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3. a) 70 000 000 5 000 000 300 000 8000 400 3
b) 60 000 000 000 4 000 000 000 300 000 000 8 000 000 400 000 70 000 200 4
c) 90 000 000 9 000 000 300 000 300 20 7
5. a) 881 462 has 80 thousands, so 10 000 more will be
90 thousands. I replace the second 8 with 9: 891 462.
b) 2 183 486 has 100 thousands, so 100 000 less will leave
0 hundred thousands. I replace 1 with 0: 2 083 486.
c) 746 000 has 0 millions, so 1 000 000 more will mean
I write a 1 in front of the 7: 1 746 000.
d) 624 327 207 has 4 millions, so 1 000 000 less will leave
3 millions. I replace 4 with 3: 623 327 207.
6 276 089
24 342 584
2 460 069 018
6. 1 000 000 000 200 000 000 70 000 000 4 000 000
900 000 10 000 5000
1000 thousands or
100 ten-thousands
20 000
4 000 000
900 000
5 000 000 000
Numbers Every Day
Students should use place-value concepts to explain how they
rounded each time.
475 500; 475 000; 480 000
3 045 300; 3 045 000; 3 050 000
40 500; 40 000; 40 000
16 944 500; 16 945 000; 16 940 000
Remind students how to use Base Ten Blocks to
model numbers. As a class, discuss what Base
Ten Blocks for larger and larger place values
would look like. Ask:
• Suppose there were Base Ten Blocks for ten
thousand and one hundred thousand. What
would they look like?
(The ones place is represented by unit cubes. The tens
place is represented by rods, which are ten unit cubes
in a row. The hundreds place is represented by flats,
which are ten rods. The thousands place, which is ones
in the thousands period, is represented by a cube. The
thousands cube is ten hundred flats. A ten thousand
block would be a rod. It would be 10 thousand cubes
in a row. Similarly, a hundred thousand block would
be a flat. It would be 100 thousand cubes arranged
in a square.)
The patterns in the periods in a place-value
chart are similar to the patterns in the shapes of
the Base Ten Blocks. Within each period in the
place-value chart, the digits (from right to left)
are ones, tens, hundreds. With Base Ten Blocks,
the blocks that represent ones are cubes, the
blocks that represent tens are rods, and the
blocks that represent hundreds are flats.
Practice
Assessment Focus: Question 10
Students should understand that the mystery
number has a 7 in the millions place. They
realize that they must find two sets of three same
odd-number digits that added to 7 make 31.
Unit 2 • Lesson 2 • Student page 37
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Home
8.
Billions
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T
Millions
O
1
H
2
T
0
Thousands
O
0
H
4
0
T
9
0
O
2
0
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Units
H
3
0
T
8
0
O
6
0
9. The student did not realize that the 3 is in the millions place
1 274 915 000
Two hundred eighty million
and that the digits in the thousands period are all 0.
The number is three million one hundred forty-six.
10. I know the number has 7 digits, and the first digit is 7.
Since all digits are odd, and the digits in the thousands
period are the same, I wrote all possible numbers, then
checked to see which digits added to make 31.
7 111 111 I can tell the sum is less than 31.
7 111 333 I can tell the sum is less than 31.
7 333 333 I can tell the sum is less than 31.
7 111 555 The sum is 25.
7 111 777 The sum is 4 7 3 1 31.
So, I know another number is 7 777 111.
7 333 555 The sum is 7 3 3 3 5 31.
So, I know another number is 7 555 333.
7 111 999 The sum is 37.
I know that any other combination of odd numbers will give
a sum that is greater than 31, so I need not check anymore.
REFLECT: The number has 7 digits, so I know that the first digit,
5, is in the millions place. The digits 4, 8, and 7 are in the
thousands period, so their values are 400 000, 80 000, and
7000. I know that the last 3 digits are in the units period, so
their values are 300, 0, and 2.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand the organization
of large numbers into periods.
Extra Support: Provide students with place-value charts
to record large numbers.
Students can use Step-by-Step 2 (Master 2.10) to complete
question 10.
Accuracy of procedures
✔ Students can use place-value concepts
to read large numbers and to represent
large numbers in a variety of forms.
Extra Practice: Have students research to find more large
numbers used in the context of world records. Students record
the numbers in standard and expanded forms.
Students can complete Extra Practice 1 (Master 2.22).
Extension: Challenge students to find the names of some
periods beyond the trillions. (Answer: quadrillion, quintillion,
sextillion, septillion, octillion, nonillion, decillion)
Recording and Reporting
Master 2.2 Ongoing Observations:
Whole Numbers
10
Unit 2 • Lesson 2 • Student page 38