Our five-year old is in kindergarten and has mastered what they teach for addition/subtraction (he's way past the single digits they are still working on...). He's very interested in multiplication and division. I'm not sure how to best explain these concepts/teach him the basics.
Suggestions for methods or resources? I'd like to feed this interest while it exists, rather than waiting for school to get to it in a year or more.
Of course, you could purchase supplementary curricula, and just pick up mathematics from his mastery level and follow him forward. That would be the most straightforward. But if you don't want to actually accelerate his instruction, just give him age-appropriate mathematical play, then...
For concepts, rather than pursuing computational fluency, I think the most kid-friendly approaches involve everyday context, like dividing trading cards for a group of friends, determining how many smiley fries you need to put in the oven in order for everyone in the family to have a specified amount, and scaling up or down for cooking. Counting pips on playing cards can also be fun, or figuring out how many shoes there are in the family if each person has a certain number of pairs, etc. Comparison shopping with unit pricing is also a useful and natural activity.
A fun and inexpensive DIY is to take two mirror tiles and tape them together along one edge, securely enough that they won't easily separate, but loosely enough that the tape will act as a hinge. (Obviously, tape around the remaining edges too, and maybe some contact paper across the non-reflective side, to reduce the chances of broken glass incidents.) put an object inside the angle between the two mirrored faces, and experiment with how many images you see as the angle increases/decreases. Put multiple objects inside the angle, and you can now play with multiplying by the number of reflections.
I was taught and taught my DS7 multiplication via repeat additions, but it's not mathematically correct.
I agree that concept is more important than fluency for that age. Another idea would be to teach him coins, and there are tons of games that involves money and multiplication/division. e.g. if you have 100 quarters, how much $ do you have?
I think skip counting is often a precursor to multiplication.
I've had this question too. My son loves multiplication and taught himself to multiply while I was sitting around trying to figure out how to teach it to him.
He said he skip counted to teach himself the tables. It made sense to him. He was 5 as well. From doing that he had no problem figuring out 3x5 = 5x3 so it worked for him.
I was leaning toward using math blocks or physical objects to show it.
Have you looked at education unboxed?
These are all great ideas, thank you!
aeh - I used piles of books tonight to teach multiplication and it worked! He caught on in about two-three minutes. (Gulp. This is the child I was second guessing assessing later this spring.) He also was able to take the concept in his head to do multiples of ten. (He's been into tens lately.) We did a few division problems with books and he got that, too.
I'll look at education unboxed, puffin. Is it something you'd recommend?
I used Cheerios and green peas. I placed 1 green pea on the tray and said "1 green pea". Then I stated "1 green pea 1 time is 1 green pea." Then I added another green pea. "1 green pea two times is how many green peas?" He said "2". Then I would state, "Yes. 1 two times is 2." Then I added another green pea. "1 green pea three times is how many green peas?" He said "Three". I said yes, "1 green pea three times is 3". He loved it and would then eat the green peas. Repeat with 2 at a time, then 3, etc. He grabbed onto the concept very quickly. By keeping consistent with the vocabulary, it was easy for him to move from "2 two times is 4" to "2 times 2 is 4".
For division, I gave him 20 dried lima beans. I told him division was taking a group of something and dividing it into piles of that number. For example, 20/2 means you make piles of 2 beans until you have no more beans. I gave him the 20 beans and he made 10 piles of 2. Repeat with 20/4 and 20/5.
Sorry - no workbooks - just playing with food.
Love it! This boy gets more than enough worksheets at school. We'll stick with objects and wordplay for now.
I use the education unboxed videos for me then work with the kids with cuisinere rods.
Multiplication - we taught skip counting and then repeated addition. Since your son is getting the concept quickly, you can expand his basics to 0 times tables (this worked well using the repeated addition method - add nothing 8 times and you are left with nothing. add nothing 100 times and you have nothing etc). Then, introduce 1 times tables, 100 times tables, then 5 times tables and 2 times tables. We did skip counting by the corresponding number before starting on each table.
When it came to memorizing them all, DS had big trouble with 7 times tables. I finally bought a mnemonics based program called "Times Tales" and he picked it up on the 3rd day of using that program. After this, I bought Singapore Math, Miquon with cuisenaire rods and DreamBox to reinforce the concepts.
As for division, we waited a bit for the multiplication to sink in. then, I used food analogies - a box of 20 oranges and 2 friends and each had to get an equal share because it would be unfair otherwise - how many would each get? The concept of being "fair" while distributing a group of things amongst friends seemed to click. For variety, we varied the food that we were discussing, sometimes it was a bunch of Hot wheels, sometimes it was a group of birds sitting on a branch - but to explain that division meant equal parts, we always stuck to the "be fair to the recipients" rule. Division came to DS much quickly than other concepts because we used stick figures with names written on them and gave each of them an equal and fair share of the food or toy in question.