Warm Up
• Which Standard for Mathematical Practice do
you feel is most important? Why do you think
it is the most important?
Powers of Ten
Alignment Lesson
2
20
200
2,000
• Take a look at the numbers above!!
• How are they alike?
• How are they different?
2
20
200
2,000
• Let’s use base ten pieces to model these
numbers.
2,000
200
20
2
2 x 1,000 = 2,000
2 groups of 1,000
2 x 100 = 200
2 groups of 100
2 x 10 = 20
2 groups of 10
2x1=2
2 groups of 1
2,000
200
20
2
2 x 1,000 = 2,000
2 groups of 1,000
2 x 100 = 200
2 groups of 100
2 x 10 = 20
2 groups of 10
2x1=2
2 groups of 1
•In which direction did the digit 2 move when we multiplied by 10 (instead of 1)?
•To the left, the 2 moved from the ones place to the tens place
•How many places did the 2 move in this direction?
•One place
•In which direction did the digit 2 move when we multiplied by 100 (instead of 10)?
•To the left, the 2 moved from the tens place to the hundreds place
•How many places did the 2 move in this direction?
•One place
•In which direction did the digit 2 move when we multiplied by 1,000 (instead of 100)?
•To the left, the 2 moved from the hundreds place to the thousands place
•How many places did the 2 moved in this direction?
•One place
Math Talk
Can you create a general rule or
relationship for what we’ve just
observed?
• Rule: A digit in one place represents ten times
as much as it represents in the place to its right.
-or• A digit in one place represents 1/10 of what it
represents in the place to its left.
Think about this…
• Ten of the smaller place value make one of the
next place value to the left. Therefore a digit in
one place represents ten times as much as it
represents in the place to its right. For example:
• 10 ones make 1 ten (10 units make 1 rod) so 20 is ten times
as big as 2 and the value of the 2 is ten times as much in 20
as it in 2
• The same is true for 200, 10 tens make 1 hundred (10 rods
make 1 flat) so 200 is ten times as big as 20 and the value of
the 2 in two hundred is ten times as much as it is in 20
X
3
30
300
3,000
2
2x3
=6
2 x 30
= 2 x 3 x 10
= 6 x 10
= 60
2 x 300
= 2 x 3 x 100
= 6 x 100
600
2 x 3,000
= 2 x 3 x 1,000
= 6 x 1000
= 6,000
20
20 x 3
= 2 x 10 x 3
= 6 x 10
= 60
20 x 30
= 2 x 10 x 3 x10
= 6 x 100
= 600
20 x 300
= 2 x10 x 3 x 100
= 6 x 1,000
= 6,000
20 x 3,000
= 2 x 10 x 3 x 1,000
= 6 x 10,000
= 60,000
200
200 x 3
= 2 x 100 x 3
= 6 x 100
= 600
200 x 30
= 2 x 100 x 3 x 10
= 6 x 1,000
= 6,000
200 x 300
= 2 x 100 x 3 x 100
= 6 x 10,000
= 60,000
200 x 3,000
= 2 x 100 x 3 x 1,000
= 6 x 100,000
= 600,000
2,000
2,000 x 3 =
2 x 1,000 x 3=
6 x 1,000
6,000
2,000 x 30
= 2 x 1,000 x 3 x 10
= 6 x 10,000
= 60,000
2,000 x 300
= 2 x 1,000 x 3 x 100
= 6 x 100,000
= 600,000
2,000 x 3,000
= 2 x 1,000 x 3 x 1,000
= 6 x 1,000,000
= 6,000,000
What patterns do you see in each row and column?
What general rules(s) for multiplying numbers with zeros can you
create?
Homework
Day 2, “Powers of Ten
Journal Prompt”