Page 90 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Instructional Tips
Teachers can:
• use a variety of strategies, including representing using visual models, patterning, and coding, to build students’ understanding of the relationship between the sign and size of an exponent and the value of a power;
• begin the learning with patterns involving bases that are natural numbers, then extend the learning to bases that are integers, unit fractions, and proper and improper fractions;
• extend a pattern from numeric bases to variable bases to build students’ understanding of how to generalize the relationship between the sign and size of an exponent and the value of a power;
• create opportunities to illustrate why scientific notation can be useful for representing extremely
large and extremely small numbers, including negative numbers; for example, instead of writing 0.000 000 002 5 m, it is simpler and more efficient to write 2.5 × 10−9 m.
Teacher Prompts
• What happens to the value of a power when the size of the exponent decreases by 1?
• What happens to the exponent of the power when the value of the power is multiplied by the base of the power? (For example, what happens to the exponent of 74 when you multiply this
power by 7?)
• What is the value of a power with an exponent of 0? How do you know?
• How would you show in a different way that 3−2 = 19?
• What are some situations where you have noticed numbers written in scientific notation?
• What do you notice when you divide or multiply a number repeatedly by 10? What is the
connection to showing this in scientific notation?
• How would you use patterning to write 23.7 × 105 in scientific notation?
Sample Tasks
1. Give students different base numbers. Have each student make their own patterning chart like those in the example above.
2. Have students use powers to form as many expressions equal to 1000 as they can.
3. Have students determine, using a strategy of their choice, which number is smaller, −4 × 103 or 4 × 10−3.
4. Have students explain how they would write 0.005 689 and 479 000 in scientific notation.
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