1. Northcote Glenfield Birkenhead Cluster
Lead Teacher Workshop
Northcote Glenfield Birkenhead Cluster
Thursday September
A Closer Look at The Geometry Measurement Strand of NZC
Mathematics facilitators:
Christine Hardie
Michelle Wetherall
Heather Lewis

2. Queen Esmerelda’s Coins
Queen Esmerelda has 20 gold coins. She puts them in four piles.
The first pile had four more coins than the second
The second pile had one less coin than the third
The fourth pile had twice as many coins as the second.
How many gold coins did Esmerelda put in each pile?
Hint: which pile shall we call n? n
n-1 n
2(n-1)
5n = 20, therefore n = 4

3. Objectives 8.45-9.15 Discussion – National Standards implementation
Module 9 + Rich Task – Engaging Learners with Mathematics
Morning Tea
Written Recording
Progressions
As evidence to support teacher OTJ
Questioning – how to enable and extend students 3

4. Challenges & Opportunites
At your table groups, discuss:
How you have used the lead teacher sessions to support your teachers with implementation of the Standards
Challenges?
Opportunities?
List any support you feel you would benefit from over the next term, eg:
Reporting to parents at end of year
Moderation
OTJs

5. Engaging learners with mathematics
Ministry Professional Development
Modules – Jigsaw Activity
Module 7 & 9
Engaging learners with mathematics

6. Using Different Problem Types
The expectations defined by the standards include how a student solves a given problem, not only the student’s ability to solve it so….
Provide tasks with multiple possible solution strategies

7. Different Problem Types
1. Martin opened his book and noticed that the sum of the two pages was 173.
What page numbers were showing? =
open-ended
procedural
Open ended problems are something they need to think about, not simply a disguised way of practising already demonstrated algorithms

8.
Measurement is important in providing links between strands of mathematics. For example, it provides a rich and meaningful context for the use of number skills and of spatial concepts.
Measurement also provides links between mathematics and other school subjects. Measuring skills, especially estimating, have an important place in many games and sports. In addition to being required in many science investigations they also play a part in some artistic and musical experiences.

9. Ttributes co Five phases L1 L4/5 Identifying the attribute
Volume / Capacity
Time
Ttributes co
Five phases
Identifying the attribute
Comparing and Ordering
Non-Standard UnitsL1/2
Standard Units L2/3
Applying & Interpreting L1
L4/5

10. Key ideas when teaching non-standard units
focus on the process of repeatedly using a unit as a measuring device.
Generalise principals of counting to measuring.
Develop key ideas how units work:
- Units are a part of the attribute being measured.
- Units must be the same size.
- Units must fit together with no overlaps or gaps, ‘tiling’
N.B.children tend to choose units matching the shape
- Units can be partitioned (e.g. halves) and joined.
- Choose appropriate units of measure.
- Understand the limitations of non-standard units.
Estimation should be encouraged early.

11. Standard Units Misconceptions when using standard rulers
Measure the length of the stick with the broken ruler.
What do you think counters (stages 1-4), and adders (stages 5-6) would do?
Need time to study the instruments used before using the instruments to measure!
Why might EA and AC thinkers struggle with mm on a ruler?

12. Level 2 Old Curriculum
M2:1 carry out practical measuring tasks, using appropriate metric units for length, mass, and capacity;
Level 2 New Curriculum
GM1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature and time.

13. Key ideas when Teaching Level 2 Numeracy Stage 5
Extend understanding of non-standard units;
- Units can be partitioned or joined,
- Choose appropriate units of measure
- Understand the limitations of non-standard units).
Create ‘measurement devices’ before more structured instruments are introduced.
Progress to simple standard units. (A diversity of metric units are required at Level 3).
Consider numeracy links when using units (standard or non-standard).

14. Key Ideas when Teaching Level 3 Numeracy Stage 6
Strong focus on diverse range of standard units, specifically the metric system. Choose appropriately.
Know the names, prefixes (cenit- milli – kilo) and ‘feel’ for the size of units.
Use scaled instruments such as rulers and protractors effectively and read graduated containers.
Connect place value understanding to relationships between units of the same attribute e.g. 1cm is one tenth of 1 metre.
Begin to see relationships between length and area or length and volume for rectangles and cuboids.
(second AO in the new curriculum)

15. Effective Teaching Cycle
Assess
Analyse data
Plan
Teach
Practice/Apply

16. Fitting It In – FIO Measurement L2
Book 9, page 13
As you do this task, consider what written recording would provide evidence to illustrate how the problem is solved. Make sure one of you is responsible for recording everyone’s ideas

17. Consider possible responses and use the progressions in the Standards to identify next learning steps.
Bigger, smaller
Cubes, etc.
cm and mm
Whole number cm
- halves etc.

18. How rich was this task?
It must be accessible to everyone at the start.
It needs to allow further challenges and be extendable.
It should invite learners to make decisions.
It should involve learners in speculating, hypothesis making and testing, proving and explaining, reflecting, interpreting.
It should not restrict learners from searching in other directions.
It should promote discussion and communication.
It should encourage originality/invention.
It should encourage 'what if' and 'what if not' questions.
It should have an element of surprise.
It should be enjoyable.
Ahmed (1987), page 20

19. How rich was this task?
It must be accessible to everyone at the start.
It needs to allow further challenges and be extendable.
It should invite learners to make decisions.
It should involve learners in speculating, hypothesis making and testing, proving and explaining, reflecting, interpreting.
It should not restrict learners from searching in other directions.
It should promote discussion and communication.
It should encourage originality/invention.
It should encourage 'what if' and 'what if not' questions.
It should have an element of surprise.
It should be enjoyable.
Ahmed (1987), page 20

20. Turning a terrific task into a terrific lesson
In your groups, consider…
Mathematical opportunities
Possible responses
‘Enablers’ and ‘Extenders’

21. Using rich tasks to engage learners in mathematics
As you do this task, consider what written recording would provide evidence to illustrate how the problem is solved. Make sure one of you is responsible for recording everyone’s ideas
The Sweet-tooth Company has hired you to design boxes to hold sixty-four sugar cubes. Each cube has edges of 2 cm, just like multilink cubes. The boxes have to be the shape of boxes (cuboids) as there should not be sugar cubes sticking out. What sizes of boxes could they have? Do not make the boxes, just sketch rough plans of them showing the length of the edges.How many different boxes could be made? How could this be worked out without having to build each shape with cubes?
The Managing Director now walks into the design room to say that market researchers say that 2cm cubes make the consumer’s tea too sweet – how many 1cm cubes could you fit into the box you have designed?

22. Which of the rich task criteria did this problem meet?
It must be accessible to everyone at the start.
It needs to allow further challenges and be extendable.
It should invite learners to make decisions.
It should involve learners in speculating, hypothesis making and testing, proving and explaining, reflecting, interpreting.
It should not restrict learners from searching in other directions.
It should promote discussion and communication.
It should encourage originality/invention.
It should encourage 'what if' and 'what if not' questions.
It should have an element of surprise.
It should be enjoyable.
Ahmed (1987), page 20
However, keeping mathematics interesting and fun should not be at the expense of content.

23. Turning a terrific task into a terrific lesson
Select an engaging problem that is both achievable and challenging.
Know the mathematical opportunities provided in the problem.
Consider possible responses from the children.
Consider ‘enablers’ and ‘extenders’ to make the task both achievable and challenging.
Formatively assess what a child can do and..
Identify next learning steps.

24. Jack and the Beanstalk learning centre

25. If you always do what you’ve always done -
Thought for the day
If you always do what you’ve always done -
you’ll always get what you’ve always got.