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Level Three > Number and Algebra

# Time for Breakfast

Achievement Objectives:

Achievement Objective: NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
AO elaboration and other teaching resources

Purpose:

This unit encourages students to assess the validity of a set of statements and then plan and carry out investigations to find out whether the statements are true. Students then carry out statistical investigations of their own.

Specific Learning Outcomes:

plan a statistical investigation to assess the reasonableness of a statement

carry out a statistical investigation to assess the reasonableness of a statement

check the reasonableness of answers obtained using a calculator by calculating mentally and using approximations

Description of mathematics:

In order to assess the validity of statements students will need to identify and agree upon the assumptions underlying the statements and the way in which the statements’ accuracy is to be assessed. For example, what will be used as an average lifespan?

Students will also need to have an understanding of the term average. The word average is used in two ways and students need to understand the distinction between these. Sometimes the term average is used in the same way as the statistical term, mean. The mean is calculated by adding all the numbers together and dividing by the number of numbers. The word average can also be used in everyday language, to mean something that is not out of the ordinary.

Required Resource Materials:
The statistics New Zealand website may be useful to find average ages and other relevant information: www.stats.govt.nz. Based on mortality in 2000-2002, a newborn girl can expect to live 81.1 years and a newborn boy 76.3 years
Copymaster 2: Investigation Example
Copymaster 3: Investigation Template
Calculators
Activity:

### Getting Started

1. Begin a discussion about the activities students engage in to get ready for school in the mornings.
What do you need to do to get ready in the mornings?
How long does it take you to get ready?
How long do you spend in the shower? Brushing your hair? Having breakfast?
Does it take you the same amount of time every morning?

2. Introduce the text for the McDonalds advertisement contained in Copymaster 1.

3. Introduce / review the concept of averages with the group.
What is an average? What is a mean?
Ensure students understand the difference between the two ways the word average can be used and the statistical term mean (outlined in the description of the mathematics section above).
Show / remind the students how an average is calculated by asking a group of students how long they spend eating their breakfast each morning, listing these values, and then carrying out the calculation of the average.

4. Encourage the students to consider the validity of the statements.
Do you think these statements are accurate?
How would we check their accuracy?

5. Split the class into groups and assign each group one of the seven statements. Tell the groups their task is to check whether the statement is accurate. As the students work ask them to record the assumptions they are making. These will include:
• the estimated length of the activity each day
• whether the activity occurs for the same amount of time on weekends and week days
• the length of an average lifetime

6. Once the groups have finished checking the accuracy of the statements, gather together as a class to discuss the results.
Do you think the statement is accurate?
How did you work that out?
What calculations were involved?

7. Make a list of the assumptions each group has made.

### Exploring

Over the next few days have the groups of students carry out their own statistical investigations about the average time spent on various activities:

1. Discuss the average amount of time spent on a variety of activities. Encourage students to identify activities they would like to find out about.
How long in a lifetime do you think you would spend watching TV?
How long do you think you would spend riding your bike?

2. Use the assumptions listed previously to discuss the assumptions that will need to be made. As a class decide the assumptions that will be used by all groups and list these clearly. For example the average lifespan is 81 years for females and 76 years for males. Some assumptions will be particular for a statement and so groups will have to make some assumptions themselves.

3. Place the students into groups.

4. Groups list questions for investigation. For example:
In an average lifetime how long will be spent reading?
In an average lifetime how long will be spent eating?

5. Show students the worked example of the investigation, Copymaster 2 and explain the process they will follow to answer their question.

6. Groups work to answer their questions using the investigation template, Copymaster 3. This will take some time with some and you may need to have several small group / whole class discussions to help students through this process.

As students work, encourage them to use mental strategies to estimate answers before they are calculated, and confirm the results of calculations. Discuss the strategies students are using and compare strategies used by different students.
What do you think the answer will be? How did you work that out?
Do you think the answer Jack got using the calculator is about right? How could you check?
That’s a good way to work that out. Did anybody use a different method?

### Reflecting

Once groups have answered their questions, have the groups swap questions (without the assumptions, calculations and answer) and work out the answers to each other’s questions. Compare the different answers obtained to see how close these are, and use these differences to discuss the different assumptions each group made to answer the question.
What answer did you get to the question?
How close was your answer to the conclusion of the investigating group?
Why do you think the answers you got were different?
What assumptions did each group make that were the same? Why?
What assumptions did each group make that were different? Why?

AttachmentSize
TimeForBreakfastCM1.pdf48.27 KB
TimeForBreakfastCM2.pdf54.47 KB
TimeForBreakfastCM3.pdf26.94 KB