Mini Workshop

I haven't had much time to post in the last few weeks as I've been busy working on developing my student's abilities to work in small groups together and to explain and justify mathematically in order to problem solve. 

Today we were a little stretched for time so I did a mini workshop with Group 2 around basic fractions. They loved this as they got to write on the table with whiteboard markers. We were looking at halves and quarters of shapes and then sets. 

I asked them, "If I have 16 counters and that is my whole, can you draw what halves would look like? Quarters? (and for those that finished quickly) Eighths? I asked them to write an equation next to their representation which proved that the pieces made the whole.

Here are my girls next to their work:

Creating Problem Solvers

Everyday when my students work with me they are challenged with Mathematical word problems. They are put in mixed ability groups within their main group and asked to solve a problem given to them anyway they can this includes using materials if they so choose. My students can find this very challenging at times but as they get more practice on how to approach these problems they are really working their hardest to get the right answer. They have such expressions of accomplishment when they do manage to work out tricky problems, which is so great to see.

Here are some photos of my groups working on problems. They are concentrating hard :-)

Introducing My Students!

For the first half of this year I am working with 5 fabulous groups of students. Below are some photos of my groups. More will be added soon.

Welcome to 2015

This year I will once again be working with many wonderful children to help accelerate their learning in Mathematics. Please check back regularly as I will be posting teaching strategies and activities I use with my Maths groups and the learning journey of my students.

Miss Breen :-)

P.s. Here is the yearbook page with all my fantastic kids from last year.

Fractions of sets

This term I am focusing on Fractions, Decimals and Percentages with my students. The students are started to see the connection and relationship between these three areas i.e. that 0.2 is the same as 20% which is the same as 1/5. They are also learning how to simplify fractions and about equivalency at the same time.

So on Monday we started using paper strips to work out the fraction of a certain number of chocolate bars each person would get.

Example:
Miss Breen has 4 Chocolate bars left over at the end of the school term. She wants to share them out with the 5 children that were the best helpers that week. How much chocolate will each child get?

The paper strips helped the students to think about the chocolate bars as wholes before they broke them up into fractions and shared them out. We had a few tries, much trial and error before they began to realise that it was a good idea to start by breaking each whole paper strip into the number of people from each problem.

Once the students understood that each problem related to parts of a whole we moved onto the fractional equations. The students were still free to draw pictures but they began to use multiplication and division as a way to work out their answers.

Here are some photos from this week, of the students from all my groups working on these types of problems.

p.s. I let my kids draw on the tables with Whiteboard markers, it makes for a great working space :-)

Understanding Fractions - Group 7

Today I asked Group 7 (Yr 5/6) to show me fractions in more than one way (multiple representations). This group of students are lacking understanding of the key idea that fractions is about parts of a whole. They are learning that the whole could be five, the whole could be 100, the whole could be a set of objects (discrete), just repeated numbers added together, or even a shape (continuous) but they can all show the same fractional number related to the whole.

In the photos below I asked the students to show me four quarters, this is only the beginning of these lessons so as they progress we will use other materials as well so that they get experience of fractions in many forms.

• The multi-link cubes stuck together are fractions of a shape 
• the groups are fractions in sets 
• The numbers represent equal sharing creating a whole using numbers

Group 7 Problem Solving

Today my group (7) began working on a problem solving task (about workers packing cherries into boxes and cartons) near the end of their session. This group is very enthusiastic about mathematics so we have a lot of cooks in the kitchen as the saying goes. I'm sharing this video to show what is working well and what needs improvement with this group dynamic. 

As you'll see the girls take over quite a bit so we are working on listening to each other more and taking turns with sharing ideas. Jarome tries to share his thinking - that they can use their basic facts to help work out larger numbers when he says, "8 + 4 is 12" in reference to the problem where they are trying to work out 80 + 40, though he is talked over. It also shows how important it is for us as teachers to listen to what our students are muttering or saying within a group especially the quiet ones, as they usually know more than they let on. 

They are very engaged in this task. However, as we continue the task in the next session I will need to go over the expectations of working in a group and also the importance of reading the problem. They have come a long way with their communication in mathematics and they will surely continue to improve :-)

Subitising and Quick Images

One of the many things I have learned while being a Maths Support Teacher is the value of Subitising and Quick Images. Now if you aren't sure what subitising means, here's a definition:

Subitising

We often recognise the number associated with a particular pattern straight away, even before we have had time to "count" the items.

The process of immediately recognising how many items are in a small group is called subitising. This name comes from the Italian word subito, which means "immediately" or "right now". When playing a game with dice we normally recognise the number of dots immediately.

By "chunking" information, subitising contributes to early forms of grouping. The process of subitising can also be used with seeing parts in the whole.

If you look at the dot pattern for five you become aware of seeing it also as four and one, or three and two. Domino patterns capture this idea of subitising playing an advanced-organising role. People can see each side of the domino as four individual dots and as "one four". They see the domino as composed of two groups of four and as "one eight".

The notion of units within units is important for separating and combining numbers as well as for multiplication, division and measurement. Subitising contributes to part-whole (sometimes called part-part-whole) number relations.

Interpreting number in terms of part-whole relationships makes it possible for children to think about a number as being made up of other numbers.

Reference: 

State of New South Wales, Department of Education and Training. (2009). Count Me in Too: 

          Subitising.  Retrieved from http://www.curriculumsupport.education.nsw.gov.au/

          countmein/learning_framework_subitising.html

I use subitising quick images as a warm up with every group of students I work with. I created my own set of cards so that I would be able to include more unstructured patterns. By having unstructured and structured dots on one card this leads students to think multiplicatively and decompose numbers (combine dots in various ways) to make groups.

Here is a photo of some of the cards I made:

2d and 3d Geometric shapes can also be used in quick images. This helps promote the use of mathematics vocabulary and also helps them to recognise properties of shapes. With 3d images you can ask students to build them with blocks which helps them to think about parts of the picture/image that they can't see.

Geometric Quick Images to use can be found on the below link:

Click Here

Here are some photos of Group 6 using multi-link cubes to make 3d images of cube arrangements.

How to use quick images:

The students are told that they are going to be shown a card with black dots or shapes or cubes (depending on what you are showing them) on it for three seconds. Their job is to try to work out how many dots are on the page or to describe what the picture was made up of. Then they are shown the card for 3 seconds. After some wait time they are shown the card for another 3 seconds to check their answer. They are using both perceptual and conceptual subitising in this example. The teacher then elicits responses by asking questions such as: 

What did you see? How did you know? How did you count them/add them? 

Below is a short exemplar video of two of my students discussing what they saw after viewing the card in the top right corner of the above photo.  

NB: My students are very familiar with quick images so are now much better at identifying groups of dots quickly. However, at the start of the intervention they would identify individual dots rather than groups, count in ones or skip count and draw the patterns in order to get the answer. Their use of mathematics vocabulary and the concept of 'groups of' (Multiplication) and using equations which you will hear in the video, has been developed over time.

The Egg Couch

Last week I had the chance to interact with other Math Support Teachers from around New Zealand at our Seminar Days. I was shown this fabulous idea of using the below image as a basis for a Mathematical investigation:

Source: Eggs Sofa by Fulvio Bonavia http://adsoftheworld.com/media/print/axn_sonys_satellite_tv_channel_eggs_sofa

Yesterday I used this image for the first time with a class of Year 7 students. Each group were given the image and asked to list down all the things they noticed about the picture i.e.I notice the eggs are in trays, there are lines going down etc. 

Once they had written down the things they noticed, they were then asked to write down any questions under 'I wonder' i.e. I wonder who made this couch? how is it stuck together? etc.

Then we had a quick discussion on the types of questions they had come up with. Are they mathematical, scientific, general?

From here they were asked to make predictions of how many eggs they thought there may be altogether. We discussed what a prediction was and an example of a good prediction versus a silly prediction.

The groups made their predictions and then started thinking about how they would go about completing this investigation i.e. what strategies could we use?

We ran out of time so unfortunately we didn't get any further however, this is great because investigations take time and this helps the students learn perseverance when attempting to solve challenging mathematical problems.

I will be using this same image with my groups, so check back in the next couple of weeks to see how they undertook the challenge : - )

Here are some photo's of room 7 working on the problem:

Here are a couple of photo's of some of my year 7 and 8 students working on their piece of the egg couch:

Is There Another Way?

My students have been working very hard with me ever since they started their groups a few weeks ago. We have spent some time learning what Multiplication looks like as an array, using Animal Strips. I use this material as it is an excellent way for the students to see what the groups are made up of i.e. 9 is made up of 5 and 4, 8 is made up of 5 and 3 etc and it moves them away from counting in ones or skip counting and towards looking at groups of/sets of/lots of instead. While my students are still getting a grasp of their multiplication facts, using this materials enables them to break down the numbers into the Multiplication tables they do already know like 5 and 3 or 5 and 2 and 2 (4). 

This leads them into learning the strategies of Place Value Partitioning (breaking up the tens and ones) and Rounding and Compensating (rounding to the nearest ten and then subtracting the groups you added in the beginning). As my students generally have some knowledge of written strategies like algorithms, we look at those as well, which I teach them can be another tool to check their answer with but it should be one of many ways they know how to solve a problem.

Below are some photos of my year 7 & 8's - Group 8 (Trinaye, Michaela, Katelyn, Aisea, Harrison & Jerome) working with these Animal Strips to develop their understanding of Multiplication and related strategies; followed by a problem solving session where they needed to extract what the questions were asking them and then use their knowledge of these strategies to solve each problem. They were able to demonstrate all three strategies and are becoming much better at identifying the maths question within all the 'words' of each problem.

These questions were taken from the Mathematics Assessment Resource Banks (ARBS) Copyright 2011 Ministry of Education, Wellington, New Zealand.

The first question for example is: 

"Hohepa worked in a store for 16 hours a week for 7 weeks over Christmas. Show how to work out how many hours he worked over that time"