Paraphrased from a homeschool math discussion forum:
“Help! My daughter struggles with arithmetic. I guess she is like me: just not a math person. She is an outstanding reader. When we do word problems, she usually has no trouble. She’s a whiz at strategy games and beats her dad at chess every time. But numbers — yikes! When we play Yahtzee, she gets lost trying to add up her score. The simple basics of adding and subtracting confuse her.
“Since I find math difficult myself, it’s hard for me to know what she needs. What’s missing to make it click for her? She used to think math was fun and tested well above grade level, but I listened to some well-meaning advice and totally changed the way we were schooling. I switched from using workbooks and games to using Saxon math, and she got extremely frustrated. Now she hates math.”
Not a Math Person?
Please don’t tell your daughter she has to be either a math person or a language person. It is quite possible to be both. It sounds to me as though she has a very mathematical mind, if she is so good at strategy games and chess. Numbers are only a tiny part of math, even if they are the part that fills elementary textbooks. And if she can analyze a word problem, she is way ahead of many kids her age!
Since her problem shows up in adding and subtracting, it could be a couple of things. Perhaps she does not understand the concepts of putting things together or taking them away — but surely that is NOT true, because she does well with word problems and was doing well with the workbooks you used before. Maybe she loses track of the numbers, especially when she tries to count in her head. If she isn’t sure of her math facts, she probably gets flustered when she has to deal with larger numbers.
Here’s my best guess: I think your daughter’s problem is that she has not quite internalized the place value system. She knows it on a surface level, but she needs to know it down in her bones. This is a key to understanding more math than you would think at first glance.
First Steps to Recovery
- Drop the Saxon textbook, if you have not already done so. That book carries too much emotional baggage at this point.
- Go to the library and check out Family Math if they have it, or The I Hate Mathematics! Book or Math For Smarty Pants, for a more interesting approach to mathematical thinking. Order them through library loan if you have to. Play around with math for awhile before you attempt to do textbooky work again.
- Meanwhile, pick up a cheap workbook for practicing with numbers, or try a few online worksheets from my math resource page.
- Whenever you are ready to try another textbook — next school year, perhaps? — look for one that will focus on conceptual understanding and word problems. I like the Primary Math series, but as you found out before, what works for someone else will not necessarily work for your daughter. If you get a chance to attend a curriculum fair, you may want to take her with you to look around at all the possibilities. Once you decide which math program to try, be sure to use their placement test, so you start working at just the right level.
Learn Math by Playing Games
- Because the number 10 is the foundation of our place value system, your daughter needs to work on the sums that make 10 until she knows them instantly. If you say “6” she needs to be able to say “4” right back at you. At her age, this won’t take long, but it is super-important.
- Practice with a math card game like Tens Concentration.
- Practice the math facts until she is confident, and then practice them some more. Try the game that is worth 1,000 worksheets.
- Play some of the advanced games at the end of my number bonds article.
Practice Mental Math Skills
- Talk about how the pairs that make 10 can help her with mental addition and subtraction. If she needs to add 5+8, she knows that:
- Or here is another way to look at the same problem. (There are many ways to approach any math problem!) To figure out 5+8, your daughter could ask herself, “How many more does 8 need to make 10?”
- If she needs to figure out 13-7, she can do it backwards:
Be sure to notice that you are taking away the 3 and the 4, not taking away the 3 and then adding the 4!
- It may help to use M&Ms or toothpicks to model the numbers, so she can move them around and find the 10. Practice this until she starts thinking in 10s and can immediately recognize them:
And so forth.
- “Finding the 10” may sound too simple for a student your daughter’s age, but this is the most important step, because our number system is set up in tens. In our base 10 place value system:
Moving On to Bigger Numbers
- Now use these same tricks to add or subtract some larger numbers, like her Yahtzee scores. Work in place value columns, but do it differently from what the textbook had her doing. No “carrying” allowed!
- If she is going to add, say, 273+596, have her work from the bigger parts of the numbers to the smaller:
That should give her 7 hundreds, 16 tens, and 9 ones. She can even write it that way, with the 16 in the tens place, as an interim step — have her write the numbers with a wide space between place value columns to allow for this. And then she can easily see that those 16 tens are the same as one more hundred plus 6 tens.
- For subtraction, try the same sort of trick. The next time she needs to subtract something like 462-175, work from the big part to the small part. Start with the hundreds:
Does she understand that 3 hundreds and 6 tens is the same as 36 tens? Now she is ready to take away the 7 tens.
Finally, take away the 5 ones.
- She can work in her head if she wants, but she will probably want to write down the numbers as she goes through the steps, at least until she gets used to working this way. The main thing is to give her a different approach from what the textbook did — no “borrowing”! — and set her free from those negative feelings about math.
Please let me know if these ideas help, or if you have any more questions. Best wishes to you and your daughter on the great adventure of learning math!
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