Minds On…
Action!
Consolidate
Debrief
Concept Practice
Description
• Review 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.
Materials
• place value mats
• centicubes
• BLM 7.1, 7.2
Whole Class
Place a transparency of BLM 7.1 on the overhead projector and hand out
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 = 10 2
Represent as a power of base 10: 100 000 = 10 × 10 × 10 × 10 × 10 = 10
5
Assessment
Opportunities student copies. Prompt students to name the columns with place values from correctly. more numbers, prompting different students to correctly read the new number.
Whole Class
Individual Æ
Æ
Æ
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 Applying Concepts 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
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
Write one of the numbers from the chart on the board and ask, In how many different forms can you represent the number 574?
Ask: How do you determine the exponent of the base 10?
The final form of 574 in expanded form with powers Æ 5 × 10 2 and in scientific notation 5.74 × 10 exercises with students.
Practise
2
Demonstrate Understanding
Students complete BLM 7.2 individually.
+ 7 × 10
To reinforce understanding of the different forms, complete two or three
1 + 4,
Among the possibilities are jobs involving money, cell or bacteria counts, outer space, and astronomy.
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.
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.
Explain in your math journal what you think the exponent of base 10 would be for the number 1 or 1
100
= 0.01 or 1
10000
= 0.0001.
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 ×
10 3 , 5.001 × 10 4
Pose this question for students who need a challenge.
TIPS: Section 3 – Grade 8 © Queen’s Printer for Ontario, 2003 Page 24

Name:
Date:
Sample Numbers Place Value
Hundred millions
Ten thousands
Units
Decimal
TIPS: Section 3 – Grade 8 © Queen’s Printer for Ontario, 2003 Page 25

Name:
Date:
Complete the charts.
Standard Form 894 87.65 1 000 326
Expanded
Expanded Form with Powers
Word Form five hundred million and four tenths forty-seven and six tenths seventy-eight million
Expanded
Expanded Form with Powers seven thousandths Word Form
Expanded
Expanded Form with Powers 6 × 10 2 + 8
Scientific Notation 6.054 × 10 3
TIPS: Section 3 – Grade 8 © Queen’s Printer for Ontario, 2003 Page 26