Sharp EL-531RHB Operation Manual

SCIENTIFIC CALCULATOR

TEACHER’S GUIDE

EL-531RH

Contents

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

Introduction

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 generate large amounts of data from which patterns can be spotted, and predictions can be made and tested. This is an important aspect of the dev elopment of mental methods 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.

This Teacher’s Guide presents several classroom activities that make use of Sharp scientific calculators. The purpose of these activities is not to introduce the calculator 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 always be considered as a first resort when tackling calculations introduced in these activities. The development of trial and improvement methods ar e supported by the activities as well. We hope you will find them interesting and useful for reinforcing your students’ understanding of mathematical concepts.

* Mike Askew & Dylan Williams (1995) Recent Research in Mathematics Education HMSO

≈Read Before Using≈

1. KEY LAY OUT

How to Operate

2nd function ke y

Pressing this key will enable the functions written in yellow above the calculator buttons.

ON/C, OFF key Direct function

2nd function

Written in yellow above the ON/C key

Mode ke y

This calculator can operate in three different modes as follows.

[Normal mode]

[STAT-1 mode]

•Mode = 0; normal mode for performing normal arithmetic and function calculations.

•Mode = 1; STAT-1 mode for performing 1-variable statistical calculations.

[STAT-2 mode]

RESET

2. RESET SWITCH

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.

NO TE:

Pressing the reset switch will erase any data stored in memory.

•Mode = 2; STAT-2 mode for performing 2-variable statistical calculations.

Reset switch

RESET

Number Bowling

Junior high school

•••••••• •••••••••••••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

• •••• • ••••• ••• •••Using the calculator • • • •••••••• • • ••••

Calculator functions used: Subtraction, addition, last answer memory

A: Using subtraction

Press the following buttons and then start operation.

(1) Enter a 3-digit number.

638

(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.

638=

ANS-8=

ANS-30=

DEG

(4) Knock down the pin of the hundreds column.

600

ANS-600=

DEG

Number Bowling

B: Using addition

Press the following buttons and then start operation.

Junior high school

(1) Enter a 3-digit number.

638

(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.

300

638=

DEG

ANS+2=

DEG

ANS+60=

DEG

ANS+300=

• • • • • • • • • • • 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.

Down to One

Junior high school

•••••••• •••••••••••••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 n umber 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.

• •••• • ••••• ••• •••Using the calculator • • • •••••••• • • ••••

Calculator functions used: Subtraction, division, last answer memory

Press the following buttons and then start operation.

Suppose the random number you generate is 567.

Example A:

567 9

567÷9=

ANS÷7=

DEG

The answer is 1 and the game is finished.

ANS-8=

DEG

Down to One

Press the following buttons and then start operation.

Junior high school

Example B:

DEG

567÷7=

567 7

ANS-9=

DEG

ANS÷8=

DEG

You want to subtract 8 from 9, but you cannot since you have already used 8 once. So...

ANS÷3=

DEG

ANS-2=

DEG

The calculator displays 1 and the game is finished.

• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •

Students should be encouraged to estimate the results of calculations and think about the appropriate 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 calculator 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 100.

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 10, 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.

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.

• •••• • ••••• ••• •••Using the calculator • • • •••••••• • • ••••

Calculator functions used: Addition, subtraction

Press the following buttons and then start operation.

Example A:

To reverse the order of 58:

58 27

Solution: Add 27 to 58 to get 85. Now try using a 3-digit number.

Example B:

Enter 432 into the calculator

432

234

85-58=

DEG

58+27=

DEG

432+234=

DEG

234+198=

Solution: Add 198 to 234 to get 432.

Reverse the Order

Junior high school

• • • • • • • • • • • 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 generalization:

(10a + b) + N = (10b + a) N = (10b + a) - (10a + 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.

Different Products

Junior high school

•••••••• •••••••••••••Objective •••••••• •••••••••••••

Estimate and approximate solutions to problems.

• •••••••• ••••••Explanation of the activity ••••• •••••••••

Have the class make up multiplication problems using the digits 1, 2, 3 and 4. Each digit can only be used once. Find out what the largest product among the possible answers will be.

While working on this activity, students should practice their skills of mental estimation. They should also be interpreting and generalizing their answers.

• •••• • ••••• ••• •••Using the calculator • • • •••••••• • • ••••

Calculator functions used: Multiplication

Press the following buttons and then start operation.

What is the largest number you can make by pressing the keys and once and only once?

Example:

DEG

2 34

2 341

Can you make a larger number? Using algebra, for any four digits a, b, c, d, where a < b < c < d, the largest product is given by: (10d + a) x (10c + b).

Ans: The largest product is given by

41 32

12X34=

2X341=

41X32=

Different Products

Junior high school

• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •

This activity could be introduced to the whole class by asking students to individually make up any multiplication using only the digits 1, 2, 3 and 4. The different multiplication problems and their answers can then be compar ed and students can be set the task of finding the largest product. Students should be encouraged to estimate the answers to the various multiplication problems.

•••• ••• ••• ••• ••Points for students to discuss • • • ••••• •• ••••

Students can explore other sets of four numbers, generalizing the rule to find the largest product using words or symbols. After generalizing, explain the rule that for any four digits a, b, c, d, where a < b < c < d, the largest product is given by:

(10d + a) x (10c + b). If the investigation is extended to the five digits 1, 2, 3, 4, 5, then the largest product is given by: 431 x 52 = 22412. For some students it may be appropriate to begin with only three digits.

Further Ideas

• Find the largest product for any number of digits.

• Find the smallest product for any number of digits.

• Find the different sums that can be made by adding the digits 1, 2 and 3 once and only once. For example 12 + 3 = 15. What happens for other sets of 3-digit numbers?

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