We started our summative assessment discussing some of the activities we had done in our unit that we felt helped us understand our central idea a lot and those not so much.
For this summative, we had two parts:
Part 1: Show understanding of central idea brainstorm with connections
The children are given are central idea and time to reflect on what
they understand about it giving examples to support.
(I use this idea for every maths unit. To see my reasoning behind it,
see this previous blog past Positive Summative Maths Assessment Idea)
The advantages of giving a summative like this:
° Every child feels like a successful mathematician
° Allows for a meaningful reflection on what they have learnt
° They feel proud when they see everything they have understood
° Pride when sharing with the parents and they are likely to discuss with their parents their learning rather than the negative sharing of looking at mistakes made in a traditional summative maths assessment
° Gives them an opportunity to make connections between the concepts explored
° The strong mathematicians are given an opportunity to show what they know. Unlike a traditional maths assessment this style does not cater to the upper-middle mathematicians- it caters to everyone and reflects the differentiation and personal enquiries taking place throughout the unit.
Part 2: I wanted to give the children another opportunity to take ownership of their learning, to think creatively in maths and to apply their new understandings, so I came with with this idea.
In small groups/partners, created 3 probability games.
° 1 game must have a low probability of winning
° 1 game must have an even chance of winning
° 1 game must have a high probability of winning
Quite often children latch on to their first idea and run with it without giving thought to other possibilities. To thwart this, the groups needed to create 2 x low, 2 x even and 2 x high probability games. Then they needed to select the best game from each category to present to the other Year 6 class. This helped them to understand that when thinking creatively, we should explore more than one idea. It also gave them an opportunity to evaluate the games to determine which might be more successful.
Creative Maths Thinking!!!
'EVEN PROBABILITY OF WINNING' GAMES WE CREATED:
I love how creative kids can be when we give them opportunities. This group created an 'even' probability game.
You flicked a ping pong through the toilet roll. It would first bounce on the yellow backboard and then land on either a black or white square. This is how they determined it was an even / 50-50 probability of winning.
They even thought of creating a storage area where you can keep the whiteboard for scoring, a texta and the ping pong ball!!!! Amazing!!!! :)
The other creative and clever addition to the game was the storage drawer they created under the flap to keep the whiteboard scorecard, texta and ping pong ball in :)
In this chance game, the player was blindfolded (amazing what you can make with some cardboard and iPod headphones!) There were different coloured rods in the bowl they had made. This game had an even probability of winning. There were 6 black rods and 6 coloured. You needed to pull out a coloured rod to win.
Each player pulls out 1 scrabble tile each and drops them in a cup at the same time. The cups are balanced on the lid.
Then, each player pulls out 2 scrabble tiles each and repeats.
The game continues (doubling the amount of times pulled and dropped) until the cups fall to the ground.
Whichever cups falls and touches the ground first wins.
'LOW PROBABILITY OF WINNING' GAMES:
This game involved skill and probability. You needed to toss a counter from 1 metre away on to the board. If the counter was touching the blob of blutack, you won.
We wondered how much probability was involved in this game compared to skill. Quite an interesting debate!
Each player need to roll a 20-sided die. What it landed on was the number of steps you could take. The winner was the player who got to the end first.
Blindly pull out a green counter and without looking try to place it on the centre blutack on the board.
The reason for the other blutack blobs?
- To trick people into thinking they are the centre blobs.
Out of all the counters only 1 in 35 was green so it was an extremely low probability of winning. The funny aspect to the game was you didn't even know what colour you had pulled out till you had finished trying to blindly place it in the centre.
You had a choice of two bins to toss the ball into. One bin had a higher probability of winning because it was closer and larger than the other.
'HIGH PROBABILITY OF WINNING' GAMES:
Different coloured tennis balls. They explained:
° 80% chance of pulling out a yellow
° 10% chance of pulling out an orange
° 10% chance of pulling a marked ball
I liked the creative thinking in this high probability game.
1. Roll 2 dice.
2. Pull out the corresponding card.
3. Pull a red counter out and place it on the card and you win. (Only one blue counter amongst all the reds. Yes, a VERY high chance of winning!)
Choose a shape to kick or throw a ball into.
Later, we wondered about the probability involved. We decided we would all have a different perspective. If you were sporty you might see this as a high probability of winning; if you weren't sporty you might see it is low.
Interesting. But is that a perception of luck or mathematical probability we were left wondering.
1. Roll 2 dice. Subtract the lower die throw from the higher die roll.
2. Pull out that number of cards from the pack.
3. Whichever player draws the highest card wins.
We debated whether this really was a high probability or an even probability.
We invited the another class to come and play our games. After playing the 3 games at each stand, the players were then asked to complete a small questionnaire to think which games they felt had the low, the even and the high chance of winning. The children would then let them know if they were correct or not. If not, they explained what the probability actually was and in doing so were given a further opportunity to reflect on their conceptual understandings.
When we had finished sharing our games, we gathered together and examined the questionnaires. We discussed the results and what we noticed.
Were people able to determine the probability well or not?
Some examples of their game designs and explanations of the probability involved:
- They felt really proud of their creative games (rightly so).
- Maths can be creative thinking. I'd never thought of that before.
- Probability can be tricky to measure precisely, but it is always measurable.
- I love maths now compared to last year.
Being our last maths activity for the year, I thought that was the best way to close the year.
Sample assessment feedback given (based on Learner Profile attributes):