Sharp EL-531RH User manual

SCIENTIFIC CALCULATOR
TEACHER’S GUIDE
JULY 1999EL-531RH

1
Contents
Generating Sequences………………………………………………………………………p.39
Train Journeys………………………………………………………………………………p.41
Simulated Dice……………………………………………………………………………p.43
Mean Dice Scores…………………………………………………………………………p.45
Again and Again……………………………………………………………………………p.47
Fibonacci……………………………………………………………………………………p.49
Factorizing Quadratics……………………………………………………………………p.51
Triples………………………………………………………………………………………p.53
Teacher’s Guide Part 1has already been completed.This guide presents Part 2 beginning on page
39 (marked with ). We encourage you to put this guide to good use.
Introduction………………………………………………………………………………………………p.2
How to Operate…………………………………………………………………………………p.3
Number of Bowling…………………………………………………………………………………p.4
Down to One…………………………………………………………………………………p.6
Reverse the Order…………………………………………………………………………………p.8
Different Products…………………………………………………………………………………p.10
Sums and Products…………………………………………………………………………………p.12
Target 100……………………………………………………………………………………p.14
Ordering Fractions…………………………………………………………………………………p.16
Addting Fractions…………………………………………………………………………………p.18
Halfway Between…………………………………………………………………………………p.20
Near Integers…………………………………………………………………………………p.22
Reshaping Cuboids…………………………………………………………………………………p.24
Function Tables…………………………………………………………………………………p.26
Palindromes…………………………………………………………………………………p.28
Trial and Improvement………………………………………………………………………p.30
Last Digits…………………………………………………………………………………p.32
A Question and Interest……………………………………………………………………p.34
Getting Even…………………………………………………………………………………p.37

2
The use of calculators as a classroom teaching tool is becoming more and more
popular.Contrary to the belief that their use encourages dependency and inhibits
the development of mental skills,research has proven that calculators are highly
unlikely to harm achievement in mathematics and using them can actually improve
the students’ performance and attitude.* Calculators allow students to quickly gen-
erate large amounts of data from which patterns can be spotted,and predictions can
be made and tested.This is an important aspect of the development of mental meth-
ods of calculation.Therefore,priority must be given to create new ways to exploit
the potential of the calculator as an effective learning tool in the classroom.
ThisTeacher’s Guide presents several classroom activities that make use of Sharp
scientific calculators.The purpose of these activities is not to introduce the calcula-
tor as a device to relieve the burden of performing difficult calculations,but rather
to develop the students understanding of mathematical concepts and explore areas
of mathematics that would otherwise be inaccessible.Mental methods should al-
ways be considered as a first resort when tackling calculations introduced in these
activities.The development of trial and improvement methods are supported by the
activities as well.We hope you will find them interesting and useful for reinforcing
your students’ understanding of mathematical concepts.
* MikeAskew & DylanWilliams (1995) Recent Research in Mathematics Education HMSO
Introduction

3
How to Operate
2nd function key
Pressing this key will enable the functions written
in yellow above the calculator buttons.
ON/C,OFF key
Direct function
Mode key
This calculator can operate in three different
modes as follows.
<Example>
Written in yellow
above the ON/C key
<Power on> <Power off>
1.KEY LAYOUT
•Mode = 0;normal mode for
performing normal arithmetic
and function calculations.
•Mode = 1;STAT-1 mode for
performing 1-variable
statistical calculations.
•Mode = 2;STAT-2 mode for
performing 2-variable
statistical calculations.
If the calculator fails to operate normally,press the reset
switch on the back to reinitialise the unit.The display format
and calculation mode will return to their initial settings.
RESET
2. RESET SWITCH Reset switch
RESET
2nd function
[Normal mode]
[STAT-1 mode]
[STAT-2 mode]
NOTE:
Pressing the reset switch will erase any data stored in memory.
≈Read Before Using≈

4
Number Bowling Junior high school
•••••••••••••••••Using the calculator • • • ••••••••••••••
Calculator functions used:Subtraction,addition,last answer memory
•••••••••••••••••••••Objective •••••••••••••••••••••
Read whole numbers and understand that the position of a digit signifies its value.
Understand and use the concept of place value in whole numbers.
•••••••••••••••Explanation of the activity ••••••••••••••
Think of a 3-digit number and enter it into your calculator.
Pretend each digit is a“bowling pin.”
Knock down each pin one at a time,so that your calculator display shows 0.
A: Using subtraction
B:Using addition
(1) Enter a 3-digit number.
(2) Knock down one digit,or“pin”;i.e.change the last
digit to a 0.
(3) Knock down the next pin;i.e.change the tens column
digit to 0.
(4) Knock down the pin of the hundreds column.
A: Using subtraction
638
8
30
600
Press the following buttons and then start operation.
638= DEG
ANS-8= DEG
ANS-600=DEG
ANS-30= DEG

5
Junior high school
(1) Enter a 3-digit number.
(2) Knock down one digit,or pin;i.e.change the last digit
to a 0,except this time,do so by adding a number to
the last digit to make it 0.
(3) Knock down the next pin;i.e.change the tens column
digit to 0.
(4) Knock down the pin of the hundreds column.
B:Using addition
Number Bowling
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
This activity is a good game for students to play in pairs.
One student enters a number in the calculator,and the other student has to knock each digit,or
“pin,” down.
Example:
638 - 8 = 630
630 - 30 = 600
600 - 600 = 0
•••••••••••••••Points for students to discuss • • • •••••••••••
It is important for students to talk about what they are doing and use the appropriate language,for
example:“six hundred and thirty,minus thirty,equals six hundred.” Students should be challenged
to vary the starting point;i.e.sometimes starting with the hundreds digit and sometimes with the
tens digit.
Further Ideas
• Play the game using 2-,4-,or 5-digit numbers according to the ability of the students.
2
60
300
Press the following buttons and then start operation.
638 638= DEG
ANS+2= DEG
ANS+60= DEG
ANS+300=DEG

6
Down to One Junior high school
•••••••••••••••••Using the calculator • • • ••••••••••••••
Calculator functions used:Subtraction,division,last answer memory
•••••••••••••••••••••Objective •••••••••••••••••••••
Develop a variety of mental methods of computation.
Develop the use of the four operations to solve problems.
Use sequence methods of computation when appropriate to a problem.
Estimate and approximate solutions to problems.
•••••••••••••••Explanation of the activity ••••••••••••••
Use the calculator to generate a 3-digit random number.
The aim is to get the calculator to display the number 1 .
Players can use any of the numbers 1 – 9 together with any of the keys below:
, , , , , ,
You cannot put numbers together to make 2- or 3-digit numbers.
You can use each number only once.
The first player to get his/her calculator display to show 1 scores five points.
If after an agreed time limit no player has reached 1 ,the player who is closest scores two points.
While working on this activity,students should develop their skills of mental mathematics and their
fluency with numerical calculations.
Suppose the random number you generate is 567.
Example A:
The answer is 1 and the game is finished.
567 9
7
8
Press the following buttons and then start operation.
567÷9= DEG
ANS÷7= DEG
ANS-8= DEG

7
Junior high school
Down to One
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
Students should be encouraged to estimate the results of calculations and think about the appro-
priate operations and numbers to use during the game.Let’s start with 864,for example.This
number is divisible by 9,6,3 and 2.The equation 846 ÷9 could therefore be a possible first step.
This will prompt students to test the divisibility of numbers.Students should also be encouraged to
think about the various strategies they use.
The game could be played between small group of students.
•••••••••••••••Points for students to discuss • • • •••••••••••
For some students,it may be more appropriate to start with a 2-digit number.In this case,the calcula-
tor should be set to fixed decimal place mode by pressing the [2ndF] key once and then pressing the
[ .] key,which has FSE written in yellow above it,until FIX is displayed at the top of the calculator
screen.And press [2ndF] [TAB] and [0] keys.Doing this will round answers to 0 decimal places.The
starting number can then be generated by multiplying a random number by 1 00.
Further Ideas
• Play the game using decimal starting numbers.
• Give the students a shuffled set of cards numbered from 1 to 9 and a shuffled set of
cards numbered 1 0,20,30,40,50.Students choose five cards from the first set,and
two cards from the second set.The calculator is then used to generate a random three
digit integer,and the students have to make this total by using the numbers on the cards.
Example B:
You want to subtract 8 from 9,but you cannot since you have already used 8 once.
So...
The calculator displays 1 and the game is finished.
9
8
3
2

8
Reverse the Order
Junior high school
•••••••••••••••••••••Objective •••••••••••••••••••••
Develop a variety of mental methods of computation.
Estimate and approximate solutions to problems.
•••••••••••••••Explanation of the activity ••••••••••••••
Enter any 2-digit number into the calculator.
Reverse the order of the digits through simple calculator operations.
While working on this activity, students should develop their skills of mental mathematics.
They should also be interpreting and generalizing their answers.
Example A:
To reverse the order of 58:
Solution:Add 27 to 58 to get 85.
Now try using a 3-digit number.
Example B:
Enter 432 into the calculator
Solution:Add 1 98 to 234 to get 432.
58 27
432 234
234
1 98
Press the following buttons and then start operation.
85 58
•••••••••••••••••Usingthecalculator • • • ••••••••••••••
Calculator functions used: Addition, subtraction
DEG
DEG
DEG
DEG

9
Junior high school
Reverse the Order
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
This activity is probably best introduced orally to a group of students.Ask the students to enter
any two digit number into their calculators.Then,ask them to find a simple way to reverse the
order of the digits of these numbers.Students may do this by using inverse operations.
•••••••••••••••Points for students to discuss • • • •••••••••••
After trying an example,the students can talk about the operations and numbers that they used.
This discussion should lead to the generalization that one way to reverse the order of the digits is
to add or subtract a multiple of 9.More able students could be asked to try and prove this gener-
alization:
( 1 0a+ b) + N = ( 1 0b+ a)
N = ( 1 0b+ a) - ( 1 0a+ b)
N = 9b- 9a= 9(b- a)
Further Ideas
Try using the activity with 3-digit numbers,4-digit numbers,etc.
Choose any 2-digit number,reverse it,and then add the reversed number to the original.
What happens?Try this with 3-digit numbers or 4-digit numbers,etc.