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Starter of the Day. Name a number that has exactly 10 factors. What number can not be written as consecutive sum? [ eg 26 = 12 + 13, 15 = 1+2+3+4+5, most can]. Work and Study Skills Numeracy Unit Standards. Ngatea Teacher Day, June 15 th Hauraki Plains College

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starter of the day
Starter of the Day
  • Name a number that has exactly 10 factors.
  • What number can not be written as consecutive sum?

[eg 26 = 12 + 13, 15 = 1+2+3+4+5, most can]

work and study skills numeracy unit standards

Work and Study SkillsNumeracy Unit Standards

Ngatea Teacher Day, June 15thHauraki Plains College

Jim Hogan, Sandra Cathcart, Brenda McNaughton

Faculty of Education

Team Solutions, Auckland University

burning questions
Burning Questions

What is burning in your head that needs to be answered this session?

objectives de jour
Objectives de jour
  • To enhance teacher knowledge and understanding of numeracy unit standards
  • To experience a selection of problems
  • To develop teacher capability for using

these standards effectively

war plan
War Plan
  • Most minutes on the general nature of
  • 10 minutes on Number and recording
  • 10 minutes on Measure and recording
  • 10 minutes on Statistics and recording
  • 10 minute wrap up
nzqa website
NZQA Website

Contains everything being used in this .ppt.

Google “numeracy standards nzqa”

There may well be more efficient ways!

what is a problem
What is a problem?

In the context of numeracy of course and mathematics in general.

Have a chat about this.

definition of a problem from clarifications
Definition of a Problem from clarifications

A problem is a question where the pathway to the solution is not given.

The learner works out for themselves how to solve the problem and selects the strategies to use in order to do so.

Problems have a purpose and are relevant to the learner.

hogan s interpretation
Hogan’s Interpretation
  • A problem is a question where the student:-
    • Selects the method of solution
    • Uses the result in some way

The purpose is the use.

a useless problem
A Useless Problem

Add the prices of these items to find the total amount of money Fred needed at the shop.

Pie $3.50, Chips $3.00, Drink $2.50

Why is this not a problem?

a useful problem
A Useful Problem

Fred had $10 and wondered if he had enough to buy these items for lunch.

Pie $3.50, Chips $3.00, Drink $2.50

Why does this now work as a problem?

six squared resource
Six Squared Resource

I do not have a copy (yet) but just run the


lenseover every problem before

using it as assessment evidence.

adult learning progressions
Adult Learning Progressions

Remember these are Work and Study Skills standards. They are designed for use by adults in all sorts of occupations.

Hence the relevance statements and “naturally occurring evidence comments.

An apprentice chef would use food contexts.

x one off assessments x
X One-off Assessments X

Sorry, no use.

Hence, while the o/d Unit Standards might be “practice” or “in class work” they (generally) can not be used for valid evidence.

classroom work
Classroom Work
  • Real contexts may include “classroom”.
  • A classroom is not just a mathematics classroom.
  • Hence this is a SCHOOL WIDE learning consideration. (Signed and verified)
over time

This does not mean more pay!

This means the student has learned and remembered how to use the mathematics involved in solving this sort of problem.

So over a 2 or 3 month period evidence is collected.

This demonstrates learned skills and knowledge.


Use them and always ask “Is my answer reasonable?”

Preferable the Casio 82au Plus because 25% of 60 looks just like that and a fraction looks like a fraction and it has an S<=>D button.

It is the thinkingby selection and use that is important here not the calculation.

one step solution
One Step Solution

Does not mean a whole lot of single step trivia. Give students appropriate and relevant problems.

Eg Fred wants to paint the fence outside the classroom and needs to cost the job for the caretaker.

This is a many step problem. Each step is evidence for the numeracy standards.

In this case, NUMBER and MEASUREMENT

and probably WRITING as well.

orally visually or written
Orally, Visually or Written

The evidence can be spoken, noticed or written.

It could be a video.

It could be a computer .ppt

Encourage imagination….


Of course an assessor must be certain the work is by that particular student (and verified).

How can this be assured if a student does number or measurement in an out of school context?

With care, planning and the knowledge of parents or associates. We have to accept and trust but where there is doubt say “No”.


Evidence is to be verified. This is a two step check system designed for industry buy we have to use it in school.

Record oral evidence by notes and signing.

Record visual evidence by notes and signing.

You are a registered teacher!

portfolio of evidence
Portfolio of Evidence

A moderator is only going to check your decisions concerning the evidence.

Please carefully indicate which evidence is being used and why.

A moderator is moderating your decisions.

Only give them the evidence you used.

recording sheets
Recording Sheets

Get the latest downloads from NZQA.

Which brings us to evidence requirements.


See Number US 26623 Standards, Outcome 1.

All clearly stated.

measurement us 26627
Measurement US 26627

A measurement is not a measurement unless it has units.

Correct units.

A student selects their own measuring device for the purpose and reads it to appropriate accuracy.

range for measurement
Range for Measurement

See standard, all clearly stated.

Conversions and estimation.

Location using direction and distance.

GPS, Navman, Google Maps, all good. How about navigating in a flight simulator?

capacity or volume
Capacity or Volume?

Capacity is a liquid measure or how much a container will hold.

Volume is a spacial measure which could be used for liquids but is generally referring to the “amount of 3d space”.

Either is OK for this standard.

interpreting statistics
Interpreting Statistics

The range involves

- general features of data

- measures of centre

- extremes, shape, trends

Appropriate conclusions are drawn from the evidence.

conclusions where from
Conclusions… where from?

Lists, tables, graphs, diagrams, pictures, text.

Which reminds me of the Hungry Planet.


pathways from my workshop 1
Pathways from my Workshop 1

Low ability Y10 students, how do they get numeracy?

Students who have 10 numeracy credits ONLY – now what?

Students who have 14 credits all at Achievement level and NCEA L1.

Now what?

expectation and relationship
Expectation and Relationship

I think that a course with Numeracy standards should also offer some credits in Achievement Standards.






aims from jen hudson jh
Aims from Jen Hudson (JH)
  • To build student’s confidence in mathematical abilities and skills
  • Prepare them for real world by incorporating life skills
  • Use Brainstorming to get ‘by-in’ as they help plan the unit
  • Use of Projects to collect the evidence: personal choice & the more they do the more they get out of it (including evidence)
year plan jh
Year Plan JH
  • Began with Themed Unit booklet & test – Amusement Park (NZAMT)
    • Use the Assessment as a tool to understanding collecting evidence
  • Themed projects – On Holiday & Going Flatting
  • Achievement Standards :
    • 1.1 Numeric Reasoning
    • 1.10 Multi-Variate Data
    • 1.5 Measurement?
    • Bi-Variate Data?
    • Geometric Transformations?
themed unit amusement park jh
Themed Unit – Amusement Park JH
  • NZAMT website( for Amusement Park Unit booklet & Assessment
    • Supplement with notes and practicing of skills from Units In Maths textbook and Beta textbook
    • Complete individual portions of the booklet after completing practice
    • Test at the end of topic
    • Go through the assessment with students as they record evidence they have shown in the test
    • ALL students able to achieve some success and tick off some boxes on the Number Unit Standard
themed unit on holiday jh
Themed Unit – ON HOLIDAY JH
  • Brainstorm group & class activity
  • Use ‘On Holiday’ and ‘Earning Money’ books by Faye Cowin to develop and practice skills
  • Develop Project parameters as a class
  • Computer room – to research & collect info
    • Travel
    • Accommodation
    • Holiday Activities
    • Food
  • Project Presentations – poster, brochure, PowerPoint
  • Oral Presentation
  • Recording of evidence
  • ALL students who submitted a project, collected some evidence
themed unit going flatting jh
  • Brainstorm group & class activity
  • Explore career options –
    • Schooling needed
    • Income
    • Job prospect
    • How to get into the career
  • Budget
    • Find a job
    • Find a flat
    • Other expenses
  • Sprucing up the flat (measurement)
    • Carpeting
    • Wallpapering
    • Curtains
quotes from students end of term 1 jh
Quotes from Students – End of Term 1 JH
  • I really enjoy maths class this year, I don’t feel like cabbage at maths anymore. I’m more confident with maths. I LOVE doing projects to help with our evidence to get our credits for Level 1.
  • The assignments are fun because it is like real life.
as 1 1 numeric reasoning jh
AS 1.1 Numeric Reasoning JH
  • About 75% of students achieved
  • Worked to develop the Number skills all year
  • Only spent 4 concentrated weeks to revise before testing
  • Only focused on the Achieve level..hmmmm?
numeracy resources
Numeracy Resources
  • Adult numeracy progressions.
  • This is where the standards come from. Level 5 of the progressions across the board.
  • This correlates to NZC CL 4 or being multiplicative, in broad terms.
thank you
Thank you!

Kia kaha and try something new. Remember that for low success students previous mathematics pedogogy did not work.

Involve student!

See BES Mathematics for more ideas.