Maths with big numbers

[momtobaby]

Dear EL moms and dads,

I was just wondering if you could share some ideas on how to teach your toddler maths with big numbers (for eg. addition and subtraction using 2 digit and 3 digit numbers) . My toddler is 2.5 years old now and we have been doing addition and subtraction using 1 digit numbers. She cannot add two digits in her head yet, she needs to count them physically. Is there any way I can teach her how to do the same without counting physically the number of objects she need to add or take away?She knows how to count quantities to a 100. I mean, if you give her 100 items she will count the items in order till 100 or how much ever qty I gave her. With the current method of counting4 items to add them up will get difficult as we move on to bigger numbers. Any advice will be much appreciated. Thanks a lot in advance.
Regards,
momtobaby

[Tamsyn]

Using cuisenaire rods with a centimeter ruler helped my kids start adding without counting.  We went to the dollar store and bought them each a ruler and they were excited to use them.  By lining a 5-rod up with a 6-rod, they can immediately see that it is 11, and so on.  My kids love playing with manipulatives, and their mental math has improved as well.

[Korrale4kq]

Emphasis place vaue. Write the equations on grid paper or paper with colums. Adding 345+428 is just like adding 5+8, 4+2, 3+4.

[Mandabplus3]

Yes I agree teach place value
 Teach it strongly and teach it with NO thought of teaching addition or subtraction for the moment. Put the equations aside and teach place value then add the equations back in once you have it sorted.
I taught place value to my 6 year old ( at age 5 from memory) using Montessori place value cards. They overlap so you can put them together by stacking the 600 and the 70 and the 3 to get the number 673. Pure genius. I printed mine the first time lost them and en just made then myself after but I would recommend buying the full set. Their large wooden. Numbers are beautiful to work with. ( postage killed it as an option for me!) my boy learnt place numbers looking on as I taught his sister and then figured out what it all means on the right start abacus.
If you just want to teach large number additions and subtraction use an abacus. If you want them to understand why teach place value, even better do both 
To teach place value I called out numbers and we built them then pulled them apart and examined the parts. After she could do that independently I would ask her to built a number then add ten more or add 1 more or take 100 away.

[Tamsyn]

I haven't done a lot with Math-U-See besides buy the manipulative blocks and make a decimal street poster, but it really did help my kids with place value.  The sample lesson on the primer page was really helpful for that:  http://store.mathusee.com/catalog/general-math/primer/

Here is a link to our decimal street poster:  http://www.professional-mothering.com/2011/01/decimal-street.html

Naturally you don't have to have the blocks to do something like this.  My Mom said that some of her older kids didn't really understand place value until they got to play with some base 10 blocks.

[lzp11]

I am teaching place value to my 3.5 year old using place value cards and a rightstart abacus and she seems to be getting on with it quite well.  We just bought some cheap cards from ebay and they are working for us.

If you are not familiar with Rightstart, they suggest teaching a different way of counting to help understand large numbers -
11 becomes ten-one
20 is two-ten, 21 is two-ten-one
84 is eight-ten-four etc

We use the abacus to make sense of these numbers.  We are practicing skip counting in 10s using both the 'normal' and the 'rightstart' way of counting (I just ask - what is the other name for this number?).  Then I ask her to find "eight-ten" by pushing across eight of the rows of ten and then add however many additional beads are needed. 

We are not yet doing addition with larger numbers but I think this will provide a really good basis for it.  Using the abacus has been a very good visual method for teaching addition up to 10 as well, without counting, as she can subsitize the answer by looking at the abacus.

[momtobaby]

Thanks everyone for the lovely ideas.....I have already introduced place value to my baby. We bought this place value flip book and now she can read large numbers using them (for eg. the number 21,345 she will read it as 21 thousand 3 hundred and 45 ). I also made my own base 10 blocks and we do make large numbers using them. I was more interested to know how to get my child to start doing mental maths, because even now if I ask her what 2+3 she will have to coint the numbers of items to get the answer. Do you think if I continue with the place value games she will eventually get it?

[TeachingMyToddlers]

How funny that I run across this topic, I JUST made a set of these cards for my kids a few days ago. I took some pictures tonight so anyone considering it can see the materials I used.

http://teachingmytoddlers.blogspot.com/2013/01/teaching-place-value-diy-montessori-way.html

[Kerileanne99]

TmT-
I love that you have done it in LMs colors
Great work. 
If you are a bit lazier like myself, I found one a few months ago on Confessions of a Homeschooler. I emailed the file to Kinkos and then picked it up   It ended up costing about $6.00, but Alex played with it forever! She also did a money one on this same link if anyone is interested:
http://shared.confessionsofahomeschooler.com/math/PlaceValueBoard.pdf

Momtobaby:
When Alex was at that point in addition and subtraction, where I knew she had a firm grasp on the concept, but needed practice and non-counting practice, I approached it a couple of different ways.
We use an abacus with focus on grouping by fives and tens, a hundreds board, and flashcards for memorizing math facts up to ten.  I would show her the cards or give her equations, stressing commutative property. If she knew it she would shout it, but if not I allowed her to work it out on the abacus, her fingers, or manipulatives.  This also helps them learn it. and of course, when I ask her a question such as what is four plus two, I also say, or four plus two. i did this for all equations in arithmetic.
At the same time we worked on patterns using the hundreds chart and abacus: looking at the rows and columns. For example, I would say what is five plus three? Now add ten, and ten more, etc...
That way when your child has the 0-10 facts down, it is a simple jump to doing the same thing for larger numbers. Also highly recommend the RS, 'math' way of counting as Izp11 mentioned...

Also, lots of skip counting practice, counting forwards and backwards (at least as often!). Whenever Alex had to wait for something I had her count as quickly as she could both forwards and backwards, which also works wonders with patience stretching! We practiced daily on the abacus, moving beads whilst counting, by 1's, 2's, 3's, 5's, 10's, etc., both forwards and backwards.

And of course, Singapore style number bonds: a big circle at the top with two 'legs' with circles to show the relationship between the parts of the equations. I think this really helps quickly learn to do the operations 'forwards' and 'backwards', and she still loves to segment equations...

And if all else fails, back up a bit...ask equations that involve adding only ones, then do adding twos, etc...this is how such drill books as Kumon encourages mastery, and I can see how it would be very effective...I would do this all the way up through the ten facts. Possibly as we did using a worksheet with number stamps instead of writing, then reinforcing the patterns on the hundreds board for bigger numbers.

When you get to addition with regrouping, I LOVE the RS methods for reorganizing and thinking in terms of grouping in fives and tens.

Oh!
And invest in card games and board games. Definitely Hi-Ho Cherry-o, Sum Swamp, chutes and ladders, and some of the RS games, plus a pack of cards like UNO that can be used for all sorts of games!
 
Hope that's along the lines of what you are looking for

[Jenene]

Tamsyn, your place value street is so cute.  My son would have loved this. 

[Chip201]

For practicing big numbers and speeding up your mental math try: www.calculationrankings.com

Chip

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