We spent 1 tutorial covering some aspects of these sub-strands, gaining a strong understanding of beginning elements of both statistics and probability. We looked at a range of activities that can be used as appropriate learning experiences for students to being to develop an understanding of these element. The first activity involved finding the probability of flipping a coin 3 times in any combination. Initially, we worked to find how many different combinations this may produce. Using a three-diagram, we found there would be 8 possible combinations (HHH, HHT, HTH, HTT, TTT, TTH, THT, THH). Next we took an A4 board consisting of 3 levels, to find the probability of flipping a combination. The board finished on 4 possible squares marked A, B, C and D. Squares A and D resulted in flipping either 3 heads in a row or 3 tails in a row. We used an MAB block to mark the result of each flip, and conducted the test 20 times, with 1 person flipping and 1 person marking. At the conclusion of the 20th test, our board reflected the image :
Questions could then be posed to being higher order thinking of the results.
- "Why were squares A and D relatively lower than squares B and C?"
- "What combination resulted in the largest outcome?"
The next step involved connecting the entire classes stacks of MAB blocks for each square together. As there were 13 groups of 2 conducting the activity, we were now comparing 260 tests instead of 20 tests. The results reflected similarly to that of previous activity. We concluded by stating that the probability of flipping either 3 heads or 3 tails in a row was relatively smaller than that of the other 6 possible combinations. Students conducting this activity will begin to formulate an understanding of how probability can be explored using a very basic process.
The next activity involved Smarties (every child's favourite treat). In small groups of 4, we each received a box of smarties. We were posed the following questions:
- "What do you think is the most common smartie colour?"
- "How many smarties do you think is in a typical box?"
- "What do the smarties look like in your box?"
As a group we each answered these questions and recorded the answers. From here, we could see what colours the group individuals thought may be the most common, how many we each thought may be in our box, and finally, what each group members box looked like. We each arranged the smarties from our boxes on the table, in colour groups (see image on the left). We then went through a list of questions where the answers related solely on our box of smarties. Students taking part in this activity should be posed similar questions, as each question only requires a yes or no answer. An example of questions could be as follows:
- Is it possible to select from your packet:
- A red smartie?
- A green smartie?
- A brown smartie?
- 4 blue smarties
- 10 orange smarties?
- Which colour has the greatest chance of being selected from your packet? The least chance?
From these questions, students can begin to look at the statistics, primarily what the chance is of pulling out a certain colour of smartie, as young students can correctly classify an event as impossible, possible or certain. From the image above, we can count 12 smarties that were pulled from the box. Since there are 5 green smarties, it would be safe to presume that the chance of pulling a green smartie out of this particular box would be 5:12. Similarly, we can see there are 3 red smarties, therefor we can presume that the chance of pulling a red smartie out of the box would be 3:12 (older students will even begin to simplify this to 1:4).
We then combined all 4 group members smarties together to form a larger group of 52 smarties. From here, we discussed how students could be posed similar questions to the ones above in relation to the larger group. In our group, we were able to add smarties to each individual colour group (green, purple, red, yellow, orange, blue, brown and pink) and count the total number of each colour. From this data we found that the most common colour was green (12) and the least common was pink (3). Statistically, we could presume that the chance of pulling a green smartie from the pile would be 12:52 (or 3:13), and the chance of pulling a pink smartie from the pile is 3:52. Students could then be given the task of graphing this data into a bar graph to see the results. Our groups data was graphed as follows:
It is important that the production of the graph is not the endpoint of the exercise, but a stimulus for discussion about what can be interpreted from the data as presented (Marshall & Swan, 2006, p.18).
The final activity we looked at involved finding the probability landing on a particular colour with a spinner. We used 3 different circular game boards for this activity, each consisting of different probabilities for landing on a colour. Below the spinner were kites, each representing a different colour available to land on. Once a colour was landed on, a sticker was placed on the kite of that colours string. The exercise ended once 1 kites string was completely covered. Before any spinners were spun, we first discussed the statistics involved for landing on a particular colour on each game board. The first board was divided into 4 segments (see image on right). An analysis by students could be that there are equal portions of red and blue, and that each colour has a 50% chance of being landed on. This activity works to develop students ability to explore probability, and understand statistics. By placing a paperclip in the centre, and using a pen to hold it down, a spinner is created. We now spun the spinner until one entire kite string was covered in stickers. The result looked as follows:
In the image above we can see that, although relatively close, we landed more times on blue than we did red. The other game boards consisted of circles broken into more portions differing in size. in one example, the spinner consisted of mostly red portions, with a single blue portion covering approximately 20%. In this example, what would be the probability of landing on blue? What colour would we expect to land on more times? Students will begin to develop an understanding through the exercises which will assist in exploring probability and statistics.
