Party, Party, Party
In this unit we conduct a number of investigations using a party theme. In the unit the students spend time counting, comparing, organising, analysing, displaying and interpreting data. While discussing the data we take the opportunity to use and reinforce early additive strategies for combining numbers.
- pose questions for investigation
- collect category data
- display data in tally charts, uniform pictograms & bar charts
- make statements about data displays
At Level 2 you can expect the students to be posing a greater range of questions. They will also be helped to understand some of the issues involved in conducting surveys and learn new methods for collecting data. While at Level 1 the students collected data and chose their own ways to display their findings, at Level 2 they will be introduced to uniform pictograms, tally charts and bar charts. More emphasis here will also be placed on the discussion of the data and the making of sensible statements from both the student’s own displays and the displays of others.
In a uniform pictograph the pictures are drawn on uniform pieces of paper. This means that the number of objects in each category now bears a direct relationship to the "size" of each category on the display. An example is shown in the diagram below.
In a further development the pictures can be displayed on a chart with axes and titles. The vertical axis can be numbered to match the pictures.
In a bar chart the pictures are replaced with vertical straight lines or rectangles. The position of these rectangles indicates what they represent and the height of these rectangles tells how many of that object there are. It should be noted that the numbers label the points on the vertical axis, not the spaces between them. Notice too, in a convention used for discrete data, there are gaps between the columns.
The example above shows the types of shoes worn in the class on a particular day. There are three types of shoes: jandals, sneakers, and boots. The height of the corresponding rectangles shows that there are 6 lots of jandals, 15 lots of sneakers and 3 boots.
A tally chart provides a quick method of recording data as events happen. So if the students are counting different coloured cars as they pass the school, a tally chart would be an appropriate means of recording the data. Note that it is usual to put down vertical strokes until there are four. Then the fifth stroke is drawn across the previous four. This process is continued until all the required data has been collected. The advantage of this method of tallying is that it enables the number of objects to be counted quickly and easily at the end.
In the example above, in the time that we were recording cars, there were 11 red cars, 4 yellow cars, 18 white cars and 5 black ones and 22 cars of other colours.
At Number Framework Stage 5, Early Additive, the students have begun to recognise that numbers are abstract units that can be treated simultaneously as wholes or can be partitioned and recombined. A characteristic of this stage is the derivation of results from known facts such as finding addition answers by using 'doubles' or 'ten facts'. Students may also respond to the tally chart data by applying simple multiplication of 5s.
most common, least common, altogether, less, more,
tahi, rua, toru, wha, rima, ono, whitu, waru, iwa, tekau....tekau ma tahi, tekau ma rua.... rua tekau, toru tekau....
tasi, lua, tolu, fa, lima, ono, fitu, valu, iva, sefulu... sefulu-tasi, sefulu-lua, ..........lua- sefulu, tolu-sefulu
Session 1: Balloons
Today we make a pictograph about our favourite balloon shapes.
- Take a bag of balloons and spread out. Discuss shapes. Students choose favourite shape (or colour if different shaped balloons are not available) and draw it on a piece of paper (one eighth of an A4).
- Whole class discuss ways to display the data. If matching pictures in 1:1 lines (Pictogram) is not suggested, teacher will need to direct them to this.
- Students attach their drawing to the class chart.
- Discuss information shown on pictogram. These could be recorded as "speech" bubbles around the chart.
- Talk about the need to label the axes and give the chart a title so that others could make sense of the display.
- Ask questions about the results that require students to combine sets:
How many students liked long wiggly balloons?
How many students liked long straight balloons?
How many students liked long balloons altogether?
How can you add the numbers together?
How many students liked balloons that were not long?
How many more students liked long wiggly balloons than long straight balloons? (Model and reinforce the use of subtraction or addition rather than counting on or back to solve this type of question.)
Try to find questions that will allow students to use strategies such as near doubles and adding to make 10s.
Session 2: Party Questions
- Students brainstorm "how many" type questions around the party focus. For example:
- Which is your favourite birthday cake?
- What is your favourite birthday game?
- How many birthdays have you been to this year?
- Where do you like to have your birthday?
- What would you like to be given for your birthday?
- What types of food do you like to have on your birthday?
- How many people might come to your birthday?
- Each group selects one of the questions and is given a partially prepared piece of chart paper.
- The group need to record on the chart paper the title and the choices.
- The students enter their data on their own chart using either sticky labels or prepared rectangles of paper which are glued onto the chart to form a pictograph.
- When each group has completed recording their data they move to another group’s "graph" and record the relevant data. Repeat as time allows.
- Teacher roams questioning for understanding and ensuring that the students are able to correctly construct a pictogram.
- Groups return to their original question to examine and discuss findings.
- Share as a class.
- Again, emphasise questions that require students to operate with the numbers in their display. Rather than asking How many students... ask How many students liked cakes that were not Chocolate cake?
Session 3: Chips
Today we use tally marks to record the number of chips in a snack bag.
- Display a snack bag of chips and ask the students to guess how many chips they think are in the bag.
- Teacher models using tally marks to track how many chips she/he eats.
- Distribute individual bags of chips.
- Students eat chips and use tally marks to record the number of chips in each bag by adding the total of the tally marks each student in the group recorded.
- Share the tallies.
- Using a prepared bar graph outline the teacher constructs a bar graph with the information from the individual tallies.
- Discuss features of the graph and summarise the information shown.
What was the most common number of chips?
What was the least common number of chips?
How many more chips were there in the packet with the most than there were in the one with the least?
- As a class challenge, try to work out how many chips the class ate altogether.
How many chips did the boys eat?
How many chips did the girls eat?
Discuss strategies for adding the numbers together (for example: combine the numbers that add to 'tidy' numbers; add the tens and then the ones; use doubles or near doubles).
Session 4: Lollies
- Using a bag of mixed sweets to focus questions, the class brainstorms possible questions.
- Which is the least favourite lolly?
- How many different kinds of lollies are there in the bag?
- What colour lollies are there in the bag?
Questions are recorded on strips of paper.
- Groups of four select a question to be answered and place it on the desk with a sheet for recording tally marks. Students divide the tally sheet into categories.
- Students move around the class recording choices under relevant categories.
- When they have completed everyone’s tally they return to their question.
- Students use the tally chart to construct a bar chart.
- Students prepare statements about the chart to share with the class.
- Share charts as a class.
- Model questions that they could ask and answer about the results.
How many students liked soft lollies?
How many students liked wrapped lollies?
How many students liked either yellow or green lollies?
Today we plan our own investigation from a party prop display.
- Use "party props" to generate discussion about parties.
- Brainstorm possible questions to investigate. You may need to model possible questions as you display party props. For example:
Here are some balloons. Gosh I’m hopeless at blowing up balloons. It probably takes me 12 or more breaths to blow it up. How many breaths does it take you?
- In pairs students select a question to investigate and plan how they are going to collect the data. One idea is to use tally charts and to circulate aksing their classmates the survey question. This sounds chaotic but usually works very well and takes little more than five noisy minutes.
- Once the data is collected the pairs need to display the data using either a pictograph or a bar chart. Ask them to write a couple of questions (to which they have worked out the answers) to accompany their graph.
- Share survey results. Students can be challenged to answer the questions on each other's data displays.