Introducing Fractions

Today I introduced our new central idea for our Proportion and Ratio Unit. 

First, I asked kids to read and discuss what they thought were the KEY words from within the CI. Then, on post it notes, I got my students to write down what they knew about fractions. 

Some kids could recall prior knowledge from previous Grade 1. 

Other students were open enough to admit that they don't know... yet. So pleasing to see growth mindset developing in the way they think about maths.

I then showed them this video I made using Lego Movie as a provocation. I wanted to see if this would give me more insight into the students prior knowledge. 

I asked them to answer these questions:

1. What are the problems the gorilla and the monkey face?

2. How would they solve the problems?

There responses to this showed me that some students already have a good understanding about the concept of equal sharing and knowledge of using vocabulary such as half or thirds to represent whole -part amounts.

Most could write the symbols, but some had difficulty using fractions to represent the correct amount. e.g. 3/1 is half a cake.

Interestingly, some students who said that they didn't know anything about fractions, were able to solve this problem.

This always reminds me of the importance of formative assessment and getting students to share their initial understandings .


              

                      

Using the Summative Task as the Provocation

I was struggling to come up with a provocation or ideas for our Shape and Space Unit. We are doing a unit the looks at monuments, so I wanted to try and incorporate some kind of building or creating into the unit. 

This unit really made me think how about how I could make it engaging for students. I didn't want to just go through property after property of different shapes. I wanted to give the students ownership of their learning and make them have to use the knowledge they have gained in some way. 

So I thought, what if I give the students the summative task as the provocation for the unit. One that requires them to draw a structure or monument that has to incorporate certain properties?

I have never tried this before, but I thought no harm in trying... I hope!

First, I used the Teaching Student Centered Mathematics text (a wonderful resource), to find out what learning outcomes or big ideas that I need to address at a Grade 2 level. 

I then gave my students time to go through the outcomes and identify what they knew already and what they needed to know. This also turned out to be great formative assessment task that allowed me to find out my students prior knowledge. It also allowed me to challenge those students how needed it. 

Here are some of the student going through the expectations. 

I told students that it is ok not to know any of them... just write I don't know it yet! 

I also gave students time to try and draw it ... most found this challenging.


The kids are now really keen to go and find out what these outcomes mean and then use their acquired knowledge to draw their monument.

I am not sure how this will work out. My one reservation is that, does it give students the scope to inquire? As I mentioned earlier I was really having trouble thinking of how I would get them to do that. Time will tell if this works out.

If you have any ideas then please share.

... I will post again with how it worked out.

Tech Provocation for Multiplication

This is my first attempt at using tech, in this case Lego Movie Maker, to create a provocation for a maths lesson. In terms of engagement it was a big success, students found it really fun when reflecting at the end of the lesson.

Here is the video: (in hindsight I probably should have just kept them multiplying in rows of 3 rather than changing to rows of 4, but hey... next time!)

To start the lesson I showed them the movie and asked them to come a questions that they could ask after watching this video. 

Here is an example of some student responses. As always, they tend to come up with better questions than I do.

My favourite was.."How many lego holes did they take up on the board?" - I hadn't thought of that!

Next, I ask them to show me the equations using different operations that this movie shows. 

Examples of responses:

3x4

6x2

4x4+2

To lead into the next lesson I got the idea of asking them to look at the last clip and show me how they could find out how many man there were only using multiplication and subtraction?

In all in an engaging lesson. I am going to try to use tech as a means of providing provocations in the future. 

In my next lesson I am going to ask students to create their own movies to show multiplication facts that they are having trouble with. 

Reflection on the activity:

1. engaging

2. great way to explore maths questions

3. great way to differentiate the lesson

4. students learn what it really means to multiply sets.

5. provided me with a different angle to start my next lesson on.

Feel free to post any ideas you may have!

Provocation Tables for Multiplication and Division

As part of a formative assessment/provocation for the start of our new unit on multiplication and division, I set up four different stations. Each station was designed to provide me with different information to help me plan where to take my students next.

Table 1:

This question was designed to see how students would solve this problem. Students responses varied from...

5+5+5+5+5=24
or
5+5=10, 5+5=10, 10+10=20, 20+5=25
to
5x5=25

Table 2.


This activity was designed to see if students could conceptually visualise multiplication facts.

I really liked this students response. Showing creativity in his maths thinking.


Table 3:

Note: Students knew we have 21 students.

This station was set up to check students understanding of division. I purposely used words such as 'divide' and 'equal groups' to gauge their knowledge of these concepts.

Many students required the use of materials to solve this problem.

Some were about to use their knowledge of multiplication.

Others found it too challenging and wrote 'I don't know?'

Table 4:

For this activity I purposely used the word 'operation'. I wasn't sure if it was too challenging, but I wanted to find out what students knew what it meant. Some required help, but once I had explained it to them, they were then able to provide an answer.

Some students wrote 5x5x5, 2x2x2 and 4x4

Others used addition e.g. 5+5+5

Some students wrote 'I don't know?'

GREAT!!!!!! I always encourage and praise my students for being courageous enough to share that they don't know. I constantly refer to our Maths Essential Agreement that states, "mistakes are good" and "it's ok not to know". Too often maths is seen as a competition to see who can answer questions the fastest, even among 2nd Graders. It is so important that students are able to feel comfortable to share their level of understanding.

An example of a student recording their thinking.

During the activity I asked students to revisit the 'reflection table' to write down any new wonderings they may have.

Pleasing to see students using materials to help them solve problems. It is so important that students don't view using materials as a sign that they don't understand. One student even said, "I am just using them to check"

Provocation for Data Handling Unit

After presenting my students with a pre-assessment to gauge their level of understanding, I found that nearly all...except one wrote I don't know...yet! This then made me think that I need to really build a good visual and conceptual understanding. 

So I emptied out boxes of linking cubes and posed the question

Show me visually what is the most common colour?

I explained that I didn't want to know how many of each colour their were. I wanted to be able to 'see' their answer.

Without any prompting this team automatically started to organise into colours. They didn't do that in the pre-assessment I gave them 5 minutes earlier!

This team sorted and then counted. We discussed that the question required them to show me the answer visually. 

This team organised them straight into lines.

This team tried to go up, but soon struck a problem!

This group took a different route. They individually started to make groups of colours. After they finished the class reflected that it was difficult to see which was the most common colour. Someone then said if they made them all the same shape, then it might be easier!

My next question was, how could you have organised this better to make it even easier for me to see the answer. 

The result...

After about an hour of engaged students. I then shared that they basically just did the pre-assessment task without any help. They all went... really... we did? We discussed that all you have to do now is replace the coloured cubes with numbers. 

We also then reflected on how we could improve these visual graphs even more.

"Add" numbers at the top was one suggestion. 

We then talked about where we could add numbers, introducing X and Y axis.

On our reflection wall we shared what we had learnt from todays inquiry.

You need to organise your data

You need to show things in the same way, like using lines or shapes

You need to be accurate

You need to start from zero

You need to answer the question