![Page 1: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/1.jpg)
A workshop at
Homi Bhabha Centre for Science Education,
Mumbai, India
22–23 February 2011
Elisabeth Rystedt and Johan Häggström
National Center for Mathematics Education, NCM,
Gothenburg, Sweden
![Page 2: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/2.jpg)
Teacher
Pupils: 10–16 years old
Mathematics and the Swedish language
Educational inspector in mathematics at The National
Agency for Education
National Center for Mathematics Education, NCM
Project leader of a national network
![Page 3: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/3.jpg)
Math lab at NCM
The book Matematikverkstad
In-service projects
Lectures
Conferences
Courses: all over Sweden, in some places in Norway + London, Brussels, Mexico City …
Advisors
Research overview
![Page 4: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/4.jpg)
Teacher in mathematics and science
Mathematics teacher educator
Research in mathematics education
Editor of Nordic Studies in Mathematics Education
Learning study – professional development
![Page 5: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/5.jpg)
![Page 6: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/6.jpg)
![Page 7: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/7.jpg)
How can I take the ideas and change them, so it will be possible toconduct them together with my pupils?
![Page 8: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/8.jpg)
![Page 9: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/9.jpg)
![Page 10: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/10.jpg)
![Page 11: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/11.jpg)
Gothenburg
Stockholm
![Page 12: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/12.jpg)
![Page 13: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/13.jpg)
![Page 14: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/14.jpg)
Population 9 000 000 1 161 000 000
Population
density, inh/km
22 353
Area
km
450 000 3 290 000
”Big cities” Stockholm
1,2–2 milj
Mumbai
14–20 milj
![Page 15: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/15.jpg)
![Page 16: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/16.jpg)
![Page 17: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/17.jpg)
![Page 18: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/18.jpg)
![Page 19: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/19.jpg)
![Page 20: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/20.jpg)
![Page 21: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/21.jpg)
![Page 22: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/22.jpg)
The only things required for
this game are pens and paper
and also an ordinary dice
Each participant will draw a
square which is in turn
divided into 3 3 squares
In other words: a lot of
people and only one dice for
all!
+
+ + =mental math
![Page 23: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/23.jpg)
![Page 24: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/24.jpg)
Why will it be a favourite game?
How can you vary the game?
Think of these two questions while
we play the game …
![Page 25: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/25.jpg)
Why will it be a favourite game?
It has to be quiet (and it will be!)
It´s easy to understand the rules and it´s
easy to carry it through
It will reveal which pupils have a good
number sense
![Page 26: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/26.jpg)
How can you vary the game?
Make smaller grids, e.g. 2 2 squares
Make grids for e.g. subtraction
Appoint different masters by playing in different languages
Use a ten-sided dice instead (change the total, e.g. 5000)
If you are going to learn to count in a new language it´s more natural to count to ten.
![Page 27: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/27.jpg)
http://www.zompist.com/numbers.shtml
1 3 5 4
2 8
7
6 9 10
![Page 28: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/28.jpg)
How can you vary the game?
Put a decimal point in the grid
Change the total, e.g. 5
+
.
.
.
.
![Page 29: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/29.jpg)
4-sided 6-sided 8-sided 10-sided 12-sided 20-sided 30-sided 100-sided
… and a lot more of different kinds
![Page 30: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/30.jpg)
![Page 31: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/31.jpg)
What?
An inspiring furnished and
with hands-on materials
well-filled place
A way to work hands-on
A way to relate to
mathematical
education
![Page 32: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/32.jpg)
A lot of photos from Swedish
schools, showing WHAT a math
lab can look like.
![Page 33: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/33.jpg)
Make use of the walls, windows, floors
and ceilings
Different kinds of shelves: some old, some
new, some big, some small, some open,
some covered
Boxes, tins and drawers
Water
Interiors
![Page 34: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/34.jpg)
![Page 35: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/35.jpg)
Make use of the walls,
windows, floors and ceilings …
![Page 36: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/36.jpg)
![Page 37: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/37.jpg)
![Page 38: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/38.jpg)
Pink horses 8 %
Grey horses 28 %
![Page 39: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/39.jpg)
![Page 40: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/40.jpg)
![Page 41: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/41.jpg)
![Page 42: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/42.jpg)
![Page 43: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/43.jpg)
![Page 44: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/44.jpg)
![Page 45: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/45.jpg)
cloth pegs
![Page 46: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/46.jpg)
![Page 47: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/47.jpg)
![Page 48: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/48.jpg)
![Page 49: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/49.jpg)
![Page 50: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/50.jpg)
![Page 51: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/51.jpg)
![Page 52: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/52.jpg)
![Page 53: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/53.jpg)
![Page 54: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/54.jpg)
![Page 55: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/55.jpg)
A half square metre …
![Page 56: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/56.jpg)
![Page 57: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/57.jpg)
![Page 58: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/58.jpg)
![Page 59: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/59.jpg)
![Page 60: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/60.jpg)
![Page 61: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/61.jpg)
![Page 62: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/62.jpg)
![Page 63: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/63.jpg)
Different kinds of shelves:
some old, some new
some big, some small
some open, some covered
![Page 64: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/64.jpg)
![Page 65: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/65.jpg)
![Page 66: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/66.jpg)
![Page 67: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/67.jpg)
![Page 68: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/68.jpg)
![Page 69: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/69.jpg)
![Page 70: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/70.jpg)
![Page 71: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/71.jpg)
![Page 72: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/72.jpg)
![Page 73: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/73.jpg)
![Page 74: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/74.jpg)
![Page 75: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/75.jpg)
![Page 76: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/76.jpg)
![Page 77: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/77.jpg)
![Page 78: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/78.jpg)
![Page 79: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/79.jpg)
![Page 80: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/80.jpg)
![Page 81: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/81.jpg)
![Page 82: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/82.jpg)
![Page 83: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/83.jpg)
![Page 84: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/84.jpg)
![Page 85: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/85.jpg)
![Page 86: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/86.jpg)
![Page 87: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/87.jpg)
![Page 88: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/88.jpg)
![Page 89: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/89.jpg)
![Page 90: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/90.jpg)
![Page 91: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/91.jpg)
![Page 92: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/92.jpg)
![Page 93: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/93.jpg)
![Page 94: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/94.jpg)
![Page 95: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/95.jpg)
Boxes, tins and drawers …
![Page 96: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/96.jpg)
Cardboard boxes wrapped in wallpaper
![Page 97: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/97.jpg)
![Page 98: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/98.jpg)
![Page 99: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/99.jpg)
![Page 100: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/100.jpg)
![Page 101: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/101.jpg)
![Page 102: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/102.jpg)
![Page 103: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/103.jpg)
![Page 104: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/104.jpg)
![Page 105: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/105.jpg)
Water …
![Page 106: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/106.jpg)
![Page 107: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/107.jpg)
![Page 108: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/108.jpg)
![Page 109: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/109.jpg)
![Page 110: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/110.jpg)
![Page 111: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/111.jpg)
![Page 112: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/112.jpg)
Interiors …
![Page 113: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/113.jpg)
![Page 114: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/114.jpg)
![Page 115: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/115.jpg)
![Page 116: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/116.jpg)
![Page 117: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/117.jpg)
Probably the
smallest math lab
in Stockholm …
![Page 118: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/118.jpg)
Probably the
second smallest
math lab in
Stockholm …
![Page 119: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/119.jpg)
![Page 120: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/120.jpg)
![Page 121: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/121.jpg)
![Page 122: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/122.jpg)
![Page 123: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/123.jpg)
![Page 124: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/124.jpg)
![Page 125: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/125.jpg)
![Page 126: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/126.jpg)
![Page 127: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/127.jpg)
![Page 128: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/128.jpg)
![Page 129: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/129.jpg)
![Page 130: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/130.jpg)
How tall are you?
![Page 131: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/131.jpg)
Some Swedish words:
Cirkel
Rektangel
Triangel
Kvadrat
![Page 132: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/132.jpg)
More Swedish words:
Addition
Subtraktion
Multiplikation
Division
![Page 133: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/133.jpg)
What number is missing?
1, 2, ?, 4, …
What is the next number?
1, 1, 2, 3, 5, 8, 13, 21, ?
![Page 134: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/134.jpg)
Box files
![Page 135: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/135.jpg)
The maths grocery/shopExtremely popular!
Use empty packages
Let the pupils produce groceries
Use money
![Page 136: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/136.jpg)
To …
reach educational goals
increase the interest in – and knowledge in – mathematics
create variation
make the subject mathematics visible
broaden the approach to mathematics
draw out curiosity and creativity
individualize – both extra support and extra challenges
support language development
develop different competences
…
![Page 137: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/137.jpg)
matches
straws bamboo sticks
Trunks of
trees –
not too big :-)
You may use …
![Page 138: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/138.jpg)
All you need is 12 sticks of the same
length
= a length unit = l.u.
= an area unit = a.u.
![Page 139: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/139.jpg)
perimeter
area
= 12 l.u.
= 9 a.u.
![Page 140: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/140.jpg)
perimeter = 12 l.u.
area = 8 a.u.
![Page 141: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/141.jpg)
Instructions:
1. It always has to be the perimeter 12 l.u.
Challenges:
Try to find polygons with 7, 6, 5, 4 and 3 a.u.
2. It has to be one polygon every time
Definition of a
polygon:
plane figure
bounded by a
closed path
a finite sequence of
strait line segments
![Page 142: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/142.jpg)
area = 7 a.u.
![Page 143: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/143.jpg)
area = 6 a.u.
![Page 144: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/144.jpg)
area = 5 a.u.
![Page 145: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/145.jpg)
area = 4 a.u. ?
![Page 146: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/146.jpg)
A common question: Is it ok to use triangles?
Yes, it is ok. But what triangle to use?
A right-angled triangle? (half a square)
The hypotenuse is longer than one stick
2 1,414
![Page 147: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/147.jpg)
A common question: Is it ok to use triangles?
An equilateral triangle?
Yes, it is ok. But what triangle to use?
Is the area 1/2 a.u.?
No, the area is less than 1/2 a.u. because the altitude is less than 1 l.u.
The area 0,43 a.u.
![Page 148: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/148.jpg)
Area: = =base · altitude 2
1 3
2·
2 3
4 0,43 a.u.
1 1
1
x
60°
60°
60°
Area of an equilateral triangle?
b
a c
a2 + b2 = c2
Altitude: x2 = 12 – (1/2)2 x = 32
![Page 149: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/149.jpg)
a
b
c
sin( ) = a = c · sin( )ac
1 1
1
x
60°
60°
60°
32
x =1 · sin(60o) = l.u.
Area of an equilateral triangle?
Area: = =base · altitude 2
1 3
2·
2 3
4 0,43 a.u.
![Page 150: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/150.jpg)
area = 4 a.u.
![Page 151: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/151.jpg)
area = 4 a.u.
![Page 152: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/152.jpg)
area = 6 a.u.
3 – 4 – 5
Egyptian triangle
Proof: Pythagorean theorem
32 + 42 = 52
![Page 153: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/153.jpg)
area = 5 a.u.
![Page 154: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/154.jpg)
area = 4 a.u.
![Page 155: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/155.jpg)
area = 3 a.u.
![Page 156: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/156.jpg)
Summary:
Easy to find material (sticks)
Easy to introduce the activity
The material is necessary
More mathematical content than you perhaps first realized
It can be a challenge even for gifted pupils
One perimeter – several areas
…
![Page 157: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/157.jpg)
![Page 158: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/158.jpg)
12 sticks to each pupil or pair of pupils.
Basic understanding of the concepts of perimeter and area
measuring and logical reasoning
length and area units, polygons
Ask the pupils what they know about perimeter and area. What do they think about the connection between perimeter and area? If one is altered, what happens with the other? Hypotheses?
I have to talk more about area units before we start next time I use this activity.
In figures with the same perimeter the areas can differ.
To avoid the common mistake when pupils think that if you alter the area the perimeter (always) will alter at the same time.
We will use the activity ”Area with sticks”
Were your hypotheses correct? Why or why not?
How can you express the connection between perimeter and area in general? Give some examples.
They can use the maths hands-on workshop journal.
Ask them to give an example of their own.
![Page 159: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/159.jpg)
Cheap material
Little storage space
A lot of different mathematical contents:
Perimeter
Area
Pythagoras
Geometrical figures
Patterns
Algebra
Logical thinking
Spatial reasoning
…
![Page 160: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/160.jpg)
![Page 161: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/161.jpg)
A tessellation is created when a shape is repeated over and over
again covering a plane without any gaps or overlaps
![Page 162: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/162.jpg)
![Page 163: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/163.jpg)
![Page 164: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/164.jpg)
![Page 165: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/165.jpg)
![Page 166: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/166.jpg)
Maurits Cornelis Escher, a Dutch artist, 1898–1972
![Page 167: Johan Häggström Elisabeth Rystedt - NCM:s och Nämnarens ...ncm.gu.se/media/maut/india/Math_lab_1.pdf · Elisabeth Rystedt and Johan Häggström National Center for Mathematics](https://reader034.vdocument.in/reader034/viewer/2022042320/5f0a63f27e708231d42b66fd/html5/thumbnails/167.jpg)
1 = ett
2 = två
3 = tre
4 = fyra
5 = fem
6 = sex