Developing Rich Mathematical Tasks – Mathematical starting point
What if’s‌.
On 24 January 2011 there were 550 days to go until the opening ceremony for the Olympics
If you are an athlete preparing for this event how much time do you have left?
The Paralympics will take place 33days later. What date will this be?
What if the family and friends of international athletes want to be watching TV in their own countries to support them?
What do you know that would help you to begin with? Eg this is more than a year away Less than 2 years 7 more days before the end of January It will be after 2011 Grouping in 30s might help to work out approx how many months Questions and tasks What is the day and date for these events? Will the opening ceremonys be in 2012 or 2013- how do you know? About how many weeks or months is this? So what time of the year will they take place How old will you be for each opening ceremony? What time of day does the opening ceremony start for the competing countries? Between now and then we have 11 Nov 2011 (11/11/11) what other interesting dates are there between now and then? Eg 21/02/2012 What do you know
Desired outcomes for learning Can the children use their number sense and understanding/ fact recall of days in a month and year to begin to predict the month the event will fall in?
Possible Processes Recalling facts about measuring of time: weeks, months, year Adding and subtracting time differences and considering time zones
The Hampshire Mathematics Advisory Team MB/Jan 2008
Developing Rich Mathematical Tasks – Context
What was the impact on children’s learning?
What the teacher did
What the learners did
The Hampshire Mathematics Advisory Team MB/Jan 2008
Developing Rich Mathematical Tasks – Mathematical starting point
What if’s….
Change the money They have more money? They have less money? They want to visit on the 29th July but go to the most expensive event They want to visit on the 29th July but go to the most cheapest event
Venue: Aquatic centre Change the distance They live further away? Change the event / day They want to see as many gold medals being won as possible (not necessarily swimming?
Questions and tasks
A family of 4 from Basingstoke want to visit the Olympics on Sunday 29th July 2012 to watch the swimming. They have been saving up and have £150 to spend on their trip. Have they got enough money to travel to the venue, buy their tickets, buy lunch and drinks and have a souvenir each?
Desired outcomes for learning Researching information train prices, ticket prices, souvenir prices Calculating possible total costs inc food Check solution fits all constraints
Possible Processes List all possibilities Answer the main question giving reasons and explaining thinking Predictions and estimating Taking a systematic approach Communicate and explain The Hampshire Mathematics Advisory Team MB/Jan 2008
Developing Rich Mathematical Tasks –
Context
What was the impact on children’s learning?
What the teacher did
What the learners did
The Hampshire Mathematics Advisory Team MB/Jan 2008
Developing Rich Mathematical Tasks – Mathematical starting point
What if’s….
Olympic Rings and nations’ flags
… the flags chosen are more / less complex in design?
… children sort by predominant colour? … children sort by number of colours used? … children order flags by proportion / percentage of a colour?
Questions and tasks Every participating nation’s flag has a least one of the colours of the 5 Olympic rings. How can the flags of the nations be sorted … using a Venn diagram; using a Carroll diagram; using a branching tree diagram?
Desired outcomes for learning Sort accurately according to described criteria Recognise symmetry - one line / two or more lines / rotational Calculate and represent fractions (proportion), percentages or ratios
Which nations flags are symmetrical in some way? What proportion / percentage of a nation’s flag do the colours represent? (use 1cm2 paper; graphing paper dependent on level of demand) What are the ratios of the coloured areas on nations’ flags?
Possible Processes Determine and refine own criteria for sorting Work systematically Recognise and use alternative approaches / strategies Find ways of calculating fractions, percentages, ratios
Developing Rich Mathematical Tasks – Mathematical starting point
What if’s….
What if you only had 2 or 3 or 4 rings? Can you predict the answer for any number of rings? What if not all of the rings are equal in size? What if the rings were not rings – triangles? Squares? Any other shape? Can you create the exact pattern of rings (overlaps) from a set of coloured paper rings?
Questions and tasks The five Olympic rings overlap so that they enclose nine separate spaces. Try arranging the rings in different ways. How many spaces are enclosed each time? How many different ways can you find? What is the greatest number of spaces that can be made with five rings?
Desired outcomes for learning Working systematically. Finding rules and patterns. Making predictions.
Possible Processes Using hoops to investigate practically. Using ICT (geometry package) Recording outcomes pictorially – using photographs. Recording in a table. Working outdoors – on a large scale.
The Hampshire Mathematics Advisory Team MB/Jan 2008
Developing Rich Mathematical Tasks –
Context
What was the impact on children’s learning?
What the teacher did
What the learners did
The Hampshire Mathematics Advisory Team MB/Jan 2008