Please find assessment details for term 1 for students enrolled in Infinity Squared.
If you are the students’ regular numeracy and mathematics teacher feel free to add this information to your assessment notes.
Please note that students will also be sent a copy of their assessment via WebCT if they are still enrolled in the course. I would be greatly encouraged if you discussed these notes with them.
Thanks,
Marietta Sansom-Gower
Infinity Squared Teacher
CELO
PERTHPRIMARY SCHOOL
Infinity SquaredTERM 1, 2006Ms. Marietta Sansom-Gower
Student Name:
Task / Number Attempted / Comments / Being Numerate / Being Information LiterateWarming Up Problems / 10/10 / Simple Subtraction- Solved using most obvious solution in his second check – explained his guesses properly.
InheritanceSolved the inheritance problem and when prompted to explain his answer and the 31 shares he did so correctly.
How could you plant 4 treesCame up with a hemisphere for the planting of 3 trees which is correct – just a triangular pyramid with equal curves.
Bag of Ballsneeded to explain his answer in more detail – did so with prompting. Used the language of chance by talking about “worst case” and “best case” scenario’s. Very good explanation when asked.
Half full/Half emptyLots of questions about this but the questions are taking him further from the easiest solution. Still trying to solve the problem scientifically – using the theory of displacement.
Number squareCleverly used excel including formulas to attempt to work out the 65 number square, made a few attempts. Sent another 5 trials but still not quite there – really showing perseverance on this one which is admirable.
Finally got this correct – apparently with the aid of grogono.com.
Turning CirclesAbsolutely correct – looked at the circles and assumed 2 revolutions – did not look at it from the circumference calculation point of view. Stated that they made a representation of that on the computer – if they did using the information of “twice the diameter” then the two revolutions would have been precise.
ExplorationAssumed that a bearer can die – not suitable – needs to rethink the problem. Fellow student Doug sent in a response for both of them that proved that it can be done with 2 bearers.
GrapefruitAsked how many decimals the answer required – so must be on the wrong track. He then sent me an excel spreadsheet showing the first part of the equation and then the second part of the equation. He must have done a lot of guessing and checking and then when these were equal he realised that he had the correct values. The only problem is that he didn’t really explain it very well, I can obviously work it out but others may not be able to. Sent another email explaining what he had done using algebra – very clear and nice work.
Names and FacesWorked this one out with Teagan and did a more efficient job of this than I did – extremely logical. / Josh clearly selects from his repertoire of problem solving strategies (Standard 3 lower). Through the terminology (e.g. use of words such as contradict, worst case, best case scenario) and information tools (predominantly excel but also websites) that Josh has used, he has shown that he cannot only communicate mathematically but that he has identified the purpose for the communications. The manner in which he has solved problems, particularly through his use of excel has challenged my mathematical thinking (Standard 3 Upper).
Josh has a huge repertoire of styles to describe and explains his answers from tables to sentences to excel spreadsheets which is fantastic. On rare occasions he had to be prompted to provide a better explanation but this is continually improving. / Josh has selected and used information tools to organise and analyse information, this was clearly evidenced by the excel spreadsheet produced for the horse race problem. He has created products (predominantly excel spreadsheets) to communicate his understanding; examples of this was the spreadsheet for the number square problem as well as his solution to the grapefruit problem (however this one required greater explanation). He also accessed grogono.com in order to solve the number square problem thus demonstrating that he can access information as well as utilise and evaluate it (Standard 3 Middle). He has produced a homepage, contributed to discussion forums and from the information provided by WebCT Josh has accessed the calendar. No reports of irresponsible use of the course have been received.
It must be noted that other than the trigonometry challenge the course has not as yet demanded students to utilise a wide range of tools nor create products.
First 20 Mathematics and Logic Problems / 11/20 / Find 24 Sent an excellent email explaining how he got all the correct answers for this one. He stated that for the first request he guessed one number out, then corrected and from that he found all the others knowing that 11, 12 and 13 would be near the numbers.
What 2 digit Got this one and explained it clearly using steps and calculations which was excellent. Horse Race Got this one and explained it beautifully and logically. Used terms such as “contradict” which was great.
Palindromes Josh got this correct with 15051.
Shoes and Keys Josh first got the answer that it would be 30 minutes but seemed to think that this was too easy so then he guessed 35 minutes – his email sounded as though he confused himself as he worked through it. No new answer and explanation received.
Red, White and Blue Solved and provided every possible solution for the second and harder part of this problem but did not give the simple answer for the easier first part of the problem.
Speedy Made an estimate of 2 minutes 30 seconds which is reasonable as a mathematical average – I responded with some information about how to work out speed using the scientific formula of distance divided by time. Given the formula for speed Josh has worked out that the speed is 0.44km/h – which was absolutely correct. He then had trouble working out what the time would be _ I sent a message explaining how to do this and convert it to mins and seconds.
Prime Number Josh started with 777 but stated that is divisible by 111. Then 775 which is obviously divisible by 5. Why he goes to 772 next I have no idea but states that this obviously is divisible because it is an even number and is then left with 773 which is correct.
A farmer and his wife Got this with 12 moves – made another nice excel document to show how he did this.
Watermelons Josh solved this problem really well, he looked at how much would be made by selling all the melons at $3, $2, and then the combination of both – which explains the problem.
A Knight’s Tour Found the solution on the net – but worked out logically for himself why it could not begin and end on diagonally opposite corners because they are the same colour and a knights moves alternates from black to white.
Trigonometry Challenge / 0
Infinity SquaredTERM 1, 2006Ms. Marietta Sansom-Gower
Student Name:
Task / Number Completed / Comments / Being Numerate / Being Information LiterateWarming Up Problems / 6/10 / Simple SubtractionSent a response with a clear sum which was correct.
InheritanceDouglas explained how he got the 31 shares to work out the widow’s inheritance correctly.
How could you plant 4 treesgot the equilateral triangle based pyramid worked out
Half full/Half empty Scientific idea of throwing the barrel in water and checking by using the theory of displacement. Nice idea. Again still working on the theory of displacement which is not necessary for solving the problem.
Number squareGot it correct with Josh using “grogono maths”?
ExplorationNeeded to clarify whether the explorer carries food. Really doing a great job, is onto the idea that the bearers can turn back but still got to the point that a bearer dies. Needs to work out how to explain his answer. Sent another attempt which was a little difficult to understand and people were referred to as numbers – it was all calculated which made it confusing but is on the right track however has solved it using 3 bearers and has now been given a clue that it can be solved using 2 bearers but is having trouble seeing how. Is improving at using written language to explain his solutions.
The third bearer he included really did nothing for the explorer and he could not see this, he also seemed to think that the bearers had to go back and forward each day instead of being able to travel forward a day or two and then back a day or two.
Really trying to work out how it can be done with 2 bearers.
Got it done with two bearers – absolutely spot on. / Doug has shown that he can communicate mathematically and provide reasoning for his mathematical understandings.
He has drawn upon different mathematical problem solving strategies such as using algebra, guess and check in order to solve problems. Doug’s communication and explanations of the his solutions have improved and continued to improve over the course of term 1. / From the information provided by WebCT Doug has read the problem pages, emails, discussion pages and has accessed the calendar. He has produced a homepage and has partaken in the discussions. It is clear that he understands that information tools and products are used to access and communicate information.
Doug has initiated the use of tools in solving problems, sometimes with the aid of other students but this is good and shows resourcefulness. It must be noted that other than the trigonometry challenge the course has not as yet demanded students to utilise a wide range of tools nor create products.
First 20 Mathematics and Logic Problems / 3/20 / What 2 digit Doug guessed this as 18 by guess and check – not sure how he got it. I explained to him that the digits in 18 are 1 and 8 and so the product of its digits is 8 as 1 x 8 = 8, then double this is 16 so it doesn’t work – have not as yet received another guess.
Horse Race Stated that he got a hint from Josh and then he sent me an email stating what the clues indicate and which ones contradict and from this concluded that the answer is 11.
Palindromes Doug sent in 15151 as an answer which is a palindrome but it is not the next largest – have prompted him in relation to this.
Shoes and Keys Douglas stated that he received help from his support teacher and worked this out correctly – he laid it out nicely in his email so that it showed what each assistant was doing at what time.
Speedy Used mathematics to average a guess of 2.5 mins which is a fair estimate when one does not know about the formula for speed – have sent him details for this so will see what he comes up with.
Prime Number Doug’s first guess was 777. Again prompted him that this was not a prime number. Has now solved it as 773.
Trigonometry Challenge / 0
Infinity SquaredTERM 1, 2006Ms. Marietta Sansom-Gower
Student Name:
Task / Number Completed / Comments / Being Numerate / Being Information LiterateWarming Up Problems / 6/10 / Simple SubtractionGot the correct answer for the simple subtraction answer.
How could you plant 4 trees Spoke about using a cone and place one at the tip and 3 evenly spread around the base – asked her if she knew the shape made if one drew a straight line from each tree to each other tree.
Bag of BallsA clear explanation of the solution.
Half full/Half emptyAsked one interesting question about the barrel question. Finally figured it out with tipping the barrel on a 45º angle and this is correct.
Turning Circles Teagan drew two circles – so made a model and got the answer of 2.5 rotations each time – questioned the sizes of the circles that she made. With the help of her support teacher to work out the circumference of the circles Teagan then discovered that the little circle would go around the larger circle twice – regardless of whether it was on the inside or outside.
ExplorationGave the idea of a bearer going ahead of the explorer and leaving 2 days worth of food for the Explorer. This is an innovative solution however it means that at the end of the first day the Explorer must carry 5 days worth of food which is not possible given the rules of the problem.
Names and FacesWorked this one out with Josh and did a more efficient job of this than I did – extremely logical. / Teagan can clearly and confidently use mathematical language to explain reasoning and numerical understanding (Standard 3, Middle). She has drawn on a number of strategies in order to solve problems. / From the information provided by WebCT Teagan read the problem pages, emails, discussion pages and has accessed the calendar. It is clear that Teagan understood that information tools and products are used to access and communicate information.
Teagan has not initiated the use of tools in solving problems. It must be noted that other than the trigonometry challenge the course has not as yet demanded students to utilise a wide range of tools nor create products.
First 20 Mathematics and Logic Problems / 0
Trigonometry Challenge / 0