What do you do with What do you do with the smart alecs?the smart alecs?

Numeracy approaches to Numeracy approaches to teaching high ability teaching high ability

students.students.

Who are we?Who are we?

HoD & Assistant HoD Maths Taradale HSHoD & Assistant HoD Maths Taradale HS 2003 - Began using numeracy 2003 - Began using numeracy

programmes, initially to support low ability programmes, initially to support low ability students in junior schoolstudents in junior school

2004 - Extended to incorporate other 2004 - Extended to incorporate other junior classesjunior classes

2005 - Part of pilot secondary numeracy 2005 - Part of pilot secondary numeracy project for year 9 studentsproject for year 9 students

2006 – Year 2 school in SNP 2006 – Year 2 school in SNP 2007 – Year 3 school in SNP 2007 – Year 3 school in SNP

Past experience tells us….Past experience tells us….

Stages 4 – 5Stages 4 – 5 yr 9 students, will have yr 9 students, will have difficulty coping with achievement difficulty coping with achievement standards in yr 11. They are best suited to standards in yr 11. They are best suited to a unit standard coursea unit standard course

Stage 6Stage 6 students have the most potential students have the most potential for movement and this is the group we can for movement and this is the group we can make the most difference to.make the most difference to.

Stages 7 – 8Stages 7 – 8 students will cope well with students will cope well with achievement standards at yr 11. They are achievement standards at yr 11. They are likely to continue successfully with likely to continue successfully with mathematics in yrs 12 – 13mathematics in yrs 12 – 13

And we must…And we must…

establish effective practice in year 9 to establish effective practice in year 9 to ensure our ensure our understanding of student understanding of student abilityability is as complete as possible is as complete as possible

establish establish good lines of communicationgood lines of communication with contributing schools, to avoid mass with contributing schools, to avoid mass math testing on arrivalmath testing on arrival

triangulate our assessment datatriangulate our assessment data during year 9 and not rely totally on during year 9 and not rely totally on numeracy data. (At THS we do class numeracy data. (At THS we do class assessments and AsTTle testing)assessments and AsTTle testing)

Moving studentsMoving students

Ideally, before we teach “formal” algebra in Ideally, before we teach “formal” algebra in preparation for NCEA Level 1, we require all preparation for NCEA Level 1, we require all of our students to be at strategy; of our students to be at strategy;

stage 7stage 7 add/sub, add/sub,

stage 8stage 8 mult/div, mult/div,

stage 8stage 8 ratio/proportion ratio/proportion Also, we identify knowledge hotspots by Also, we identify knowledge hotspots by

analysing data effectively and teach analysing data effectively and teach accordinglyaccordingly

However…..However…..

Student misconceptions can impact Student misconceptions can impact on the development of algebraic on the development of algebraic

thinkingthinking Before Before stage 7stage 7 it is imperative that it is imperative that

students can confidently students can confidently playplay with with whole numberswhole numbers

At At stages 7+stages 7+ both decimal both decimal understanding and playing with understanding and playing with allall numbers are strong indicators of numbers are strong indicators of student readiness for higher level student readiness for higher level algebraic thinkingalgebraic thinking

Therefore… Therefore…

use a use a variety of methodsvariety of methods so so students are given opportunities to students are given opportunities to reach the highest stages in strategy reach the highest stages in strategy and knowledgeand knowledge

develop develop classroom and teaching classroom and teaching structuresstructures that facilitate student that facilitate student progressprogress

Teacher toolbox should include;Teacher toolbox should include;

Starters, games, etc for filling Starters, games, etc for filling knowledge hotspots knowledge hotspots

Grouping based on strategy, in order Grouping based on strategy, in order to encourage total student to encourage total student participation in;participation in;– Teacher instruction Teacher instruction – Group workGroup work– Individual work Individual work

Nuts & bolts 1Nuts & bolts 1

StartersStarters Place value 1 starterPlace value 1 starter Place value 2 starterPlace value 2 starter Decimal StarterDecimal Starter

Nuts and bolts 2Nuts and bolts 2

Strategy linked to knowledgeStrategy linked to knowledge

Adapting resourcesAdapting resources Move to decimalsMove to decimals Move to decimals 2Move to decimals 2 Move to decimals 3Move to decimals 3

Garden BedsGarden Beds

Tell the story of a gardener who Tell the story of a gardener who wants to protect some plants by wants to protect some plants by placing a border of tiles around the placing a border of tiles around the edge. edge.

Here are 5 plants in a row.Here are 5 plants in a row.Could you help me place the tiles Could you help me place the tiles around the edge? around the edge?

Garden bedsGarden beds www.curriculum.edu.au/maths300 www.curriculum.edu.au/maths300

Time ProblemsTime Problems

Time ProblemTime Problem www.nzmaths.co.nz www.nzmaths.co.nz

So, what do you do So, what do you do with the smart alecs?with the smart alecs?

PlanPlan, adapt, research & , adapt, research & askask

Time ProblemTime Problem

The ProblemThe Problem We have a group of unfortunate people here. We have a group of unfortunate people here.

They all have an exam to do. It starts at 9:30 pm They all have an exam to do. It starts at 9:30 pm sharp. Which of them will get there in time for the sharp. Which of them will get there in time for the start of the exam? Here’s the problem. start of the exam? Here’s the problem.

Derek’s watch is 15 minutes fast but he thinks Derek’s watch is 15 minutes fast but he thinks that it is 10 minutes fast.that it is 10 minutes fast.

Marilyn’s watch is 15 minutes fast but she thinks Marilyn’s watch is 15 minutes fast but she thinks it is 20 minutes fast.it is 20 minutes fast.

Sara’s watch is 15 minutes slow but she thinks it Sara’s watch is 15 minutes slow but she thinks it is 10 minutes fast.is 10 minutes fast.

Tim’s watch is 15 minutes slow but he thinks that Tim’s watch is 15 minutes slow but he thinks that it is 10 minutes slow.it is 10 minutes slow.