Using Number Bonds

Do you use number bonds?  Here are a few ideas on how to use them to teach number sense.
Ever done this:
Line up 10 beans. Line up 10 more beans below the first 10. As you point to each row, say, "Does this row have the same number of beans as this row?" Usually children will quickly say yes. Now spread out the beans in the first row. Ask again, "Does this row have the same number of beans as this row?" And then...they say....no. As they point to the top row, they add, "this row has more."
This is an example of conservation of number. According to Piaget, children develop this concept at  developmental age 7. When children have conservation, they realize that just by spreading out the beans, you don't get more.
Now lets think about addition. Isn't that what we are doing? We take a set, divide it into 2 sets and put an equal sign in the middle.  Here's the problem...When we divide the group into 2 sets, we are "spreading" out the counters.  Children without conservation now see it as more!!!!! So when they read 3+2=5, in their mind they see...3+2 is more than 5! This leads to great confusion about the concept of equal.
So what do we do....? We have addition in our standards. Here's a great way to develop conservation using Number Bonds. Be sure and read all the way to the bottom of this post to grab the FREE number bond mats and the numeral cards!

Number Bonds Conceptual Level

To begin the lesson invite the children to place a given number of counters in the large rectangle. Say, "I have 5 bears." Have the children repeat it back to you.

Now, using the same 5 bears, divide the bears into 2 groups. Say, "I have 2 bears, I have 3 bears." 
Again, have the children repeat it back to you.

Last, move all of the bears back to the rectangle and say, "I have 5 bears." Children repeat.  By moving the bears back to the original location, the children see that the number of bears doesn't change just by spreading them out. Repeat with various ways to make 5.

Transitioning to Abstract Level

Once the children are fluent with dividing sets and have developed the understanding that they don't have more just by spreading them out, they are ready to transition to abstract. (This could be several months, more or less, for the children.) Invite the children to place a given number of counters on the new number bond mat. Say, "I have 5 bears." Invite the children to repeat after you.

Divide the bears into 2 sets using the circles. Say, "I have 2 bears, I have 3 bears." Again, the children repeat.

Demonstrate adding the "2" and "3" to show how many bears are in each circle.  Ask, "How many are there all together?" Since the children have developed fluency with dividing sets and have conservation of number, they should know that there are 5 altogether. Model your thinking as you show how you add the "5".  Repeat with other combination for 5. 
Once the children become fluent with this step. Transition to writing the number sentence on dry erase boards.
Be sure and grab these FREE number bonds and numeral cards below!
Here are the Peek at My Week-Mail plans.  I think I have shared how I lay them out in the past few peek at my week posts, so I am not going to do that. If this is your first time reading these plans, look back at other peek at my week plans to see how they are organized.


Presenting on the road can be very lonely. I love people! But, when I am traveling I often find myself alone. I’m not telling you this so that you will somehow feel sorry for me, but so that you will know just how excited I get when I realize I am NOT going to be alone! So you can only imagine how super excited I was when I received a message from Katie of Little Warriors, that I was going to be working in her school district on Friday! When she went to sign up for her sessions on Thursday night, she saw my name in the listings! I didn’t know that she worked in the district where I was presenting! Now, if we had put two and two together, we could have planned to get a cup of coffee (or a diet coke!) or something together, but it was still fun to see her on Friday!