This is a companion downloadable PDF resource for Natural Maths Strategies downloadable PDF resource 1. This downloadable PDF resource provides the tools needed to make an informed and accurate assessment of individual student's level of mathematical competence. Annotated work samples, from students working with the Natural Maths Strategies program, illustrate how to interpret students' work for assessment purposes. The authors have also provided learning horizons, that identify the developmental stages that underpin each of the "big ideas" in the Natural Maths Strategies program. These can be used as the basis of informed planning and direct teaching.

Discussing a work sample with the individual student is like having an intensive interview. The student might explain what they are doing and thinking. Clarification can be sought and questions that will stretch the student to think further or differently can be asked. For example, if a student uses a chunking strategy, they can be asked if there is an alternative way that they could make the calculation, as a check. Or they might try number splitting, but be unsure of how the number should be partitioned to make the calculation simpler. Listening to what the student can do and finding out what they do know and then nudging them to think a little further or a little differently provides further information on which informed planning can be based.

Through intensive interviews and annotation of work samples it is possible to make informed decisions about what to do next either for the whole class, a specific group or an individual student.

For example, we might ask:

• Is the specific mathematical big idea involved being developed?
• Are there any misconceptions that need to be worked on?
• Is the intellectual level challenging enough or too challenging?

Answers to questions such as these point the way for future lessons