In this unit data about sporting activities is collected and presented using dot plots and bar graphs.
The key idea of statistical investigations at level 3 is telling the class story with supporting evidence. Students build on the ideas from level two and their understanding of the PPDAC (Problem, Plan, Data, Analysis, Conclusion) cycle – see Planning a statistical investigation – level 3 for a full description of all the phases of the PPDAC cycle. Key transitions at this level include posing summary investigative questions and collecting and displaying multivariate and time series data.
Summary or time series investigative questions will be posed and explored. Summary investigative questions need to be about the group of interest and have an aggregate focus. For example, What types of lunch-time activities do the students in year 5 like doing? What are the heart rates of students in our class?
Data displays build on the use of frequency plots from level two and can be formalised into dot plots and bar graphs. Students should be encouraged to show a second variable, for example, by using colour. They may like to look at boys’ and girls’ lunch-time activity preferences.
Students will be making summary statements. For example, the most common resting heart rate for our class is 70 beats per minute, four people have a resting heart rate of 66 beats per minute (read the data), or most students (16 students out of the 27 in our class) have a resting heart rate between 65 and 75 beats per minute (read between the data). Teachers should be encouraging students to read beyond the data by asking questions such as: “If a new student joined our class, what resting heart rate do you think they would have?”
Dot plots
Dot plots are used to display the distribution of a numerical variable (for example, hours of sleep) in which each dot represents a value of the variable (for example, 8 hours). If a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value. Sometimes the dot plot is drawn using crosses instead of dots. Dot plots also be used for categorical data (i.e. data that can be organised into distinct categories, such as types of preferred lunchtime activities).
Bar graphs
In a bar graph equal-width rectangles (bars) represent each category or value for the variable. The height of these bars tells how many of that object there are. The bars can be vertical, as shown in the example below, or horizontal.
The bar graphabove 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 bars shows that there are six lots of jandals, 15 lots of sneakers and three lots of boots. 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 (category and whole number data), there are gaps between the bars. A histogram, which features bars without gaps, is used to present continuous, numerical data that has been organised into continuous intervals (e.g. average temperature inside the classroom over the course of a day). Histograms are covered further at late Level 3 and at Level 4.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The context for this unit can be adapted to suit the interests and experiences of your students. The statistical enquiry process can be applied to many topics and selecting ones that are of interest to your students should always be a priority. Consider how you could make links between this unit and learning from another curriculum area. For example, to complement learning about conservation and the life cycle of plants, you could frame the unit around creating a graph showing native plants found in the bush, or birds observed in the local environment. Comparisons to the amount of birds could be made from one day to the next, or at two different times of the day.
Te reo Māori vocabulary terms such as kauwhata ira (dot plot, dot graph), kauwhata pou (bar graph), tauanga (statistics), kohikohi raraunga (data collection), raraunga whakarōpū (category data), and raraunga (data) could be introduced in this unit and used throughout other mathematical learning. Numbers in te reo Māori can be used alongside numbers in English.
Session 1
We begin the session by looking at our resting heart rate and our heart rate after we’ve done some exercise. We display this data using dot plots. Discuss with the students what they already know about dot plots graphs. Show and discuss some examples. These could be found in media (e.g. newspapers, CensusAtSchools data) or in texts. Briefly refer to the important features (e.g. title, y and x-axis, scale, regular intervals, type of data displayed - number or category). Explain that you are going to collaborate (mahi tahi) and create a dot plot. You have chosen a dot plot because you want to display number/numerical data.
Session 2-3
In these two sessions we focus on the use of bar graphs to display results of categorical data.
Discuss with the students what they already know about bar graphs. Show and discuss some examples. These could be found in media (e.g. newspapers, CensusAtSchools data) or in texts. Briefly refer to the important features (e.g. title, y and x-axis, scale, regular intervals, type of data displayed - number or category). Explain that you are going to collaborate (mahi tahi) and create a bar graph. You have chosen a bar graph because you want to display category/categorical data
Session 4-5
Over the next two days the students gather information around the theme of sports. They use the PPDAC cycle to collect, display and share the information with others.
Remind them to include the variable and the group in any statements they make about the data, and if the data is numerical to also include values and units. Give students the opportunity to share their learning with others within the class or as a whole class group.
Dear family and whānau,
At school this week we have been gathering information about our heart rates. We have displayed the data using a dot plot. A dot plot is useful for arranging numerical data in a display. Ask your child to share with you how we found our heart rates and then can you place the heart rates of your family on the chart below.
We have been solving heart-beat problems with the help of calculators. Here’s one for you to work on with your child:
How many times does your child’s heart beat in a week?
Printed from https://nzmaths.co.nz/resource/sports at 10:59pm on the 4th May 2024