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Four Quarters Make A Dollar - How to Build Number Sense

Updated: Oct 28, 2022

Does math make sense? And how can you make sense of it?

In our recent newsletters, we shared some ideas on building number sense. As a challenge, we asked our members to compute "36 x 25" without using long multiplication. It's quite tricky, and we were very happy to receive excellent solutions from both students and tutors!

Here, we present two solutions:

Solution 1: Recognize that 36 and 25 are both perfect squares.

36 x 25

= (6x6) x (5x5)

= (6x5) x (6x5)

= 30 x 30

= 900.

Solution 2: Use the fact that 4x25=100. Why is that? Because 4 quarters make a dollar!!

36 x 25

= (9x4) x 25

= 9 x (4x25)

= 9 x 100

= 900.

These solutions show that we can use the multiplication chart in different ways -- it's not just for multiplying two numbers together (9x4=36), but also for factoring a number (36=9x4). Indeed, when we look at a problem differently, we may find easy solutions.

It's important to memorize your multiplication chart by heart, so you can use it at ease. Having trouble memorizing it? Check out our earlier blog on the subject and learn some tricks!

Now, can you compute"48 x 25" without long multiplication? How about "64 x 125" ?

Challenge yourself! Have fun!