31 May 2011

Thinkers and Problem Solvers

We are rounding up our fractions unit and we'll soon be ready to move onto our final unit about Shape and Space..........but before we shift focus, we did a couple of interesting investigations today.

I asked students to share a jug of water between three people and then four people. It was interesting to see how tricky it was to share that last bit of water exactly. The students decided the fraction had to be precise! Students would fill each glass half full quickly, but then take greater care to share the last bit out. Using your eye as a judge can be tricky. We did this activity because this was an example of a real situation in which we use fractions. In reality it's probably the way most of us use fractions. I heard one student say that he hadn't realised how much he used fractions in his everyday life until this unit. When recording the fraction, this provided us with a good reminder that the denominator tells us how many the parts the whole is shared into. The light bulb went on for one student today when he said fractions are like dividing as you're sharing.

After this I set a task that involved two chocolate bars that needed to be shared out between three people. Now this was a challenge! Students struggled with the idea that they really had to persevere on this one and see themselves as thinkerand problem solvers, not to be defeated when the first attempts didn't work out. (I asked the students which Learner Profile they matched.) We stopped half way through to give each other some hints. At the end of the lesson we shared our ideas and learned from each other. This task can be worked on many different levels which made it suitable for everyone.

Just to finish off today here are some more wonderful examples of contours the students are sharing in class. More to come tomorrow.

30 May 2011

Personal Connections (Homework) 30.5.11

This week's tasks are:

  • 2 handwriting sheets (The sheets are coming tomorrow, I'm out of routine today so I forgot to hand them out!)
  • Typing
  • Reading & Spelling
  • Enjoying the long weekend.

Thank you for all the contour and compass map photos. They really are great. We'll take a proper look tomorrow. Today was an intense writing day with unit assessments and finishing off poetry!

25 May 2011

Fractions and Contours

Key Understanding: We use fraction words and symbols to describe parts of a whole. The whole can be an object, a collection or a quantity. 

On Tuesday I gave students a quick assessment in their maths journals. I gave them a paper  'part' and asked them to draw the 'whole'. Here's one of D's pages:

We revised the term numerator and denominator too. The students are realising the denominator tells us how many parts there are and the numerator how many of the parts are being referred to. We're also making sure we know the words and symbols for different fractions like a third & 1/3 and one tenth & 1/10. We explored how to show our diagrams as calculations too, as a way to introduce the addition of fractions.

Some new fraction kits arrived in school this week, so today we have been building with fractions. This has been a great way to see how many fraction combinations we can create to make a whole. It was interesting to see students beginning to realise that certain combinations work together e.g. thirds & sixths or fifths & tenths. By playing with the shapes they have seen, for example, how a third is equivalent to two sixths. The students have also been using the kits to add fractions together. 

We had a good discussion about this problem: If one pot of cream costs 30 chf, how much did it cost my friend to buy this box on offer?

The solutions offered by the students reminded me how this type of application question can be a challenge, but also why students need such opportunities to apply their mathematical skills.

This week's Personal Connections task is very 'hands on'. Have a look at G in action building his mountain, then adding the contour lines and finally mapping it. You can also check out his explanation of contour lines on the wiki. What a great inspiration for the students in the class to see.

23 May 2011

Personal Connections (Homework) 23.5.11

This week:
  • No handwriting for a week, but please keep typing.
  • Try out the Contour Lines and/or Make a Compass activities at home. Instructions have gone home tonight.
  • Complete the wiki post for each activity.
  • Visit and play this contour activity sent in by GB.
Please send in a photo of you in action if you can!
  • Reading and spelling

19 May 2011

Exploring Fractions

Key Understandings: 

  • We can partition objects and collections into two or more equal sized parts and the partitioning can be done in different ways.
  • The same fractional quantity can be represented with a lot of different fractions. We say fractions are equivalent when they represent the same quantity.

It's been a busy two days of fractions in the Middies! We started Wednesday by discussing the times we used fractions in our everyday lives. Some examples included the letter 't' is three quarters the size of the letter 'l', cookies need half cup and quarter cup measurements when mixing ingredients and you only make a 3/4 blow into your recorder.

From here we took a variety of paper shapes and explored ways to shade half of each shape. At first the students used straight forward folds to make two parts. Then they discovered if you folded a shape into four quarters, two of these quarters were the same as a half. The investigation continued with one student splitting a square into sixteen smaller squares and shading in eight of these, one student tried to fold a circle into thirty two parts and then shaded in sixteen of these, the possibilities became much more exciting. This is a great exploration into equivalent fractions.

Here's a question to discuss: Would you rather have a quarter of a delicious cake or 4/16 of the same cake?

To ensure students don't just see just fractions as paper shapes, we have another investigation happening in class. Students are using measuring cups (1, 1/2, 1/3 & 1/4) to work out different ways to measure quantity. For example DB and H discovered they could measure out 1 1/2 cups of rice by using three 1/2 cups or 1 whole cup and two 1/4 cups or  six 1/4 cups or even three 1/3 cups and a 1/2 cup. It was interesting watching the pair realise that the cupfuls had to be level in order for it to be a fair measurement. H and M discovered a book all about cookie making in the library today with lots of fractions as measurements. Maybe we can try out some cooking..................

Our final investigation of the week presents the students with a series of 4 x 4 grids. They then have to find different ways of splitting the grids into halves, quarters or eighths. Here's C explaining how to split a grid into quarters in today's Celebration of Learning.

It is always satisfying when what we've been learning continues to interest students beyond our immediate lessons in school. Here's a photo of G sharing the book he brought in this week about multiplication.

17 May 2011

Continuing our Lorzenpark Inquiry

We spent all of this morning out and about working on our weather delayed Lorzenpark maps. Our first job was to orientate our map outlines and discover which way pointed north. After this we undertook our features survey to help the students pay attention to the variety and number of things in the park. Students completed a tick list and made a tally. This data could then be included on their maps. Students also begun to realise they needed a key in order to be able to remember what they had mapped. Some of the maps have become really detailed and complicated. The pathways were much more accurate this time too, but we discovered it was really important to walk the route and make adjustments as we moved. Even I had to make changes to the scale of some of the things I drew on my map. We used a wiki post to look back on our mistakes and successes.

Our next step will be to decide upon the symbols and colours we are going to use for our individual maps and then make a neater copy of the draft. We will also measure the pathways and see if we can add a distance scale to our map.

As a follow on to our direction discussion this morning, at lunch time DB noticed that we needed to head in a southerly direction to reach Teuflibach and DT followed the way with a compass. If you have a simple compass at home, please bring it in and we can test it out. I'm wondering if there are more directions than north, south, east and west?

16 May 2011

Personal Connections (Homework) 16.5.11

This week:
  • Handwriting 5-10 mins
  • Typing Practice 5-10 mins
  • Reading
  • Tracks spelling for those students in allocated groups
  • Visit the wiki and complete the year book post
  • Visit the wiki and explore the imaginary maps. Start to think of ideas for your own story map for next week. 
If you have time, check out this site that compares country land areas and try some geography games.

14 May 2011

Part Two: Lorzenpark Mapping Inquiry....but not quite yet

Thursday started with Plan A..............We finished off our initial maps of Lorzenpark, shared these maps and the difficulties of map making. Then we looked at an outline map I had made from the Google Map photo so that this time everyone started off with the same sized and shaped map. You'll see our maps hanging in the classroom and the size and scale varies greatly. From here our next task would be to survey all the features in the park with a tally list and add the paths and major features to make a draft map. We would also start measuring distance using the trundle wheel.......but then it poured with rain just as we were poised with our clipboards ready to go!

Lorzenpark Map Outline
So then to plan B! (Being flexible must be at the top of any teacher's CV!) I directed Miss Kathy on a quest to find a left over chocolate egg from Easter, but my instructions were so vague she had no clue where to go in the classroom. It was really quite funny watching Miss Kathy wandering around trying to go in the right direction. Gradually my instructions became more detailed and the egg was discovered. The students quickly realised that I needed to give very specific directions in order for Miss Kathy to know where to go! We brainstormed all the terms I had used to arrive at the correct destination. We were surprised how varied the vocabulary was (and how connected it was to maths too). I got students to model quarter and half turns, connecting the angle to the turn as well. 

Next each student choose a secret destination in the classroom. Using the language of direction, they wrote a list of directions in order to reach the chosen spot. Then came the test, with students testing out their directions on another student. It became clear that some of our instructions needed adapting as students headed off in the wrong direction, into furniture or never quite reaching far enough! Students made changes such as being specific about the length of a pace, and tried again with more success!

Each student then took a moment to reflect on the process of giving and receiving directions in their unit journal.

In the afternoon we completed journal entries for the week, thinking about the things we had learned. Miss Kathy then introduced us all to the program ScratchScratch is a software application which allows us to make simple and complex programmes for animating objects on screen. We experimented with the program  to move a character around the screen using directions, a perfect ICT connection to and application of our work in the morning. We also discovered you could use the program in your own mother tongue language. Finally, all the students headed off in the direction of the swimming pool!

image: ictatnhs.wordpress.com

10 May 2011


This week's Key Understanding (or what we are learning about):
When we split something into two equal-sized parts, we say we have halved it and that each part is half the original thing.

We've been having some interesting discussions about fractions here in the Middies. It all started out when we noticed the different ways we could split our colourful 4 x 4 square carpet. This led on to today's questions:

What is a fraction?
Where have you seen fractions?

With a little help from a video on Brain Pop, a maths dictionary and lots of ideas from the students we realised lots of the same words kept appearing:
equal, parts, share, fair, whole
Getting the words 'right' is so important as we build our knowledge of mathematics. I showed the students a picture of one whole cake split into two parts and asked them could I label the portions each as a half. That made it really clear that the two portions needed to be equal to be halves. I had to laugh when a student said there would be lots of complaints if I kept the bigger piece, it wouldn't be fair! K made the link that sharing was also dividing.

From here we went on investigating, this time using paper strips to make fractions. I first asked students to share the paper strip into two halves. Easily done and labelled, how about four equal parts? Some students, not all, realised you could fold the sheet in half, and half again. To make sure we understood the language of fractions, we labelled each portion with the words 'a quarter' and 'a fourth' and with the symbol 1/4. (DZ had found out the top number is called the numerator and the bottom number the denominator. Check our Maths Masters Blog for a film he watched.) I then asked the students to discover if they could then make eight equal parts.......we continued until it began to get tricky to fold the paper. Students noticed the pattern too and described what was happening to the denominator. The challenge was, can you make 1/64?  

Things to consider that came out of our discussions. I noted these points for further discussion: 
  • Is a fraction less or more than 0? 
  • Is a fraction less than 1? 
  • Can you share something into a mix of fractions e.g. 1/2, 1/4 and 1/4? Does it have to be only be one 'type' of fraction?

We finished off by looking at the origami film on Maths Masters and noticed how many examples of fraction vocabulary appeared. Keep an ear open for how many times your family uses the language of fractions in your everyday lives. 

P.S. Thank you to AL who brought in a ruler today so we could compare the measuring units of inches and centimetres.

09 May 2011

Start the Week

Here are the tasks for this week's Personal Connections (Homework):
1. Handwriting Practice
First students should practice a line of any letter I corrected in last week's tasks.
Today I went thorough the whole of the practice task for tonight. Students should look at the practice sheet and copy the exercises. I will look at Tuesday's sheet in class tomorrow, but I will not do the whole task. Students should then repeat and complete.
2. Typing Practice
3. Spelling Group Practice
4. Complete the two wiki post discussions. It's important that this is done before we learn too much as it is a pre-assessment!

Today we started learning about mapping skills by drawing a series of maps. We started off by taking toy house furniture and making a bird's eye drawing of the pieces. We learned how we can make a key in different ways, by using pictures, symbols, colours or numbers. Our maps were exactly to scale as students were asked to measure the pieces. From here we went on to map our bedrooms and make maps of our routes to school. We have learned that all maps must have a title and a key. As we finish each map, they are going on display outside the classroom.

05 May 2011

Here and There

Today really was the day that we launched into our new unit 'Here and There'. It comes under the theme of Where We Are in Place and Time with a geographical, language and mathematical focus. Our central idea is:

Maps are visual representations of place and help us locate where we are in relation to other places.

As the weather was so beautiful today we headed outside after Miss Kathy told us that she had noticed that the Google Map of the area around our school was completely out of date when she zoomed in. Our unit aim is therefore to create up to date maps of this area so accessible to us.

We walked all around Lorzenpark using our research skills. We paid attention to the park's shape, layout and its many special features. (I discovered that's a word we need to investigate further.) It's amazing how many things we noticed when we observed carefully. We gathered together our data and made a huge list back in the classroom. We noticed things like points where paths cross seem to be marked by a pattern of trees, gravelled pathways are curved, one surfaced road was straight, there are signs to tell you about the park rules, that land has been allocated for different uses such as flower meadows and farm land, some trees are planted in a straight line, there are lots of bins, that areas with benches have little alcoves and that we needed to use words like left, right, next to, behind, straight ahead, turn, at an angle.... to describe the location of the objects. Miss Kathy took lots of photos of our exploration to remind us of what we had seen.

Using this information students worked with a partner to create their own maps. It quickly became clear it was difficult to decide where to start on the paper and the problem of not having a piece of paper big enough, so some students started taping sheets together! Scale has already become apparent. Questions arose naturally as the students worked. How big should we draw the objects on the page? How can we remember the exact shape of the pathways? How shall we represent the things we saw? How can we make this task fair so we each have a turn to draw and decide how the map is made?

We will come back to these maps next week to discuss the map making experience and take the inquiry one step further. T brought in a huge atlas today which was fantastic timing. We found out that an atlas is a collection of maps from all over the world, but that T's also has lots of other fascinating information about maps. We read that cartographers have made maps for over 4000 years. People have made maps to show our three dimensional world in a flat format.

Thank you for all the maps that have been sent in. Our fascinating collection is growing. This week the students have been spending time just browsing our information books and maps. Some students noticed there are grids on some maps, that there are different types of maps like weather maps, some maps have photos of places and that maps seem to tell us how to get to a place. K spotted a map of world religions in school too. We've also started asking and recording questions about maps, helped by N's book 'Why is the sky blue?' Don't forget to start checking the new wiki to learn more.

N, DZ and DB were inspired and have developed their own map inquiry.They've started labelling a Swiss map with places they know. They will then label these locations to inform us why they went there or why they know the place. I will ask other students to add to this map or even bring their own maps of countries to start up their own maps to build up a picture of familiar places, if they so wish.

I can really see this inquiry unfolding. We'll need to understand measurement on maps. We stated counting footpaths in by paces and discovered we all had different numbers. We'll need to look at scale, key symbols, how you show flat and sloped land, the importance of accuracy, as well as orientation and compass directions. However, today we also discovered how there's an art to folding up a large map!

I have asked students to complete two discussion posts on the wiki over the weekend. This is a pre-assessment so it should be based on what each student knows right now. I have reminded them of using the three checks before they post.

A very interesting discussion came out of the need to find a big enough piece of cardboard to build our world map puzzle on. DZ and I had measured out the dimensions on the box, 810 mm x 540 mm, but today we noticed there were measurements in inches too. I asked the students if the puzzle would be the same size if I used these measurements instead. Some uncertainty and confused faces! We went on to discuss metric and imperial measurements, units and measuring systems in different countries, vocabulary such as width and length, as well as converting the measurement in millimetres to centimetres 81 cm x 54 cm and metres 0.81 m x 0.54 m. (There was a flutter of excitement from some students when the decimal numbers appeared!) I've asked if one student could find a ruler at home with inches so we can see and compare the units.

P.S. Come and check out the students' maps of the world on our wall. It's fascinating to see how they went about this independent task.