Using Open Ended Tasks in the Mathematics Classroom

Glenroy West Primary School19th May, 2010

Northern Metropolitan Region, DEECDAdrian Berenger

Part 1: Types of Questions Closed Questions are those which require an answer or response to be given from memory.

Open Questions require students to think more deeply and to give a response which involves more than recalling a fact or reproducing a skill. Usually more than one possible answer.

Mother’s Day Bill

• $711 was the total bill• Mum & Dad, Brother and his Wife and 2

children, Sister and her Boyfriend, and me• Who pays what?

Buying Shoes

• You go with a friend to buy shoes. Each pair cost $80

• The sale offers $100 off if you buy 3 pairs.• Your friend gets 2 pairs and you get only one.• Who pays what?

Making Shapes

• Minimum Properties of Shapes• Construct a quadrilateral that has two pairs of

adjacent sides equal.• What shapes are possible?

Closed to Open12 cm

3 cm

Calculate the Perimeter and Area of the rectangle.

I want to make a garden in the shape of a rectangle. I have 30 metres of fence for my garden. What might be the area of the garden?

Garden paving• Peter wants to pave an area using 16 square

paving stones and 16 straight border pieces.• Each stone is 1m2 and each border piece is 1m.• What different arrangements are possible?• On the way home, Peter carelessly breaks several

of the paving stones. What is the maximum number of broken stones possible in order to still be able to use all his 16 border pieces?

• Draw all possible arrangements.

Bloom’s Taxonomy

Can the student GENERATE new products, ideas or ways of viewing things?

Can the student JUSTIFY a decision or course of action?

Can the student DIFFERENTIATE between constituent parts?

Can the student USE the new knowledge in another familiar situation?

Can the student EXPLAIN ideas or concepts?

Can a student RECALL information?

Why do we use Open Tasks?

• To draw out misconceptions• To encourage deeper thinking• To develop problem solving • To cater for mixed ability

levels

Creating Open-Ended Tasks

‘Any closed questions can be reformulated to create an open

ended questions using one of two methods’.

(Sullivan & Lilburn 1997)

• There are 11 more students enrolled at the school this term. What’s possible?

• How many whole number pairs sum to 11?

Misconceptions with =

8 + 3 = ? + 4• 7 because 8 and 3

equals 11 and so does 4 and 7

• 7 because 4 is one more than 3 so ? must be one less than 8

• 11

Totals

• 11 + 0• 10 + 1• 9 + 2• 8 + 3• 7 + 4• 6 + 5

• 10 + 0• 9 + 1• 8 + 2• 7 + 3• 6 + 4• 5 + 5

• 9 + 0• 8 + 1• 7 + 2• 6 + 3• 5 + 4

• 8 + 0• 7 + 1• 6 + 2• 5 + 3• 4 + 4

• 7 + 0• 6 + 1• 5 + 2• 4 + 3

• 6 + 0• 5 + 1• 4 + 2• 3 + 3

11 678910

• A maths teacher always likes to have his class working together in groups but no matter if he suggests his students work in groups of 2, 3 or 4 there is always one student on their own. How many students might there be in this teacher’s class?

Other Questions with Numbers

Other Questions with Numbers

What scores are possible from 4 darts?

10 7 3 1

Method 1

TRADITIONAL

249 + 173

• Omit enough information so that, although the answer remains the same, the digits required to achieve the answer becomes variable.

OPEN-ENDED

2** + *7* 422

Method 1 (continued)

TRADITIONALTwo fifths of 250 students borrow books from the library each day. Calculate the number of students who borrow books each day.

Find the missing angle on this trapezoid40◦

140◦

OPEN-ENDEDTwo fifths of the students in a school borrow books from the library each day. How many students might there be in the school and how many of them borrow books each day?

What might the angles on this trapezoid be?

Method 2• Work backwards from the answer. Begin with a

closed task. Calculate the answer, then work backwards and using the context of the question, create a question that would allow multiple responses to achieve the same answer.

TRADITIONAL

The following numbers represents the temperature of 5 consecutive days in Melbourne: 44◦C, 42◦C, 36◦C, 22◦C, 29◦C. Find the average temperature.

OPEN-ENDED

The average temperature over five consecutive days in Melbourne was 35◦C. The highest temperature was 44◦C. What might the temperature have been on the other days?

Method 2 (continued)

TRADITIONAL

What is the volume of the cylinder?

35.0X 0.5

4cm

6 cm

OPEN-ENDED

The answer is 17.5 What might the question be?What might the dimensions of a cylinder prism that has a volume of 300 cm3?

Summing Up!

Open Ended Maths Activities2nd Edition

Peter Sullivan and Pat LilburnOxford

• Resources

Thinking Tools for the Mathematics Classroom.

Sue GunninghamHawker Brownlow Education

Part 2: Creating Open-Ended Questions

• 8 closed questions to open questions in pairs• Hot dots

Video: 7X13=28