Mystery numbers – bar model video

A challenging mystery numbers question where you are only told the sum and difference of the two numbers. The numbers are small so you can fairly easily use trial and improvement in this question but like many questions, when trying to use the bar model approach, it’s not really about the calculations it’s more about can you see a picture to make generalisation so that whenever you see a similar type of question, your understanding and reasoning skills allow you to solve the problem with the help of visual approaches like bar models.

Question

Annand thinks of two different numbers. When he adds the two numbers he gets 17. When he subtracts one number from the other, he gets 9. What are the two numbers?

When reading this question, it may not be very clear as to how you would use the bar model approach. What do we start off with? Should I draw a part-whole model? If I do then where do I show the subtraction part of the question? In this example, it is better to use the comparison model. Is there a reason why? We are trying to represent two different numbers, yes we can combine them to show the sum but then how would we show the difference between them with one bar? Some may also start off with the part-whole model (to show the sum) before moving to the comparison model (to show the difference) then realising that…actually, I just needed to draw the comparison model to show everything I need in this problem.

This isn’t your typical sum or difference or even sum and difference question though, as you will see in the video, there still needs to be more work to be done for you to solve this 3 step word problem but hopefully, the video is clear enough for us to understand how to solve these types of problems in general.

Proportionality with mystery numbers

What are the problems you may discuss with your class by looking at this model we have in the video? Is 4 really bigger than 9? Then why do you think we have this in our mode;? Do let us know what you think…