgage and refinance. Teach the realities of how much money is needed for daily expenses – multiple maths skills are used in these.
Conversion: Are you using a recipe with imperial measures but only have metric scales? Get your kids to do the conversion. Are you shopping online and have to pay in US dollars – get your kids to do the currency conversion. Better still, if you get the opportunity to travel overseas, teach them how exchange rates work.
Fractions: So, your kids are going to have to share some things – teach them how to divide things equally between them. Cut up a piece of fruit or sandwich and tell the name of the shapes and parts. Teach older children how to multiply a recipe to make enough for your crowd of visitors (or your large family) – how much is 2 x ¾ cup of flour, etc.
5. Word problems
Word problems are probably one of the things most neglected when teaching maths, and that’s because most of the time they’re hard! One way to make them easy is to make up your own, so you can begin to see how each story has an equation behind it. Choose an equation, and make up a story that includes each number and process involved. This will take a bit of practice, but after a while it’s a lot of fun and will demystify word problems. Give it a go!
Another help is to get a dedicated word problems book and do word problems on a regular basis – preferably daily. Start with one a day, perhaps first thing in the morning while brains are fresh and uncluttered.
6. Teach them to check their work
The bane of my maths teaching life was getting my kids to check their work. It saves everyone so much time and angst, often making the difference between passing and failing a test. Drum this practice into your children! Before you check their tests or lessons, make sure they have checked their answers – it’s as much a habit for you as it is for them.
So how do they do it? Firstly, you both need to differentiate between computational errors and conceptual errors. Computational errors are a result of not copying a problem correctly, mistakes with adding, etc. They may understand how to do something but get it wrong due to carelessness. Don’t let your child fail at maths due to avoidable computational errors! They can avoid these by general training in carefulness, checking they have copied the problem accurately, then, check every step by redoing.
A grid notebook will help your child line up columns which will reduce computational errors. It’s also useful for drawing tables, graphs, etc and generally assist with neatness.
Computational errors will slow him down and you’ll waste time that you could be spending on improving conceptual errors (mistakes made due to not understanding a concept).
7. Do a quick 2 minute review of previous lesson
After you’ve done some maths drill, spend a few minutes going over the previous lesson. Ask your child what he remembers learning and to teach you how to do it. If this is too much for him, redo a practice problem together to demonstrate the concept if necessary. Don’t spend too much time on this, as it will most likely be revisited in the next lesson anyway, but it’s a good habit for your child to learn to pay attention if he knows he has to give an account of it the next day.
8. Learn and use mathematical terminology
Learning proper maths terminology goes a long way in building confidence and clarity of understanding.
9. Make sure they understand the concept
Mastery is important if a child is to move forward with maths skills. Practice a concept until the child understands, and can explain it to you, or teach someone else how to do it.
10. Use a number line.
Using a number line is not only helpful for beginning counting, but is invaluable when learning negative numbers and plotting graphs. When teaching adding and subtracting positive and negative numbers, find a good simple explanation that your child understands and stick with it.