Module 9--Division strategies
TEKS: 4.4E, 4.4F, 4.4G, 4.4H
VOCABULARY
REMAINDER--tHE NUMBER LEFT OVER WHEN A NUMBER CANNOT BE DIVIDED
EQUALLY.
cOMPATIBLE NUMBERS--nUMBERS THAT ARE EASY TO COMPUTE MENTALLY,
AND, IN DIVIDING, WORK OUT WITH NO REMAINDER.
THINGS TO KNOW
**Dividing is just putting numbers into groups, and is the opposite of multiplying. Instead of trying to find the total in multiplying, dividing means you start with the total and find out how many are in each group.
**Interpreting Remainders can be tricky! Let’s say the problem is 13 divided by 4. You would get 3 remainder 1. But… depending on the word problem, your answer could either be 3, 4 or 3 remainder 1. Deciding which answer is correct is the real problem....Look at the following examples:
*There are 13 pieces of candy in a bowl. Four students want to share the candy equally. How many pieces can each student have if they have the same amount? For this problem, the answer would just be 3. If the students all want the same amount, each one can only have 3. (There will still be one left over, but no one would get that piece.)
*There are 13 students who need to get to school. 4 students fit in each car. How many cars do you need? In this case, your answer must be 4, because 3 isn’t enough and you can’t have a remainder 1 car.
*There are 13 cans of food that will be placed on 4 shelves. If all the cans are put on a shelf, how many would each shelf get? This one could be answered two ways--1. Each shelf has 3, with one leftover (remainder). 2. Each shelf has 3, and one shelf has the leftover added to it, making 4 on that shelf.
Dividing Using Place Value
This method lets you use your basic facts to solve harder problems.
Let’s say that you know the fact 15 ÷ 3 = 5.
If you think of 150 as being 15 tens, you would know that…
150 ÷ 3 = 15 tens divided by 3 = 5 tens, or 50.
1500 ÷ 3 = 15 hundreds divided by 3 = 5 hundreds, or 500.
15,000 ÷ 3 = 15 thousands divided by 3 = 5 thousands, or 5000.
Compatible Numbers
Another tricky thing to understand when dividing is Compatible Numbers. The purpose of this is great--it uses numbers close to the actual numbers, that will divide evenly with no remainders, in order to get an estimate. The tricky part is knowing which numbers to use. There isn’t a set pattern for doing this. Compatible numbers is NOT the same as rounding, although they are both used for getting an estimate. Knowing your basic facts is a big help!
Let’s start off easy-- 65 ÷ 9 = ?
Generally, you leave the divisor alone. Changing both numbers can end up changing the quotient too much. So that means we would leave the 9 alone. Think of your multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. Is there one that is close to the 65? Yes--63. We would know that our compatible fact is 63 ÷ 9 = 7, so 65 ÷ 9 is about 7.
Ready for a harder one? 1718 ÷ 4 = ?
Leave the divisor 4 alone, then think of basic facts that would get close to 1718…
Think: 16÷ 4 = 4 and 20 ÷ 4 = 5
so using the place value strategy above,
our compatible facts are: 1600 ÷ 4 = 400 and 2000 ÷ 4 = 500.
Now, which compatible fact is closer to 1718 ÷ 4? That’s the one you would use!
Division and the Distributive Property
We learned about the Distributive Property during our Multiplication Unit. Now we will be using it in reverse! Let’s look at it using a basic fact that we already know the answer to first…
20 ÷ 5 = 4
We can break the 20 into smaller parts that add up to 20...the “trick” is to make sure the parts are divisible by 5. I would choose 15 & 5 for this example. (10 & 10 would also work)
20 ÷ 5 = 4→ (15 ÷ 5) + (5 ÷ 5)
3 + 1 = 4
Now for bigger numbers! 84 ÷ 7 = ??
Since this isn’t a basic fact, I have to think of some facts that would add up to 84. There are several possible ways to break this up! I would start with 70 ÷ 7 = 10 and then see how much of the 84 I have left to use. 84-70= 14 and voila! 14 ÷ 7 = 2.
84 ÷ 7 = (70 ÷ 7) + (14 ÷ 7)
10 + 2 = 12
IXL LESSONS THAT REVIEW THIS MODULE:
▢E.7 ▢E.20 ▢E.15 ▢E.25 ▢E.26