How Likely is That?

# 1. What Does our Village Look Like? Suggested Learning Intentions

• To understand the difference between a population and a sample
• To design and conduct a survey
• To gather and evaluate categorical and numerical data and represent it using fractions, decimals, and percentages

Sample Success Criteria

• I can explain the difference between a population and a sample
• I can collect information based on questions that I pose
• I can explain the difference between numerical and categorical data
• I can use manipulatives to model the data and explain my thinking
• I can use fractions, decimals, and percentages to represent survey results

Our World's Population

Invite students to estimate the size of the world’s population. Ask them to record their estimates in their workbook, using both words and numbers. Students may use terms such as millions and billions while having little understanding of where these numbers sit within a place-value system. Once students had a chance to record their answers, draw up a place value chart on the board for students to come up and record their predictions. Once your class has made several predictions, click on the world clock. This world clock continuously ticks over to demonstrate how quickly the world’s population is increasing. It also helps students to understand just how large the world’s population is.

This activity supports students' understanding that it would be costly and impractical to collect and analyse data from every person in the world, and therefore we take smaller samples of a population and use these samples to make inferences about a population. A sample is a small selection of a population – it is not the entire population.

If Our World Were a Village

This activity involves exploring different ways in which the world’s population can be categorised.

Introduce students to the book ‘If the World Were a Village’, written by David J Smith (2010). This book explores characteristics of the world’s population as applied to a village of 100 people.

Students select up to three facts and represent them on a poster or digital presentation shared on a class collaboration platform. Conduct a real or virtual gallery walk to share their learning.

Enable students by modelling how to display their data as a pictograph or bar graph.

Extend students by encouraging them to think about the different ways in which the data could be displayed. For example, could they display their data in decimals and/or fractions?

In this activity, students create and refine a survey. Students work in small groups to design and conduct a survey to determine the individual characteristics of their classroom (or another class) and then present the data using the approach from ‘If the World were a Village’ (i.e., describe their classroom as if it were made up of 100 people). Students collect numerical and categorical data. At the beginning of the activity, list on a board all the possible numerical and categorical data sets that could be surveyed. Examples of data sets are:

 Categorical Data Numerical Data Eye colour Hair colour Religion practiced Favourite fruit/drink/cereal Gender (M/F/other) Dominant hand (left/right/ambidextrous) Number of siblings Shoe size Height

When creating the list, you can either go into the class with a prepared list or create one on the board as a class. If you plan to create one as a class, prepare a small list to prompt student responses. Be selective about the categories that students can use to survey one another. Be mindful of your school’s demographic and potential sensitivities amongst your school’s community.

Note that we can collect categorical (qualitative) and numerical (quantitative) data. Categorical data is used when data can be divided into groups, for example brands of running shoes that people prefer. Numerical data represent numbers and can be further divided into two subsets: discrete and continuous. An example of discrete data is the number of children in a family. Common examples of continuous data are weight, height, and temperature.

Students can work in groups to survey some of their peers. Each group of students selects one numerical and one categorical datum option to survey their classroom. Where possible, each survey question should have five possible answers (four categories and ‘other’). Notable exceptions include dominant hand and gender.

Ensure that students are aware that we are not surveying every student in the class during this lesson - we are taking a sample from the population and that from this sample we will make inferences.

Students survey 20 students. This number allows us to generalise, where each person surveyed represents 5% of the population.

Students collect their survey data in a frequency table. This information is then displayed in a Fractions/Decimals/Percentages table.  Once students have converted their survey data into a fraction, a decimal and a percentage, they represent this information in a pie chart. Using the 100-person pie chart ('At Level' Pie Chart task available in the Materials and texts section above), students display their data by colouring in the appropriate number of people to represent the correct percentage. Students then draw a line connecting the ‘people’ to the centre of the circle to create a segment.

Enable students to work as a small group to create a survey with one piece of categorical data (one question). Students collect survey results from ten students and represent the data using a frequency table.

Model how to complete a Fractions/Decimals/Percentage table, providing support based on students' understanding of fractions, decimals, and percentages. Students can display their data using the ten-people pie chart ('Enable' Pie Chart Task available in Materials and texts), where each circle on the pie chart represents one person from their survey. Encourage students to talk about their data in terms of a fraction, e.g., ‘three out of ten people had brown hair’.

Extend students by encouraging them to survey any number of respondents other than 10, 20 or 25. Encourage students to work in groups and collect their survey data in a frequency table. They then display this information in a Fractions/Decimals/Percentage table.  Students convert unit fractions into a percentage using a calculator, for example if they collect 23 responses: 100% divided into 23 equal pieces is equivalent to 4.3%. Therefore, each response is 4.3% of the whole survey.

Students multiply this part by the number of responses they collected for each choice. This percentage shows how many parts out of 100. This data can then be represented as hundredths and written on a place value column; this produces the decimal.

Students display their data on a blank pie chart ('Extend' Pie Chart Task available in Materials and texts section above). These students partition 360 degrees by dividing the whole into 100 parts (1 part or 1% = 3.6 degrees) and determining the correct number of parts (multiplying) for each given percentage. Students will require a protractor and knowledge of how to use it. Example teacher-student conversation

Teacher: If 100% is 360 degrees, what would 50% be?

Student: 180 degrees.

Teacher: How did you do that?

Student: I halved it.

Teacher: You divided into 2 pieces. If you had 25%, what would you do?

Student: Divide it into 4 pieces.

Teacher: If you had 1%, how many pieces would you have to divide the 360 degrees into?

Student: 100.

In this way you can lead the students to the understanding that they must divide 360 by 100 to work out how many degrees 1% is worth (3.6 degrees) and then if they have 17%, they need 17 groups of 1% or 17 × 3.6.

This stage supports students to develop their capacity to develop a question, conduct a survey and use this data to fill in a Fractions/Decimals/Percentage table. Students represent their findings using a pie chart. Ask students to write a summary of the data represented in their pie chart. When describing their data support students with the following sentence starters.

 Categorical Data Numerical Data Most students selected… In general, more students preferred…  The least popular drink for students in (e.g., 7A) is ...  Most students in our class are ... (i.e., left-handed) The mode for this set of data is… The mean for this set of data is… The mean number of siblings in this class is…  The average number of siblings per student in our class is…  The median for this set of data is…  After sorting my data from smallest to largest I found that the median number is…  The range for this set of data is…  The range of (i.e., shoe size) in our class spanned ... (e.g., 4 sizes) Throughout Stage 1, students have explored the use of pie charts to represent their data. Have students reflect on the pie charts they have created and those of their classmates.

Ask: Were there any things you learned about your classmates? Did you expect x amount of people to prefer y? Do you think these displays reasonably represent your class?

Encourage students to interrogate their data and their findings. Have them consider if they surveyed only specific sub-groups of the population. For example, did they survey only their friendship group or a specific gender group? Lead students to see that it is important when surveying populations to survey the variations within a population, to ensure all voices are heard.

Freund, M. et al., 2019. The prevalence and correlates of gambling in secondary school students in Victoria, Australia, 2017. [Online]