Over the next while, I will be posting samples from actual reports I have made to parents of my tutoring students. Today’s topic is some practical suggestions for a child who is struggling with primary-level math. Hope you’ll find some helpful tips here!
Addition of Double-Digit (or Larger) Numbers
J was sure he wouldn’t be able to add double-digit numbers. So I showed him some practical ways to make it easier. We started with double-digit numbers that don’t require carrying (numbers added don’t add to more than 9 in any column). I emphasized that it is important to line up the numbers carefully so as not to become confused. To help him, we used cm graph paper (the squares are large enough for his handwriting of each number to fit in each square; there are different sizes of graph paper available, so choose a size that fits the child’s handwriting size). Then I had him add–starting with the ones column, then the tens column … and then I put down hundreds … and even thousands and ten thousands columns. He was very impressed that he could successfully add such large numbers! Building confidence is so important. Once he feels very confident with adding this way, we’ll talk about place value, and then introduce carrying.
J also doesn’t seem to clearly understand how easy it is to add 5 to 10s. For example: 20 + 5 = 25. You can help him practice this at home by using dimes and nickles. For example, have him count 5 dimes and then add a nickle. This usually helps children catch onto this concept easily.
We practised counting coins — pennies, nickels, dimes and quarters. But while J can count them, it is much more difficult for him to try and figure out what coins to use for a given price. But, as with most children, he likes using coins, so this is something you can easily do with him for practice. Just write down a price–or “play store” and have him choose what he’d like to buy for the prices you’ve marked on items (for example, 38 cents or 55 cents), and have him figure out which coins to use. Let him figure out different combinations. For example: for 38 cents he could use 25 + 10 + 3 pennies OR 10 + 10 + 5 + 5 + 5 + 3 pennies. I realize that officially we don’t use pennies anymore in Canada, but we still need to be able to figure out whether to round up or down, so if you have pennies, it’s good to use them … and besides …
J also needs practice with rounding in math. Using pennies, nickles and dimes is a great way to practice rounding! For example, 18 cents: dime, nickel, 3 pennies. To round, we want to just end up with dimes. So count the pennies and nickel. That’s “5 or more” so we round up and it becomes 20 cents (2 dimes). But if it was 13 cents (dime, 3 pennies), we can count the pennies and since they are “less than 5” we round down to 10.
Please also note: When rounding, always ask if the number to be rounded is “less than 5” or “5 or more.” Be careful NOT to say, “less than 5 or more than 5” as that leaves out the 5!
J can generally do “> greater than”, “< less than”, and “= equal to”. However, I noticed that he said 7685 = 7865. I asked him to explain it, and he said that both numbers each contained a 7, a 6, an 8, and a 5. He didn’t seem to realize that just because the numbers contain the same digits, doesn’t mean that they are the same numbers if the digits are in a different order. So we talked about that and did some practice. This is something you’ll want to keep an eye on as you work with him. Really emphasize the “ones, tens, hundreds…” Use the graph paper, as discussed above, so he can clearly see the difference. Have him write the digits in different orders and read them aloud. If he is having difficulties reading the numbers, write abbreviations at the top of each column: th (thousands), h (hundreds), t (tens), o (ones).
What Calculation Method Should We Use?
In the workbook you are using with J, a wide variety of methods are presented for doing certain kinds of calculations, for example, double-digit addition. This can be confusing OR it can be helpful (for parents as well as for the student). My feeling is this:
- First try the simplest/standard method.
- If your child is having difficulty with the simple method, try one (or more, if needed) of the other methods, until you find one that your child “gets”–and then do lots of practice with that. Once your child understands the overall concept, it is wise to go back and learn the simple/standard method, as the child will no doubt run into it at various points later in math–and in “real life.” Note: You may discover that the method that helps your child understand the concept is different than the method that you think is easiest/most helpful. We all learn in different ways–so you as a parent may very well end up learning some surprising new ways to deal with a concept!
- If your child “gets” the simple/standard method, but finds the concept very intriguing, encourage “exploration” of some of the other methods. Learning a variety of approaches can actually help to prepare the child for more complex mathematical concepts in future, as well as using them in “real life” applications.
J seems to have some difficulty with counting backwards … and especially counting backwards “over decade breaks” (for example: 62, 61, 60, 59, 58). This is a good thing to practice by using “real” learning opportunities. For example, as you walk along a sidewalk, count each square, starting with a number like 33 or 54 or whatever, and count backwards from square to square, making sure to go back into the next “decade.” You can also use things like “100 number charts” (with numbers in rows of 10), and count backwards, pointing at each number as you say it. Or you can use dot-to-dot pictures that go up to at least 50, but start at the end number and draw the dot-to-dot line backward to the beginning, counting aloud from number to number. Or you can use calendars and count backwards from the end of the month (eg 31) to the beginning (1). There are lots of different fun ways to learn to count backwards–just keep your eyes open for ideas!
Writing Numbers Backwards
J tends to write some numbers backwards. As he tends to be a “hands-on” kind of learner, try having him “write” these numbers with his finger on a textured surface (such as a piece of sandpaper or a textured fabric or on a sidewalk) so he can “feel” the number–or he could write in sand, or in finger paints, or in shaving cream. Or have him “trace” magnetic or foam or plastic numbers, first with his eyes open, and then with his eyes closed. Another idea is to have him close his eyes and you can “write” the number on the palm of his hand with your fingertip (or you could “write” it on his back) so he can get the feel of the number. Also, have him “write” it in the air (or on a window or other surface that has condensation on it–kids love this!) with his finger.
Learning Arithmetic Facts
J really needs to learn his number facts, and it would be great if he could learn his “doubles” first, as he can then use them to easily calculate other number facts. Some methods to learn them: Repeat them over and over (aloud and/or written). Say them as you do an activity, such as bouncing or tossing a ball, climbing stairs, jumping on the trampoline, etc. “Sing” or “chant” them. There are CDs available that have songs or chants for number facts, or you can make up your own. There are lots of free number fact apps available for your smartphone, tablet or cell phone–and many of them have a “game” approach which really appeals to lots of children. Of course, there are also flash cards available very inexpensively at dollar stores or thrift stores–or you can use an ordinary deck of cards (just use the number cards) to practice addition, subtraction or multiplication facts; just draw two cards at a time. Dice also work well, as do dominoes.
What practical math tips have worked well with your child/ren? Why not share them with us in the comments? Thank you!