Making Evaluations

Purpose

In this unit students evaluate statements made about the findings of statistical investigations. In evaluating the statement students look at how the results of the investigation support the findings. 

Specific Learning Outcomes
  • Agree or disagree with a statement made about the findings of statistical investigations
  • Give a reason for their evaluation of the statement
  • Complete a statistical investigation by collecting, displaying and discussing data
Description of Mathematics

In this unit students evaluate statements made about the findings of statistical investigations. Students will look at the results and decide if they would have made the same conclusion about the findings. Students will agree or disagree with the findings, or they may conclude that the results do not have enough information for the conclusion to be made. This interpretation of the results is the beginning of critically analyzing statistical investigations.

Required Resource Materials
Copymaster 2: Library Bar Graph

Copymaster 3: Line Graph

Copymaster 1: Lunchtime Places

Copymaster 4: Lunchtime Activities

Key Vocabulary

 evaluation, conclusion, opinion, statistical investigation, recommendation, average, census, multivariate data

Activity

Getting Started

  1. Explain the following scenario to the students. “The teachers at Sunshine school wanted to know where the most children play at lunchtime. After one lunchtime they asked all the children where they had spent most of the lunchtime and made a bar graph. Show the students the bar graph of results in Copymaster 1.
  2. Read the conclusions to the students and ask if they agree, disagree or can’t tell from the results.
    1. The library is equally popular with juniors and seniors.
    2. Everyone’s favourite is the adventure playground.
    3. The juniors play on the concrete because the seniors take over the sports field.
    4. The treehouse doesn’t hold many people.
    5. The sandpit is more popular with juniors.
  3. Discuss with the students how they evaluated the conclusions. Encourage students to check the data supports the conclusion by looking at the numbers and facts, for example 5 juniors and 5 seniors spent time in the library and these numbers are the same so it is equally popular with juniors and seniors.
  4. Ask students to check if there is enough information to make the conclusion, for example, we can’t tell from the results if more people could fit in the tree house because the survey doesn’t say why people chose different areas. Ask students to check that conclusions are not just opinions.
  5. Discuss with the students that survey results can lead to further investigations, for example in this survey it would appropriate to ask juniors why they don’t chose to play on the sports field.

Exploring

In the next few sessions students will evaluate the findings others have made from statistical investigations.

Activity 1

  1. Provide the students with the graph in Copymaster 2.  It shows what children at school wanted most in their new library. 
  2. Ask the students to each individually write some recommendations based on the survey results.
  3. Have the students work in pairs to discuss and evaluate the recommendations each other made. Encourage students to refer to the data results and discuss if they agree with each other’s recommendations.

Activity 2

  1. Provide the students with the time series graph in Copymaster 3. Explain the local swimming pool is trying to work out when the different pool facilities were being used the most.   The graph shows the average number of users in the 3 facilities over a month.
  2. Ask the students to each individually write some statements about the patterns of use of the different facilities over a typical week.
  3. Ask the students to work in pairs to evaluate the conclusions each other made. Students should be able to support their conclusions and evaluations using the data.

Activity 3

  1. Provide the students with the graph in Copymaster 4. Explain a class did a survey to find out what activities boys and girls did at lunchtime. The class asked their classmates each day for a week and then averaged the results.
  2. Provide the students with the questions that the class wanted to know from their survey:
    1. What is more popular the sports equipment or the playground equipment?
    2. Is there an activity that girls like more than boys?
    3. Is there an activity that boys like more than girls?
    4. If the teachers didn’t organise activities like sports practice and production rehearsal who would this affect the most?
    5. Should the library only be open on wet days?
    6. When the production is over what might girls and boys chose to do?
    7. Who is more interested in sports?
  3. Ask the students to answer the questions and then compare their statements with other students.  Some questions may not be able to be answered by the survey.

Reflecting

In this final session show students the results of the 2009 Census at School survey that asked about 1000 students how they carry their school bag to school. The results were:

Method
Percentage
Two straps, one on each shoulder
63%
One strap, over one shoulder
26%
One strap, going diagonally across your body
9%
Hold in your hand(s)
2%

Use this as a starter for students to investigate the idea further. Ask the students to design a survey that involves multivariate data for example girls/boys, different ages, how they get to school. Students should make conclusions from their own investigations and then work in pairs to discuss and evaluate their conclusions


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