Mattot- Multiplying and Dividing powers of 10

"Moshe spoke to the people, saying, 'Arm men from among yourselves for the army that they may be against Midian to inflict Hashem's vengeance against Midian. A thousand from a tribe, a thousand from a tribe, for all the tribes of Israel shall you send the army.' 
So there were delivered from the thousands of the Children of Israel, a thousand from each tribe, twelve thousand armed for the army. Moshe sent them- a thousand from each tribe for the army- them and Pinchas son of Elazar the Kohen to the army, and the sacred vessels and the trumpets for sounding under his authority." ~Bamidbar 31;3-6

"Moshe, Elazar the Kohen, and all the leaders of the assembly went out to meet them outside the camp. Moshe was angry with the commanders of the legion, the officers of the thousands and the officers of the hundreds, who came from the army of the battle." ~Bamidbar 31;13-14

Math Connection:
For younger students, and even some older students, calculations with big numbers can be scary. The larger the number, the more room there is for errors. It is helpful for students to identify patterns in the way numbers work in order to help reduce anxiety and make calculations easier, and even faster. When dealing with multiplication and division of numbers that are powers of 10 (tens, hundreds, thousands,...), there is a simple trick that you can use to make the calculations easier. If you remove (or ignore) any extra zeros at the end of the number that aren't needed for the purpose of your calculation, you can multiply or divide as you normally would with your truncated number, and then add back your extra zeros onto the end of your product or quotient from your calculation. 

Some examples:

4,000 x 4: Set aside the 3 zeros at the end, leaving 4 x 4 = 16, and then add back the 3 zeros, making it 16,000.

650,000 x 2: Set aside the 4 zeros at the end, leaving 65 x 2 = 130, and then add back the 4 zeros, making it 1,300,000.

For multiplication, if both numbers are powers of 10, you can still set aside the zeros from the end of both numbers to simplify your calculation. After your calculation, you add all of the zeros from both numbers back to the end of your product. For example, 2,000 x 80 can be calculated by multiplying 2 x 8 = 16, and then add back on the 4 zeros (3 from 2,000 and 1 from 80), making it 160,000.

6,200 + 2: Set aside the 2 zeros at the end, leaving 62 + 2 = 31, and then add back the 2 zeros, making it 3,100. 

43,000 + 5: Here, 43 is not evenly divisible by 5, so we will take away just 2 zeros at the end, leaving 430 + 5 = 86, and then add back the 2 zeros, making it 8,600.

For division, if both numbers are powers of 10, you can permanently remove the same number of zeros from the end of both numbers to simplify your calculation. For example, 24,000 + 300 is the same as 2,400 + 30, which is the same as 240 + 3 (all of which = 80).

Parsha Connection:
In this week's parsha, we have both multiplication and division with powers of 10. First, when Moshe instructions the Children of Israel to create an army with 1,000 men from each of the twelve tribes, we can confirm the total of 12,000 that is given in the text. 

1,000 x 12: Remove the 3 zeros at the end, leaving 1 x 12 = 12, and then add back the 3 zeros, making it 12,000 men.

When they return from battle, Moshe is "angry with the commanders of the legion, the officers of the thousands and the officers of the hundreds, who came from the army of the battle." How many commanders were there?

Officers of the thousands:
12,000 + 1,000: Here, we have 3 zeros at the end of both numbers (dividend and divisor), so we can remove the 3 zeros from both, and are left with 12 + 1 = 12 commanders overseeing the thousands.

Officers of the hundreds:
12,000 + 100: Here, we have 2 zeros that we can take away from both numbers, leaving us with 120 + 1 = 120 commanders overseeing the hundreds.

So, there were 132 commanders (12 + 120) with whom Moshe was angry following the battle with Midian.

Everyday Connection:

Working with a committee on planning for a large event? What if you have 237 people attending your event and your tables each seat 8 people? How many tables will you need? Using estimation and our division trick, we can quickly calculate how many tables you'll need.

237 is just 3 short of 240. To calculate 240 + 8, let's use our trick- 24 + 8 = 3, then add the zero back, and we know that we need to set 30 tables for the event.

And what if you want to estimate a food budget for the event? Let's say $30 per person. Now we can use estimation and our multiplication trick to see if our food budget is realistic.

Again, we'll use 240. To calculate 240 x 30, we'll do 24 x 3 = 72, then add our 2 zeros back, and we have an estimate of $7,200, if you spend $30 per person.