Bereishit- Place Value and Regrouping

Addition and Place Values:
When younger children begin learning to add (and subtract) multi-digit numbers, the algorithms alone for these calculations can be confusing. As a starting point, children first need to understand the meaning behind what each digit in a number represents. As they expand their understanding, it is helpful for children to recognize the pattern of every three place values from the decimal point moving towards the left. Larger decimal place values come later, but, again, understanding the pattern of place value will help students pick up the larger picture of what's happening with the numbers.

Basic place values to the millions:

The biggest hurdle for students to overcome is that each place value can't have more than 9 of it's kind, and every time you reach a group of 10, you have reached the next place value and need to "regroup" your numbers.

*10 ones = 1 ten and 0 ones [10]
*10 tens = 1 hundred and 0 tens and 0 ones [100]
*10 hundreds = 1 thousand and 0 hundreds and 0 tens and 0 ones [1,000]
*10 thousands = 1 ten-thousand and 0 thousands and 0 hundreds and 0 tens and 0 ones [10,000]
*10 ten-thousands = 1 hundred-thousand and 0 ten-thousands and 0 thousands and 0 hundreds and 0 tens and 0 ones [100,000]
*10 hundred-thousands = 1 million and 0 hundred-thousands and 0 ten-thousands and 0 thousands and 0 hundreds and 0 tens and 0 ones [1,000,000]

It helps for children to visualize this concept using manipulatives such as base-10 blocks, which have models for ones, tens, hundreds, and thousands. Paper clips are a good make-shift manipulative, since students can clip and unclip into and out of groups of 10, 100, etc. as they make sense of the numbers.

One key that is critical for students to remember is that they need to line up the place values- you can only add ones with ones, tens with tens, hundreds with hundreds, etc. (and then regroup as needed).

Parsha Connection:
Chapter 5 of this week's parsha gives details of the direct lineage from Adam to Noah. We are given information on names and ages for this direct line of descendants. We are given enough information about each person to provide 9 sample addition problems, where we can check the numbers that we are given in the parsha.

As a first step, let's organize the individual pieces of information that we are given. As we organize information for each person, we can check the math.

1st generation:
"This is the account of the descendants of Adam- on the day of G-d's creating of Man, He made him in the likeness of G-d. He created them male and female. He blessed them and called their name Man on the day they were created- when Adam had lived one hundred and thirty years, he begot in his likeness and his image, and he named him Seth. And the days of Adam after begetting Seth were eight hundred years, and he begot sons and daughters. All the days that Adam lived were nine hundred and thirty years; and he died." ~Bereishit 5;1-5

Adam was 130 years old when Seth was born.
Adam lived 800 years after Seth was born.
Adam died at 930 years old

  130
+800 
  930    so this works

2nd generation:
"Seth lived one hundred and five years and begot Enosh. And Seth lived eight hundred and seven years after begetting Enosh, and he begot sons and daughters. All the days of Seth were nine hundred and twelve years; and he died." ~Bereishit 5;6-8

Seth was 105 years old when Enosh was born.
Seth lived 807 years after Enosh was born.
Seth died at 912 years old

  105
+807
  912    so this works

The above example offers regrouping in the ones (to tens) digits.

3rd generation:
"Enosh lived ninety years, and begot Kenan. And Enosh lived eight hundred and fifteen years after begetting Kenan, and he begot sons and daughters. All the days of Enosh were nine hundred and five years; and he died." ~Bereishit 5;9-11

Enosh was 90 years old when Kenan was born.
Enosh lived 815 years after Kenan was born.
Enosh died at 905 years old

   90
+815
  905    so this works

The above example offers a sample with different sized numbers (one tens and one hundreds), which offers a good check on understanding lining up the place values. Also, we have regrouping in the tens (to hundreds) digits here.

4th generation:
"Kenan lived seventy years, and begot Mahalalel. And Kenan lived eight hundred and forty years after begetting Mahalalel, and he begot sons and daughters. All the days of Kenan were nine hundred and ten years; and he died." ~Bereishit 5;11-14

Kenan was 70 years old when Mahalalel was born.
Kenan lived 840 years after Mahalalel was born.
Kenan died at 910 years old

   70
+840
  910    so this works

Again, here we have different sized numbers and regrouping in the tens (to hundreds) digits.

5th generation:
"Mahalalel lived sixty-five years, and begot Jared. And Mahalalel lived eight hundred and thirty years after begetting Jared, and he begot sons and daughters. All the days of Mahalalal were eight hundred and ninety-five years; and he died."  ~Bereishit 5;15-17

Mahalalel was 65 years old when Jared was born.
Mahalalel lived 830 years after Jared was born.
Mahalalel died at 895 years old

   65
+830
  895    so this works

Again, here we have different sized numbers.

6th generation:

"Jared lived one hundred and sixty-two years, and begot Enoch. And Jared lived eight hundred years after begetting Enoch and he begot sons and daughters. All the days of Jared came to nine hundred and sixty-two years; and he died." ~Bereishit 5;18-20

Jared was 162 years old when Enoch was born.
Jared lived 800 years after Enoch was born.
Jared died at 962 years old

  162
+800
  962    so this works

7th generation:
"Enoch lived sixty-five years, and begot Methuselah. Enoch walked with G-d for three hundred years after begetting Mehuselah; and he begot sons and daughters. All the days of Enoch were three hundred and sixty-five years. And Enoch walked with G-d; then he was no more, for G-d had taken him." ~Bereishit 5;21-24

Enoch was 65 years old when Methuselah was born.
Enoch lived 300 years after Methuselah was born.
Enoch died at 365 years old

   65
+300
  365    so this works

8th generation:

"Methuselah lived one hundred and eighty-seven years and begot Lamech. And Methuselah lived seven hundred and eighty-two years after begetting Lamech, and he begot sons and daughters. All the days of Methuselah were nine hundred and sixty-nine years; and he died." ~Bereishit 5;25-27

Methuselah was 187 years old when Lamech was born.
Methuselah lived 782 years after Lamech was born.
Methuselah died at 969 years old

  187
+782
  969    so this works

Again, here we have regrouping in the tens (to hundreds) digits.

9th generation:
"Lamech lived one hundred and eighty-two years, and he begot a son. And he called his name Noah, saying, 'This one will bring us ease from our work and from the toil of our hands, from the ground which Hashem had cursed.' Lamech lived five hundred and ninety-five years after begetting Noah, and he begot sons and daughters. All the days of Lamech were seven hundred and seventy-seven years; and he died." ~Bereishit 5;28-31

Lamech was 182 years old when Noah was born.
Lamech lived 595 years after Noah was born.
Lamech died at 777 years old

  182
+595
  777    so this works

Again, here we have regrouping in the tens (to hundreds) digits.

10th generation:
"When Noah was five hundred years old, Noah begot Shem, Ham, and Japheth." ~Bereishit 5;32

Noah was 500 years old when Shem, Ham, and Japheth were born.

Follow-up Activities:
If you take this base information and use it to try to place the births and deaths in a timeline, students can calculate how old each person was at the births of successive descendants, as well as how old each of the descendants was at the time of death of their ancestors. These calculations will offer students more, similar calculation practice.

For an added exercise, having students identify which numbers to use for these different comparative calculations offers practice with problem solving and identifying important information.