A guide to the wonders of grade 5
Today we looked at the relationship between skip counting by 7s and by 70s. We noted a pattern that is identifiable by anyone, regardless of their familiarity with math or numbers. There is simply a 0 behind every number skip counted by 70 as opposed to 7, where there is not.
But why is that 0 there and how can I use this knowledge for long division? Of course, the 0 is there in order to bump the other digits 1 place in the place value chart and therefore it means: multiplied by 10. So when we look at a question that was on the assessment last week, 586/7, we can see the use of skip counting this way. In order to approach 586, we can think to our multiplication charts to see what big chunk of 586 we can divide first. We want to divide our big value digits first, and we know that 56 is the highest number along the 7s multiplication row without going over. And since we know the relationship between place value, we know that this really means 56 tens, or 560. We can then figure out the quotient of that problem by saying that 7x(8x10)=560, so therefore 560/7=(8x10) or... 80 By dividing that big chunk, we can now focus on the remaining number. The difference between 586 and 560 is 26. We know 7 fits in 26 3 full times, leaving us with 5. So, we have 80 and 3 from our 2 first divisions, making 83 the whole number quotient for this problem. Rather than declaring the remaining 5 as a "remainder", let's break it into a fraction! Students know to practice 1 long division problem at home tonight, and that is 473 divided by 6. If helping them, feel free to introduce other methods, but see if they can show you the breakdown method. It is not so different from the standard algorithm.
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