Bird table visitors


Following this weekend’s Great Garden Birdwatch and with Spring just around the corner (I’ve always been an optimist), it might be opportune to set up a bird table or bird feeder(s) within sight of a classroom window to do a bit of statistical analysis on the avian visitors.

The most interesting investigations are those which seek to test an hypothesis or which aim to answer a question (preferably posed by the children). For example, does the type of food we put out affect the species of birds which visit? If a bird has to eat its own weight in food each day, how many visits does a blue tit have to make? Does the weather affect the number of types of visitor? Do different species feed at different times of day? Are there some combinations of visitors which are less likely than others (eg do blackbirds never visit at the same time as thrushes?).

Once the children start gathering data, they may start speculating on other questions or hypotheses.

Where Maths Grows on Trees

Where Maths Grows on Trees

Find out how one school in Morocco is using a grove of olive trees planted in their school playground to teach students about maths.

The students care for the trees, harvest the oil, visit the camel-driven olive press and sell the resulting oil in their local market, all using maths.

This video is inspiring – and has been described as: “…a fantastic film! A great insight into teaching methods using the environment as a sustainable and inspirational resource. It is heartening to see such recognition and validation of this brilliant initiative.”

Where Maths Grows on Trees [Teachers TV]

Allotment Maths

See the NCETM website

After months of planning I eventually succeeded in creating an allotment in the grounds of St Joseph’s primary school. As Yr 6 teacher & Numeracy Coordinator I wanted to make concrete links for children between numeracy skills & the outdoor environment.

Previous to starting the project the children

  • Investigated the dimensions of the allotment boxes by measuring the depth, width & length.
  • Calculated the perimeter and area of one box.
  • Estimated how many of a particular vegetable they would be able to grow in one allotment box.
  • Made calculations for 2 boxes, 4 boxes, 6 boxes etc by multiplying original calculation.

1st November 2007 – Lesson 1

This involved:

  • Pupils investigating the size & type of various vegetables suitable for growing in our allotment
  • Using strategies to calculate the amount of space each type of vegetable would take in the allotment

View the video ‘Allotment Project – Part 1’

It was very interesting observing the various types of strategies pupils used to measure amount of space vegetable would take up. For most it was the first time they had ever used 3D objects in this context & some made the error of measuring the length of the vegetable as opposed to the largest slice of area.

View the video ‘Reflections after the lesson’

We were also surprised at how many pupils were unable to name the various vegetables. This made us think of possible future lesson developments:

  • To investigate diets of the children in the class, looking particularly at their vegetable intake. Linking this to maths through recording and analysis of the data collected from home surveys. This project would also have many other cross-curricula links.

15th November 2007 – Lesson 2

This involved:-

  • Using plans which they had produced previous to lesson showing patterns of vegetables which would produce the greatest yield pupils worked in groups setting out life-size templates onto the allotment
  • Recorded patterns
  • Predicted & calculated total cost of crop

View the video ‘Allotment Project – Part 2’Evaluation
Children demonstrated their team work skills as they verbalised their ideas for a pattern & negotiated the final pattern with their peers. It was an effective activity in which children were able to use their skills of estimating and then checking their estimate using calculators in a ‘real life’ context. Profit and loss calculations around maximum crop yield fascinated the children, creating some fantastic mathematical patterns.

Does maximum crop yield have links to symmetrical planting? What do you think?

After the activity pupils were able to state what the found easy/difficult & what they would do differently if they repeated the activity.

View the video ‘Back in the Classroom’

In conclusion, I feel the project met my objectives for the children as definite but also meaningful links between maths & the outdoors were made for the children.  They applied various mathematical skills in a ‘real life’ exercise.

View the video ‘Summing Up’

The experience of this project has made me think about the way I teach other maths topics, as I have seen such a positive affect on the children’s maths achievement. As a school we have built upon these experiences and intend to extend the idea of ‘doing maths outdoors’.

Val Douglass
St Joseph’s Primary School

Angles in Nature

Outdoor Maths: Looking at different angles in nature


Recently, I observed a super lesson about angles. I knew things were looking up the moment I arrived in the classroom. To begin with, the teacher had this written on her board:

If you look, the focus is on the maths. Very often, teachers assume that “outdoor learning” is the focus or the subject. It shouldn’t be. It’s a place. It’s also very clear what the learning intention of the activity is. Very often going outside is conveyed to the children as a treat. It shouldn’t be. In Scotland it is now expected that frequent, regular opportunities will occur where the learning takes place outside.

When we went out, the teacher briefly encouraged the children to recall the different angles they have studied. The teacher and children made different angles with their bodies. Naturally, acute angles look remarkable like crocodile jaws!

Next the children worked in pairs to look for different angles in nature. Immediately the children twigged that trees are full of angles…

One pair of children noticed that even one fork in a branch had three angles…

Another pair decided to make angles from separate sticks. These are their photos…

A right angle

An obtuse angle

An acute angle

The conversation also developed around other natural angles which moved. For example, the antenna on a snail…

Two children found a branch that made a moving angle…

Acute angle

Obtuse angle

Right angle (my fault – the angle of the camera is wrong)

Back in the class, the follow up discussions remained interesting. The children had enjoyed exploring angles. They came up with the next steps of working out the sizes of angles by measuring them. Here the Carpenter app on the iPad has an excellent large protractor. An older class had tried measuring the angles of branches and found it surprisingly tricky, as illustrated below – I haven’t been very accurate here!

An interesting investigation which leads up to looking at self-repeating patterns and fractals in nature is to find out if the branches in a tree all have approximately the same angle or whether there is substantial variation? Any thoughts about this are welcome!

Stick Logic




One ongoing challenge for teachers is ensuring that children who finish earlier than others have something meaningful to move onto. There’s lots of possibilities outside and this stick activity is one such example. It can be completed in pairs or by children working alone. It helps if children know they can look at the work that others are doing.

Take 1: 5 triangles – not bad for starters!

The children need to find 9 sticks of about the same length. Conveniently I have a big stash of cut sticks. If you do not have such luxury items, then challenge children to find or create 9 sticks of equal length. Twigs are fine too.

Take 2: A 4 triangle option

Take 3: 7 triangles – getting better

The challenge is pretty simple: how many triangles is it possible to make using 9 sticks? I have no idea, but the photos give you an indication of how I went about the task.

Take 4: I can spot 10 triangles

This logic activity can also be ongoing over several days. I like coming up with variations on a theme and asking children to do the same. For example, what differences would we discover if:

  • We used 9 sticks of different lengths
  • We used less than 9 sticks or more than 9 sticks – Is there a pattern to what we discover?
  • We chose a different shape to create, e.g. a square

Take 5: If only I had moved the middle stick up a bit! 16 triangles

Take 6: I can count 18 triangles but I’m getting fuzzy eyes!

All-in-all it can be quite an absorbing task. I’m not sure this is the maximum number possible. If you better 18, I’d love to know how! Oh and add a link to the picture!

Scale and Patterns with Sticks

Scale and Geometric Patterns with Sticks

Creative Learning

3 MAY 2011 · 2 COMMENTS


Last week I was visiting a school where the P5-7 class had just begun to look at scale. This is a super topic that lends itself naturally to outdoor work. With the Scottish experiences and outcomes, there is no mention of scale within Level 1 in the Maths or Numeracy curriculum areas, however, common sense suggests that a little bit of previous work can pay dividends and links nicely to art and geography activities.

A few months ago, I bought some sticks from the Forest School Company, Muddy Faces. This may sound shocking. After all, sticks are there to be picked up from under a tree and played with. However, my big bag of sticks was being well-used at a local primary school and I didn’t want to remove these. Furthermore I noticed that the sticks I bought came in specific pre-cut lengths, unlike picked-up sticks.

The sticks are cut to approximately 60cm and 30cm respectively or 1ft and 2ft lengths. So this is ideal for some initial explorations into simple scale. As you can see, a square can be made and doubled in size…

Children can make different shapes, any shape, using a small set of sticks and then the large. Or the other way round…

These shapes can be carefully and accurately copied onto squared paper, with the children deciding the scale, e.g. 1cm on paper = one 30cm stick, 2cm on paper = one 60cm stick. Once simple shapes have been created, they can be enlarged with more sticks like this…

Or this…

And this…

The concept of repetition in pattern work is geometrically interesting. There is the potential to increase or decrease any shape infinitely based upon each new term being generated by the rule of the repetitions or replications.

Letting children decide a rule of replication can lead to all sorts of interesting patterns. For older children, the recurrence can be examined by looking at the perimeter and area of each square and seeing how this is affected by the pattern, e.g.

Perimeter = 4m, Area = 1 sq m
Perimeter = 8m, Area = 4 sq m
Perimeter = 12m, Area = 9 sq m
Perimeter = 16m, Area = 16 sq m
Perimeter = 20m, Area = 25 sq m

This can be plotted on graph paper and can help lead to interesting mathematical discussions.

One of the reasons, I think this works well is the speed and ease at which patterns can be created. There’s no mess from chalk, no rubbing out of pencil lines, no laborious sewing of patches, and so children can easily play with the designs. As you can see, I had a lot of fun in my back garden…

Taking a pattern and creating patterns within and beyond patterns…

The only limit is the space and number of sticks available…

My supply of 72 small and 72 large sticks seems to be working well with classes of up to 25 children. I think a few more might be needed with larger classes. It’s great for cooperative group work.

And for devising puzzles and challenges…

Leaf Logic – Creative Learning

Leaf logic is ane exercise where the srudents agther as many different possible leaves.  Then they try and form a Caroll diagram to sort the properties:

With older kids two way tables can be used to get more criteria.

Read the original at

Building on this idea you could look at leaves and the number of points; I think there will be a predominance of Fibonacci numbers.