20170616 calc prog v4 postpresent

何明華會督銀禧中學

STEM: Using Calculator Programming to Solve Mathematics Problems & Learn Coding

Background

Rationale

Implementation

Phase 1: Pilot

Next Step


• “Integrate and apply knowledge and

skills across disciplines to solve

AUTHENTIC problems” (EDB 2016)

Question:

What are the AUTHENTIC problems students face?


Scratch Games?Scratch Games?

3D Printing?

3D Printing?

Robot?Robot?


• “Integrate and apply knowledge and

skills across disciplines to solve

AUTHENTIC problems” (EDB 2016)

Question:

What are the devices students use most frequently

which is related to learning & teaching?


PC?PC?Smart Phone?Smart Phone?

Tablet?Tablet?


• F4 Maths: Calculator Programming for

DSE

– Quadratic Equation

– Simultaneous Linear Equations

– Cosine Formulae


– This is the AUTHENTIC PROBLEM students facing

– Calculator is the most frequently device used by students which is related to (Maths) learning & teaching.


• Students NEED these programs

(Authentic Problem) but….

– Mathematics: not teaching / only teach how to

enter

– ICT: not teaching


?��A: ? ��B: ?��C:

-A/B��-C/A�� -C/B


Level 4Students can identify users’ need, then design & develop a programStudents can identify users’ need, then design & develop a program

Level 3Students can write a program given a known situationStudents can write a program given a known situation

Level 2Students understand the inputted programStudents understand the inputted program

Level 1Students can input a given programStudents can input a given program

Level 0Students know nothing about calculator programmingStudents know nothing about calculator programming


• Introduce the Calculator Programming

Curriculum

– Maths x ICT

– F3

– Part of the STEM initiative


Background

Rationale

Implementation

Phase 1: Pilot

Next Step


• Aims:– Nurture students’ problem solving mindset

– Coding

– Solving Maths problems

• Tool:– Casio 50FHII


Background

Rationale

Implementation

Phase 1: Pilot

Next Step


• Target Students: F3– Adequate Maths Knowledge

– Ready to apply calculator programming in F4

• Chapters1. Flowchart

2. Programming Introduction

3. Simple Programming

4. Control Structure

5. Design Your Own Maths Program

6. Calculator Games


• Basic Operations

1. Editing /Running /

Deleting a Program

2. Typing Special Characters

3. Inserting /Overwriting

Characters

4. Meaning of symbols


• Using Mathematics

Topics as Examples

1. Pythagoras Theorem

2. Co-Geo (Rotation above

the origin)

3. Angle Sum of Polygons


1. Pythagoras Theorem

• ICT Elements:

– Input/Output Analysis

– Coding

• Maths Elements:

– Pyth Thm


2. Rotation

• ICT Elements:

– Coding

– Testing

– Flowchart

• Maths Elements:

– Deducing the General Case

– Rotation



• Procedural

• Selection

• Iteration

– Not implemented in the

pilot phase


Problem Solving Procedures

1. What is your actual need? (Spot the

problem, define the problem)

2. Problem Analysis

3. Algorithm Design

4. Implementation

5. Testing/Debugging


Is there any Maths Formulae I want to

“programmize”?

Warm Up:

– Co-Geo

– Simultaneous Equations


Co-Geo (F3 Maths)

– Input: x1,y1,x2,y2

– What do you want to find?

– What else can you find?


Co-Geo (F3 Maths)


Co-Geo (F4 Advanced Version

Modified by an ICT Student)


Simultaneous Linear Equation (F2 Maths)

– What are the inputs?

– What are the outputs?


Step 1 :

Solve

2x+3y-4=0

5x+6y-7=0

Step 2 :

Solve

Ax+By+C=0

Dx+Ey+F=0




?��A: ?��B: ?��C:

?��D: ?��X: ?��Y:

(CX-YB)/(DB-XA)��

(CD-YA)/(AX-BD)


Simultaneous Linear Equation (F4 Version)


Next Step:

Is there any Maths Formulae I want to

“programmize”?

- Volume of Sphere?

- Compound Interest?


Basic:

1.Random Number

2.Throwing a Dice

3. Lucky Draw (from a class of N

students)


1.Throwing a Dice

FIX 0:1+5Ran#

• ICT Elements:

– Manipulation of Random

Number

• Maths Elements:

– If 0<x<1, how to manipulation

x such that the output lies

between 1 and 6 inclusive?


2. Lucky Draw

? �� A:FIX 0:1+ARan#

• ICT Elements:

– Use of variables

• Maths Elements:

– If 0<x<1, how to manipulation

x such that the output lies

between 1 and N inclusive?


Advanced:

1.Slot Machine (老虎機老虎機老虎機老虎機)

2. Liar’s Dice (大話骰大話骰大話骰大話骰)

3. Shooting Duck (射鴨仔射鴨仔射鴨仔射鴨仔)


1. Slot Machine (老虎機老虎機老虎機老虎機)

- Output: 111-777

• Maths Elements:– Concept of place value

• ICT Elements:– Algorithm Design


2. Liar’s Dice (大話骰大話骰大話骰大話骰)

- Output: Simulating 3 Dices

- Modified from Slot Machine

• Maths Elements:

– Concept of place value

• ICT Elements:

– Algorithm Design


3. Shooting Duck (射鴨仔射鴨仔射鴨仔射鴨仔)- 1111111111 represents 10 wooden

logs.

- Player has to guess which log had

duck hidden by choosing the log

number (1-9)

- E.g. “3” is chosen.

If duck is there: 1111111211

If duck is not there: 11111111011


1. Shooting Duck (Simplified version)

• Maths Elements:

– Concept of place value

? �� A:

1111111111+10^(A-1)*(-1)^(1000Ran#)



? �� A:

1111111111+10^(A-1)*(-1)^(1000Ran#)

E.g. A=3

Possible Outcomes:

1111111111+100=1111111211

1111111111-100=1111111011



? �� A:

1111111111+10^(A-1)*(-1)^(1000Ran#)

Follow up Questions:

- Why?

- What is the behavior of (-1)n?

- What is the probability of shooting a duck? (1/10? ½?)

- What if I input “10”?



• Maths Elements:– Behavior of (-1)n

– Place value

– Probability

• ICT Elements:– Coding

– Limitation of a program

? �� A:

1111111111+10^(A-1)*(-1)^(1000Ran#)


Next Step:

Design Your Own Game!

(Maker Rationale)


Background

Rationale

Implementation

Phase 1: Pilot

Next Step


• Pilot (~4 hrs)

1. Flowchart



4. Control Structure (Not implemented)

5. Design Your Own Maths Program (Partially implemented)

6. Calculator Games (Partially implemented)


• Full Curriculum (~7 hours)

1. Flowchart




5. Design Your Own Maths Program

6. Calculator Games


What are the Aims?

• Solve Maths Problems?

• Understanding Programming Concept?

• Understanding Calculator Programming Concept (For

DSE)?

• Raise their interest in both Maths & Coding?

STEM = high tech ?


Background

Rationale

Implementation

Phase 1: Pilot

Next Step


1. Implement the Full Curriculum

- In normal lesson time?

- As ECA?

2. Supports in F4


Programs:A1 [Quad Eqt] : Delta,Root1,Root2,h,k,sum of roots, prod of roots

A2 [Linear Eqt]: x,y,Slope,x-int,y-int

A3 [Factor Thm]: (ax+b)(cx2+dx+e)

A4 [Co-Geo]: m, dist, ax+by+c=0, section formula

B1 [Cos Formula]: Input SAS, Find area & S

B2 [Cos Formula]: Input SSS, Find area (Heron) & Angle

B3 [AS/GS]: Input a, r/d, n, output T(n), S(n), sum to infinity

B4 [Circle]: x2+y2+Dx+Ey+F=0, input D,E,F, output center, r

20170616 calc prog v4 postpresent

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