Problem Solving: This Problem Solving Bundle contains 13 Beautiful Problems to solve in the form of A4 posters, task cards, black line versions and a PowerPoint file for easy display and discussion. The puzzles are great for Math Walls, Bulletin Boards, for 'early finishers', homework etc,etc.
The 13 tried and true puzzles included in this problem solving pack are great for all kinds of learners. They have been selected for their ability to engage students, promote discussion and encourage the practice of solving problem skills.
* 13 color A4 poster size puzzles
* 1 PowerPoint with ALL the Puzzles
* Two 1/2 sized color versions of each puzzle for small group work
* Two 1/2 sized line versions of each puzzle.
(Check out the PREVIEW to get a good look)
These puzzles are ideal for group work, as a challenge for early finishers, as a way to add an extra dimension to homework or as a wall display that’s focused on problem solving skills.
You’ll find more than enough puzzles here to introduce one problem solving task per week for a whole term!
Reasons for Puzzles:
Teaching problem solving skills is more than something that’s just for the moment, just for the classroom. This kind of abstract thinking is so much more!
As a teacher, I’ve been collecting problem solving activities since the earliest days of my teaching career. They were scribbled down in old notebooks and on bits of scrap paper,tucked away to help future students. Why?
* Abstract problem solving
* Real world problem solving
* Future thinking
This download is a collection public domain puzzles I have found that work really well with students. I have presented the puzzles so they are colorful, bright, easily interpreted, child friendly, printable and ready for classroom use.
About Problem Solving:
Throughout history mathematicians have dedicated their lives to solving problems. They have spent countless hours alone in quiet reflection exploring solutions and assembling groups of like minded people to answer their questions.
These meetings of the minds included those members of the group going through this incredibly rich and complex process in which they share, discuss, argue, prove, disprove, refine, fight, hypothesise, expand, learn new things, consider new possibilities, draw correlations, encourage different ways of looking at a problem, refine ideas, support, inspire, offer encouragement, draw diagrams, discard diagrams that don't give a solution, justify, test, hypothesise, critique, joke, help each other through the tough times, commiserate failed attempts and celebrate successes. And they NEVER, EVER, EVER turned to the answers at the back of the book :) What’s the best part? It can all happen with your students too!
Why No Answer Sheet?
When it comes to Math teaching there’s something to be said for idealism.
Math is a vast field of human endeavor filled with problems to be solved and patterns to find. These activities are designed to have students work mathematically. Real Math is not a collection of exercises on a page where all the information needed is in the question and the numbers only need to be 'massaged' until your answer is the same as the one in the back of the book. These puzzles are 'hard fun'. They are designed to promote engagement with problem solving and authentic discussion around finding the best solution.
My other reason for not including the answers is so as to not deprive students of the 'A-ha' moment. That feeling of working on something, persevering, getting frustrated, wanting to make the puzzle fly, walking away, coming back with fresh eyes and eventually... the sense of satisfaction when you get when you solve it. It is the moment of insight where, for the briefest of time, all the pieces fall into place and you realize you've got it. Some call it the Eureka Moment. The reward is in the discovery, and discovery is more likely to happen if you are not tempted to turn to the answers at the back of the book.
Thirdly, despite popular misconception, teachers are not the fountain of all knowledge. I have always had no problem admitting I don't know the answer but have all the skills to work it out. It is important to demonstrate this.
So when a student comes and pleads with you to give them the answer just say, 'Who am I to deprive you of the Ah-ha Moment?' hehehe
A Possible Process
Over the years I have tried many ways to introduce problems and this process works very well. Feel free to try it out.
Stage 1 - Introduce the Problem
Choose a puzzle from the set, project the electronic version onto a large screen and explain the basic parameters of the problem. Encourage students to clarify the parts of the task they are unsure of then set them free to find a solution.
Stage 2 - Work Like a Mathematician - (Think - Pair - Square)
The students spend 10 to 15 minutes working quietly on their own seeking to find a solution to the puzzle. You will need to gauge the mood of the group as to how long the students work this way. You may find the natives get a little restless. (Think)
Next, the students join with a partner to share and discuss their findings. (Pair)
Students then form groups of four to share and discuss their findings. (Square)
Stage 3 - Share Findings with the Mathematics Community
Turn the electronic version of the puzzle back on and have students from each group elect a member of their group to share and explain their findings. Seize and discuss any teachable moments as they arise.
Stage 4 - Put it Out There
In the world of Mathematics, once an answer is discovered, a group of experts check the answer for accuracy and publish it for all mathematicians and interested people to see.
Mathematicians all over the world can then check the theory and proof to make sure everything 'adds up'. They can learn from the workings, study the methods used, think about the findings and work out ways to improve upon the answer. Some mathematicians even use the new discovery in a way to advance their own work.
Create a wall display, partner with other teachers, seek opportunities to put it on the web. Find creative ways to publish your findings!
Stage 5 - Make a Class Book
Once the term is over put all the puzzles into a loose leaf folder and add it to the class library. Over the years you’ll find that these books become some of the most loved and borrowed.
Creating Problem Seekers:
The other hope I have for these puzzles is that they might light a small flame in the minds of some students and teachers so they go on to become problem seekers - i.e. people who actively seek out problems and dedicate their time to solve.
The one thing we can be sure of is that people will face all sorts problems in their day to day lives and will continue to do so throughout their lifetime. We cannot be certain of the nature of many of the problems they will face so it is important to equip students with skills that are transportable over time and place. These puzzles help with logical and systematic thinking, perseverance, observation and analysis. They will help to create problem seekers!
Taking it Further:
After several weeks of exploring this type of puzzle, students must find a similar type of puzzle to challenge their classmates. I set the parameter, 'The teacher most likely hasn't seen'. I then show possible search terms to use in Google as well as how to do a site:edu or file:pdf search. This way not all students come in with a puzzle from the first page of Google or Pinterest.
Last Thoughts (for now)
Puzzles teach flexibility, the ability to stick with a problem, perseverance, logical thinking and they increase the frustration barrier. After using puzzles like these, you’ll observe students taking on new ideas and molding their ideas in the face of new evidence.
The other great thing about these puzzles is that it’s often the students who don’t naturally succeed in standard classroom activities are suddenly masters of these! They are natural puzzle seekers.
Math is the science of patterns and puzzles can ignite a passion for those patterns.
“Go forth and seek problems to solve!”