# Number Sense

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Hello,

How did you get your child to develop number sense?  What games did you do?  I don't want worksheets.

I have a child who is a bit flexible with numbers.  So, this child can say 1+1+2 = 4, but I want to work on moving numbers around.  For example, if given 21 - 16, this child would break 16 into 10 and 6, then subtract 10 from 21, then subtract 5 from 11, then subtract 1.  I think this is fine, but I want this child to realize that 21 - 16 is the same as 20-15.

To be more clear, this child knows her math facts (addition to 10; 1+9, 2+8, etc).  However, when I ask what is 90-82, this child borrows from the tens digit to subtract 2 from 10.  Which is fine, but I want this child to realize that since 2 and 8 make ten, then the answer is 8.  I hope I am making sense.

It seems that I want this child to make a leap.  Applying the math facts she knows.

Any ideas/games?  Thanks in advance.

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Number sense develops over time, as long as children are not permitted to use a calculator.

Aside from doing actual math problems, children develop number sense through card and dice games, baking/cooking, shopping and making change, sharing items among family members, sorting toys/items, arranging things in patterns, doing crafts (lots of math in crochet).

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We use Rightstart, and it does quite a bit of that.

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Singapore math does a great job of developing number sense.  We also used blocks so that they physically manipulate them to see how it worked.  We didn't use unifix blocks-just plain ones.

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Cuisenaire rods are fabulous for that.  You can pair them up with Education Unboxed or Gattegno Math for activities to help them visualize better.

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Ok. Thanks everyone.

I think I'm a little worried about something.  I noticed in BA 2A that BA was teaching addition in different ways.  My child generally resorted to the first way this child learned how to add. I'm seeing the same thing in BA 2B which seems to be about subtraction.

I guess just give it more time?

Kiara - which rightstart would help my child with this leap.  This child has done A and I have B.  Would B help?

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I think time, yes.
DS does Right Start and one thing I like is that the beginning of each level goes over ways to add/subtract again in the review lessons.  DS can do this no problem, but having the lessons reintroduced over and over helps him to practice the various methods and internalize them better.

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Remember when your children were infants and everyone would tell you to do a running commentary of everything you were doing so your child would hear tons of language and hopefully talk soon and have a larger vocabulary?

I do the same thing when I do example math problems when they are older. I may even model more than one way and show that no matter what way I do it, I still get the same answer. I say outloud, every step I have to go through to get the answer mentally.

So for example, if I wanted to show the correlation between 21-16 and 20-15, I would say something like, " If I take one away from both numbers, I get 20-15 which is much easier to get the answer for in my head. I know it is the same problem because I took the same amount away from both of the original numbers. So I know the answer is 5."

Other thing I often did was have them do a problem and explain to me how they came up with the answer. Then ask them to show me another way they could have solved it. As someone else said Cuisenaire rods are fabulous for seeing the correlations between numbers.

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She's quite young. Number sense takes time and time and time to develop. However, you can try picking up the Peggy Kaye book Games for Math, which is right about her speed, and simply having her spend more time working with numbers - adding up scores on games (even if not specifically math games), cooking, doing basic carpentry and sewing (lots of measuring!), and always, always estimating answers in her curriculum before she solves them. That last step is tedious, but I'm convinced it's crucial.

Note: Any number games that involve dice, like shut-the-box, can be done using special ten or twelve sided dice instead of six sided dice, once she gets the basics down.

Quote

To be more clear, this child knows her math facts (addition to 10; 1+9, 2+8, etc).  However, when I ask what is 90-82, this child borrows from the tens digit to subtract 2 from 10.  Which is fine, but I want this child to realize that since 2 and 8 make ten, then the answer is 8.  I hope I am making sense.

One question - does she know how to subtract by counting up? Using her fingers (or not) and saying "83, 84, 85, 86, 87, 88, 89, 90! That's eight!", I mean? Maybe more time spent modeling this will help her make the leap to "Okay, 2 and 8 is 10, so 90 takeaway 82 is 8."

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We just played lots of regular games that involve math, and also implemented a weekly allowance system which often required multiple ways of having to make change to enable me to pay them (because I often didn't have correct change). As "sweet2ndchance" said above, I would talk about easy ways to make 10's, to add or subtract, ways I thought about the math in my head etc... We also did a lot with base 10 blocks, cuisenaire rods, and other manipulatives to talk through and show different ways of solving problems. It will come in time!

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4 minutes ago, Tanaqui said:

She's quite young. Number sense takes time and time and time to develop. However, you can try picking up the Peggy Kaye book Games for Math, which is right about her speed, and simply having her spend more time working with numbers - adding up scores on games (even if not specifically math games), cooking, doing basic carpentry and sewing (lots of measuring!), and always, always estimating answers in her curriculum before she solves them. That last step is tedious, but I'm convinced it's crucial.

Note: Any number games that involve dice, like shut-the-box, can be done using special ten or twelve sided dice instead of six sided dice, once she gets the basics down.

One question - does she know how to subtract by counting up? Using her fingers (or not) and saying "83, 84, 85, 86, 87, 88, 89, 90! That's eight!", I mean? Maybe more time spent modeling this will help her make the leap to "Okay, 2 and 8 is 10, so 90 takeaway 82 is 8."

I don't think that is how she does it.  she just said that she borrowed from the tens digit to make the 0 a 10, then she knew 10 - 2 was 8.  Which is great.

I think I will talk more about it.  If we want our kids to, then I should start as well.  ?

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Keep going with RS; it has lessons for exactly what you are asking (it may be in level B or C, depending on edition).  When people complain that RS teaches too many ways of doing things, it's really just giving them strategies and tools to manipulate numbers the way you are describing.  I think people can miss the big picture of RS.

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10 minutes ago, domestic_engineer said:

Keep going with RS; it has lessons for exactly what you are asking (it may be in level B or C, depending on edition).  When people complain that RS teaches too many ways of doing things, it's really just giving them strategies and tools to manipulate numbers the way you are describing.  I think people can miss the big picture of RS.

Ok. I'll give RS B a try then.  Thanks.

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I do lots of activities with the RS Abacus, c rods, ten frames, and number bonds. Any method you use first start with add/sub within ten. Then add more tens but set the whole tens off to the side that you don't really need. This emphasizes that the part of the add/sub you're actually calculating is the same as add/sub within ten. You can do two problems side by side with the manipulatives to illustrate this point more, like 90-8 and 10-8 then go through the steps simultaneously. Hopefully that makes sense to you.

If you do want to look at worksheets after awhile check out Greg Tang's website for free sheets that target that skill.

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4 minutes ago, desertflower said:

Ok. I'll give RS B a try then.  Thanks.

Don't forget to do the games; that will provide the practice using the tools.  If you have 1st edition of RS, then you'll need to be more pro-active in finding the games in the game book; 2nd edition will tell you when to introduce new games & which ones to introduce.

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16 minutes ago, domestic_engineer said:

Don't forget to do the games; that will provide the practice using the tools.  If you have 1st edition of RS, then you'll need to be more pro-active in finding the games in the game book; 2nd edition will tell you when to introduce new games & which ones to introduce.

Ok Thanks.  Yes, we do like the card games.  In fact the game go to the dump and education unboxed are probably how she learned her basic math facts.

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1 hour ago, ClemsonDana said:

Singapore math does a great job of developing number sense.  We also used blocks so that they physically manipulate them to see how it worked.  We didn't use unifix blocks-just plain ones.

Ok.  This is good to know since we are using SM too.  ?

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22 minutes ago, Sarah0000 said:

I do lots of activities with the RS Abacus, c rods, ten frames, and number bonds. Any method you use first start with add/sub within ten. Then add more tens but set the whole tens off to the side that you don't really need. This emphasizes that the part of the add/sub you're actually calculating is the same as add/sub within ten. You can do two problems side by side with the manipulatives to illustrate this point more, like 90-8 and 10-8 then go through the steps simultaneously. Hopefully that makes sense to you.

If you do want to look at worksheets after awhile check out Greg Tang's website for free sheets that target that skill.

Yes. That makes sense.  I've done this, before.  probably just need more practice.  Glad I'm on the right track.

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1 hour ago, HomeAgain said:

I think time, yes.
DS does Right Start and one thing I like is that the beginning of each level goes over ways to add/subtract again in the review lessons.  DS can do this no problem, but having the lessons reintroduced over and over helps him to practice the various methods and internalize them better.

How far along is your child in RS?

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1 hour ago, sweet2ndchance said:

Remember when your children were infants and everyone would tell you to do a running commentary of everything you were doing so your child would hear tons of language and hopefully talk soon and have a larger vocabulary?

I do the same thing when I do example math problems when they are older. I may even model more than one way and show that no matter what way I do it, I still get the same answer. I say outloud, every step I have to go through to get the answer mentally.

So for example, if I wanted to show the correlation between 21-16 and 20-15, I would say something like, " If I take one away from both numbers, I get 20-15 which is much easier to get the answer for in my head. I know it is the same problem because I took the same amount away from both of the original numbers. So I know the answer is 5."

Other thing I often did was have them do a problem and explain to me how they came up with the answer. Then ask them to show me another way they could have solved it. As someone else said Cuisenaire rods are fabulous for seeing the correlations between numbers.

I will ask her for another way to solve it.  That is such a good point.  I don't like explaining how I got an answer, but I guess if I won't my kids to, I'm going to have to too!

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We also use SM, which I find has helped a ton with number sense.

I've also found that once DD feels comfortable with doing addition or subtraction in one way, she will default to the more familiar way. So we review the BA pages that show the different strategies used (I only have 2B handy right now, but like page 35 of the 2B guide), and we'll talk about when one strategy might be faster than the others. I also explain that when we are teaching our brains to do things in a different way, it doesn't feel quite as quick and easy at first; but if we take the time to practice it, it will become quicker and easier.

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4 minutes ago, JIN MOUSA said:

We also use SM, which I find has helped a ton with number sense.

I've also found that once DD feels comfortable with doing addition or subtraction in one way, she will default to the more familiar way. So we review the BA pages that show the different strategies used (I only have 2B handy right now, but like page 35 of the 2B guide), and we'll talk about when one strategy might be faster than the others. I also explain that when we are teaching our brains to do things in a different way, it doesn't feel quite as quick and easy at first; but if we take the time to practice it, it will become quicker and easier.

Yes, I will probably have to do the same thing.  That is what I had to do with addition in BA 2A.  I've also learn so much!

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45 minutes ago, desertflower said:

How far along is your child in RS?

He's in the middle of E.  I looked ahead to F and it has the same sort of review at the beginning, too.

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• 2 weeks later...

You might like the Math Express Speed Maths workbooks by Singapore Math.  There are 6 levels, and they teach mental math strategies.

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I thought I had added this to my original post in this thread but I guess I didn't.

Taking one from each original number to simplify the problem is an algebraic thinking concept. It is the same concept as taking and x from both sides of an algebra problem to simplify before solving. Some kids can see this intuitively with no instruction. They are natural algebraic thinkers. Some kids can be taught from a young age to see numbers and equations this way. Then there will always be some that just cannot wrap their brains around the concept at all no matter what you try. Their brains are just not wired to think algebraically yet and it may be years before they are ready. If they can accurately solve age appropriate problems and have been introduced to algebraic thinking, I would let them solve the problem whatever way they feel confident solving the problem and just keep touching on the idea of how to do it faster. Eventually it should click when they are ready to understand it but there is no need to frustrate them by making them solve it that way before they are ready to understand it.

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Ok. Thanks Everyone.

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RightStart B is *amazing* at establishing number sende and facility of manipulating numbers in the base ten system! It uses lots of games, very little writing/worksheets, and lots of concrete manipulatives.

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