30
Comparing numbers. Change of quantities
Textbook, pp. 138–142
GoalCompare integers; calculate the change of a quantity.
New words
comparison · taqqoslashchange · o‘zgarishgreater · kattasmaller · kichik
Explanation
On the number line the number further right is greater. So every positive number is greater than zero and zero is greater than every negative number. Of two negative numbers the one with the smaller modulus is greater: −2 > −5 because −2 is further right. For example −1 > −100 even though 1 < 100. The change of a quantity is final value minus initial value: change = final − initial. A positive change is an increase and a negative change is a decrease.
Worked examples
−7 and −3: −3 is further right, so −7 < −3. Increasing order: −8 < −2 < 0 < 5.
In the morning −6 °C, at noon +4 °C. From −6 to 0 is 6 degrees and from 0 to +4 is 4 more: the change is +10, i.e. 6 + 4 = 10, so it warmed by 10 °C.
Class activity
“Temperature table”: groups get a 5-day temperature table (−8, −2, 0, 3, −5). They order the days from coldest to warmest and calculate the changes between consecutive days.
Practice
1
Compare −7 and −3 (>, <).
<
2
Write −2, 5, −8, 0 in increasing order.
−8, −2, 0, 5
3
The temperature was −6 °C in the morning and +4 °C at noon. By how many degrees did it change?
10
4
Why is −1 > −100 even though 1 < 100?
−1 lies further right than −100 on the number line: owing 100 is worse than owing 1.