The purpose of this activity is to engage students in using standard measuring tools in a non-standard manner.
This activity assumes the students have experience in the following areas:
- Recalling basic addition and subtraction facts.
- Working with metric units of length, especially metres, centimetres, and millimetres.
- Converting between centimetres (cm) and millimetres (mm).
- Using a ruler to measure length and distance.
- Adding and subtracting decimals to 1 decimal place, e.g., 4.3 + 12.8 = 17.1.
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
How long is this piece of string?
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Make sense
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
- Do I understand the situation and the words? (Students may need support to recognise that the string is aligned with the 1.2 cm mark on the ruler, not on zero.)
- What are the important words and symbols? (Students may need support with understanding the meaning of cm and mm, and the relative size of the units.)
- What will my solution look like? (The solution will be a measure expressed in either centimetres, millimetres, or a combination of both units.)
Plan approach
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
- What strategy might I use to solve this problem? (Acting out with a real ruler, drawing a diagram, and using equations are potentially useful strategies.)
- What makes the problem tricky? (Students should note that one end of the string is not aligning with zero on the rule. Students might also suggest that sometimes string is not straight.)
- What are the maths skills I need to work this out?
- Can I estimate how long the string is before I measure it?
- What tools (digital or physical) could help my investigation?
Take action
Allow students time to work through their strategy and find a solution to the problem.
- Is my strategy working? Does it give me a sensible answer?
- Does my answer seem correct? Is it close to my estimation?
- How could I make sure that I haven’t missed anything?
- How do my results look the same or different to others? Why could this be? (Students might use different units to represent the length of string.)
- Is there another possible answer or way to solve it that might be more efficient?
Convince yourself and others
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
- What is the solution?
- Is my working clear for someone else to follow?
- How would I convince someone else I am correct?
- What could I find out next?
- Is there some mathematics that I need to learn from this problem?
Examples of work
Work sample 1
The student recognises one end of the string is not on zero, makes an equal length, and measures the length of it on a ruler by aligning one end with one.
Click on the image to enlarge it. Click again to close. 
Work sample 2
The student counts units of one millimetre from the start of the string. They organise the units into parts, 8 millimetres, 10 millimetres, and 6 millimetres. By adding millimetres and converting 10 millimetres to 1 centimetre they express the length of the string as 2 cm and 4 mm.
Click on the image to enlarge it. Click again to close. 
