IfSR - Multiplicative thinking

Interview for Student Reasoning - Multiplicative thinking (IfSR-MT) is an on demand assessment that enables teachers to hear and see how students apply their mathematical understandings of multiplicative thinking. IfSR-MT is divided into 4sections:

  • Section 1: Strategies for sharing and forming groups
  • Section 2: Flexible strategies with single digit numbers
  • Section 3: Flexible strategies with multi digit numbers
  • Section 4: Flexible strategies with rational numbers

More information on each section is available below.

Assessment guide and materials

The Assessment guide and student materials document (PDF 254KB) (staff only) supports teachers to administer the assessment.

The first part of the document outlines:

  • the purpose of the assessment
  • details on how to prepare for, administer and lodge the assessment
  • a summary of related syllabus outcomes and links to the National Numeracy Learning Progression.

The second part of the document details the materials required for each of the 4 sections for the assessment. Templates for printable resources are available in separate section documents below.

Syllabus and IfSR item mapping tool

The Syllabus and IfSR item mapping tool (XLSX 769KB) (staff only) maps the top response to each IfSR item against the NSW Mathematics K-10 syllabus.

Section 1: Strategies for sharing and forming groups

Sharing and forming groups are characterised by sharing equally and working with a unit (one-to-many relationships). When working towards Early Stage 1 outcomes and beyond, students may use manipulatives and mental strategies to model and solve problems in multiplicative situations.

Section 2: Flexible strategies with single digit numbers

Flexible strategies with single-digit numbers are characterised by the development of a range of flexible strategies such as using renaming, doubles and known facts that can be used for mental computation. When working towards Stage 1 outcomes and beyond, students apply a range of mental strategies in various multiplicative situations and represent thinking in a range of ways.

Section 3: Flexible strategies with multi digit numbers

Flexible strategies with multi-digit numbers are characterised by using appropriate mental strategies such as using known and derived facts, strategically partitioning and applying number properties. When working towards Stage 2 outcomes and beyond, students select and apply from an extended range of ideas to support a broader range of multiplicative contexts.

Section 4: Flexible strategies with rational numbers

Flexible strategies with rational numbers are characterised by the application and extension of whole number place value knowledge, using known facts, strategically partitioning and the application of real number properties. When working towards Stage 3 and 4 outcomes and beyond, students work flexibly and efficiently exploring ideas that work in whole numbers and those that are unique when working with fractions and/or decimals.

Online tool

Teachers administer the assessment using the online tool for entering student responses. The online tool is available via ALAN.

The ALAN helpdesk has solutions for all ‘How to' questions for administering the assessment.

Multi-select response feature

An additional feature in IfSR-MT enables teachers to select multiple flexible strategies to acknowledge students’ thinking. This feature is available in sections 2, 3 and 4.

When a teacher selects one or more strategies from the list, the information is recorded in the Student Assessment Analysis. This allows teachers to analyse the range of flexible strategies students are using, and to make informed decisions about next steps for each student. This can also assist in identifying if there is an over reliance on some strategies.

This short preparation video 'How to navigate the online assessment' helps teachers familiarise themselves with the online tool.

Navigating IfSR Multiplicative thinking (IfSR-MT)

The Interview for Student Reasoning - IfSR - is an online, on-demand diagnostic numeracy assessment. The IfSR informs teachers of the way a student reasons and uses their mathematical knowledge.

What is IfSR - Multiplicative thinking?

IfSR- Multiplicative thinking or IfSR-MT is an online assessment that enables a teacher to gain insights into how a student reasons and works flexibly with numbers in multiplicative situations.

From the insights a teacher can establish where students are in their learning in order to target their teaching. The tool enables a teacher to monitor student progress through the use of PLAN2. There are 4 sections in IfSR-MT. Each section has 2 subsections.

All items are aligned to the Mathematics K-10 syllabus and the National Numeracy Learning Progressions.

Who is IfSR-MT for?

The assessment is designed to be delivered flexibly to assess individuals or groups of students K-10 to identify their reasoning skills in Multiplicative thinking. You can select students who you would like to gather more information on.

It is designed to supplement existing school practices and inform your decision making within the teaching and learning cycle to identify how students construct their mathematical understandings and to help you tailor your teaching more specifically to student needs.

How do I administer the online assessment?

Select the year level, class, or group. Select the student, then choose to begin or continue the assessment for the student you are working with. Confirm the student and section by selecting the ‘Start’ or ‘Continue’ button, to start or resume the assessment.

The IfSR-MT assessment has been modularised to give you flexibility in assessing sub-skills for targeted teaching. This allows you to select the starting point when beginning each section.

When administering each question, you will see: the sub-section being assessed, any materials that may be required, and instructions for the task. Read the questions to the student that are marked with a speech bubble icon.

How are responses recorded in the tool?

Record student responses by selecting an option from the response panel. You can record a comment, noting the student’s behaviour. This will assist you when analysing the results.

Select the ‘Flag’ button to mark and draw your attention to particular tasks. Select ‘Next’ to move to the next question. Responses will be saved automatically.

What is the multi-select response option?

In IfSR-MT, there is an additional feature that enables teachers to select multiple flexible strategies to acknowledge students’ thinking. This feature is available in section 2, 3 and 4.

When you select one or more strategies from the list, the information is recorded in the Student Assessment Analysis. This allows you to analyse the range of flexible strategies students are utilising, to make informed decisions about next steps for each student. This can also assist in identifying if there is an over reliance on some strategies.

How do I navigate the assessment?

The progress bar displays the count of completed tasks out of the total number of tasks for that section. Move to a specific task by selecting ‘Go to’.

How do I review individual student progress?

View the number of questions in the sub-section and navigate to a specific question if needed. Answered questions display in blue, not answered in white, and flagged with a black triangle in the top left corner. Close the progress bar to return to the assessment.

To pause the interview without completion, select the ‘Exit’ button in the top right corner. This will save your progress and close the assessment screen.

How do I finalise responses and lodge the assessment?

To lodge the assessment, select ‘Finish Interview’. Lodgement will not be possible until all tasks have been responded to.

Navigate to any unanswered tasks or mark all unanswered tasks remaining as ‘Not given’, noting a reason and any additional comments. You can also Save and exit to lodge responses at a later time or finalise student responses by selecting ‘Lodge’ once all responses have been recorded.

Once lodged, student responses cannot be modified.

How do I access student analysis history and responses?

View the status of an assessment and access a student analysis for each section assessed from the main page of the online tool. Here you can continue, re-assess, or begin a new assessment. Re-assessment of a section can occur at any time.

A Student Assessment Analysis can be downloaded in the online tool for each section assessed. The analysis can assist in making decisions about the next steps in learning to meet the needs of individual students.

Where else can I analyse student responses?

IfSR-MT maps student responses to the National Numeracy Learning Progression in PLAN2. Direct links to Class observations and cohort snapshot are available via the ‘Class analysis’ button.

The Area of focus template in PLAN2 is aligned with IfSR-MT to enable you to target your teaching.

For further information on the Interview for Student Reasoning diagnostic numeracy assessment, please visit the ALAN help desk or the IfSR web page.

Professional learning

Becoming mathematicians: flexible multiplicative thinking: professional learning video and accompanying resources examining the components, or "molecules" of multiplicative thinking.

See the IfSR-Number and place value and IfSR-Additive thinking web pages for related professional learning options.

Improving reading and numeracy course: Multiplicative thinking (K-8)

This professional learning course supports teachers to understand and implement evidence-based teaching strategies for multiplicative thinking and access, adapt and implement universal resources to support effective teaching practice.

  • Access ‘Improving reading & numeracy: Multiplicative thinking (K-8)' via MyPL (course code NR31653).

Multiplicative strategies: blended learning

This professional learning focuses on understanding of the development of multiplicative thinking and practical ideas for classroom application.

Additional resources

Flexible strategies (in 4 parts)

Resources supporting the evidence-based teaching of numeracy more broadly are available via:


Visit the Interview for Student Reasoning web page for information on the purpose of the assessment suite.

Visit the Literacy and numeracy professional learning web page for more professional learning opportunities in the practical application of evidence-based teaching of numeracy.

Visit the ALAN helpdesk for solutions relating to administering the assessment.

Join the Interview for Student Reasoning channel in the Numeracy NSW statewide staffroom in MS Teams.

About this resource

Advice on use

IfSR - Multiplicative thinking (IfSR-MT) is part of a suite of teacher-led online numeracy assessments administered by the classroom teacher to individual students through one-to-one interviews. They can be administered at any point in time to reveal what a student knows, ways a student reasons with and thinks about mathematical tasks, and as a tool to investigate the gaps in a student’s mathematical knowledge.

  • The assessment is modularised to give teachers flexibility in assessing sub-skills for targeted teaching.
  • The administration is flexible and adaptable to enable teachers to gather information on a student's conceptual knowledge in numeracy.
  • IfSR - MT does not need to be administered within a specific timeframe or from beginning to end.
  • Teachers tailor the administration of the assessment to suit the needs of individual students by selecting either a section, sub-section or specific tasks. For example, a teacher may select to administer only a small group of tasks in one section.
  • The teacher decides on tasks and/or sections by reviewing existing assessment such as classroom observations and/or teacher judgement.

This resource may be used across the curriculum where it supports the teaching and learning of numeracy skills aligned to syllabus outcomes.

For further advice on use, please see the IfSR-MT assessment guide.


When using these resources in the classroom, it is important for teachers to consider the needs of all students, including Aboriginal and EAL/D learners.

EAL/D learners will require explicit language support and scaffolding, informed by the Enhanced EAL/D enhanced teaching and learning cycle and the student’s phase on the EAL/D Learning Progressions. For further information visit the English as an additional language or dialect education webpage.

Learning adjustments enable students with disability and additional learning and support needs to access syllabus outcomes and content on the same basis as their peers. Teachers can use a range of adjustments to ensure a personalised approach to student learning.

A range of tools to identify, assess and challenge high potential and gifted learners are available to support teachers in the classroom. Identifying contributors to achievement helps teachers identify and target areas for students’ growth and improvement. A differentiation adjustment tool can be used to plan effective teaching strategies.

Alignment to system priorities and/or needs

These resources reflect the following existing frameworks:

Alignment to School Excellence Framework

These resources support the School Excellence Framework and clearly align to the following domains and themes:

Learning domain

  • Assessment: Formative Assessment, Summative Assessment
  • Student Performance Measures: Internal and external measures against syllabus standards

Teaching domain

  • Effective classroom practice: Lesson planning, Explicit teaching, Feedback
  • Data Skills and Use: Data Analysis, Data Use in Teaching
  • Learning and development: Expertise and innovation

Research base

Centre for Education Statistics and Evaluation (2020). What works best: 2020 Update, CESE website

Clarke D, Clarke B and Roche A. (2011) ‘Building Teachers’ Expertise in Understanding, assessing and developing children’s mathematical thinking: the power of task based, one-to-one assessment interviews’, ZDM Mathematics Education 43:901-913

Department of Education and Training, Victoria (n.d.) Assessments for Common Misunderstandings, DET Victoria website

Hurst C and Hurrell D (2016) Assessing Children’s Multiplicative Thinking Mathematics Education Research Group of Australasia

Lamon, S (1999) Teaching Fractions and Ratios for Understanding – Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum and Assoc

Siemon D, Beswick K, Brady K, Clark J, Faragher R, and Warren E (2019) Teaching Mathematics: Foundations to middle years. Oxford University Press

Booker G, Bond D, Sparrow L and Swan P (2014). Teaching primary mathematics. Frenchs Forest, NSW: Pearson Australia

Vale C, Bragg L A, Widjaja W, Herbert S, and Loong E Y-K (2017). ‘Children's mathematical reasoning: opportunities for developing understanding and creative thinking’, Australian Primary Mathematics Classroom, 22(1), 3


Comments and feedback to contribute to evaluation and support ongoing resource development can be provided via Literacy and Numeracy resource feedback form.

Reviewed by: Literacy and Numeracy team

Last updated: January 2023

Anticipated resource review date: January 2024


  • Numeracy

Business Unit:

  • Educational Standards
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