structuring numeracy lessons to engage all students: 5-10 peter sullivan
Post on 14-Dec-2015
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Overview
• We will work through three lessons I have taught this year as part of classroom modelling in years 5-10.
• The lessons are structured to maximise engagement of all students, especially those who experience difficulty and those who complete the work quickly.
• I will ask you to examine the commonalities and differences between the lessons and identify key teacher actions in supporting this lesson structure.
• I will ask you to reflect upon what implications for leading whole school Numeracy improvement.
Assumptions
• We do not want to tell the students what to do before they have had a chance to explore their own strategy
• We want to step back to allow ALL students to engage with the task for themselves
• We want them to see new ways of thinking about the mathematics
• There is no need to hurry• We want them to know they can learn (as distinct
from knowing they can be taught)
• Some people came for a sports day. • When the people were put into groups of 3
there was 1 person left over. • When they were lined up in rows of 4 there
were two people left over. • How many people might have come to the
sports day?
OLOM Coburg 2013
OLOM Coburg 2013
Multiplication content descriptions• Year 4: Develop efficient mental and written
strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
• Year 5: Solve problems involving division by a one digit number, including those that result in a remainder
• Year 6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
OLOM Coburg 2013
Patterns
• Explore and describe number patterns resulting from performing multiplication (ACMNA081)
• Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)
Some “enabling” prompts
• Some people came for a sports day. When they were lined up in rows of 4 there were two people left over. How many people might have come to the sports day?
• • Some people came for a sports day. When the
people were put into groups of 3 there was no-one left over. When they were lined up in rows of 4 there was no-one left over. How many people might have come to the sports day?
OLOM Coburg 2013
An extending prompt
• Some people came for a sports day. When the people were put into groups of 3 there was 1 person left over.
• When they were lined up in rows of 4 there was 1 person left over.
• When they were lined up in columns of 5 there was 1 person left over.
• How many people might have come to the sports day?
OLOM Coburg 2013
The “consolidating” task
• I have some counters. • When I put them into groups of 5 there was 2
left over. • When they were lined up in rows of 6 there
was the same number in each column and none left over.
• How many counters might I have?
OLOM Coburg 2013
In this lesson, I need you to
• show how you get your answers• keep trying even if it is difficult (it is meant to
be)• explain your thinking• listen to other students
To start
• Write a sentence with 5 words, with the mean of the number of letters in the words being 4.
To start
• Write a sentence with 5 words, with the mean of the number of letters in the words being 4.
To start
• Write a sentence with 5 words, with the mean of the number of letters in the words being 4.
Next
• Seven people went fishing. • The mean number of fish the people
caught was 5, and the median was 4.• How many fish might each person have
caught?
Next
• Seven people went fishing. • The mean number of fish the people
caught was 5, and the median was 4.• How many fish might each person have
caught?
And now
• Seven people went fishing. • The mean number of fish the people
caught was 5, the median was 4• How many fish might each person have
caught?
• Seven people went fishing. • The mean number of fish the people caught
was 5, the median was 4 and the mode was 3.• How many fish might each person have
caught?
• Seven people went fishing. • The mean number of fish the people caught
was 5, the median was 4 and the mode was 3.• How many fish might each person have
caught?
If you are stuck
• A family of 5 people has a mean age of 20. What might be the ages of the people in the family?
If you are finished
• How many different answers are there?• What is the highest number of fish that
anyone might have caught?
Now try this
• The mean age of a family of 5 people is 24. The median age is 15. What might be the ages of the people in the family?
The key task
Four lines meet in such a way as to create a square. One of the points of intersection is
(-3, 2)What might be the co-ordinates of the other points of intersection? Give the equations of the four lines.
How might you run that class?
• How much would you tell the students?• What approach do you recommend to
doing this task?• How much confusion can you cope with?• When is challenge and uncertainty
productive?• What is meant by “cognitive activation”?
Numeracy keynote SA
Quotes from PISA in Focus 37• When students believe that investing effort in
learning will make a difference, they score significantly higher in mathematics.
• Teachers’ use of cognitive-activation strategies, such as giving students problems that require them to think for an extended time, presenting problems for which there is no immediately obvious way of arriving at a solution, and helping students to learn from their mistakes, is associated with students’ drive.
Responses
Four lines meet in such a way as to create a square. One of the points of intersection is
(-3, 2)What might be the co-ordinates of the other points of intersection? Give the equations of the four lines.
On this sheet draw the letter of your name and give the co-ordinates of the points at the ends of each line.
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