Sequence, knows and processes

NZQA Numeracy year 10 :

• Formulate a mathematical/statistical approach in meaningful problems
• Use maths/stats to address numeracy demands
• Explain the reasonableness of responses

Aim is support learners to value, develop and apply key skills

Australia created a flowchart to support assessment

Translate into mathematical representations

(principles, concepts, techniques to proceed)

Select and apply concepts and techniques

(accurate use and setting out of procedures)

(procedures are relevant to the task)

Consider reasonableness of what/why/how

(Judge their answer in relation to question

Strengths and limitations in their pathway)

Coherent and concise organisation

Correct use of appropriate vocabularly

Correct use of conventions

1. Randomly select 3 or 4 single digits
2. Using all digits every time:

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• Create different number sentences
• Mark these off on the 0-100 number board

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Be creative with properties of number

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9 2 5 1

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25 36 72 100

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High Schools are adapting this “recallNreason” routine

A DDSW High School sharing their adaptations – Year 11 and 12

2015 – 2018 working with High Schools on numeracy disposition

Bob’s bakery reports a profit of $6405.70

Karen’s Bakery reports a profit of $4070.95

How much more money did Bob’s bakery make

than Karen’s bakery

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$ 

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Rush

Won’t

A Year 5 simple routine question

1 in 4 “extension” students failed to do it

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What was the issue here?

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A question from Aus Year 8 Numeracy

Rush

Won’t

Janine is writing a list of numbers that follows these rules

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Select all the numbers below that follow all these rules?

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7042 6302 7402 7123 7312 6142

The number must

• be even
• lie between 6200 and 7400
• Have digits that add to 13

A Year 3 simple routine question

What was the issue here?

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Effective teaching will teach and monitor through all these task types

Problem solving and reasoning only happen when students are working on tasks that they don’t immediately know how to solve and is not merely repeating an argument developed by someone else, it must be their own. Peter Sullivan, 2014

It is through tasks, more than in any other way, that opportunities to learn are made equitable and accessible to students Anthony and Walshaw, 2011

Routines evolved from impact of 2015-2109 work to support schools

Pedagogy to reflect the disciplinary and inter-disciplinary nature of the curriculum content

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• Collaborating
• Developing language
• Engaging with feedback
• Explicit Instruction
• Learning Goals
• Making connections
• Metacognition
• Practising
• Questioning
• Releasing responsibility

Assessments- Ensuring we assess t

Working with Intermediates and High Schools in AUS and NZ

2012-14 13-15 14-16 15-17 16-18 17-19 18-22*

Control Schools

Nation

Like Schools

Three year moving average of Year 9 Numeracy

Phases

1 Rich routines

• moveNprove (unit and strand)
• recallNreason games (basics)
• revistNretain (basics – num/strand)

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2 Open tasks

3 Assessment

• PSMT each semester
• Unit tests (60%, 20%, 20%)
• Basic test snapshots

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4 Numeracy across all Key learning Areas

Target = 100

����RecallNReason

÷

Turn a game into a problem solving experience

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How could you place the digits 3, 4, 5 , 6 into these boxes to make the answer closest to 100

Improving participation and performance for all students

These routines have evolved over the last 8 years

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They pepper a typical week

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They last 5-10 minutes

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They promote the proficiencies

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They build retention

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They support positive disposition

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Which of the following statements do you agree with?

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1. If 𝑥 = 5 then 𝑥 + 5 = 25
2. If 𝑥 = 3 then 𝑥 + 3 = 6 - 𝑥
3. If 𝑥 = 5 then 5 - 𝑥 = 0
4. If 𝑥 = 3 then 𝑥 + 3 = 9 - 𝑥

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moveNprove for group/pair discussions

• Choose terms from the cloud and write some expressions from the cloud below that equal

5 a + 9

3a

4a

2

6

a

3

2a

7

2a

4

5a

1

8

a

����Maths Leadership Series� ���

recallNreason

• Academically rich games
• Whole class or target groups
• Promotes fluency and reasoning
• Can be used for formative assessment
• Offers variety and engagement

Number Boxes Years 1 to 8

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Materials: 6 sided dice, pen and paper

Maths concepts: computation, place value

Aim: Be the closest to the target number

1. Choose which number box layout you want to play and decide on a specific target number to aim for, e.g. 200
2. Players take turns to roll a dice and place it somewhere in one of their boxes.
3. Once the number has been placed, it cannot be moved. One number on any given round may be “thrown away” and written in the throw away box instead.
4. Play continues until all of the boxes are full. Players justify which number is closest to the target number.

Target = 200

5

6

2

4

3

1

6

����RecallNReason

6

(50 x 4) + (2 x 4) = 208

(30 x 6) + (1 x 6) = 186

����RecallNReason : Number Boxes game

A 5 min self directed task once a week to encourage discussion

���One Maths HOD has been creating and rippling out in Years 9 to 12

����Maths Leadership Series� ���

revisitNretain

• Questions flash up on screen (3-5)
• One every 20 seconds
• Students jot down answers
• Teacher moves around room observing
• One question chosen for discussion

( errors, efficient strategies, inefficient strategies)

By putting in just one pair of brackets, make as many different answers to this as you can. Write each answer as an equation

3 + 4 x 8 – 6 ÷ 2

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Try this first…

3 + 4 x 8 – 6

Not done yet….

Set your work out in a way that convinces me that you have found all possible answers

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A revisitNretain – one question we saw all kids do

For delivery each day is made into a slide deck

3 or 4 questions over 2 minutes

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Teacher observes responses

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Teacher focuses on one question

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Mathematical discourse activated

Here Year 9s are going back to Year 8

revisitNretain

Progress Outcome:

Recognise, read, write, represent, compare and order decimals (to three places)

10.56 10.57 10.58 …

13.743 13.843 13.943…

5.64 5.54 5.44…

What “Do” practices does this routine activate?

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N

y3 y4

One example of basics without conceptual understanding

Richard Cowan (2011) pointed out that there is a high correlation between the calculation skills of addition and subtraction and the performance of maths among primary school students

43 – 29

given to 9082 tamariki in May 2024

y5 y6

y7 y8

39%

18%

66%

����Maths Leadership Series� ���

moveNprove

https://bit.ly/7to10moveNproves

Year 9s first “Table Debate” moveNprove

A task for you to try in pairs

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1. Choose your question (with bracket)

eg 35 – (3 x 5)

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2. Create an expression that gives the same solution eg 15 + (2 x 2.5)

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3. Create an expression that gives a different solution eg 20 – (15 x 1)

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You can create 3 wrong like the example

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Year 8s on the Gold Coast working in pairs

A process that can be used as an exit pass

What expression will find the area of this shape

1. Draw and label two separate rectangles

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An explicit routine for creating their own

2. Calculate the area of each

3. Join your two shapes together

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4. Add in the other correct missing measurements

5. Make 1 correct, 1 incorrect

Year 9s having a first attempt at 1 right 3 wrong

����Maths Leadership Series� ���

discussNdefend

• Create a culture that values and enables student voice
• Guiding students to have both self-agency and self-efficacy
• Have opportunities to practice productive maths talk in a ‘safe non threatening environment’
• Use as a ‘hook’ to generate doubt or curiosity

SHS teachers finding and adapting these great free resources

An activity to get students to notice what is the same and different. This could include either mathematical images or solution methods. ��

2 websites:

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Same or different

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Same but different math

�What’s the same, What’s different?

A hexagon has six equal length sides.

Cutting a corner off a square makes a pentagon.

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Always, Sometimes, Never

• Sort the statements: which are always true, sometimes true, or never true?

• For the “sometimes true” statements, can you explain when they are true?

Squares have two diagonals that meet at right angles

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����TLF Maths Capability Series

Summing Up

https://arbs.nzcer.org.nz/

Generic username : arb

Password: guide

But it is much better to create your own username and password

Where to go to make some – ARBS

e.g. Folded measurements

Folded measurements (Level 4 Measurement ARB)

Where to go to make some – 1 . ARBS

Links for Australian Schools

TLF Maths: ideas and insights | Facebook

General links to resources – currently at home

https://bit.ly/rapidroutines

https://bit.ly/7to10moveNproves

digital recourse collection -