Primary Mathematics and Numeracy 2
Assignment 2: Analysis
Introduction:
This paper presents an analysis of Abhi’s mathematical thinking and his abilities to solve handshake problem.
About Student:
Abhi is a stage 3 student from Year 6, who recently attempted his selective school test. Having a conversation with his parents helped me to know that Abhi enjoys doing maths and is working at appropriate stage level. Abhi states that his most interesting topics in maths are place value, angles and geometry (I-04), as they are easy to understand (I-05). Whereas, he hates fractions and decimals (I-06) as he found them to be very confusing (I-07).
The Handshake Problem:
You entered a room in which there were six other people standing. If everyone
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Then I started with 2 people as a single person cannot shake hand with himself. I made a table with a number of people and possible number of handshakes they can have. I started with 2 people and went down till 7 as there are 7 people in the room including me. Number of people Number of possible handshakes
2 1
3 3
4 6
5 10
6 15
7 21
While calculating a possible number of handshakes, I observed a number pattern i.e, possible number of handshakes between 4 people is equal to an earlier number of people(3) + number of their corresponding handshakes (3) which is 6.
Similarly, for 5 people = earlier number of people (4) + number of their corresponding handshakes (6) = 10
Hence, a total number of handshakes between 7 people are 21.
From the question, it says that 3 more people entered the room which means there are 10 people in total. I continued above table till 10 to calculate the total number of handshakes between 10 people
8 28
9 36
10 45
Hence, total number of handshakes between 10 people are 45
Solution 2:
I named 7 people as A, B, C, D, E, F, G and represented each handshake with a pair of letters. For example, a handshake between A and B will be represented by
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He applied his familiar concept of addition and related it to a new situation to obtain a solution (WS-05). Abhi was able to remember the concept of addition and other problem-solving strategies he learned earlier, through retention and transferred it to a new situation (WS-05, WS-02, OB-14) using his higher-order thinking skills (WS-06) (Krathwohl, 2002). Abhi also demonstrated his critical thinking skills (WS-08) by making a wise decision and giving an appropriate reason for his solution (Collins, 2014).
Fluency:
Abhi checked his solution and corrected it once, without the help of diagram as he identified specific number pattern from previous solution (WS-01). Abhi recalled his factual knowledge in addition and reduced problem-solving strategy steps by using possible arithmetic operations (WS-05, WS-06), which resulted in the qualitative solution strategy (Silver, 2013) (WS-05, OB-13, OB-14, and OB-15).
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