The purpose of this activity is to engage students in applying their number knowledge and strategies to solve a problem.
This activity assumes the students have experience in the following areas:
- Applying the place value of whole numbers to 4 digits.
- Adding and subtracting whole numbers using mental, pencil and paper, and digital strategies.
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.
During a cricket match, the commentator announced the there were 7542 people at the grounds.
Only 7281 tickets had been sold.
How many people (players, officials and workers) were at the match without a ticket? Show your working.
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 need to recognise that the difference between the larger and smaller numbers of people is required.)
- What do I know about the two numbers that might be helpful?
- What will my solution look like? (The solution will be the number of non-ticketed people, and calculations that show how the number was found.)
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 math skills will I need to solve the problem? (Note that differences can be found by adding on or subtracting.)
- What strategies will be useful to solve a problem like this? (Place value tables might be useful though some students may choose to represent the place values diagrammatically.)
- Do I have a sense of how big the answer can and cannot be? What is a reasonable estimate?
- 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.
- Have I shown my workings in a step-by-step, systematic way?
- Have I looked for efficient ways to find the difference?
- Have I tried different strategies? Did I get the same answer?
- How could I check my answer is correct?
- How do my results look different or different to others? Why could this be?
- Do others have better ways to solve the problem?
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.
- Is my working clear for someone else to follow?
- How would I convince someone else I am correct? Can I justify what I did?
- Is my strategy the most efficient way to solve the problem? What strategy works best? Why?
- Would my strategy work in a different situation? What kind of situation is this problem about?
- Is there some mathematics I need to learn or practise to solve similar problems?
- What have I noticed that seems to work all the time in these types of problem?
Examples of work
Work sample 1
The student solves a difference problem with 3-digit numbers by adding in parts from the smallest to largest number.
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Work sample 2
The student solves a difference problem with 3-digit numbers by subtraction, using strategies such as rounding and compensating.
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