Before the problem is created some background information is needed about the data that is available. This is activity is useful for the first time scatterplots are introduced to students.
This activity uses six different sets of data cards. Each set of data cards contains a sample of 40 Year 9 students selected at random from the Census at School database in 2005.
Teacher activity/ dialogue
Possible student outcome/dialogue
Hand out the pre-prepared data card sets. Tell the students only that each set is a sample of 40 Year 9 students from the 2005 Census at School database.
Get the students to look at the cards and make notes about what they notice. Split them up by colour.
Explain that each data card is for one person and gives 5 pieces of information about that person. What do you think the pieces of information are?
Draw an outline of the data card on the board and collate ideas.
Complete the outline as the variables are ascertained by the class.
Discuss the variables with the class. What was the survey question that was asked in the Census at School questionnaire for each of the variables?
# gender - 1. Are you: male/female
#circumwrist – What is your wrist circumference? (cm)
#circumneck – What is your neck circumference? (cm)
#year - What year level are you?
# age - 2. How old are you?
Discussion on sample and population. It is worthwhile now having a discussion about the sample of cards they have in front of them. Ask the students to describe what they think the cards represent.
Need to distinguish at this point that we want to use the sample to make decisions about the population.
Brainstorm some investigative questions that could be asked of these samples of data cards about the population.
At this stage accept all questions that are suggested. If the students appear to be suggesting just one type of question, e.g. comparison only, encourage them to come up with summary and relationship type questions. It would be useful to categorise the questions into the three different types.
Refining the investigative questions
It maybe that you might want to explore some of the summary or comparison questions that have been raised by the students. However, this activity is focusing on relationship questions.
At this point we want to take the relationship investigative question that was (possibly) posed.
I wonder if wrist size and neck size are related.
We want to make sure the population we are interested in (i.e. that our sample came from) is reflected in the investigative question. This is the population about which we want to make inferences.
Questioning the investigative question(s)
Can this question be answered by the data you have? Is there sufficient data?
Who would be interested in the outcome of this investigation?
cards have mostly 2 digit numbers across the middle
That the bottom part of the card has two numbers in it Hopefully the students will:
-come up with at least the gender
-see that the wrist/neck values, one is twice the other
-guess what the two variables at the bottom might be by the fact that they are repeated on many cards, and 9 is on all of them wrist/neck card
wrist circ. left, neck circ. right
year level/age bottom
Survey question: question that was asked to get the data
Investigative question: question that is asked of the data
It is possible that some students will think that they are all from the same class? Probably not with 40, but maybe all from the same school… challenge this notion, 40 students from a total of 33,000. Is it likely that they will even know one another?? What is the population that the sample came from? It is the 2005 Census at School database which contains 33,000 Year 5-10 students from all over New Zealand. Question: does this database represent all Year 5-10 students in New Zealand?
Wrist/neck – I wonder …
If boys tend to have bigger necks than girls,
What the typical wrist size is for a year 9 student,
If wrist size and neck size are related
I wonder if there is a relationship between wrist circumference and neck circumference of Year 9 boys and girls in the 2005 NZ Census at School database.
Once the investigative question is posed and is suitable it is important to get down the key information about the data. This can include but is not limited to:
What type of graph(s) will be used to display the data? What are you looking for in these graphs? What do you expect to see?
These data are from the 2005 NZ Census at School database. 40 Year 9 students were selected using the random sampler. As the sample is random all Year 9 students had an equal chance of being selected. Students are a mixture of boys and girls. The investigative question focuses on neck and wrist circumference. The survey questions asked to get these data were#circumwrist – What is your wrist circumference? (cm)
#circumneck – What is your neck circumference? (cm)
Will use a scatterplot to look for a relationship. Expect to see some sort of relationship, think as your wrist gets bigger expect neck to too.
Data cards are given to groups of students. It maybe that you can use different coloured paper and sort the sets so that boys are one colour and girls are another (for example – to bring in a third variable).
Get the students to look through the cards, checking for any unusual values. Students need to decide if these values are “realistic” or “unrealistic”. Discussion on why/why not and whether they should be kept for the analysis.
The data needs to be cleaned. Reference Level 5.
Students need to think about what values might be appropriate for the different variables (neck and wrist). They can have a look at their cards and discuss any they think are not suitable. It maybe that they need to make these measurements of themselves to see how they really work.
Typical examples of incorrect values – wrist and neck circumference are interesting, anything below 10 cm for wrist is pretty small, get students to check their own and find this out, also neck is roughly double the wrist, this maybe clear from just looking through, some of these will be picked up once the data is graphed.
Next stage is to develop the graph.
Get the students to sort the data cards using the wrist data. They could build a dot plot below the x axis.
From here grow the scatterplot, move the card from the wrist position to the neck position.
Hope that the students realise as they get higher wrists, they have to move further up, also get to see that for any given wrist there are a number of different neck circumferences, leading to the idea that when making predictions there isn’t one right value.
This picture shows the data cards with the wrist values sorted below the x axis. Cards in the bottom left are those that are not realistic so have been left out of the analysis.
This picture shows the data cards placed in position. There is a group of cards at the bottom that were unrealistic. Students should write about which cards they didn’t use and why.
When I made the dot plot of wrist circumferences I didn’t include five cards because the values of the wrists were too small. They were 3.5, 5.5, 5.7,6 and 6. When I made the scatterplot I excluded another four cards. 15/10 and 16.5/12 as the neck was smaller than the wrist, 20/0 as there was no neck measurement and 15/20 as that just didn’t seem realistic. I had noticed that neck was about double the wrist.
Get the students to place a piece of string to show the pattern of the data.
This picture shows the pattern of the data placed on top.
Data cards can be glued to the graph and the graphs placed on the wall. In addition the pattern can be cellotaped onto the graph.
Remember that there are six different samples so there will be slightly different pictures of the data.
Assuming this is possibly the first time students have really been focused on relationship questions get them to write down things they noticed as they created their graphs. They should note down their ideas.
You may like to use two further pieces of string to indicate the spread.
Get the students to walk around and look at other graphs that other students have made. Get them to compare and contrast the other graphs with their graph.
Things they might notice include:
That the smaller the neck the smaller the wrist circumference
That there are lots of wrist and neck sizes the same
Some of the data cards were “invalid” indicating incorrect measurements
That the data cards seem to follow a pattern.
These data suggest that there appears to be a relationship between wrist and neck circumference. There is an upward pattern in the plot, which means that people with bigger wrists tend to have bigger necks. The relationship is quite strong as this pattern is quite clear. Neck circumference appears to be twice the wrist circumference.
What is the difference between the investigative question and the survey question?
What were the benefits of growing the scatterplot? Do you think you need to do this more times for the students to get a good picture/idea of the relationship idea that a scatterplot shows?
This resource contains 15 pages of scatterplots. Most have a short story with the variables listed and the data set given. This is usually on one page. On a second page are the title, variables and then the scatterplots. With each graph(s) there is the starter: What we notice about the graph(s):
The main aim of this activity is to get students to describe what they see in the graphs before they get hung up on drawing lines of best fit, making calculations or in fact have much in the way of analysis tools. Trying to get through to them the need to draw the graph first.
Photocopy the pages for use in class. The write-on pages need to be copied multiple times, the story pages only once. Make about eight copies of each write-on page. (64 activities, standard class 15 pairs @ 4 each is 60 activities)
Set up the different stories around the class. Split the class into pairs. Each pair should endeavour to do at least 4 different stories. (allow about 5 mins per story then move to next one)
Suggested groupings might be:
Pair 1 do 1, 2, 3, 4 Pair 2 do 2, 3, 4, 1
Pair 3 do 2, 3, 4, 5 Pair 4 do 3, 4, 5, 2
Pair 5 do 3, 4, 5, 6 Pair 6 do 4, 5, 6, 3
Pair 7 do 4, 5, 6, 7 Pair 8 do 5, 6, 7, 4
Pair 9 do 5, 6, 7, 8 Pair 10 do 6, 7, 8, 5
Pair 11 do 6, 7, 8, 1 Pair 12 do 7, 8, 1, 6
Pair 13 do 7, 8, 1, 2 Pair 14 do 8, 1, 2, 7
Pair 15 do 8, 1, 2, 3 Pair 16 do 1, 2, 3, 8
At the end the pairings will join up to compare and contrast what they have found (that is why the pairs are not doing the same activity at the same time).
Pair 1 and 2 together etc.
Any additional pairs double up.
Smoking and cancer (2 pages – 1 write-on)
World population figures (2 pages – 1 write-on)
Olympic games long jump gold medal (2 pages – 1 write-on)
High jump world records men (2 pages – 1 write-on)
Global mean temperatures (3 pages – 1 write-on)
Alligator (1 write-on page)
Cattle (1 write-on page)
Body fat (2 pages – 1 write-on)
Focus in this activity is on the analysis of the graph, initial not icing’s that students do.
Get pairs of students to compare and contrast with another pair of students who have done the same activity.