Today, I'm going to help a mom with a math facts problem. Her daughter is going to knock off 1st grade math in preparation for first grade, but she hit a wall on subtracting numbers up to 20.

Let's take 19 - 7. Your child can't get it? OK, here's what you do.

There are really 3 problems here, and not one. The first problem is 19 - 7. This problem is way too hard, and math geniuses don't bother to solve this, because they know that math is all about cheating and shortcuts and being lazy. That's what makes them math geniuses. The second problem is to figure out an easier way to do this. That's the real problem. One answer is 10 + 9 - 7. Some kids will come up with a different problem each time, like 10 + 5 + 4 - 4 - 3, or 10 + 4 - 4 + 4 - 3 or whatever.

The third problem is to solve the easier problem, which is easy because it's an easier problem. 9 - 7 = 2, and add 10 back and you've got 12.

Of course, this brings up 2 new problems, one for the parent and one for the child.

The parent's problem is that 19 - 7 is totally doable, and you know it is, and you know kids who can do this. You just don't know how to get there and your daughter is now crying because she can see that you expect her to get this problem, as does the book, and it's totally frustrating. When she was one year old, she would happily stumble around like a drunk trying to walk, and she was smiling and the parents were all excited and laughing and totally excited because she stood on one leg for .3 of a second. Then math books come along and we totally crush this natural love of learning out of the child.

I think the biggest problem all along is the parent problem. Don't ask for 9 + 7 = ? or 19 - 7 = ?, just ask for a better, easier, cheaty problem. You'll get something from your child, usually not what you expect, and that's OK, because the kid owns the problem is about to fall over again, which is also totally OK. Then when they announce 10 + 8 - 7, which is totally wrong, and get 3, which is also totally wrong, you're going to be 100% excited and announce GOOD JOB, but the kid just got it wrong and will have to do it again.

If I can get all parents to spend 10 minutes with their children on every simple math problem and be excited about wrong answers, math scores in this country would double. I say 10 minutes because we're no longer trying to memorize or count, we're trying to think, and this makes every problem really hard and take a long time. So instead of plowing through 30 math facts and learning nothing, your child might only do 4 or 5 math facts - or even worse - only 1 - and end up with a great tool set.

But back to the last problem which is the child's problem. Getting from 19 - 7 to 10 + 9 - 7 = 2 is a skill that requires some practice, so you'll have to back track to "the second half" numbers, which are 6 to 9 and start over will 6 + 5 = 5 + 5 + 1, and 7 + 7 = 5 + 2 + 5 + 2 (until your child memorizes doubles on their own). If you do problems this way, you not only teach your child math facts, because kids can't help but learn them, but you teach higher order math analysis which is needed beyond 1st grade.

If you can do math facts properly like I describe above, then your child is prepared for what comes next, because all math after that involves breaking down and analyzing.

When I wrote Test Prep Math Level 2 and Test Prep Math Level 3, this is what I was thinking. (These books are way to hard for 1st grade, by the way.) My target is 2nd through 4th grade kids who will be facing the 4th Grade Train Wreck. The forth grade train wreck is what happens when the child spends 3 years doing math facts and ends up unable to think. Sometimes it hits in 5th grade and sometimes 7th.. The focus of these books is problem analysis, going slow, only doing a few problems at a time, and doing them over. I added other key skills for both parent and child, including spending a long time trying to figure out what my goofy convoluted questions are asking, solving multiple problems at once in one problem, learning abstract thinking, having to check the answer and redo a problem, and trying to solve a clock problem when one of the main characters has a time machine (Level 3).

My son was doing a clock problem out of his 3rd grade school math book. "If Suzie finished her homework at 4:15, and it took her 45 minutes. When did she start?" He brought me his book and showed me this problem and we both burst out laughing.

Here's a question from Level 3 that is entirely doable, but might need a few tries and take a long time.

In the center of Metroville,
there is a super villain named Destructovil breaking into the Metroville
bank. Rubberband girl got a distress
call on her cell phone, but she is on the south end of the city in a train
station. There is a train leaving at
3:00 pm that will take her to the Metroville bank. The train takes 12 minutes to go from the
train station to the bank. She has to
wait 4 minutes for the train. Speedy Man
is in the next town over, but he can get to the bank in 8 minutes because he is
Speedy Man. First, he needs to finish
his cup of lemonade because he's too thirsty to be speedy. That will take 7 minutes. It is a very large cup of lemonade. Destructovil's getaway car is coming to pick
him up at exactly 3:14 pm. Who will save
the bank?

Bonus Question: Who is Rubberband girl?I should advertise these books more. They completely reorient kids and parents back to real math from the garbage that is in math text books. There is another section that has problems that look like this:

35 + 26 = 8 F + 5

3 F – 16 = 33 - ?Then they get really hard after that, especially when I introduce a third equation involving G and "not F".

I through this last section in, 120 problems in all, for the following reasons: COGAT Test Prep books cost about $30 and are usually too easy. Many kids have to take the COGAT between 2nd and 3rd grade and there is very little material on the market. Plus, as a micro publisher, my publishing costs are higher than I would like. So I put in the equivalent of a test prep book, just for the quantitative section of the test, with all questions 4 TIMES as hard as what I expect to be on the test.

My poor 7 year old had to be the editor because my 10 year old was in charge of question themes and character development. He ended up on that roll after pointing out that some of my questions were lame. After getting every problem wrong multiple times, the little guy ended up way beyond the 99th percentile and lately we've been covering arithmetic operations on fractions because I've run out on ideas. The older kid ended up at the 95% level, which is great because he hates math. It was a huge and welcome leap to 95%, but we have some work to do. By the way, he hates math because we practiced math facts, and when we began working ahead in math, I expected him to get the answers correct.

I'm not sure how a parent is going to fair with an 8 year old on that question with "F" in it. It took my child (the test prep poster child) about 2 weeks before he could do these, and then only after making a lot of progress on the first section to pick up the skills needed. My 4th grader couldn't get algebra type questions at all out of his SAT test prep book (there are articles in here some where on why I was experimenting with this) and this question type totally solved the problem.

Amazing blog and so awesome that you share. In the week since I read this blog and started spending time with my daughter and son, I can already see the benefits.

ReplyDeleteQuick question....what sequence of topics did you follow when teaching math in the 3-6 age group...like start off with addition, subtraction, skip by 2s, skip by 10s...?

Also my daughter's preschool uses the abacus for adding. Any opinion on that versus finger counting?

How do you progress to mental math addition?

Thanks,

ML

I answered your question in the next article. I think my kids used the abacus in school at some point. I never taught anything related to arithmetic. By the time my child was doing something like 34 - 27, he had his own models at work that he build on his own.

DeleteThanks much.

ReplyDelete- ML

Norwood, My son is somewhere on the 50th question of your book Test Prep Math Level 3 and I have to compliment you on not only trying to keep them jogging their comprehension skills but also keeping their humor going. I often catch him chuckling or rolling with laughter (farm jokes and party balloons where mom will not be very happy).

ReplyDeleteHe loves to work his way through it because it is almost like Sadlier Oxford. Every once in a while he may make an error because he is not in the 'mood'. However, he loves your bonus questions and loves to challenge you for example missing details in a question (#44 , I think) to computation error in one (you may need to edit that or may have done so already with the next edition).

I have to keep him off that book and how I wish you have the next level ready soon.

The next level is 5th grade mathematics, which is really good, so I'm not doing a Level 4. I'm thinking about a level 1. Any issues with the solutions, feel free to send me the question # so I can add it to the next addition.

Delete