How Can You Measure This?

Purpose

In this unit students, working in groups of 2 to 4, carry out and report on a series of investigations involving decisions about how to measure something. The suggested investigations ask: What’s In a Newspaper?, Are You a Square?, How Far Do You Walk? and How Thick Is It?

Specific Learning Outcomes
  • make estimates of lengths and areas
  • measure using a variety of techniques to check their estimates
Description of Mathematics

Measuring skills:
Students will need to be proficient and accurate using rulers and tape measures. They will also need to understand how to combine several measurements appropriately to achieve a result. Relationships between kilometres, metres, centimetres and millimeters will be examined.

Calculations:
All four operations on measurements will be used in this unit. The calculations will involve: large numbers and decimals, conversion to fractions and the choice of appropriate levels of accuracy of measurement and of fraction conversion. Calculator use may also be included in the unit.

In this unit students, working in groups of 2 to 4, carry out and report on a series of investigations involving decisions about how to measure something. The four investigations suggested are:

What’s In a Newspaper?
Students calculate what fraction of a newspaper is devoted to news, sport, advertisements and other categories of information.

Are You a Square?
Students determine whether their height is equal to, greater or less than, the distance from end to end of their outstretched arms.

How Far Do You Walk?
Students work out approximately how far they walk in one year.

How Thick Is It?
Students decide how to measure a length that cannot be measured directly – for example the thickness of a wall of their classroom.

In each investigation the students follow the same sequence:

  1. Make sure they understand the problem
  2. Discuss and decide on three different strategies for tackling the problem
  3. Complete a table to assess the merits of each strategy
  4. Use the best strategy for conducting the investigation
  5. Record their methods and results
Required Resource Materials
Calculators

Large card for displaying results and methods.

Table for comparing strategies (Strategy copymaster)

Newspapers

Rulers

Tape measures

Activity

The sessions are described on the assumptions that students will complete a different investigation on each of the first four days, with discussion of all investigations on Friday. However it is much more likely that two or at most three investigations will occupy those four days, especially if they are asked to record and present their findings. You may prefer to select from the suggestions.

Session 1

What is in a newspaper?

  1. Give each group a newspaper. (They need not all be the same. The class can compare the same newspaper on different days of the week, or different newspapers.) What does a newspaper contain? News, advertisements, sport… Decide on a number of categories that all groups will use.
  2. The challenge is to determine what fraction of the newspaper is devoted to each of these categories. Ask for some suggestions as to how this can be done (e.g. numbers of pages and part-pages, length of columns, area…).
  3. Explain that each group will decide on three different ways of working out the fractions, and will then compare these ways by completing the table. They will then use the best strategy, carry out the investigation, and describe and record what they did and what they found out. This may form the basis of group reports to the class.
  4. Groups discuss and decide on three strategies, complete the Comparison Chart, conduct the investigation, and write up their findings.

Session 2

Are you a square?

  1. Have one or two students come to the front and stretch their arms out. Does it look as though they are as wide as they are tall – i.e. are they square? Ask for suggestions as to how these two distances could be measured. (Decide whether to allow cutting a piece of string to equal the height and then using this to compare; a very effective method but it involves no standard measurements). Groups need to determine whether they are Square, Landscape or Portrait. How near will the two measurements need to be to count as ‘equal’?
  2. Groups discuss and decide on three strategies, complete the Comparison Chart, conduct the investigation, and write up their findings.

Session 3

How Far Do You Walk?

  1. Discuss all the reasons why students walk during a day. Are there days (for example weekends) when they do more, or less, walking? How far do they walk for example coming to school, or during breaks? How could they estimate or measure these distances?
  2. How far then do they walk in a year? Ask for suggestions how they could make an estimate. How accurate do they expect to be? How far do different students think they walk in a year?
  3. Groups discuss and decide on three strategies, complete the Comparison Chart, conduct the investigation, and write up their findings.

Session 4

How Thick Is It?

  1. Pose the problem: How can you measure the thickness of a wall of the classroom (or similar) when you cannot reach both sides of the wall at the same time. Ask for suggestions. How accurate an answer do they need?
  2. Groups discuss and decide on three strategies, complete the Comparison Chart, conduct the investigation, and write up their findings.

Session 5

Groups display or present orally the results of each investigation in turn. What were the findings? Were they fairly consistent with each other or not? What are the reasons for this? What unexpected difficulties did they find? How did they resolve them?

Alternately, you may prefer to reporting and discussion to take place at the end of each investigation.

Attachments

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