In this unit we take measurements of ourselves which we store in a time capsule to open and use later in the year.
- Compare the length of two objects.
- Select objects which are about the same length as a given object.
- Order three or more objects by length.
In this unit students use lengths of string to represent the lengths of different parts of the body. This enables them to compare and order different students' heights, arm lengths, etc. The comparisons can be made indirectly by (i) putting the strings representing the same body parts next to each other and (ii) by putting the strings next to the body parts. This should show the advantage of indirect comparisons, especially with regards to such things as waist measurements, which are extremely difficult to compare directly.
Although comparing is at the early stages of the measurement learning framework adults will often measure things without using measurement units.
In mathematics it is often useful to have an estimate of the size of an answer to ensure the accuracy of calculations that have been used. The comparisons of lengths in this unit lay the foundation for estimates in area and volume, and for estimates generally.
This unit is also valuable in cementing the idea of conservation of length. For instance, the string’s length is unchanged no matter where it is in the classroom and no matter how much it is rolled up. It is the conservation property that allows the students, whose height is represented by a given string length, to be tracked down. This has its parallels in real-life detective work.
In comparing three lengths, students implicitly realise the transitive nature of length. Hence if string A is longer than string B and string B is longer than string C, then string A is automatically longer than string C. There is no need to check the lengths of A and C. The difference in length follows from the first two comparisons. This ordering ability is a valuable property of numbers and has many uses throughout mathematics. When it is not present, it causes some difficulties.
- Circles of card
- Envelopes for each student's measuring information
We begin the lesson with a game, which focuses the students on height. We then move to measuring heights using string and finally we order heights. At the end of the week we will put our measuring strings in a time capsule.
- Split the class into 2 groups. Have each group form a line ready to play "shorts". To play, the students from the front of each line stand together and the class decides who is shorter. The shorter student takes the other student back to the end of their group’s line. Repeat the process with the 2 students who are now at the front of the lines.
- We are now going to measure our heights with string.
- Have the students work in pairs to help each other by cutting a piece of string to match their heights. Give them the opportunity to work out how they might do this. (Lying down works well.)
- Thread the string through two holes in a piece of card on which they have drawn a picture of their faces.
- As a whole class activity, get the students to put their strings in order at the front of the class. They can take turns to put their strings in place.
Where are you going to place your string?
Why do you think it goes there?
Who are you taller/shorter than?
Who is the tallest?
Who is the shortest?
Who is about the same height as (name)?
In the following days the students can take other measurements of themselves using measuring strings. The strings can be labelled and compared at the end of each day, with either the whole class or smaller groups. These could be left on display. At the end of the week these measurements can be placed in the time capsule (shoebox).
Body parts that can be measured and labelled include
- length of smallest finger
- length of hair
You could also spend a day exploring the following questions, which require the students to make comparisons between their own measurements. Students could make estimating before measuring.
- Which is longer – your hand or your foot?
- Which is longer – around your wrist or around your ankle?
- Which is shorter – around your head or the length of your food?
- Find measurements that are close to being the same
Strings can also be used to create a graph. Ask students to measure a particular body part such as their right foot and then glue the strings vertically along an x axis. This creates an instant graph of everyone's foot size.
- On the fifth day, you search for the mystery student. The students try to find who belongs to two particular string lengths. In preparation, you will need to cut two lots of string for all the class. These strings represent the height, and another body measurement, of one of the students in the class.
- Give each student the two lengths of string. Ask them to decide what parts of the body the two lengths represent.
- Discuss the two lengths and come to a decision to which parts of the body they represent.
- Now tell the students that they have to find the student whose body lengths are represented by the string. (They can do this by comparing string lengths with different students' heights, etc or by comparing string lengths with string lengths on display in the classroom.)
- The students report to you when they think they know to whom the string belongs. (For those students who finish early you might ask them to see if any other student has the same dimensions.)
- Conclude the week’s activity by giving students an envelope to store their pieces of string. Put the envelopes into a "Time Capsule" to be opened later in the year. The students can then make comparisons with changes in their own body measurements.