Calculate and Divide the Plunder:
"Hashem said to Moshe, saying: 'Calculate the total of the plunder of the captives, of people and animals, you, and Elazar the Kohen, and the heads of the fathers of the assembly. Divide the plunder in half, between those who undertook the battle, who go out to the army, and the entire assembly. You shall raise up a tribute to Hashem from the men of war who go out to the army, one living being of five hundred, from the people, from the cattle, from the donkeys, and from the flock. You shall take it from their half and give it to Elazar the Kohen, as a portion of Hashem. And from the half of the Children of Israel you shall take one drawn from fifty, from the people, from the cattle, from the donkeys, from the flock- from all the animals- and you shall give them to the Levites, the guardians for the charge of the Tabernacle of Hashem.'" ~Bamidbar 31:25-30
Itemization of Division of the Plunder:
"Moshe and Elazar the Kohen did as Hashem commanded Moshe. The plunder, beyond the spoils that the people of the army took as spoils was: the flock, six hundred seventy-five thousand; and cattle, seventy-two thousand; and donkeys, sixty-one thousand; and human beings, and of the women who had not known lying with a male, all the souls, thirty-two thousand. The half which was the share of those who went out to the army, was: the count of the flock, three hundred and thirty-seven thousand, five hundred- the tribute of Hashem from the flock was six hundred and seventy-five; and the cattle, thirty-six thousand- and their tribute to Hashem, seventy-two; and the donkeys, thirty thousand, five hundred- and their tribute to Hashem, sixty-one; and the human beings, sixteen thousand- and their tribute to Hashem, thirty-two people. Moshe gave the tribute that was raised up for Hashem to Elazar the Kohen, as Hashem had commanded Moshe."
From the half of the Children of Israel that Moshe had divided from the men who went to the army, and the half of the assembly was: of the flock, three hundred and thirty-seven thousand, five hundred- and the cattle, thirty-six thousand; and the donkeys, thirty thousand, five hundred; and the human beings, sixteen thousand. Moshe took from the half of the Children of Israel the one drawn from the fifty, from the people and the animals, and gave them to the Levites, the guardians of the charge of Hashem's Tabernacle, as Hashem had commanded Moshe." ~Bamidbar 31:31-47
This week's parsha is a double-parsha (we read two parshiot). For this post, I will focus on a portion from parshat Mattot. In this section, we have Hashem directing Moshe as to how the plunder of the Israelites' war with Moav was to be divided and donated. Following this, we have a section that itemizes what plunder was collected and exactly how they were divided. This set-up offers an opportunity for students to first organize the information related to how to divide the plunder and then test out their calculations on their own to see if their calculated divisions and donations match what is listed for the itemization of divisions and donations.
Some guiding questions for organizing and calculating:
- To begin, how many groups was the plunder to be divided into?
- Was this an even division?
- What/who were the groups?
- What were the categories of plunder that was being divided?
- How many were there?
- What exactly were they?
- Where was the donation from each group to be given?
- What was the calculation for donations from each group? Were there different calculations for the subgroups from each group?
- How did the calculations for donations compare within groups (looking at subgroups) and between groups?
- Can you use these questions to organize the basic set-up into a chart that will be usable for charting the actual division and donation of the plunder?
Using the chart created above, if you organize the information about the actual plunder that was collected, how do your calculations for division and donations match with the calculations given in the second quoted section above?
Problem Solving For Younger Students:
While younger students might not be able to organize a chart or perform the calculations necessary, some possible activities could be:
- As a group, with teacher guidance, identifying where information would fit into a pre-structured chart.
- Testing out donation samples for "1 out of 500" and "1 out of 50" using manipulatives.
- Note that counting out such large groupings would likely be too drawn out and tedious for most young students, but if they have pre-prepared sample groups already counted out into sub-groups of 500 and/or 50, then they can use these groups to model donating 1 from each group. Students could then use skip counting to show that, for example, 3 groups of 500 means that there were 1,500 paperclips and 3 of them would be donated.
Extension thoughts for Older Students:
- This type of information can be expressed using fractions, ratios, and percentages. How could you express the information using each of these forms?
- How might this information be displayed using graphs?
"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.
