#number bonds

[pushteacher]

https://pushteacher.co.uk/shop

[survivingparenthoodwithhumor]

When you have to learn common core math at 28 years old. Anybody heard of number bonds? I dislike them very much. My 7 year old son isn't a fan either and after a week of struggling to explain it to him I finally found a fun way to do it! You take the left sandwich and add it to the right sandwich then feed it to the top circle! Had him laughing and using his imagination!

[paulspuzzles-blog]

Solution #4

Click on the “Keep reading” thing for the solution.

The astute reader will have noticed that the middle number gets added to all four lines - which means that it cancels out when we try to make them all equal (if a+b+c = d+e+c, then a+b = d+e).  So we don’t have to worry about four lines of three numbers adding to the same total, so much as we need to worry about four pairs of numbers adding to the same total.

One way to try making those four pairs would be to start with our highest and lowest numbers - 1 and 9 - and pair them up, adding them to make 10.  From here, we can find other pairs of numbers that add to ten (good ol’ number bonds) - 2+8, 3+7 and 4+6.  We’re left with 5, which can go in the middle.  Four pairs adding to ten, and adding on the 5 gives four lines adding to 15:

So that’s our first solution.  What about the others?  Well, we could try getting our four pairs to add to different totals.  If we go too high, we hit a snag - with 13, say, we can start 9+4, 8+5, 7+6... and then have no idea what to do with 1, 2 or 3.  Similarly, if we go too low, we won’t be able to do anything with the high numbers.

But we have a small amount of wiggle room: we can put one number in the middle, essentially as a “free” space.  This could be the lowest number, 1, which gives us a new lowest number of 2 which we can add to 9 to get 11.  And we can make three more pairs that add to 11 - 3+8, 4+7 and 5+6.  Adding on the 1 gives us four lines that add to 12:

Similarly, we can put our highest number 9 in the middle.  Our new highest number is now 8, which we can pair with 1 to give 9.  And we can find three more pairs adding to 9: 2+7, 3+6 and 4+5.  Adding the central 9 to each of these gives 18:

Okay, those are three solutions.  What about the proof that these are the only three?  Let’s think: if we need four pairs of numbers adding to the same total, then the sum of all eight numbers around the edge must divide by four to share those numbers out evenly.

It so happens that if you add up the numbers 1 to 9, you get 45 (you can check this quickly with the first answer: four pairs of numbers adding to 10 gives you 40, plus 5 is 45).  If we call the middle number M, then the sum of the eight numbers around the edge is 45-M, and we’re looking for cases where this number divides cleanly by four.  The only cases where this is true are when M equals 1, 5 or 9, which makes 45-M = 44, 40 and 36 respectively.  Any other number in the middle will leave you with some of your lines of four numbers not adding up to the same amount. □

(You can even see the solutions coming out from here - 44 gives four pairs adding to 11, 40 gives four pairs adding to 10 and 36 gives four pairs adding to 9).

For me, this puzzle is a beautiful introduction to the idea of proving something mathematically - tricks like “we need to show the cases where something divides nicely by a number” show up all the time.

[appediauk-blog]

Number Pieces

If anyone has used dienes before, then they’ll appreciate the idea behind the Number Pieces app. It’s a fantastic tool when teaching addition, subtraction, number bonds, division or multiplication – or even fractions and ratio.

What The Children Do:

The children can drag-and-drop different blocks onto a screen. The blocks vary in size from 100 squares, to strips of 10 and finally 1s. Once the…

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[kidzactivities]

Number Bonds with Shells has been published on http://kidzactivities.net/number-bonds-with-shells/

[appediauk-blog]

Might Maths 1

Mighty Maths 1 is a very useful app to have in the classroom when helping children to develop their knowledge of basic mathematical topics. The app encourages children to, not only understand mathematical concepts but also to develop instant recall of various number facts. What The Children Do: Children select a mathematical concept from four possible options; subtraction and addition, number…

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[elementarymydearpenguin]

(via Teaching ten frames | homeschool)

I'm always keen to try hands on, non-paper activities and this is usually what children who are struggling with a concept need.

I know of a few still learning their number bonds to 10 who this more concrete and visually organised idea may help.

[yourhomeworkpage]

This is a collection of number bond and tables sheets to use at home. The emphasis is on practise in order to improve speed confidence.