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Peter Foxp-fox@ti.com
MAWA 2017
Coding
Critical Thinking
Reasoning
Problem Solving
Coding
Contextualise and de-contextualise problems
Coding
Persevere on a Task
Coding
Design
Build
Test
ProgrammingTI-CodesFree getting started lessons and activities, complete with teacher notes!
http://education.ti.com/aus-nz/ticodes
100 Problems worth Coding
100 Problems worth Coding
100 Problems worth Coding
What’s so special about: 739 397 ?
Special Numbers
Is 739 397 prime?Successively removing the most significant digit (left) and the resulting number is still prime!
What’s so special about: 739 397 ?
Special Number
Is 739 397 prime?Successively removing the least significant digit (right) and the resulting number is still prime!
Can you find some other numbers that are left and right reducing prime? Could you write a program to search?
Special Number
TI-Nspire is a mathematics tool and includes an ‘IsPrime’ command.
Write a program to check primality and use it as a ‘sub-routine’.
Six ‘random’ numbers are drawn consisting of a nominated quantity of ‘large’ and corresponding quantity of small numbers.Large: {25, 50, 75, 100}Small: {1, 2, 3 … 9, 10}
No RepeatsRepeats Allowed
Letters & Numbers
A three digit target number is generated. Contestants use the numbers and basic operations: { + – × ÷ ( ) } to form an equation equal to, or as close to, the target number.
Letters & Numbers
Let’s play a game!60 seconds on the clock!100 Pts = Exactly correctOne point is deducted for each unit away from
Letters & Numbers
STARTSTOP
Letters & Numbers
Sometimes it can be very difficult to solve the problem in the allocated time.
Letters & Numbers
How many points would it be worth if you could ‘buy’ an extra number?How many points would it be worth to buy an extra mathematical operator?
Letters & Numbers
Mathematical expressions can only use: + − ÷ × ()
The problem is not always solvable … particularly in 60 seconds!
Letters & Numbers
Find a rule that uses the prime factorisationof a number to predict the total quantity of factors for the given number.
Factors in their Prime
Write a program that determines the quantity of factors for a given number.
Factors in their Prime
Use the factor command to determine the prime factorisation of each of the following numbers: 36, 196, 1089, 484Check the number of factors for each.
Factors in their Prime
Use the factor command to determine the prime factorisation of each of the following numbers: 252, 300, 1575, 1452Check the number of factors for each.
Factors in their Prime
Look at the data.What part(s) of the prime factorisationshould we explore if we are seeking to find a ‘rule’ for the quantity of factors?
Factors in their Prime
Roll a die … you score the number appearing uppermost, unless it is a two. If you roll a two your out and your score is set to zero. You keep rolling, adding to your score … until you decide to ‘sit’.
Greedy Pig
Play a game, highest score wins!If you played lots of games and the overall winner was the person with the highest average score … what would be a winning strategy?
Greedy Pig
Start with any positive integer n, • If n is even then divide by 2.• If n is odd, multiply by 3 and add 1.Repeat this process... you will eventually arrive at 1. (Conjecture)
Collatz Conjecture
Collatz ConjectureNumber
x 3 + 1
= 1 ?
NO÷ 2
YESEVEN
Number
FinishYES
Input "NUMBER ",NWhile N>1
If remainder(N,2)=0 : ThenN/2→N
Else3*N+1→N
EndDisp NEnd
Let’s write some code …
Collatz Conjecture
What is the largest sequence produced by a two digit number?
Collatz Conjecture
Graph the term number against the value of the term … Why does the sequence always decrease immediately after an increase?
Collatz Conjecture
Do prime numbers generate longer sequences than composite numbers?What types of numbers generate the longest sequences?
Collatz Conjecture
Can you have a sequence with more odd numbers than even?Compare the occurrence of odd numbers and even numbers in sequences.
Collatz Conjecture
Are the any sequences that share the same value as the starting number?
Collatz Conjecture
Which numbers can be approached from above and below?
Collatz Conjecture
Write and code your own exploration.
Collatz Conjecture
Every even number greater than 2 can be written as the sum of two prime numbers.
Goldbach Conjecture
For i, 1, n
isPrime(i)
NoDisplay i,n
YesisPrime(n-i)
Next i
No sol.
No
Yes
Goldbach Conjecture
Request "Enter a number",nFor i,2,n
If isPrime(i) and isPrime(n – i) ThenDisp i, n – i
EndIfEndFor
Goldbach Conjecture
Request "Enter a number",nFor i,3,n,2
If isPrime(i) and isPrime(n – i) ThenDisp i, n – i
EndIfEndFor
Goldbach Conjecture
As the magnitude of n increases, on average, are there more or less solutions?
Goldbach Conjecture
“Every odd number greater than 5 can be written as the sum of three primes.”
Goldbach Conjecture
Is this the same conjecture?
Two points are placed randomly inside a 1cm x 1cm square. What is the average distance between the two points?
How Long
Generate a sample of size n and compute the average.
Generate multiple samples of size n and store them in a list.
How Long
A triangle with vertices A, B & C is drawn on the Cartesian plane. Point P is randomly placed within the triangle.
Chaos
Randomly select a vertex. Point P is relocated half way between the current location and the vertex. This process is repeated …
Chaos
Where will the points appear in the triangle?• Everywhere – randomly
• Selected locations forming a pattern
Chaos
1 2 3 4 5 61
Roll the dice… if the glass is empty, fill it up; if the glass is full… drink the contents. The game ends the instant all glasses are full. How many glasses would you expect to drink?
354516213
Drinking Game
Consider a list:cups:={0,0,0,0,0,0}
Drinking Game
What is this command doing?While sum(cups)<6 …
What about this set of commands?c:=randint(1,6)If cups[c]=0 Then
cups[c]:=1Elsecups[c]:=0Endif
Drinking Game
Write a program that generates a simulation of the drinking game displaying the progressive results and … when the game is over … the number of glasses consumed.
Drinking Game
Edit the program so that it generates multiple results from games and stores them in a list. Note: Do not display progressive glass status.
Drinking Game
Alex and his friend Gustav have a wager … They toss a single coin repeatedly until their selected sequence of 3 events is generated. Gustav says he would like to bet on the sequence: “H, T, H”. Alex chooses “T, T, H”. Is the game fair?
Penny’s Problem
Edit the program so that it generates multiple results from games and stores them in a list. Note: Do not display progressive glass status.
Activity coming soon …
Penny’s Problem
Factor Game
Player 1:Selects 49
Player 2:Sum of factors: {1, 7}
Player 1:Player 2:
498
Must select a number that has a proper factor available.
Factor Game
Player 1:Sum of factors: {2, 19}
Player 2:Selects 38
Player 1:Player 2:
49846
70
Factor Game
Player 1:Selects 45
Player 2:Sum of factors: {3,5,9,15}
Player 1:Player 2:
7046
11578
Factor GameYour turn…Play against a partner or play against the calculator.
Factor GameDoes an automatic scoring system change the level of thinking?
Factor GameDoes an automatic scoring system change the level of thinking?
Factor Game
Write a program … so a single user can play against the calculator. This is a level of ‘artificial intelligence’.
Josephus ProblemThe siege at Yodfat: Preferring suicide to capture, the 40 soldiers stood in a circle. Starting with the first soldier, he killed the soldier sitting to his left (soldier 2) and so forth around the circle leaving only one soldier to be captured.
Josephus ProblemThe siege at Yodfat: As Josephus lived to tell of the ritual, where was he sitting?Write a program to explore ‘any’ number of soldiers.
Josephus ProblemActivity coming soon …You may also like to explore LUA coding. A sample code in Lua (not for TI but helpful) can be found at: https://rosettacode.org/wiki/Josephus_problem#Lua
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