Page 94 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Instructional Tips
Teachers can:
• highlight the concept that any number, including an integer, can be applied to many different contexts, and that negative-number contexts can be thought of as the opposite of positive- number contexts; for example, +5 can represent how much money you have saved or added to your account, while −5 tells how much you have spent or taken out of your account;
• support students in incorporating visual representations and manipulatives to illustrate and determine location, direction, amount, and changes in these;
• emphasize the meanings of both the sign and size of an integer being used to describe location, direction, and amount when performing operations with integers.
Teacher Prompts
• Why is it sometimes helpful to use negative numbers to describe real-life situations? What does the negative sign represent in all of those situations?
• What is the purpose of benchmarks such as zero? One?
• How would you represent –50?
• How are 50 and –50 the same? different?
• If the answer is –7, what might the question be?
• How could you use a negative integer to describe an object that is 30 metres below the surface of a lake? Or to state that a company is in debt by $10 000?
Sample Tasks
1. Have students work in groups to describe scenarios in which negative integers might be used.
2. Have students describe the changes in the direction, location, and distance travelled by a train starting from 3 km west of a station and travelling to 5 km east of the station.
3. Have students represent the following:
• paying $50 from your bank account that had $400
• a temperature drop of 5 oC from 25 oC
• being paid $120 after owing $30
4. Present the following scenario: At 5:00 a.m., the temperature was −3 oC.
• Have students use a number line to determine the change in the temperature from 5:00 a.m. to 2:00 p.m. if the temperature was 6 oC at 2:00 p.m.
• Have students use counters or tiles to determine the temperature at 10:00 a.m. if the temperature rises steadily by 2 oC every hour.
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