Math Schedule

[VisionaryMom]

I'm trying to put together an overview of what we'll cover this year. Doing so is partly for my own structure needs, but I also agreed that I would come up with a schedule and topics for DH to feel better about homeschooling.

So, I worked on science, social studies, & math this morning. DS is in K. He is most advanced in math, so I'm coming up with math topics based on where I think there may be gaps. Any ideas on what I may be leaving out?

Each month I've planned for a continuous undercurrent of "math facts." He knows addition and subtraction for 1-10, but DH (and I, too, to some degree) would like him to get more automatic with them. I've also planned for a larger "unit" topic. (Just in case you're wondering if it's too much, it's not. DS would do math all day if we let him. We've bought him workbooks - his request - and we had to limit the time he spent on them.)

So, here goes...

July - (just having a slow "intro" week the last week) - Addition 1-5

August - Addition through 10; Unit - Identifying numbers through 100, place values, skip counting (mostly review stuff)

September - Subtraction Through 10; Unit - Telling Time

October - Adding 2-digit numbers; Unit - Counting Money

November - Subtracting 2-digit numbers; Unit - Measurements (English & metric)

December - Review Addition & Subtraction; Unit - Area, Volume, Diameter

January - Introduction to Multiplication (the formal language, he gets the concept); Unit - Introduction to Fractions

February - Multiplication - 0s, 1s, 2s; Unit - "Fun With Numbers" - Counting Backward, Even/Odd, Etc.

March - Multiplication - 3s, 4s; Unit - Patterns

April - Multiplication - 5s; Unit - Roman Numerals

May - Multiplication - 6s; Unit - Number Words

Thoughts? Criticisms?

[moominmamma]

There are a few unit things that I would wonder whether they'd make more sense later. I tend to prefer a mastery approach (and so do my kids), rather than introducing them at a basic level.

For instance, counting money is much easier to teach to mastery after you've learned multiplication by 5's and 10's. So are area and volume.

In my experience mastery of subtraction of multi-digit numbers is very developmental -- not simply an issue of motivation and practice. A child may get it at 5 or 6, but many kids aren't ready to truly master place value and regrouping at the level required for multi-digit addition and subtraction until they're a fair bit older.

Miranda

[VisionaryMom]

DH & I had lunch together and discussed the math units. He also felt we should perhaps push back the area & volume, rather than simply introducing him. I was trying to work in all of the areas of math, but perhaps something more akin to an introduction to 3-dimensional shapes would be better.

Counting money - I don't even really think it's necessary at this age. DC rarely see money because we use debit cards for everything. The reason I have a unit on money is in case we have to send him to a brick & mortar school. DH is still not entirely sold on homeschooling, so we have agreed that I will come up with a plan and give him an update weekly. Then we will re-assess mid-year and then again at the end of the year, so I am trying to cover what he will need to know in that event.

Every K/1st grade math curriculum I've looked at has money somewhere in it, even if it's only dollars & pennies. Maybe I could move it to next summer or try to make it a point to do some of our smaller shopping trips with cash. I will have to think about the best approach.

Okay, on the addition & subtraction. DS can do 2-digits in his head, so if I ask 12+13, he will say 25. For 2-digit subtraction, he has to think about it a bit more and sometimes go by himself for a few minutes, but he answers right. That is what he's gleaned just from observation.

When I show him the information written out, he has a harder time with it. So I've been showing him the various ways to write out math problems and what the symbols mean. I have not introduced "carrying" or "borrowing" because he does them intuitively. I know that I will need to, though, because 1) I want him to understand the full concept and 2) he will need them for 3+-digit addition and subtraction that he cannot do in his head right now.

Learning those things was the reasoning behind doing the facts as a background lesson for me. I think sitting and just doing addition and subtraction everyday for math just wouldn't be as useful. He's happy to spend his playtime doing math worksheets, but he doesn't need me to "teach" beyond the introduction of the concept.

I showed him a simple equation a few weeks ago and then gave him 5 examples. He got all of them right but wrote none of the steps. He just put "X= [answer]." When I asked him about the steps, he said he didn't need them. True, but a teacher will want them. (Believe me, I've had this conversation with a few middle school math teachers myself.) So that's what's going on there. Maybe I am wrong, and we would be better off just focusing on the facts for a while. I'm afraid of carrying out the basic operations to their logical conclusion and missing even an introduction to other areas.

Luckily for me, other areas should be much simpler to plan.

[moominmamma]

Originally Posted by VisionaryMom

Okay, on the addition & subtraction. DS can do 2-digits in his head, so if I ask 12+13, he will say 25.

I had a kid who learning multi-digit addition and subtraction algorithms at 5 quite easily. She too was doing two-digit mental math like 12 + 13 quite young. For some kids it just clicks and they easily see the connection between the regrouping they're doing in their head and the pencil-and-paper procedure for managing larger numbers. For some kids it doesn't click as easily. They can "see" their way to a solution, but they don't dissect their thinking process into steps.

If your guy can add 19 and 26 in his head, ask him how he's doing it. If he can explain that, for instance, he adds the 10 and the 20 to get 30, and then adds the 9 and the 6 to get 15, and then puts together the two answers, 30 and 15, to get a final sum of 45, he's stands a very good chance of being able to master the addition and subtraction algorithms this year. He can explain his thinking process in a step-wise way, he'll probably do well learning those step-wise algorithms and connecting them to the concepts they rely upon.

If on the other hand he says "I don't know, I just got the answer," I would think it would be much iffier whether he's ready to learn multi-digit algorithms. If it turns out he struggles to make sense of the algorithms, I would caution you against pushing him to rote-memorize them. Instead I would do what most Asian math programs do, which is to focus on addition and subtraction within 20 and multiplication within 50, exploring those inside and out with plenty of twists and games and manipulatives to ensure that he learns the basics with tangible numbers as deeply and broadly as possible. Constructing and deconstructing 10's in a kazillion ways. Working with pairs and patterns. Integrating addition and subtraction and multiplication of small numbers. That sort of thing.

In other words, it's great to have a plan, but be prepared to change things up depending on how it goes and what he seems ready for. A fair bit of math and reading stuff is developmental rather than practice and motivation related. Far better to deeply learn what "fits" his brain now than to push the envelope and risk frustration and the use of faulty or inefficient learning mechanisms.

Miranda

[kathymuggle]

You have spent a fair bit of time on adding, subtracting and multiplication - more than I would.

I think something you need to get clear on is if you intend that he memorise the times table or figure it out. There are arguments on both sides, and I will dig up a thread or two for you in a moment.

Here is one: http://www.mothering.com/discussions...highlight=math


In any event - if memorisation is the goal, I would drop the 6 times table (unless he is clamouring for it) and simply do the 0, 1,2,5,10. Save the other ones for next year.

I would spend more time focusing on fun things: pattern, fractions, lines of symmetry, tannegrams, logic games etc. Check out mathcats for some ideas.:

http://www.mathcats.com/

I would also include some books with math. Check out the Living Math site. Do not neglect math games that build skills - cards, etc.

http://www.livingmath.net/


I would seriously consider introducing chess and/or music to him - both help children develop strong math sense.

[VisionaryMom]

Originally Posted by kathymuggle

You have spent a fair bit of time on adding, subtracting and multiplication - more than I would.

I think something you need to get clear on is if you intend that he memorise the times table or figure it out. There are arguments on both sides, and I will dig up a thread or two for you in a moment.

Here is one: http://www.mothering.com/discussions...highlight=math


In any event - if memorisation is the goal, I would drop the 6 times table (unless he is clamouring for it) and simply do the 0, 1,2,5,10. Save the other ones for next year.

I have mixed feelings on memorization. I personally know adults who can't do basic multiplication and division without a calculator, and that's not something I want for DC. I think overall I feel that basic operations are just the foundation of what you need to know, just as the sound B makes and the exceptions are the basis of reading. So it's helpful if he has them learned by memorization, or at least not need to think about them, and then can use those skills in higher-level math as he moves along.

I don't know that I'll spend much time on addition & subtraction, just because as DH pointed out, he already knows most of what I have until the end of the year. I'd rather just give him some problems and then move on when he can complete them comfortably. That's my plan anyway.

I have no idea how quickly we actually will move through what I listed. That's my ideal plan for now, but it's flexible if needed. I'm not going to force either doing 100 problems a day to keep where we are or push forward if he doesn't understand.

Originally Posted by kathymuggle

I would spend more time focusing on fun things: pattern, fractions, lines of symmetry, tannegrams, logic games etc. Check out mathcats for some ideas.:

http://www.mathcats.com/

I like this site! I haven't visited it before, but I think it has some games DS will enjoy. We do lots of puzzle and logic games, tangrams, etc. I may incorporate more.

I'd love ideas for patterns. I've tried quite a few pattern books and games, and DS gets the answer quickly and without effort. Then he gets bored and moves on. He has an uncanny ability for seeing patterns. About a year ago, I was doing a word search - stress relief! - and he came up and starting pointing out words. He couldn't read them, but he would look at the list and then get this glassy-eyed stare at the puzzle to find them. He could find them faster than DH or I could, and I have to say we're good at these things. He *loves* that kind of thing. With elementary pattern books, he tends to say "duh. The answer's X" and then look at me like he can't believe I asked him that question.

Originally Posted by kathymuggle

I would also include some books with math. Check out the Living Math site. Do not neglect math games that build skills - cards, etc.

You mean like Texas Hold 'Em? He asked to play poker; maybe we could teach him card counting without getting caught. Anyway, yes we play Uno and other simple games, but we probably could add to our repertoire a bit.

Originally Posted by kathymuggle

I would seriously consider introducing chess and/or music to him - both help children develop strong math sense.

We've been gifted a piano. I just have to go pick it up from my ILs house, and I'm hoping to do that in early August. I haven't played chess in ages. I should consider introducing it to him.

[VisionaryMom]

Originally Posted by moominmamma

If your guy can add 19 and 26 in his head, ask him how he's doing it. If he can explain that, for instance, he adds the 10 and the 20 to get 30, and then adds the 9 and the 6 to get 15, and then puts together the two answers, 30 and 15, to get a final sum of 45, he's stands a very good chance of being able to master the addition and subtraction algorithms this year. He can explain his thinking process in a step-wise way, he'll probably do well learning those step-wise algorithms and connecting them to the concepts they rely upon.

If on the other hand he says "I don't know, I just got the answer," I would think it would be much iffier whether he's ready to learn multi-digit algorithms.

My husband is degreed in math, and he cannot explain how he does multi-digit operational math. Don't even get him started on his feelings about theorems. We've had this conversation before. Both DH & I are math-oriented. I can give explanations; DH can't. We've both taken highly advanced math courses. We have different strength areas, but I think the difference is in communication skills rather than math ability.

I know that DS knows what adding means. I will teach him the symbols and the generally-accepted written process. He can see patterns and connections in numbers that are intuitive to our family but I know are struggles for many people, and he mentions them to me.

I would not push a child who didn't understand what subtraction was, but I don't think that doing math on worksheets until he knows the answers more quickly is necessarily bad. The reason I'm not a fan of things like saying that he will pick up math in everyday life (and I know you're not saying this, but it's the common opposition) is that I anticipate him wanting and needing higher math later in his life. The math we all do on a daily basis is pretty minimal. Plus we're math nerds. Go, Mathletes! Puzzles and games are a hobby in our house in the same way others knit or write poetry.

Originally Posted by moominmamma

In other words, it's great to have a plan, but be prepared to change things up depending on how it goes and what he seems ready for. A fair bit of math and reading stuff is developmental rather than practice and motivation related. Far better to deeply learn what "fits" his brain now than to push the envelope and risk frustration and the use of faulty or inefficient learning mechanisms.

Oh, I know I'll need to be flexible. I may be moving too quickly, though I don't think so. If anything, I think we're moving too slowly. I explained multiplication and gave him a few word problems scenarios. He got them without trouble, so I think by the end of next year, he'll be ready to delve in. I'm honestly concerned about his desire to do math over learning to read. He's said, "no, I don't want to read. I like numbers." :sigh

[AAK]

You mentioned removing volume for a while. Which, I get if you mean calculating volume. But, while you are studying measurements--it can be fun to play with volume. Give him different sized containers and let him discover the equivalencies himself rather than just listing/memorizing them. Then, you can challenge him to figure out problems that involve volume.

Building different three-dimentional shapes is also fun and can introduce geometry without a lot of calculation.

Does he work with negative numbers? With a kid as mathematically inclined as yours seems to be, I would introduce them. Depending on how that goes, I may also give him addition sentences with negative numbers. It allows you to take a concept further.

Comparing numbers, comparing equations (greater than, less than, equal).
And, finally, how about using graphs and charts. I don't see it on your list, yet it is usually included in math curriculums.

Amy

[VisionaryMom]

Originally Posted by AAK

You mentioned removing volume for a while. Which, I get if you mean calculating volume. But, while you are studying measurements--it can be fun to play with volume. Give him different sized containers and let him discover the equivalencies himself rather than just listing/memorizing them. Then, you can challenge him to figure out problems that involve volume.

Building different three-dimentional shapes is also fun and can introduce geometry without a lot of calculation.

I like these ideas. I will try to incorporate them.

Originally Posted by AAK

Does he work with negative numbers? With a kid as mathematically inclined as yours seems to be, I would introduce them. Depending on how that goes, I may also give him addition sentences with negative numbers. It allows you to take a concept further.

He has asked some questions that have introduced negative numbers. "What happens if you try to subtract 5 from 3?" "Can there be less than zero?" So we could do more with talking about negative numbers.

Originally Posted by AAK

Comparing numbers, comparing equations (greater than, less than, equal).
And, finally, how about using graphs and charts. I don't see it on your list, yet it is usually included in math curriculums.

We've done lots of comparison problems and greater than/less than/equal. I could do something a bit more advanced with those - comparing groupings of numbers.

Yes, I did leave out charts and graphs. I thought about that later this afternoon. It's probably because I never enjoyed units on graphs and charts, so I tend not to think about it. I'm excited about everything else!

[mom2ponygirl]

Originally Posted by VisionaryMom

I'm honestly concerned about his desire to do math over learning to read. He's said, "no, I don't want to read. I like numbers." :sigh

Oh, this is easy. Go to www.livingmath.net and check out fun math books. I remember dd enjoying Penrose the Mathematical Cat and The Number Devil.

The website has listings for books based on concepts you are learning/teaching.
http://livingmath.net/ReadersbyConce...8/Default.aspx

Perhaps finding books with cool stuff about numbers will win him over. LOL

[AAK]

Originally Posted by VisionaryMom

Yes, I did leave out charts and graphs. I thought about that later this afternoon. It's probably because I never enjoyed units on graphs and charts, so I tend not to think about it. I'm excited about everything else!

Skip the workbooks stuff for graphs. Instead, make it real life learning. If he has a package of m&ms fore example, make a bar graph comparing colors or a pie chart or whatever. While waiting in line for something, pick something to count and compare--how many people are wearing sneakers vs dress shoes vs flip flops. And then, when reading show him how people use graphs to illustrate the information. Chart the weather at home and use a line graph to show patterns in temperature.

Amy

[Amanda Williams]

EXCELLENT ideas, Amy. Thank you for sharing.