Maths at KPS

We have moved beyond just using strategy stages for numeracy and learning maths problems out of context. The tools we now use come from Bruce Moody (Educational Consultant and maths guru).

The five tools are:

  1. The Key Progressions in Additive and Multiplicative Thinking
  2. The Diagnostic Questions
  3. The Flow Plans
  4. The SEED Videos
  5. Maths Recording Sheet

What to teach

  • Key Progressions

How to teach

  • Flow Plans
  • SEED Videos


  • Diagnostic Questions
  • Recording Sheet             

Note that these tools do not exclude the use of other tools, particularly the resources available on

1.Key Progressions

The Key Progressions (KPs) describe the critical aspects of the learning journey in the Number strand - and the main applications of Number to other strands. The KPs are intended as a sequence of “must do’s”. They do not exclude other teaching in Number, but are the essential elements. Each KP describes a mathematical behaviour, more than simply a search for a correct answer. In some instances, a specific student response is required. E.g. subitising is a quite different behaviour than counting even when the answer is identical. At other times, multiple pathways are acceptable, but students do not have to solve the same task in multiple ways. E.g. to solve 347-198, use of the algorithm, reversibility, or the distributive law are equally acceptable.

2. Diagnostic Questions

The Diagnostic Questions (DQ) serve to put the desired behaviour into a problem to be solved.

DQ are written to provide examples in meaningful contexts where the number choices are within an appropriate range. The DQs serve as a means of identifying an area for new learning and show students the type of problems they will master. If the teacher notes that students are in the “needs to learn” category, they will plan for student learning by drawing upon their experience, nzmaths, and using ideas from the Flow Plans and SEED Video series.

Learning will initially be scaffolded, using material and verbal prompts.  Student inconsistency is normal. As time progresses, teachers will deliberately reduce their input and increase the range of contexts and number choices within the behavioural range outlined in the key progression.

3. And 4. The Flow Plans and SEED Videos

The Flow Plans (FP) and SEED Videos (SV) serve two main purposes:

1)      They describe the importance of the new learning, identify key concepts being developed, and explain common student misconceptions. 

2)      They also provide a few useful starting activities that may be used with students. Teachers will need to use a much wider range of contexts and activities in their classrooms than those in the FPs and SVs.

Both of these resources also provide incremental learning stages within the key progression.

5. The Recording Sheet

The Recording Sheet (RS) serves to capture evidence of student progress in the “Goldilocks zone” of assessment. The RS is a “living” document that is updated as teachers note success.

Kawaha Point School
Aquarius Drive
Rotorua, New Zealand
Ph: 07 348 5864
Fax: 07 349 2581