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How do you use Base 10 blocks?

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I just bought my first set of Base 10 blocks and have no idea how to use them. Any links or guidance? We use Singapore and Miquon Math if that makes a difference. I do not have the TM for Singapore 1A/1B. Would that have spelled-out activites/suggestions?


(I don't think I have posted this question already. I had it all typed out a few days back and then got a phone call and had to leave my computer, so I am fairly certain I deleted it. :tongue_smilie:)

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I used them when we got to renaming/carrying (whatever you want to call it!). I had some poster board with columns for hundreds, tens, and ones. May have even had thousands. We counted unit blocks in the ones column and talked about only having room for 9. When we added one more, we took those away a put stick of 10 in the tens column. We also looked at having 9 tens and counting out 9 ones and then looked at what we needed to do when we added the tenth 1--renamed the 9 ones with a stick of 10--oops, too many 10s so renamed 10 10s as 1 "waffle" of 100. Anyway, we did stuff like that when learning renaming for addition and it was probably even more helpful for subtraction. One day of it was enough to "get it", so we haven't used them a lot, but they were very useful to illustrate the concept. But mostly my girls sneak them out of my room and pretend the 100's are waffles. They get very creative with their math manipulatives!

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Ds8 had trouble with subtracting one he got to double digits. So I bought the sinle squares, tens and hundreds cubes. I would go through each problem with him and show it to him.


Ex: 324 -119


I would put out three hundreds, two tens, and nine ones, then I would remove the 119. Afterwards I would also show him how to write it and work it out. For some reason this was the only way he could get it and it worked like a charm. He continued to pull tham out on his own for awhile to be sure, and ds10 has used them to work out word problems.


Ex: Sam has 20 eggs and puts them into 4 boxes.


He lays out twenty singles and then acts like he is sorting them into 4 groups. Harder problems of coarse. He struggles with word problems. If you give him the same problem in a number sentence he gets right to it, but struggles with word problems. Vast improvement recently though. Hope this helps.



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I use them to help work out problems. It would really help when SM does number bonds. You can separate out 67 + 3 to 60 + 7 + 3. THis makes it a bit easier to add.


My 6yo dd really likes counting up to add, but sometimes she counts wrong. When she uses the base 10 blocks she is a bit more accurate. They illustrate adding larger numbers together really well.


Another way I've used them is to roll a dice and add on x many. Then once you get to 10 you have to trade in and keep going. Playing this as a game really helped my older dd when it came to crossing over from 98 to 103. She could see that it is only a small difference.



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  • 2 weeks later...

I use the base 10 blocks as the basis of our math learning. I first use them for counting, showing a 1 to 1 correspondence between blocks and items to be counted. I use them to introduce the basics of adding and subtracting. I use them for more difficult concepts too, such as how to explain long division BEFORE showing it on paper (so it makes sense why we write the numbers down below, and there is no confusion as to which column to put the numbers in) and also for doing math with decimals. I use two sets of the base 10 blocks that include the red thousand cube along with the number strips (bought through Right Start, but also used in Singapore Primary Mathematics books).


I keep the rods grouped by type, with the 1s in the lid of the box, the 10s in the other lid, and the 100s lined up in the bottom of the box they came in. They all stack nicely this way when we put them away. I set them up on the table with the 1000s on the left, then each box in proper place value order. This gives a great visual for place value, something my son has never been confused on because he learned it so concretely! Then below those (ie closer to the child) I have a work area, so any time he needs to "trade in" for a larger or smaller block, he is physically putting it into the proper column.


For addition, we lay the rods out just like the problem is laid out, with the top number on top (closer to the rods) and the bottom number on the bottom (closer to the child), then starting with the 1 blocks, we scoot them together, and "trade in" if we get more than 10.


For subtraction, we start with the top number, then scoot down the number we are subtracting. So if the problem is 234-51, we scoot down 1, but since we can't subtract 5 tens from 3 tens, we have to trade in a 100 for 10 tens. Now we have 13 tens, so we scoot down 5. We don't have to scoot down any 100s, but there is only 1 left because we traded 1 in. So, the answer is what remains at the top.


I also use the full term for each number, not just the digit. When you trade in a 100, you get 10 TENS, not just 10. The new number at the top is 13 TENS, not just 13. It doesn't seem like a big deal to say just the digit (that's how I learned in school), but it really does make a difference when you get to long division.


For word problems, we use the blocks as if they were in the model method. We have a little drawn out area for the unit, and use that for the problem. For example, "Sue has 12 apples, Sally has 4 apples fewer than Sue. How many apples does Sally have?" We draw a long bar on top (ideally one that perfectly fits 12 blocks), with a smaller bar underneath that we place 4 blocks in, and an empty bar next to that to draw in a question mark. We use a large laminated piece of paper for this, then draw with dry erase markers where we need the bars.


For multiplication, we just make groups of how many we need. So for 12 x 5, we would make 5 groups of 12. At first we would also make 12 groups of 5 to see that they are the same (trading in as needed). It doesn't work when you get to larger numbers, but by then they know the method on paper and should no longer need the concrete example.


For simple division, we just divide them into groups. For 12 / 4, we start with 12, trade in the 10 for ten 1s, then divide them up putting 4 in each group. How many groups do we end up with? How many would be in each group if we divide them up into 4 equal groups instead?


For long division, we use ONLY the blocks first, but I explain it as if I was having him write it down. Like this: We have 135 / 4. That means we have 135 of something, and want to divide it up equally to 4 people. Instead of starting with the 1s like with subtraction, we are going to start with the largest block. We can't divide 100 into 4 groups, so each person will get ZERO 100s. We trade that in for 10 tens, giving us 13 tens. If we divide those up into the 4 groups, we use 12 tens with 1 ten left over (important to point this step out, so it makes sense why this step is included on the paper version of this problem). We then trade this 1 ten in for 10 ones, giving us 15 ones. We have enough to give each person 3 ones which uses up 12 ones but leaves us with 3 ones remaining. We don't have enough to divide up equally, and we don't have anything left we can trade in for, so these are called the remainder.


After doing several on his own with the blocks, I show him how it translates to doing it on paper. We do one step with the blocks, then I show him where those numbers go. We use the Math Notes paper for this, so he can clearly see the columns and he knows that you can't move digits between columns. It also helps him know where to put the numbers for the quotient, as he just has to follow the column up.


I suppose you could use base 10 blocks for fractions, but we use the Rainbow Fraction Tiles instead, as they are much more effective. He can visually see which fractions are larger, equal, or able to be reduced. I have all the tiles on the board, with the 1 at the bottom and the smallest fractions at the top. If you add 1/12 and 5/12, you count over 6/12, then you follow the "crack" after the 6th one down, seeing that it can be reduced to 1/2. When working with different denominators, you can switch the tiles around as long as they are the same total size (ie switch the 1/2 tile for two 1/4 tiles when adding 1/4 plus 1/2).


I use the base 10 blocks for decimals, with a slight change to them. I explain that decimals are tiny little numbers, so we have to make them larger, like looking into a microscope. The 1000 block now becomes the 1, the 100 block now becomes a "slice" that equals 1 tenth of one. The 10 block becomes a "stick", equal to 1 hundredth of 1. The 1 block becomes a "speck", equal to 1 thousandth of 1. We line the blocks up in the same way, with something between the 1 and the tenth to indicate a decimal point. He can clearly see that 10 thousandths make up 1 hundredth, and that 12 hundredths means 1 tenth and 2 hundredths.


I also use base 10 blocks for metric measurement -- each 1 block is 1 cm, so we can use 1s and 10s to measure things in cm. We can also use the blocks to represent grams or liters. Since he is familiar with how to trade in, he can easily figure out how to convert grams to milligrams.


I use the 1s on top of the 100 for area/perimeter. How many squares does this shape cover up? That is the area. How many pieces of fence would we need to go around this shape? That is the perimeter. You can also use the 100s to make a shape, then use the 10s to find the perimeter.


I use 1s for volume. If something is 2 units tall, 4 units long, and 3 units wide, how many blocks does it use?


We also use them to show that you can hold more weight if it is distributed (place a 100 on top of 10s).


And almost daily, we use them to build very elaborate towers. :)

Edited by Colleen in SEVA
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