PLEASE help with explaining number bonds and making 10

[babygemma]

HI there,

I totally understand the number bonds and I don't think I'm explaining "how to make 10" using the number bonds to my 6 yo ds very well.

 

For example: 6+7

 

I say make 7 a 10. what do you have to add to 7 to make a 10? he says 3. do I then make him write 3 underneath the number 6 and say what do you have to add to 3 to make 6? he says 3. should i then make some connections with 7+3 equals 10 and get the other 3 to make 13?

 

what should i say when he asks "you can also write 4+2 under 6 because 4+2 also equals 6, why does it have to be 3+3. I would say that we use the combination with number 3 because that's what you have to add to 7 to make 10.

 

This seems so long winded and I haven't even gotten into subtraction yet.

 

I also have him draw pictures to represent 6 in one color and 7 in another color and let him make 10 by circling it and counting the ones that are left. He seems to understand that just fine.

 

Any suggestions? I feel so incompetent as this is only 1st grade math. Is this really necessary for higher level math in the future?

 

Thanks very much.

[Johanna]

Do you have an abacus ??

The Right start Abacus is a great hands on visual to demonstrate this.

[Karen in CO]

I failed at first grade math with my dd. I was terrible. Finally I just gave up. really. I don't think it matters that a first grader "understands" number bonds. What matter is that he finds some way to know that 6+7=13. Keep using the manipulatives and the "facts review" until he gets it. RS has a great card game called "Go to the Dump" that is played with number cards. You play it like "Go Fish" but trying to make 10 instead of finding a match. It is a fun way to reinforce the 10 idea. Adding pennies and dimes is also great. Base 10 blocks work well and so does the RS abacus. Just use whatever he needs to do get through the problems. One day he will answer - "Oh thats easy it is 13."

 

My problem was that I wanted my dd to understand the problems the same way I do instead of waiting for it to click for her in her own way. She and I think about just about everything differently so I don't know why I was surprised that she understood math in a way that was very strange to me.

[Kathy in NC]

Try using manipulatives, if necessary (pennies, cheerios, etc.) It doesn't really matter if you use the 6 or the 7, the idea is that she is able to "break the numbers apart" to easily make a 10. So, if she wants to pull 4 of your manipulatives from the 7 to make the 6 a 10, that works! And she'll quickly see that there are now a 10 and a 3; which easily add up to 13.

 

My dd is now in algebra, but she frequently uses this method of breaking apart numbers to do math in her head. She is fast and accurate; and I'm sure it is because we really worked on these number bond problems.

 

I hope this is helpful to you.

[Kathy in NC]

This is new for you as well as your student! You can probably "see" the 10 easier and faster than your dc because you see the value in it. Let your dc experiment with it. If dc wants to break the 6 into a 2 and 4, fine...It won't take long to see that you can't make a 10 with that combination. With some of my little ones, I would have them list all the number bonds for 6 (or 7), then choose the one that would help the other make 10. My dd did best when I let her play with them using manipulatives. Frequently we used cheerios or other food, which she could eat when she was finished with the lesson.

[Lolly]

Pennies and dimes helped mine make tens. Not one ever tried adding a fives place into the number system to make room for nickels.:D Of course, fil and mil always wondered why there was change laying all over my house. They NEVER let their kids play with money.

[ereks mom]

Here's a link: http://www.mugginsmath.com/store.asp

 

Scroll down to Number Neighbors. There's a link to a demo video that explains how to play.

[Ummto4]

Hi ! I'm doing number bond with my ds6 (K-level, though).

 

I use Rightstart:thumbup: and also have Math Mammoth and Singapore (Early Bird - K level) with me.

 

Basically, your first grader should know the connection between addition and substraction, the math fact, and how to use these concepts in everyday life. MathMammoth does this explicitely within two 'HUGE' chapter (chapter I and II).

 

Math MAmmoth chapter one (addition):

- make sure your child know that addition means: adding two addends to get a total. Draw, e.g. 2 red circles and 4 red circles, then ask your child to write: 2 and 4 is 6.

- Then, replace the 'and' with '+'. Hence, you get equation 2 + 4 =6 (still in pictorial mode).

- Practice this concept using word problem, i.e. find the total of something.

- Then make one of the addend missing. 2 + __ = 6 (still in pictorial mode).

- Practice this concept using word problem, e.g. Ann has 10 shirts. Mom washes 6, how many are clean ?

- Singapore Early Bird also uses this approach. But, it also has additional approach as follows:

--> Say, you have 10 sets of cup with the saucers. But, there are only 6 saucers in the cupboard. How many are missing ? TO explain this, draw 10 cups. Draw 6 saucers directly underneath the cups. Let your child counts how many saucers are missing. Then write the equation.

- Rightstart uses partitioning and whole to part circles to explain number bond and missing addend. Start by drawing whole to part circles: one big circle on top, and two small circles underneath it. Then demonstrate partitioning, using popsicle sticks. If you have abacus, you can use that too. Place, e.g. 5 sticks on the whole/big circles, and ask your child to divide it into two parts. Each part should go to one small circle.

 

After your child knows about partitioning and writing equations based on partitioning (e.g. when partition 5, you write: 5 = 2 +3; 5 = 4+1, etc), give her either the missing addend equation , or finding total equation, and demonstrate using abacus/tally stick, combined with the whole to part circles. Basically, your child should know what she's supposed to look for: the whole (total) or the part (addend). Reinforce with word problem. My son had difficulty at first grapping this concept via Rightstart, so I added Singapore + Math Mammoth approach.

 

- Once your child knows the concept, teach the fact.

 

Rightstart teaches strategy on how to memorize the fact beautifully. First, your child should know the commutative law (1+3 = 3+1), everything with one more added means it's the next number (3 + 1 =4), and everything with two more added means it's the next even/odd number. I drilled my son these everyday: counting up, counting down, count by twos, count the even number/odd numbers up and down, as scripted in Rightstart text. First, I use abacus to help him visualizing the number, then I remove the abacus and let him count mentally.

 

Also, since it uses abacus (10 beads in a row, 5 are blue, 5 are yellow), you can easily teach: 5 blue and 1 yellow is 6, etc. My son knows this fact first time we started with abacus.

 

Hence, your child can do all these stuff in her head. What she needs to learn though, is some doubles: 3 + 3, and 4 + 4, and the nearly doublesL 3+4, and 4 + 5. That's it. Once the doubles is known, nearly double is easy (i.e. one next number after the double, when counted down)..

 

To reinforce the fact, Rightstart has lots of card games and a 'number balance'. Math mammoth also has list of sites where you can do the math games for free.

 

For teens, Rightstart B has all addition with carry over covered, and teaches strategy to visualize those addition. MathMAmmoth and Singapore uses 'ten completion' strategy when doing the carry over addition (e.g. 9+ 5 = 10 + 4). I like Rightstart better because it's much easier to visualize. I know my son visualizes abacus in his head when I quiz him orally on facts.

 

Know on to substraction:

- First, teach substraction as taking away.

- Then it includes addition and substraction equation in the same page (math mammoth does this), so your child will be able to see that substraction can also be used for finding the missing addend. As usual, the approach is pictorial, and then on to counting using number line, then just equation. Reinforce this with word problem.

- SIngapore early bird 'connects' the addition and substraction the same way using manipuliative and picture: e.g. get 4 red counter, and 5 blue counter. Ask how many counters in total. Then write the equation: 4 + 5 = 9. With the equation written, remove 4 red counter. Tell her you had 9 counters, but you removed four, how many do you have now ? Write the equation: 5 = 9-4, i.e. 9, take away 4, is 5. Now, you want to have 9, but there's only 5 counters, how many more counters do you need. Write the msising addend equation. Your child may then look at the equation and answer.

- Rightstart also teaches the same, but it has a weird scope and sequence. It does addition, missing addend, and then go straight to a couple of digit addition and mental math. Substraction is taught after that, and I'm worried my son would miss the connection b'ween the missing addend, addition and substraction v. clearly. Hence, I'll use MathMammoth scope and sequence (similar to s'pore): teach addition to 10, then substractin to 10.

- Having said that, Right start teaches something on substraction which is not yet covered ion MAthM<ammoth grade I, i.e. when you substract two large numbers which are very close in value, you better off count up. E.g. baby X was born 1998. How old was the baby X on 2004 ? Rather than substract, it's better to count up from 1998 to 2004. This explains how the better use of the missing addend concept (counting up), rather than substraction (counting down).

 

So, my advice is: if you need help explaining, get a book which explains how to explain the math concept. Rightstart is very good on this. I supplement this with math mammoth to get different perspective on to how to explain things. Math mammoth approach is more like singapore. However, math mammoth is not scripted. Righstart is scripted so it's very good for a homeschool mom like me.

 

I'm planning on doing both MathMammoth and RightStart. I basically follow the scope and sequence of math mammoth because it's mastery based. But use rightstartmath + math mammoth approach to teach math.

 

HOpe this helps.

Dian

[Johanna]

My problem was that I wanted my dd to understand the problems the same way I do instead of waiting for it to click for her in her own way. She and I think about just about everything differently so I don't know why I was surprised that she understood math in a way that was very strange to me.

 

THis is such a valid point that i am realizing as well with me kids. My first dd8 clicked right away with this sorta concpetual understanding....but my ds7...is just starting to get it a little at this point...and it couldnt be taught, he had to discover it himself. I had to learn to relax and let him come to the answer himself...and realize that he would find those "short cuts" soon enough. Sometimes, I think that conceptual understanding is pushed on a child too fast, and they just get a "glazed over " look (well, mine did :-)

So, I panicked. THen i had to remember "wait, he is only in first grade"!

[Mommy22alyns]

I feel so incompetent as this is only 1st grade math.

 

 

Hi, were you in my house this morning? ;) I wanted to poke my eyes out while trying to explain number bonds to Becca. I think I don't have it in my own head how to explain/teach it, so I keep trying to find different ways to phrase it and have it make sense to her.

[KAR120C]

And this was ages ago (lol) so I hope I'm remembering all the important bits!

 

First, we played a lot of solitaire (sometimes cooperatively), making tens. You take a regular deck and remove all the face cards and point out that an Ace is 1, then deal out whatever solitaire you like... I go with the pyramid myself but just ten stacks of cards is also good... and pick them up in pairs that make ten -- 1 and 9, 2 and 8, 3 and 7, 4 and 6, pair of 5s, or if you get a ten then it's a bonus. :) This part is just to reinforce those pairs of numbers.

 

Second, we did a TON of problems that were in the format you're talking about -- sums between 11 and 19. And the way we did it was for DS to "hold" one number (showing on his fingers) and for me to "hold" the other. We sat across the table from each other, and if for instance it was 6 + 7 then he had six fingers up and I had seven. Then every time we went through the same routine: I asked, "How many do you need to make ten?" He told me whatever he needed (and it just happens to be the number of fingers he doesn't have up... convenient, eh? LOL). I "gave" him that many, counting them out as I put each finger down, and he "took" them by putting each finger up as I counted them out. Then we looked at what I have left. In the case of 6 + 7, I would have three fingers left. So with the ten he has up and the three I have up, we have 13.

 

Third, we did the same thing with an abacus. Any abacus with ten beads per rod works fine. It's the same process as the holding-up-fingers thing, only he could do it on his own. Also since ours had six rods, I could show him that it worked for larger numbers (like 16 + 7, and 26 + 7, etc.)

 

I think it was about a week of this before it was really stuck in that little head. :)

 

After we had the making ten thing down pat, we did a sort of "part b" with making fives, using a Japanese abacus... but that gets beyond the necessary and into the geeky. LOL

 

Hope this helps!

[In The Great White North]

What's a number bond? :confused: And what math program is it from? Why are they necessary?

 

Before this forum, I never heard of number bonds.

[Suzanne in ABQ]

"Number Bonds" is the term used in Singapore Math to describe what some American math programs call "Number Families". They are any group of three numbers consisting of a "whole" and two "parts". The two parts add together to make the "whole", and you can subtract a "part" from the "whole" to "get the other part". Examples are 7/3/4, 10/6/4, 5/2/3, 8/4/4.

[Suzanne in ABQ]

I agree that manipulatives are essential until the concept sticks. Then, move to pictures and do it a lot until the pictorial concept sticks. Don't move on to the conceptual (numbers only) until he has a firm grasp of the concepts concretely and pictorially. That's the Singapore way.

 

Our dialog would go something like this:

Me: "You have six Cheerios here, and seven Cheerios there. How do you make 10 with seven?"

Him: "3?"

Me: "Yes. You need three. Where are you going to get them?"

Him: "From the six?"

Me: "Yes. That's right. So, slide three Cheerios from the 'six' pile into the 'seven' pile. . .. . Now, how many are left?"

Him: "Three"

Me: "Okay. You have ten here, and three there. How many is that altogether?"

Him: "Thirteen!"

Me: "Yes! That's right. Now, you eat these Cheerios while I set up the next problem with some frest ones."

 

 

I knew when they (dd, then ds) understood the concept because they'd jump ahead of me, and start moving the Cheerios on their own. Then, I moved to pictures of dots. I would draw the two groups of dots, and then circle the "ten", including one whole group and however many I needed from the other group to "make 10". It was easy for them to see the leftover dots, and add them to the 10 that were circled.

 

Only when they had it down this way did I move on to just using numbers (conceptual, analytical understanding). If you try to jump directly into the conceptual understanding, without spending the necessary time on the manipulatives and picturial understanding, you risk frustrating your dc, and yourself. Do what you need to do to make him successful, even if it doesn't fit your schedule. It will pay off in the long run.

[gardening momma]

Our dialog would go something like this:

Me: "You have six Cheerios here, and seven Cheerios there. How do you make 10 with seven?"

Him: "3?"

Me: "Yes. You need three. Where are you going to get them?"

Him: "From the six?"

Me: "Yes. That's right. So, slide three Cheerios from the 'six' pile into the 'seven' pile. . .. . Now, how many are left?"

Him: "Three"

Me: "Okay. You have ten here, and three there. How many is that altogether?"

Him: "Thirteen!"

Me: "Yes! That's right. Now, you eat these Cheerios while I set up the next problem with some frest ones."

 

This is basically what I was going to suggest you do. Using manipulatives, go through the process (above)...you could say that he needs to take away 3 from the 6--and if you're having him write this down, as it sounds like you are, you explain that part too (beneath the 6, write down how many you're taking away from it--and have him put in the minus sign too, then ask how many are left after he's taken 3 away from 6). Even though you say you haven't started subtraction with him yet, you really have, since you're having him take 3 from 6 to make the 7 a 10. You can go ahead and start using some subraction terminology--that might help him understand better than if you try to avoid it.

[mom31257]

This is basically what I was going to suggest you do. Using manipulatives, go through the process (above)...you could say that he needs to take away 3 from the 6--and if you're having him write this down, as it sounds like you are, you explain that part too (beneath the 6, write down how many you're taking away from it--and have him put in the minus sign too, then ask how many are left after he's taken 3 away from 6). Even though you say you haven't started subtraction with him yet, you really have, since you're having him take 3 from 6 to make the 7 a 10. You can go ahead and start using some subraction terminology--that might help him understand better than if you try to avoid it.

 

I was thinking in terms of taking the 3 away from the 6 also. Why not cross out the numbers and replace (above) them with 3 and 10? I always crossed out and changed in borrowing in subtraction, why not do it with this? If a child understands it with manipulatives, maybe they should even help decide the way to write it down. Asking the child to do it their own way can give you a better insight to the way they understand it , also.

 

Amy of GA

Darin's wife for 17 years

11yo dd

5yo ds