1. What do you do with the smart alecs? Numeracy approaches to teaching high ability students.

2. Who are we? HoD & Assistant HoD Maths Taradale HS  2003 - Began using numeracy programmes, initially to support low ability students in junior school  2004 - Extended to incorporate other junior classes  2005 - Part of pilot secondary numeracy project for year 9 students  2006 – Year 2 school in SNP  2007 – Year 3 school in SNP

3. Past experience tells us….  Stages 4 – 5 yr 9 students, will have difficulty coping with achievement standards in yr 11. They are best suited to a unit standard course  Stage 6 students have the most potential for movement and this is the group we can make the most difference to.  Stages 7 – 8 students will cope well with achievement standards at yr 11. They are likely to continue successfully with mathematics in yrs 12 – 13

4. And we must…  establish effective practice in year 9 to ensure our understanding of student ability is as complete as possible  establish good lines of communication with contributing schools, to avoid mass math testing on arrival  triangulate our assessment data during year 9 and not rely totally on numeracy data. (At THS we do class assessments and AsTTle testing)

5. Moving students  Ideally, before we teach “formal” algebra in preparation for NCEA Level 1, we require all of our students to be at strategy; stage 7 add/sub, stage 8 mult/div, stage 8 ratio/proportion  Also, we identify knowledge hotspots by analysing data effectively and teach accordingly  However…..

6. Student misconceptions can impact on the development of algebraic thinking  Before stage 7 it is imperative that students can confidently play with whole numbers  At stages 7+ both decimal understanding and playing with all numbers are strong indicators of student readiness for higher level algebraic thinking

7. Therefore…  use a variety of methods so students are given opportunities to reach the highest stages in strategy and knowledge  develop classroom and teaching structures that facilitate student progress

8. Teacher toolbox should include;  Starters, games, etc for filling knowledge hotspots  Grouping based on strategy, in order to encourage total student participation in; –Teacher instruction –Group work –Individual work

9. Nuts & bolts 1 Starters  Place value 1 starter Place value 1 starter Place value 1 starter  Place value 2 starter Place value 2 starter Place value 2 starter  Decimal Starter Decimal Starter Decimal Starter

10. Nuts and bolts 2 Strategy linked to knowledge Adapting resources  Move to decimals Move to decimals Move to decimals  Move to decimals 2 Move to decimals 2 Move to decimals 2  Move to decimals 3 Move to decimals 3 Move to decimals 3

11. Garden Beds  Tell the story of a gardener who wants to protect some plants by placing a border of tiles around the edge.  Here are 5 plants in a row. Could you help me place the tiles around the edge?  Garden beds Garden beds Garden beds  www.curriculum.edu.au/maths300 www.curriculum.edu.au/maths300

12. Time Problems  Time Problem Time Problem Time Problem  www.nzmaths.co.nz www.nzmaths.co.nz

13. So, what do you do with the smart alecs? Plan, adapt, research & ask

21. Time Problem The Problem  We have a group of unfortunate people here. They all have an exam to do. It starts at 9:30 pm sharp. Which of them will get there in time for the start of the exam? Here’s the problem.  Derek’s watch is 15 minutes fast but he thinks that it is 10 minutes fast.  Marilyn’s watch is 15 minutes fast but she thinks it is 20 minutes fast.  Sara’s watch is 15 minutes slow but she thinks it is 10 minutes fast.  Tim’s watch is 15 minutes slow but he thinks that it is 10 minutes slow.