Sharp EL-531RH Manuale utente

SCIENTIFIC CALCULATOR

TEACHER’S GUIDE

JULY 1999EL-531RH

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

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

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.

Written in yellow

above the ON/C key

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≈

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

600

Press the following buttons and then start operation.

638= DEG

ANS-8= DEG

ANS-600=DEG

ANS-30= DEG

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.

300

Press the following buttons and then start operation.

638 638= DEG

ANS+2= DEG

ANS+60= DEG

ANS+300=DEG

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

Players can use any of the numbers

– 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

scores five points.

If after an agreed time limit no player has reached

,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

and the game is finished.

567 9

Press the following buttons and then start operation.

567÷9= DEG

ANS÷7= DEG

ANS-8= DEG

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

00.

Further Ideas

• Play the game using decimal starting numbers.

• Give the students a shuffled set of cards numbered from

to 9 and a shuffled set of

cards numbered

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

and the game is finished.

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

98 to 234 to get 432.

58 27

432 234

234

Press the following buttons and then start operation.

85 58

•••••••••••••••••Usingthecalculator • • • ••••••••••••••

Calculator functions used: Addition, subtraction

DEG

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:

(

0a+ b) + N = (

0b+ a)

N = (

0b+ a) - (

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.

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