- Picture Puzzles Expand Learning Opportunities
Click an image to see it in higher resolution.
Year 8 students at Botkryka Friskola, Sweden, are exploring Square Numbers using the Free Tour Picture Puzzle of that name. One screen, two learners, concrete materials, in this case Centicubes and a challenge. These are not glorified electronic textbook exercises. Each slide show is an intellectually engaging sequence of challenges. In this case the challenges highlight the construction of square numbers from a sequence of odd numbers. This leads into finding the difference between two squares.
In this student-driven environment, the teacher has time to visit and work with many pairs during a session. That's when student insights are discovered. In this case, take a closer look at Ebba and Paulina's work. When they had to add up short sequences of odd numbers they just added in sequence. S20 was written out in preparation for the same approach, but unlike several classmates who reached for a calculator at this step, the girls noticed a short cut and wrote 40 • 10 (which technically should have been 10 • 40) and hardly had to add at all. (Dot stands for multiplication in Sweden.)
They had noticed that the first and last added to 40, so did the 2nd and the 2nd last and so on.
In the same class the teacher found that Simon and Philip had reached S20 and written out the sequence to be added like this:
continuing to 20 terms
||They intended to add this list manually but questioning by the teacher helped them see patterns in the list.
- 1 + 3 + 5 + 7 + 9 only had to be calculated once, but the answer could be used four times.
- The rest of the total would come from 5 tens, 5 twenties and 5 thirties all of which are easy to calculate.
Since the Working Mathematically objective of the lesson was to learn to ask the question Can I check this another way? these student contributions enriched the rich 5 minute whole class discussion of that question at the end of the lesson.
- Was it of any importance that it was the students who presented these discoveries to their peers?
- How could the teacher build on these discoveries in the next lesson?
- Menu Maths Refreshed
Menu Maths @ Café Conundrum has recently been recreated as a PDF file. The file contains a Café Conundrum cover page, 4 menus presenting a total of 22 investigations in a selection of content strands and assorted 'placemats' to use as game boards. You will need Poly Plug (or a substitute) because this is a hands-on learning menu.
You print the file (preferably in colour) as many times as you need, slip the pages into plastic sleeves and create Café Conundrum menu booklets which invite students from about Year 3 to choose their own investigation.
- Menu Maths is delivered by email to your chosen address.
- Menu Maths is published exclusively for your school (or yourself if it is a private order).
- Menu Maths costs just $11 for the file and it can be printed as many times as you wish.
This information, teaching notes and more has been added to the refreshed Menu Maths page. See Link List below.
- Sphinx Folding
In the previous issue we mentioned a link to David Mitchell's work at Origami Heaven on paper folding a Sphinx. We contacted David and asked for permission to modify his instructions a little because his introduction revealed some of the answers to question we wanted to investigate. David generously allowed us to produce the document in the Link List below and to distribute it through Mathematics Centre. It's first outing was at a parent evening for Caledonian Primary School. This is parents from Year 3 - 6 and some of their children. The proof is in the photos. Sphinxes can be created by folding and the number in the photo were created in about 25 minutes of a 45 minutes session.
The final challenge on the sheet is to learn to draw the smallest possible size Sphinx on the Sphinx Paper by joining dots. The challenge the parents took home was for the family to make at least three more Sphinxes so they could work with their child from the Free Tour Picture Puzzle titled Sphinx Shapes. Perhaps before the next eNews edition we will have some feedback from the school about how this played out in some homes. See Link List below.
- Caledonian PD Day
|Karren Jennings has been encouraging her staff at Caledonian Primary School toward learning to work like a mathematician for a couple of years and the time was right for a Professional Development day. Having worked with Karren on a similar curriculum shift in her previous school we were delighted to be invited to work together again. With lots of co-operation across the school and minimum employment of substitute teachers she was able to organise 3 hours for the Prep - 2 teachers, 3 more for the Y3 - 6 teachers and the parent evening. The parent evening included sessions in the classrooms as well as the group sessions we presented. Every participating family (almost 50 of them) received a Maths Showbag packed with care and creativity by the teachers.
- P - 2 teachers dug into Calculating Changes. They loved Plug Catcher, found links with Maths300 through Add Town and the Maths300 lesson Chart Strategies and were amazed at planning support available in Working Mathematically with Infants.
- Y3 - 6 teachers explored times tables and multiplication concepts through calculator activities and Uncover Counting from Calculating Changes, Times Tables Torture from Picture Puzzles and Tackling Times Tables from Maths300. They also found strong planning support in Maths With Attitude manuals.
(These are now available electronically. See Link List below.)
Parents and children from P - 2 enjoying Poly Plug activity called Buttons from Calculating Changes. Everyone has buttons, or a substitute, at home.
They also learned some card games.
Professional Development - that's what we do. You are welcome to make contact about your need.
- MAV Primary Conference
||EMBEDDING AND ASSESSING THE MATHEMATICS PROFICIENCIES CONFERENCE (Friday 23rd & Saturday 24th June)
The MAV and the Melbourne Graduate School of Education, Mathematics Education Group, have combined forces to deliver an inaugural two-day primary mathematics education conference. Day 1 is for mathematics education leaders and Day 2 is for all primary mathematics teachers. This event promises to one of the most exciting new events in your professional learning calendar and is an opportunity to learn from leaders from both organisations.
For more details access the conference web page from the Link List below.
- New Life for Maths300
In case you haven't heard yet, Maths300 now has a new home with the Australian Association of Mathematics Teachers. We are delighted that our sister site, which is built on the work of scores of teachers from Australia and overseas, is now in the care of the national organisation for mathematics teachers. The connections between our two sites are as strong as ever and AAMT is looking forward to continuing and extending the work of the previous owners.
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