1. Northern Metropolitan Region Achievement Improvement Zones Session 3: BUILDING MATHEMATICAL UNDERSTANDING Peter SullivanSue Gunningham

2. Northern Metropolitan Region Achievement Improvement Zones Reminder: we are doing this out of order

3. Northern Metropolitan Region Achievement Improvement Zones The purpose of this session is for participants to: experience some illustrative activities which contribute to building understanding of mathematics and at the same time enhance the experience of learning mathematics; and reflect on the activities and ways of incorporating such experiences into classroom teaching.

4. Northern Metropolitan Region Achievement Improvement Zones Some illustrative activities The following are five suggested activities that illustrate approaches to building understanding. They are intended to be generic, in that they can be adapted to a wide range of topics and levels.

5. Northern Metropolitan Region Achievement Improvement Zones 3a 3a 2 b × b × ab × b× b 3ab 2 3a 2 b 2

6. Northern Metropolitan Region Achievement Improvement Zones Describing relationships - Brainstorm What are some other similar puzzles that you might create (at “your” year level)?

7. Northern Metropolitan Region Achievement Improvement Zones Different representations This activity consists of a base sheet, on which clues to the four representations are given, along with small cards that are individual representations of an operation or an action. The intention is that students take turns in placing the cards into a base rectangle and to justify that placement.

8. Northern Metropolitan Region Achievement Improvement Zones Different representations- Brainstorm How might you adapt this activity to your own grade level?

9. Northern Metropolitan Region Achievement Improvement Zones Similar and different Arrange the following fraction addition questions into three groups, and write down the reason that you chose those questions in the same group:

10. Northern Metropolitan Region Achievement Improvement Zones Similar and different - Brainstorm What are some other similar concepts that you might use as the basis of such an experience?

11. Northern Metropolitan Region Achievement Improvement Zones Empty number lines Use an empty number line to work out the answer to: 37 + 29

12. Northern Metropolitan Region Achievement Improvement Zones Empty number lines - Brainstorm What are some other similar ways that you might use empty number lines?

13. Northern Metropolitan Region Achievement Improvement Zones Planning a classroom investigation By yourself, reflect for a short time of something from this session that you will try out in a class between now and the next session. This might be by making the goals for learning explicit, using a number fluency game or activity, or going beyond their current levels of thinking. You might like to make an activity like ones that we have done, and try it out. Within your school group describe what it is you will do. There will be opportunity for reporting back at the next session.

14. Northern Metropolitan Region Achievement Improvement Zones Your own way of seeing numbers What number is exactly halfway between 15 and 103?

15. Northern Metropolitan Region Achievement Improvement Zones Decimals Jigsaws

16. Northern Metropolitan Region Achievement Improvement Zones Reflecting on the experience Think Pair Share What are the opportunities in using such tasks in your classroom? What are the constraints in using such tasks in your classroom?

17. Northern Metropolitan Region Achievement Improvement Zones Planning a school or classroom investigation Before the next session, search your school storerooms, library, and classrooms for resources that might support teaching to improve the experience of learning numeracy. Make a list and report on the list at the next session