Sharp EL-531RH, Teachers Manual

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13
Junior high school
Sums and Products
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
This activity could be introduced orally.
The largest product is 25, given by 5 x 5. Some students may need to be encouraged to consider
decimal numbers to verify that the largest product is 25. More able students should be encouraged
to try and prove that this is the largest product.
One method of using the calculator is to enter the product as two numbers that can be edited.
Some students may prefer to enter the product as an expression such as 2 x (
1
0 - 2), which can be
edited.
• • • • • • • • • • • • • • • Points for students to discuss • • • • • • • • • • • • • •
Students could be encouraged to devise similar problems to give to each other involving numbers
with different sums.
Further Ideas
• Investigate products of 3, 4, 5... numbers which have the same sum. This could be explored
graphically.
(Generally, for two numbers whose sum is n, the largest product is given by (n/2)
2
, for three
numbers whose sum is n, the largest product is given by (n/3)
3
... The nearest integer to (n/e)
where e = 2.7
1
8 is the number of numbers which will give the maximum product.)
• The problem of finding two numbers whose product is a given total can be turned into a
game where students score points according to the number of trials they perform to
identify the solution. For example: The sum of two numbers is
1
0 and their product is
1
9.7
1
. What are the two numbers?
Ans: The two numbers whose product is
1
9.7
1
are 7.3 and 2.7.