I have recently been teaching lower ability Year 9 students how to calculate the mean from grouped and ungrouped data tables. I didn’t want to teach them a method to learn by rote, so I used a more investigative approach.
The third table had minimal information. Each group used their own method to find the missing values. Some chose the largest value in the range, some guessed what the results could have been in each group and one group decided to calculate two means – one using the largest value and one using the smallest.
We collected our results together on the board and discussed their accuracy. The class decided to use the middle of each range to calculate the estimated mean. They had gone from no understanding of estimated mean to formulating their own method.
I introduce order of operations by creating an imaginary Chip Shop. I usually read out orders and get the students to write down what they think they are on whiteboards. Note that when you read out the orders, the punctuation doesn’t give any hints.
‘Two fish and three chips’ – 2 fish & 3 portions of chips
‘Fish and chips twice’ – 2 fish & 2 portions of chips or 1 fish & 2 portions of chips
‘Five sausage and chips’ – 5 sausages & 5 portions of chips or 5 sausages & 1 portion of chips
This activity always prompts a ‘discussion’ as to who is correct. The misconception of what an order could mean links nicely with the misconception when working out 2 + 3 x 4. You could also adapt the idea for writing algebraic expressions.
A presentation, with questions, is downloadable in three different formats here:
A few days ago I mentioned on Twitter that I was up to something. That something was expanding the Maths Sandpit from readable blog to downloadable resource. There are now resources available on YouTube and TES resources.
Over the next couple of months I am going to go back over my blog posts and add some related resources to the appropriate sites. I hope you find them useful.