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Structuring numeracy lessons to engage all students: 5-10

Structuring numeracy lessons to engage all students: 5-10. Peter Sullivan. Overview. We will work through three lessons I have taught this year as part of classroom modelling in years 5-10.

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Structuring numeracy lessons to engage all students: 5-10

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  1. Structuring numeracy lessons to engage all students: 5-10 Peter Sullivan

  2. 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.

  3. 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)

  4. Patterns with remaindersYears 5 - 6

  5. 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

  6. 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

  7. 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) OLOM Coburg 2013

  8. 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

  9. 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

  10. 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

  11. How many fish? Year 7

  12. 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

  13. Our goal • The meaning of mean, median and mode • To explain our thinking clearly

  14. To start • Write a sentence with 5 words, with the mean of the number of letters in the words being 4.

  15. To start • Write a sentence with 5 words, with the mean of the number of letters in the words being 4.

  16. These sets of scores each have a mean of 5 5, 5, 5 4, 5, 6 3, 5, 7 1, 1, 13

  17. To start • Write a sentence with 5 words, with the mean of the number of letters in the words being 4.

  18. 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?

  19. 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?

  20. These sets of scores have a median of 10 10, 10, 10 8, 10, 12 1, 10, 11 9, 10, 200 8, 12, 10

  21. 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?

  22. 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?

  23. 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?

  24. 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?

  25. If you are finished • How many different answers are there? • What is the highest number of fish that anyone might have caught?

  26. 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?

  27. Our goal • To see the meaning of mean, median and mode • To explain our thinking clearly

  28. Co-ordinates of squares Year 8 - 9

  29. Assumptions • They have had an introduction to placing co-ordinates

  30. 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.

  31. 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”?

  32. 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. Numeracy keynote SA

  33. Where is the point (-2,3)?

  34. Where is the point (-2,3)?

  35. Show all the points which have an x value of 1

  36. Show all the points which have an x value of 1

  37. Show all the points which have a y value of -2. • What is the equation?

  38. 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.

  39. On this sheet draw the letter of your name and give the co-ordinates of the points at the ends of each line.

  40. Mark all the points where y is bigger than x

  41. What is your reaction to those lesson?

  42. What might make it difficult to teach like that in your school?

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