Day 7: The Value of Place Value
Grade 8
Description
place value and correct reading of large and small numbers from
0.001 to 999 999 999.
• Represent whole numbers using word form, expanded form, and expanded
form using powers and scientific notation.
• Review
Materials
• place value mats
• centicubes
• BLM 7.1, 7.2
Assessment
Opportunities
Minds On…
Action!
Consolidate
Debrief
Concept Practice
Whole Class Æ Connection to Jobs
Pose these questions: What jobs involve the use of very large numbers? What
is being measured by these very large numbers?
Have students volunteer their ideas and record the answers on the board.
Whole Class Æ Applying Concepts
Place a transparency of BLM 7.1 on the overhead projector and hand out
student copies. Prompt students to name the columns with place values from
hundred millions on the left to thousandths on the right of the decimal column.
Fill in BLM 7.1 on the transparency and ensure each student has it completed
correctly.
Write a number on BLM 7.1 and say the number correctly as it is being written
down, e.g., 2.47 - two and forty-seven hundredths.
Curriculum Expectations/Question & Answer/Mental Note: Repeat for
more numbers, prompting different students to correctly read the new number.
Write one of the numbers from the chart on the board and ask, In how many
different forms can you represent the number 574?
Form of the number Æ Representations
Standard form Æ 574
Word form
Æ five hundred seventy-four
Expanded form Æ 5 × 100 + 7 × 10 + 4 × 1
Students will be familiar with these three forms from previous grades. To
introduce another form which expresses the expanded form with powers, ask:
How can we represent 100 as a power of base 10? 100 = 10 × 10 = 102
Represent as a power of base 10: 100 000 = 10 × 10 × 10 × 10 × 10 = 105
Ask: How do you determine the exponent of the base 10?
The final form of 574 in expanded form with powers Æ 5 × 102 + 7 × 101 + 4,
and in scientific notation 5.74 × 102
Whole Class Æ Demonstrate Understanding
To reinforce understanding of the different forms, complete two or three
exercises with students.
Individual Æ Practise
Students complete BLM 7.2 individually.
Among the
possibilities are
jobs involving
money, cell or
bacteria counts,
outer space, and
astronomy.
Home Activity and Further Classroom Consolidation
Order all the numbers on worksheet 7.2 from smallest to largest.
In your math journal, under the heading Using Large Numbers, describe a
context where large numbers are used, where you obtained this information,
and express a number used in this situation in four different ways.
In scientific
notation, a number
looks like a
number with one
non-zero digit to
the left of the
decimal times a
power of 10, e.g.,
1.23 × 10, 9.6 ×
3
4
10 , 5.001 × 10
Explain in your math journal what you think the exponent of base 10 would be
1
1
for the number 1 or 100
= 0.01 or 10000
= 0.0001.
Pose this question
for students who
need a challenge.
TIPS: Section 3 – Grade 8
© Queen’s Printer for Ontario, 2003
Students may
need to use place
value mats and
base 10 blocks.
When reading
numbers aloud it is
important to
remember ‘and’ is
used to express a
decimal point. e.g.,
sixteen and eight
tenths - 16.8,
fourteen and nine
thousandths 14.009
No ‘and’ is used in
one thousand forty
– 1040
Students are not
expected to work
with zero or
negative
exponents until
Grade 9.
Page 24
7.1: Place Value Chart
Name:
Date:
Sample Numbers
Place Value
Hundred millions
Ten thousands
3
5
2
9
Units
.
Decimal
6
TIPS: Section 3 – Grade 8
© Queen’s Printer for Ontario, 2003
Page 25
7.2: Place Value and Representing Numbers
Name:
Date:
Complete the charts.
Standard Form
894
87.65
1 000 326
five hundred
million and four
tenths
forty-seven and six
tenths
seventy-eight
million
Word Form
Expanded Form
Expanded Form with Powers
Scientific Notation
Standard Form
Word Form
Expanded Form
Expanded Form with Powers
Scientific Notation
Standard Form
Word Form
seven thousandths
Expanded Form
6 × 102 + 8
Expanded Form with Powers
Scientific Notation
TIPS: Section 3 – Grade 8
6.054 × 103
© Queen’s Printer for Ontario, 2003
Page 26