Investigating quadrilaterals

Following on for the investigation into triangles last week with my grade 6 MYP class, I had students inquire into the interior angles of quadrilaterals today. They firstly had them identify the different types of quadrilateral and find a ways of organising and identifying when you have what type of quadrilateral.

Afterwards, they had different types of quadrilaterals and cut out the angles from these quadrilateral add them, by means of glueing it to find the rule: interior angles of quadrilaterals add up to 360 degrees.

The verdict: Another fun and easy way for students to investigate the angle rules in quadrilateral. I had them complete a traditional determining angles exercise afterwards and they found it really easy to determine based on previous knowledge. Recommended! 

Investigating triangles

During today's inquiry into triangles with my grade 6 MYP class, we reached for old-fashioned technology - and with great results! Students were really engaged throughout this activity.

I started by giving students an example of triangles with their identities written inside, and they had to label these. For example, acute and isosceles, students had to identify the acute angles within that triangle and then had to indicate the two sides that are of equal length in order to make it an isosceles triangle.

Here is a great example of two of the pieces of work the students produced:

I then asked them to use the exact same triangles (I made two copies of the same triangles), and to cut out the angles (HINT: if you are getting the students to do this activity, get the to cut it round, otherwise it becomes difficult to see where the original angle was). 

After cutting out these angles, students were asked to glue together these angles to find the pattern in the angles. 

After repeating it several times, students realised that it demonstrate that the interior angles of a triangle will always add up to 180 degrees.

The verdict: Great use of time, quick activity, but students find it so easy to remember that interior angles add up to 180 degree. Give it a go, it's so worth it!

Math class without numbers?

You are joking right? Surely that is not possible in a high school?

In an attempt to re-engage my students with sequences and series, I invited them to create a sequence using only paper and scissors. I explicitly told them that they are not allowed to write any numbers, but can model and explain their sequence using words in everyday language.

After a few moments of staring at the pieces of paper in front of them, ideas started to emerge and the previously disengaged class was not only engaged and the most surprising, the students that I struggle with most in terms of engaging, was the most engaged! Not only were they ‘hands-busy’, cutting away, they were ‘heads-busy’, as I would often hear conversations about whether this particular piece was indeed a sequence or not. 

Here is some of the work they’ve created: 

Each time the paper is folded open, it produces the sequence 1, 2, 4, so as this student commented, that if it was a infinite piece of paper, this would have produced a geometric sequence.

Considering you are starting (with the man in the middle) each additional layer, would provide a +1, so therefore this student created an arithmetic sequence.

We had discussions that ranged from what makes a pattern a sequences, and when it is a ‘normal’ arithmetic sequence and when it is a recursive arithmetic sequence. They could correct themselves on the terminology we so easily get tripped up on, one student started “this is a series of circles, oh no! I’m not adding, the pattern repeats. This is a sequence of circles…”.  (As seen below). 

One of the students referred to different terminology - she explained “this is my pattern of triangles, but when I fold my paper and bend it down, I introduce a line of symmetry”. 

Another student, produced smaller cut-outs that they arranged and re-arranged every time to create various different sequences (both arithmetic and geometric).

The verdict: This is a fun way to either introduce or reflect on sequences in mathematics. It is not very time consuming, but involves great amounts of fun! Fantastic to get students talking about what they created without feeling the 'pressure'. Highly recommended! 

Using google docs for collaborative learning in mathematics

During today's lesson with my Grade 6 class, we were looking at finding factors and multiples of specific numbers. As we were looking at finding factors, one of my students posed the question: Would an even number always have an equal number of factors? Equally: Would an odd number have an odd amount of factors?

What a brilliant question and exactly the example of how we would like MYP students to inquire into mathematics. My response was - Great!!! Let's look at what you are asking as a class together. 

We quickly made a google doc and started looking at factors. Here is an image of the work in progress:

After finding the first eighteen factors, we looked to see if it holds true, and we highlighted the outliers (as seen below). Factors of 4 was the first exception (highlighted in orange) and we suggested that maybe it is the exception to the rule. We looked further at the factors, and found that it was true for all the other factors, except for 15 and 16 as seen below: 

Thus, as a class today, through a great inquiry a student posed, we learned so much - it was a quick visual for me to see who understood the concept of factors (as they were doing it live on my screen); students inquired into a fellow classmate's question and students discussed prime factors (having only 1 and the number itself as factors) and it was a wonderful collaborative learning opportunity where we could investigate and find that there was not a pattern holding true for all factors. 

My students reminded me again today that they have so much creativity and if I give them the opportunity to inquire and explore, they develop as confident mathematicians!