Elementary School Math Tips
How can I help my child understand math concepts?
What you want to start with is making sure your child understands how numbers work. They should be able to count. They should understand that the numbers go in order and that there's a maths concept called ordinality. The child should know that if you're counting apples and you count 1-2-3-4, it means that there are four apples, that they don't have to recount them again to understand that there are four apples. The child should also be able to make mathematical estimates. So, you should be able to say, “about how many leaves are in those trees there? Are there ten or are there a thousand?” and they should be able to tell you that there are more like a thousand, or there are more like ten if it's a really sparse tree. That's the sort of thing that children have a really hard time with with maths concepts though. So to then expect that child to solve a multiplication problem and eyeball if the answer is right is impossible, if they don't really have a concept of how many is a thousand. We spend a lot of time counting when we're trying to teach place value. You've got your ones and your tens. If they don't understand ones, tens and hundreds then place, borrowing and carrying is really tricky because all they know is they're putting these little numbers up above their addition problem but they don't know why they're doing it. So, we spend a lot of time counting. We use play money. We'll count by ones and we'll count by tens and we'll see that ten ones equal a ten dollar bill and then we'll count by tens and see how they go and what if we do four tens and then one one, how many is that? For a lot of children, they have to go through this tangible process to understand, okay, you really are adding more to them. You really are taking some away. And so for us, whatever we can do to make it physical, to make them actually see things adding, things subtracting, things multiplying is helpful in children's understanding of maths concepts. It's simple things like that but it helps the children to understand what they're doing with maths, that it's not just random numbers with random answers that some teacher is telling you is right. So whatever you can do to make things concrete I think helps.
What are "manipulatives" in math?
"Manipulatives" in math is a broad term that in math applies to any tangible item you can use to demonstrate math concepts. If you go to the teacher supply store you see lots of little bears or little animals for this purpose but it can be anything. Most manipulatives are expensive and could be easily replaced with something much simpler that you have at home, a manipulative is anything tangible that can be used to demonstrate math concepts. I often encourage parents if they're trying to demonstrate with their kids that pennies are great. We often have lots of pennies hanging around. If your child has a lot of toy soliders, match box cars or other little toys in large numbers, these work well. My baby has lots of dishes, you can use anything that you can count, that you can add and you can subtract. If you have a child who's really into, say, food, cookies work really well, or jelly beans, M&Ms, Cheerios, you can use whatever will capture their imagination the smallest bit. As long as you don't mind throwing away the manipulatives afterwards because you're going to handle everything a lot.
How can I help my child understand "fractions"?
When I teach fractions, I love to use fraction manipulatives. They're circles that are cut into little pieces and they're handy to have. I also use a lot of examples when teaching fractions, so I'll talk about pie, cake or pizza. Pizza is a good example to use for teaching fractions. They understand cutting pizza into pieces. The fraction manipulatives are fun because the manipulatives are uniform and my drawings are never uniform. For the simple things like working out a fifth, you cut the pizza into five pieces and you say, "If I give you this one how many do you have? One." The top is the numerator - it's the thing that I care about - and the bottom is the denominator - how many pieces the pie is cut into total. You do this again and again, you have to do it many, many times before your child will get it. Fractions are an abstract concept. It's not the way that children think of things. They want a piece and they don't really care. Next, I begin talking about fractions as comparisons. Would you rather have a fifth or a twentieth of a pizza? I don't care or I don't know. Explain that this pizza is cut into five pieces and this pizza is cut into twenty pieces. If you can only have one piece, which one do you want? They'll almost always say they want the fifth piece because they can see that those pieces are bigger. You work that way until they start grasping fractions. They can grasp it concretely, you just have to work at it so they can grasp it conceptually.
How can I help my child understand "decimals"?
For decimals, I always start out with money. It's the kind of easiest way for them, that they know, that they understand. I start out with pennies and I'll write--everything that I do with manipulatives--I try to do the written form on paper, too. So they can kind of see how a penny is related to point one. So we'll talk about, okay, how many pennies are there in a dollar? Okay, there's a hundred. So that's the hundredths place, that's the hundredths place right here. And then, well, here's a dime. How many dimes in a dollar? Well, there's ten. So here's the tenths place, right here. And you go back and forth and you talk about it. And one of the hardest things for kids when they start doing computation with decimals is that they don't want to line them up. You know, everything goes willy-nilly. But if you say to a child, "If I have thirty cents and I have thirty dollars and I put it together, is that sixty dollars?" They'll do it on paper, no problem, they'll make is sixty dollars. But when you ask them, they'll say, "No. Not even close." And so I try to really say, "Look, you don't want to mix your dollars and your cents. You want to keep everything separate. And the way you keep it separate is by keeping that decimal point lined up for addition and subtraction." So, you kind of try to make things real for them.
How can I help my child understand "integers" or "negative numbers"?
Intergers are hard. Intergers, I would say, are the single hardest math concept that children have understanding. And part of the problem is that we've gone five or six years teaching them you can never subtract a bigger number from a smaller number, and suddenly now you can. So before you could never do five minus seven, and now you suddenly, you can and the answer's negative two, and you've never heard of a negative two, and what's going on? So a couple methods I use to talk about it. One is sometimes I use a thermometer and I say 'okay, it's five degrees and now the temperature's dropped seven degrees', and draw the lines on the thermometer, and they can count them down. You can also use a number line if the thermometer is confusing or just too much work to draw. Use a number line and literally make them hop and let them go past zero. And there's a lot of times when going past zero is a hard thing for them to do. I talk a lot about money with intergers, too. I'll say, 'look, when you're adding and subtracting with intergers you're just combining two quantities, so a positive is money that you have in your pocket, a negative is money that you owe.' So if you have six dollars but you owe eight dollars--and my vernacular is 'where you're at'--where are you at? You know, where are you? 'Oh, well I owe two.' That's right, that's a negative two. When you owe money, that's a negative two. And for some kids that really clicks. For other kids, it's hopeless and we go back to the thermometer and we'll go back to the number line and sometimes it just takes a lot of practice and a lot of work.
What are some "multiplication" tips or tricks?
Multiplication, you have your really super easy ones. You've got your times ones, and your times tens, and your times elevens. I start with those so that they feel like they know what they're doing. Most kids when they're learning addition facts will learn what they call "the doubles": four plus four, five plus five, six plus six. So then times two is really easy because they just have to recall their doubles. For the other ones- one of the things we like to do is we like to do counting by multiples. Most of the kids can count by fives, so times fives are fun. They just have to count and they get pretty good at them. If they can we try to teach them to count by threes, and count by fours, and count by sixes. It's a great skill for them to have later. Some of them get it really easily and some of them don't. There's a great trick for multiplying nines. Let's say you want to do nine times six. So, this is finger one, two, three, four, five, six, seven, eight, nine, ten. If you want to do nine times six, you put down your sixth finger. The fingers on this side of your bent finger is your tens place, and the fingers on this side of your bent finger are your ones place. So, six times nine is fifty-four. If you want to do six times three, you put down your third finger so you've got two in your tens place and seven in your ones place, so it's twenty-seven. It works great for the nines, all the way up through nine times nine, which is nine, so you've got eight on this side and one on this side.
What are some "division" tips or tricks?
With division I want them to know their times tables and then I try to teach them the flip, what they like to call in school the fact family. So if 3 x 6 is 18, then 18 divided by 3 is 6. 18 divided by 6 is 3. And some of them transition to the reverse really quickly. Others need more practice with it. They struggle with division a lot but it's mostly because they don't know their times table.
What are some "addition" tips or tricks?
When I teach addition, the first thing I do, I teach “plus ones” – and it's just counting, it's just going up one. The next thing I do is I teach “plus twos” and before I teach “plus twos”, I talk about even numbers and odd numbers and I show them on a number line how even numbers are two apart and odd numbers are two apart. So, any time you add two, you just go to the next even number or the next odd number. So, “plus ones” and “plus twos” are pretty easy. Then I do “plus tens” and I try to break out – see, nineteen is nine and ten just like twenty-nine is twenty and nine and I try to break them out – so, we do “plus tens” and they usually get “plus tens” pretty easily. And, so from there, I try to find some compromises so I'll do “plus nines” – so, I'll say, Okay I want you to think about that number plus ten so three plus ten is thirteen, you know that like that – so, you just need to take away one and it's twelve. And, so when I teach addition and subtraction, I'll give them tons and tons of sheets of “plus twos” or “plus threes” or “plus nines” – until they really kind of begin to get them in their heads. And, I'll let them hop around the sheet – if they know all the three plus nines, they can fill in all of those and then fill in all the others because all these things help them improve their recall and improve their memory – kind of get in a groove. Math facts are all about sealing them in your brain somehow, so whatever works for them. Sometimes, they'll have a completed sheet and they'll want to put it right here and kind of cheat – you know, kind of look – and I think that's fine because eventually, you'll stop looking, you'll retrieve it from your brain, you'll stop looking at that old sheet. So, whatever kind of works for them in terms of recalling these numbers over and over again, I let them do.
