Maths Fun - Exploring Real Data with Excel

This term my Year 3 class is learning to collect, organise and represent data. I feel strongly about giving students opportunities to work in real world contexts and using available tools, so try to plan Maths lessons to achieve this. Early in the term students conducted mini surveys to find out about class preferences, recording the results in tally form. They then input their results using Excel and created graphs to show what they found.

This week we worked as a class on a project using the school lost property basket. We wanted to sort through what was there and find the total value of the items in lost property. On arrival at the basket, we found additional ways to sort the items. Within the basket were lunch boxes and containers, non-school uniform clothing items, and school uniform clothing items. For the sake of our task, we decided to work only with the clothing. We carried it all to an outside space where we could sort it.

Uniform items were set out in a physical graph.

Students sorted through the clothing, initially separating the uniform from non-uniform items. Uniform items were then sorted according to type and set out to form a physical graph. We put sticky labels on items that were named, so that we could also record this data, and possibly return the items at the end of our task.

Non-uniform items were separated.

One student was responsible for being our photographer and another wrote down our findings in tally form. We counted the number of non-school uniform items, but didn't sort these, as it would be harder to determine the value of these.

On return to class we used Excel to organise our results. To begin with, we wrote out all the items and the total number we found of each item. I introduced the formula aspect of Excel, demonstrating how to calculate the total number of items with =SUM(B1:B14). We then used the uniform price list to find the cost of each item, and entered it into the spreadsheet. We used another formula =PRODUCT(B2:C2) to find the total cost for each item in column D. I demonstrated how to fill down for the rest of the items. Finally we filled right from B15 to get the total cost. Students were blown away by the total value of the lost property. It was much more than they had expected.

Working more with the data we had collected, we made a table to show what we found about labelling. We copied and pasted the first two columns from our previous table, and then added a column for the number of labeled items. We tried to make a graph with this information, but it wasn't representing what we wanted to show, so we had to consider other options. We then tried to find a formula for subtracting, and eventually discovered that we just needed to type =(B2-C2) in D2 and then fill down in order to get a column for Unlabelled. We were then able to hide column B in order to graph the results to show the total amount of each item with labeled and unlabelled displayed.

We then made one more quick graph to show the comparison of Uniform to Non-Uniform items.

We sent our findings to the Head of School and Junior School Director, as something that might be mentioned at the SRC meeting as a reminder for students to write their name on their clothing, check the lost property and take greater responsibility for their property.

The task took about 90 minutes from start to finish, and involved a lot of modelling in the classroom rather than students having a chance to work it all through for themselves on the computers. Many are now keen to have a go with Excel to create their own spreadsheets and use formulas. My plan is to try this next week, with students calculating the value of a simple summer wardrobe.

Tech Tips Tuesday

Three Simple uses for iPads in the classroom

I've been trying to think of more ways to use the iPad in the classroom. We've had a great bank of iPads that have been useless because they can't be set up without the departmental passwords (which we haven't been able to obtain), and an additional small bank of iPads that were set up before the passwords changed. I don't really understand how that works, but decided to get started with the five that were available. I was also teaching some iPad demonstration lessons for teachers in my school, and some of these ideas were born from our discussions. I needed to use what was already available on the iPads.

1. Listening Post

This is an example of old ideas with new technology! The iPad can be plugged into a transmitter for a set of headphones so students can listen to stories without disrupting others. Obviously, students can listen to stories online, or read interactive book apps, but why not have students record their own stories or readers? I had one group record their reading of a reader for another group to follow along. The trick with this is to choose a book that the recording group should read fluently, and that the listening group will be reading at an instructional level. Our iPads didn't have an audio recording app, so we just recorded with video.

2. Graphing

Students worked in small groups to conduct surveys, collect and represent the data, and present their findings to the class. We had Draw Free, so I based the survey questions around the stamp images available in this app. Questions included things like: What is our class's preferred way to travel - car, train or plane? Students used the stamps in Draw Free to represent the data in a pictograph. We then plugged the iPads into the interactive whiteboards to display the graphs while students discussed what they had found.

Tasks for students

Students cut these roles into strips, put them in a hat and selected one to determine their role in this task

Example of pictograph

3. Story Making

Prue had a great idea to make stories with felt boards, take photos and have students write their story on paper. She then printed the photos and made them into books for students to read. We took this idea and explored it with the iPads. Again, students created pictures using the felt boards. They took photos with the iPads and wrote their story on paper. We then used a story making app - Story Creator - to make the 'books'. Students inserted their photos and recorded the audio for the story. We viewed the finished products on the interactive whiteboard.

Students working cooperatively on story making task

Example of felt board story page

Why use the iPads for tasks that can be done without them?
It's true that at times it takes more effort to organise lessons around iPads (or any other ICT for that matter) but using them increases student engagement in lesson content and gives students an opportunity to develop ICT skills. Due to the limited numbers of iPads, I feel that it also leads to greater use of collaborative tasks which help students to cooperate and share both ideas and resources. Outcomes in the Australian Curriculum call for greater use of ICT as a way of demonstrating understanding and creating content.

Friday Not-so-fun

I spent Friday curled up on the couch snoozing, sculling down liquids and gobbling down food in an attempt to help my body fight what I assume is swine flu. The doctor said it is a virus and that I am contagious. Given that I had the flu injection earlier this year (which should cover me for most of the known flus they have vaccines for) I expect that it is probably swine flu. The doctor said that they aren't testing everyone for swine flu now, but only those at risk - asthmatics, elderly, pregnant women, and people with a temperature over 38 degrees Celsius.

I've been achy, coughing, and OH SO TIRED! It wasn't all bad though, as I got to enjoy a lazy day while it rained outside my window. I love the rain. And, today (Saturday), I'm actually feeling a lot better. I woke up this morning to find my feet tapping (something they do when they want to go for a run) and as I prepared my usual coffee and porridge, I looked out at the gorgeous day and felt it would be a perfect day for a bike ride. Obviously, I'm not going to put my body through any of that today - I still need to rest a little longer. But it's good to see I'm well on the road to recovery.

So, I spent even less time in the classroom this week and when I was in there, it had it's own little elements of higglety piggletiness.

Fun This Week

Chance and Data
We covered Chance and Data in Maths this week. I taught one lesson on this for my own Maths class and one lesson for Mr Tucker's class. (His relief teacher had to go to her sick child and I was off class for my executive day, so I went back on his class to fill the gap.) We explored ideas around rolling dice, pulling counters from a hat, tossing a coin, and spinning a spinner. Students really enjoyed these activities. For teachers in Australia and New Zealand, there are some great Chance and Data activities available on Scootle that allow students to explore these concepts.

Textiles and Design Projects
This week we introduced students to the next phase of their learning in our Textiles and Design Unit. We told them that they need to create an item that they can sell at school (at a fete, or market day or other). They need to consider the needs of their clientele and design something that they can make in three weeks using easily accessible resources and drawing on the skills they've learnt so far. We talked about the need to create quality items and determine a fair price. We also suggested that students speak to their proposed clientele prior to making their items in order to determine if their is a market for their product. It is exciting to see the ideas that students are coming up with and their enthusiasm in getting started with the process.

Cooperative Reading
I used my iPhone to record students thoughts about our Cooperative Reading Groups. I plan to use this information to make some adaptations. Here is a summary of their thoughts:

Good

• You can discuss your books and how you're enjoying them
  
• Learn more about how to write better stories
• Small groups with different books and we tell each other about those books
• Get to space out the reading time
• Have little groups and get to discuss your ideas and can have your own opinions
• We share our ideas with people
• Learn how to use a roster
  
• Allowed to read a book and do activities to get you more into the book and learn how to write better stories
• People are enjoying their books and having fun
• After we read we write it all down and the teacher gets to see what we're reading and then we share it with our groups too
• Get to experience new authors and how they create characters, settings and plots
  

Bad

• Most of the activities are too short
• You get through the writing activities too quickly
• Some of the Reading Response Journal sections are too easy
• It's hard to know what to write in Reading Response Journal
• Reading Response Journal is too repetitive and can get boring
  
• People with large books are having trouble finding the time to do their allocated reading AND the writing tasks.
• When there's too much talking it's hard to concentrate
  

Based on these responses, it seems that students find the discussion time very beneficial, but the Reading Response Journal needs to be re-worked. Perhaps it would be best to have a focus for each week and students write to that focus and share about that focus during their discussion groups. For example, one week might be focused on "interesting words and phrases", another on "descriptive passages", another on "characters", another on "author's style", another on "my perspective" and so on. That would mean there would be less repetition and that students would focus on these areas in greater depth.

Friday Fun

On Fridays I like to reflect on some of the more enjoyable things from the week. In my complete exhaustion it reminds me of the great learning that has taken place during the week and helps to refresh me for the week ahead.

Fun this week:

Advent Calendars - This week we made star advent calendars to count down the days until Christmas. The star was a geometrical pattern and we made colourful links - one for each of the days until Christmas. Children take off one link each day as they count down to Christmas.

"Photoshopping" with Paint - I taught students how to use MSPaint to cut a photo of themselves and paste it onto a background. I saved background files from the Creative Commons Attribute Licence page with a name that referred to the photographer. Students made their new pictures and printed it out with a sentence attributing the background to the flickr artist.

Investigating Capacity in the sandpit - Students paired off and selected a small container and a larger container. They estimated how many sand-loads of the small container would fill the larger container. After 30 minutes of focused 'work', I gave them 15 minutes playtime in the sandpit.

Great Barrier Reef Paintings - We painted an A3 sheet of paper with water colour blues. We then cut out sea creatures from bright coloured paper and glued these onto the background. Students got ideas from a flickr slideshow based on the search "Great Barrier Reef". I also took digital photographs of students pretending to swim and printed these out for students to include in their artwork.

Shivoo - On Thursday night we had our end of year concert - our Shivoo. A stage was set up in the school playground and families brought picnic baskets and picnic rugs to pread out on the lawn for our performances. The classes performed a range of great items to entertain. The Year 1 classes did "On the Good Ship Lollipop" to tie in with our "The Way We Were" unit and "Kookaburra Sits in the Old Gum Tree" to tie in with our "Are We There Yet?" unit. Once students had finished their performances, they either sat with their parents, or played with their friends. They had a ball! They wrote a journal entry about the night the next day in class.

Heads or Tails - We explored chance through the game of "Heads and Tails" and then students experimented with coins to record the way the coin landed after a number of flips.

Daintree Rainforest - After reading "Where The Forest Meets The Sea" by Jeannie Baker and discussing some facts about the rainforest, students began designing posters to encourage people to look after the Daintree Rainforest without actually writing "Protect the Daintree Rainforest". The challenge I set was to make it look so beautiful that no one would want to harm it. They got a good start to the posters and will finish them next week.

Let's Get Graphing

These lessons were follow-up to the graphing lessons last week.

As I felt that we'd ended on a negative note with our graphing (and I'd had opportunity to reflect as I wrote my blog post) I decided to revisit graphing again this week. One of the boys from my class asked to have a circle time lesson so I taught the Maths this way instead of a traditional lesson. (If you are new to circle time, you can check out the other circle time explanations by typing circle time in the blog search in the top left-hand-side of this page.)

Check In: My name is ... and I feel ... about data collection and graphing.

Mixer: Change places if... (you have a brother, you ate cereal for breakfast, you have Foxtel etc) The student in the center of the circle calls out the requirement and then has to try to find a place when students change places. The last one to find a place becomes the new caller.

Activity: Explain the difference between 'favourites' graphs (those that ask about favourite foods, colours etc) and other surveys (such as hair colour, eye colour, pets owned etc). Students pair off and select a non-favourite style survey to investigate.

Debrief: In preparation for the next day, show students how to enter data into Microsoft Excel and create a graph.

Energiser: Human Graphs. Students form lines according to criteria (eg. amount of teeth lost) and teacher takes photo. Upload images to the interactive whiteboard and discuss the graphs straight away.

Check Out: Any questions about graphing with Excel the following day.

This lesson went REALLY well, except for a couple of the survey topics. One pair chose 'type of car your parents drive' which was a bit tricky for some students to respond to. Another pair chose 'how many letters you have in your letter folder' which proved difficult since the room was set up for circle time and students had limited access to their desk trays where their folders were stored.

The human graph part was hectic, but lots of fun. I was amazed by the differences in amounts of teeth lost. Some still hadn't lost any, while one had already lost nine!

Today we created the graphs with Excel. I did another quick demonstration to review the lengthier explanation from the previous day and set students to work. (The reason I did the two explanations was because we only get 30 minutes in the lab and I knew a 5 minute explanation wouldn't be enough for a new skill, but as a review would work well.) I was impressed by how quickly and capably students worked with this task. They were very proud of their work and I encouraged them to try making their own graph with excel at home.

NOW we're ready to move on from graphs as they have been left with a positive, successful experience.

Data Collection and Graphing

This week I worked some more with my students on collecting data and presenting findings in graph format. For the first couple of graphs I offered lots of support with the data collection and some guidance with drawing up the graph. For the final graph, I encouraged the students to work in small groups to carry out their own investigations. My goal with these sessions was to demonstrate that graphing is fun and can be easily done at home with minimal resources.

Here is an outline of the sessions:

Our Favourite Ice-creams

1. As a class we chose 8 options for favourite flavoured ice-creams.
2. I provided each student with a class list.
3. Students asked each other what they're favourite flavour was and wrote the flavour (or code for the flavour) next to that person's name. They continued until they had interviewed everyone.
4. I provided each student with a blank 2cm square grid.
5. Together we wrote the title for the grid, wrote the flavours along the bottom of the grid, and wrote numbers 1-10 up the left side of the grid.
6. Students used their data collection on the class list to colour in the columns on the grid.
7. We discussed which flavour was most popular, least popular, and other information students could find out from the graph.

Cars in the School Carpark

1. We formed a list of colours we expected that cars in the carpark might be (including 'other' as a possible option).
2. We wrote this list on a piece of paper.
3. We went into the school carpark and walked along the rows adding tally marks for each car we passed.
4. Back in the classroom we wrote a numerical value for each set of tally marks.
5. I provided each student with a blank 2cm square grid.
6. Together we wrote the title for the grid, wrote the colours along the bottom of the grid, and wrote numbers 1-10 up the left side of the grid.
7. Students used their data collection to colour in the columns on the grid.
8. We discussed which car colour was most common, least common, and other information students could find out from the graph.

Group Investigations

1. We discussed possible things that students might like to investigate.
2. In teams, students decided what they would investigate and considered possible options for people to choose from. All investigations fell into the "favourites" category.
3. Students went around and collected data by questioning students.
4. Students presented findings on 2cm grid paper with title, numbers and options.
5. I discussed the information with the students in their groups.

For further improvement, I would probably ask the groups to present their findings to the class. I forgot to copy off the class lists for the group investigations, which made the data collection a bit messier for my students. I was feeling stressed by the end of it, and the kids were sick of working with their groups. Perhaps tighter structure would have made this more successful, or perhaps it would have worked better if they were in pairs instead of fours.

It would also be fun to carry out an investigation over a number of different groups of children in different schools. Definitely something to keep in mind for next time, once I have connected with a few more schools.

Some investigations to graph at home:

• Items in the dishwasher
• Toys in the toybox
• Times the television is on during the day
• Types of books on the bookshelf
• Sport statistics

Please feel free to leave your own suggestions of fun things to graph in the comments box.

Numeracy Education Day

On Friday we had our Numeracy Education Day. Students were organised into mixed-aged groups for a series of activities moving from one classroom to another. Teachers prepared a 50-minute lesson that they presented 3 times during the day - two before lunch, and one after recess. This ran similarly to the Literacy Education Day we had for Book Week.

Teachers selected math activities involving space, measurement, problem solving, and chance and data. The activities were predominately hands-on math tasks with students working in pairs or small groups. Those working with 2D shapes created pictures using tangrams or other shapes. Some students went out to measure distances in the playground using metre trundle wheels. Others created a spinning colour wheel using instructions and measurements in centimetres. One group tried to solve brain teasers like matchstick puzzles.

My group was subjected to another Circle Time! This time related to chance and data. The group consisted of children from Kindergarten to Grade 2. I organised it as follows:

Check in: Students said their name, their class, and then coloured in the appropriate square, above their classname, on a graph. We then discussed what we can determine from this graph. Which class had the most members in the group? Which had the least? etc.

Mixer: One student stood in the centre of the circle and said "I like [McDonalds]". All children who agreed with the statement changed places in the circle. The person in the centre had to try to find a spot, leaving someone else standing in the centre. The game continued until everyone was mixed up.

Activity: The Car Race - I made another graph with numbers 1-12 along the bottom and some cute little pictures I found of cars. Students then worked in pairs to roll the dice and add the two numbers together. They then coloured in the squares above this number. The 'winning car' was the first one to reach the top of the graph (where I had some cute little pictures of checkered flags!) Before beginning, I got the children to choose which car they thought would win the race.

Debrief: We went around the circle and each group told me which car won their race, and how many spaces car number one moved. We then discussed why car number one didn't get to move at all. (It is impossible to roll 1 using two dice!) We then looked at the chances of rolling the other numbers, paying particular attention to the "winning car" numbers.

Energiser: I found a toss-a-coin tool on my Smart Board, but could have settled with an 'actual' coin! We then played a game of Heads and Tails. Students put their hands on their heads if they thought the coin would come up heads, or on their tails if they thought it would come up tails. Students who got it right stayed in for the next round. Play continued until one player was left and declared winner.

Check out: Students checked out by saying their name and one thing they had learnt about Maths through this activity.

I was really satisfied with how well these activities flowed and the discussion that arose as students explored chance through the roll of dice.

For more information about circle time, click here, or search this blog for 'circle time'.