Baker's dozen
The purpose of this activity is to engage students in generalising the difference between two sequential counting numbers, in context.
This activity assumes the students have experience in the following areas:
- Counting forwards and backwards in ones from any number.
- Copying and continuing simple number patterns.
- Partitioning and regrouping numbers to make calculation efficient.
- Finding differences between whole numbers by counting up or partitioning.
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.
A bag of one dozen donuts has 12 donuts in it.
If the bag is labelled ‘a baker’s dozen’ then it has 13 in it.
Explain the difference between a dozen and a baker’s dozen.
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 what I need to do?
- Do I understand the meaning of the words? (The words ‘difference’ and ‘dozen’ may need explanation.)
- Can I express the problem in another way? (How many more are in a packet of 13 donuts than are in a packet of 12 donuts?)
- What maths will be useful to solve this problem?
- What will an answer look like? (The answer will be a number.)
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 strategies will be useful to solve a problem like this? (Drawing a diagram, making a physical model, and writing numbers in sequence are all useful.)
- What numbers and operations will I use? How might I record those operations? (Differences can be found by subtraction but young students are most likely to count on.)
- 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.
- How will I represent the number of donuts in packets of 12 and 13?
- Is there a pattern? Can I use the pattern to find the difference? How?
- How can I express my solution using diagrams, numbers, and words?
- Have I used the most efficient way 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?
- Could I use my strategy to solve more difficult difference problems?
- Can I make up and solve my own difference problems with donuts?
Examples of work
Work sample 1
The student use images and/or objects to find the difference between packs of 12 and 13 donuts.
Click on the image to enlarge it. Click again to close. 
Work sample 2
The student uses number sequence words and symbols to establish the difference between 12 and 13.
Click on the image to enlarge it. Click again to close. 