The Mathsquad Skill Problem Solving Resources aim to improve students’ ability to engage with unfamiliar problems. There are three collections of problems designed to be used over each of the first three terms. It is suggested that in Term 4, once students’ problem solving skills have been developed, teachers make use of past NAPLAN questions. Sets of past NAPLAN papers can be found here.
Term 1: Mathematical Puzzles
Term 2: Building a Problem Solving Toolbox
Term 3: Mixed Worded Questions
Why teachers will love the Mathsquad Problem Solving Resources…
- Resources are pre-made and freely available
- Problems get more difficult over time to allow for students’ improved skill level
- Problems highlight the creative and fun side of mathematics
- All problems have full solutions available
Why students will love the Mathsquad Problem Solving Resources…
- Problems are highly engaging and interesting
- Problems have a low entry and high exit point making them appropriately challenging for a range of students
- Experience solving problems and seeing solutions will improve students’ ability to solve solve worded questions in assessments and use maths more comfortably in their daily lives.
Accessing the Problem Solving Resources
All student resources, including problem solving resources, are available free of charge to mathsquad members. Membership is also free and sign up is simple. Sign up by clicking here and access the problem solving files by clicking on the download icon on the homepage and selecting the problem solving bundle.
Q. What is the general structure of the Mathematical Puzzle resources?
A. Click here for a sample puzzle page.
Q. What types of problem solving tools are included in the Problem Solving Toolbox lessons?
A. Drawing a diagram/acting it out, working systematically, finding a pattern, solve a simpler problem, use algebra.
Q. What is the structure of the Problem Solving Toolbox resources?
A. There are 5 different problem solving strategies within the booklet and each is covered over 2 weeks. The first week focuses on a collection of worded problems that can be solved using the particular strategy and the second week is a whole class open ended problem using the same strategy. The open ended problems will each be carried out in a slightly different way though for each worded question lesson it is recommended that you print out a copy of the worded questions one per student (or make them available as a PDF to be accessed electronically). It is also recommended that you begin by writing the target strategy on the board (eg. “Drawing a diagram / acting it out”) and then explain what the strategy means using examples where appropriate.
Q. What is the general structure of the worded questions within the Problem Solving Toolbox lessons?
A. Click here for a sample worded question page.
Q. What is the general structure of the open ended questions within the Problem Solving Toolbox lessons?
A. Click here for a sample open ended question page.
Q. What is the structure of sheets within the Mixed Worded Questions set?
A. Click here to see a sample selection of problems.
Q. Are solutions available?
A. Yes, however they are password protected to stop students accessing them. Click here for information on accessing the mathsquad password.
Q. I’ve already used past NAPLAN papers earlier in the year. Are there other good sets of problem solving questions?
A. Yes, click here for an excellent set of problem solving questions and click here if you’d like to see the solutions.
Q. Is there a general lesson structure you’d recommend when working through these types of application problems?
A. I think it is important that students should have the opportunity to work on application questions both independently and collaboratively. In general, I’d recommend the following structure, though timing will often need to be adjusted as it will be dependent on the task and the group of students you are working with.
- Whole class introduction of the task and once you feel the students know what to do set them off to work on the task independently.
- Give students approximately 10 minutes to work independently on the problem(s). If there are some students who are likely to find this difficult, pop by their desk to give hints or provide partial solutions to get them started.
- Give students the opportunity to work with others for a further 10 minutes. During this time look at students’ work and decide which solutions you’ll talk through with the class.
- Give students 5 minutes to write up a neat solution to one (or more) of the problems.
- If projecting students’ work is an option (maybe photographing their work and emailing it to yourself) then show some solutions and explain what makes the solution interesting or effective. If this is not an option take some time during the previous step to write up some of the students’ solutions on the whiteboard. I’d recommend that you celebrate the student who’s work it is though not have them explain their work. As the teacher you are more equipped in identifying important aspects to share with the class and also how to best communicate these ideas. That said, asking the student(s) to contribute occasionally would have positive effects on students’ confidence and feeling of being valued. It is highly recommended that you do not have students come to the board and write up their solution in front of the class. This is time consuming and little learning occurs during this process.
- Conclude the lesson by inviting the students to continue working on these problems in their own time and to submit a refined solution if they wish.
Q. Do you have any tips for helping students work effectively in a collaborative environment?
A. Setting up (and continually reinforcing) some group work protocols is going to essential. Some sample protocols are below:
- Talk one at a time
- Contribute in a meaningful way
- Listen actively
- Challenge respectfully
- Share responsibility
- Rushing through a task or question
- Being a passenger
- Seeking teacher help too early
Q. How can I maximise the likeliness that all learners contribute?
A. The below strategies could be helpful.
- Make it clear that you will ask anybody from the group to share the group’s ideas
- Ask students in the group to each use a different coloured pen so you can see how each person is contributing
- Reinforce positive behaviours in the group e.g. “I like the way Sabine is extending the ideas that Brent shared with their group”
Q. As students are working, what should the teacher be doing?
A. As students work on the task it is recommended that you:
- Ask questions requiring students to describe, explain, interpret and convince
- Avoid definitive statements, instead provide prompts for further thinking
- Don’t do the thinking for the learners, if there is something you want completed in a specific way be specific
- Give chances for groups to share ideas with other groups, an idea swap, invitations to write on the board or market place lesson.
The following phrases may also be useful:
- What have you tried so far? What was helpful?
- Can you estimate the answer?
- What information do you think you’ll need to use first?
- What makes you say that? Can you give an example?