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Problem Solving

KS2 - Problem Solving  Tasks - Click here        Solutions KS2 - Problems suitable for a Maths Fair - Click here
Questioning Skills - Click here KS2-4 Games and Logic Problems - Click here


This blog by @LeanneShawAHS  provides an extensive list of websites with problem solving resources  - Click here

Problem solving must be more than routine exercises. It cannot be viewed as an "add on" to classroom instruction but rather an important goal. Problem solving should be viewed as a means to mathematical understanding as well as a set of procedures. Engaging students in problem-centered learning will allow students to see connections within and between content areas. Students will develop the ability to employ and select appropriateness of a variety of strategies for designing solutions. Problem-centered learning creates a model where the student becomes the thinker and is engaged in a self-directed search for solutions.

Students must experience problems where flexible use of knowledge is required. Directed and focused questions must challenge students to select from a variety of strategies. Students need to analyze problems, determine what information is needed to solve them, and design solutions. Appropriate tasks should engage all students and provide opportunities for extensions that encourage students to go beyond minimum expectations. The teacher becomes a tutor or coach who facilitates the students' investigations.

The Problem Centered Classroom

A brief discussion on the merits and running of a problem centered classroom - Click here

Strategies

The Mathematical Association of America have pulled together 10 Problem Solving Strategies, which includes an Essay combined with Video examples and ideas to use in the classroom 


10 Strategies With Examples

  • #1 Engage in Successful Flailing
  • #2 Do Something
  • #3 Engage in Wishful Thinking
  • #4 Draw a Picture
  • #5 Solve a Smaller Version of the Same Problem
  • #6 Eliminate Incorrect Choices
  • #7 Perseverance is Key
  • #8 Second-Guess the Author
  • #9 Avoid Hard Work
  • #10 Go to Extremes
  • Click here

Problem Solving Strategies with examples of 6 problems each requiring a different approach - Click here

Mathematical Problem Solving Strategies: This web site contains a collection of problems, with solutions and strategies, laid out in a systematically manner to assist students / teachers with problem solving - Click here 

If you are interested in the different approaches to Problem Solving then I suggest that you take a look at this website put together by John Malouff which provides an analysis of 50 strategies.  50 Strategies
 

KS3-4 Problem Solving Resources

This free ebook from @m4thsdotcom has 16 lessons worth of problems, which require some thought and which provide a structure for a teacher to help enable their students to tackle problems independently and to think like a mathematician - Non of the problems require Higher level GCSE content - Click here

Problem Solving Strategies with examples of 6 problems each requiring a different approach - Click here

Some Maths Puzzles such as Bridge Crossing, Tower of Hanoi and many others - Click here

Assessing Problem Solving:               

Using and Applying Grid          
pMathematical Processes and Applications (MPA) Teacher Version  
MPA NC Levels included Pupil Version 1       
MPA NC Levels included Pupil Version 2

Assessment Rubrics for Problem Solving Activities:
My pdf Version     docx Version   
A very simple rubric by A Stradel - Click here
Wheel Version        
Thermometer Version        
Jigsaw Version for Younger Pupils 

Displays

NRICH produce a monthly colour poster which can be downloaded for free from the link below, you can also buy them in a larger format, please note the PowerPoint which can be downloaded from here with all the posters on - Click here

Maths Challenge Problems presented as lovely Posters - Click here
 

Great Place to Start

Require students to pose and regulate their own problem solving using these resources from Inquiry Maths - Click here

Supporting Problem Solving in Algebraic Context - Click here                
For an alternative approach using PowerPoint - Click here

Some great Problem Solving resources where Maths is placed in a 'Real Life' context, these include Bowland, Cre8ate and Nuffield Resources - Click here

GAIM materials from 1990's which was a scheme which actively encouraged teaching and learning through practical problem solving and investigations now available free - Click here

AQA 90 Problems: A superb document listing 90 problems which have been categorised by difficulty, approach and topic, which has the aim of providing a resource that enables teachers to prepare students for open, less structured problems.    For access to the 90 problems - Click here         For a commentary on 30 of the problems - Click here

OCR Problems: An excellent guide to problem solving - Click here

"if it is problem solving you are interested in I think we can help.
As a starting point you could try stealing ideas from our Task Cameos - Click here
You will find over 60 investigations here which can be used either for a pair of students - photos in each cameo show you that form - or as a whole class investigation. "Doug Williams"

 

The Liverpool Mathematical Society have produced a CDRom which comprises 250 mathematics puzzles designed for pupils from top juniors to upper sixth form arranged in ten boxes of 25 puzzles. Click here for more details

Sets of 10 related Problems
These PowerPoints comprise sets of related problems which are designed to allow for a setted or mixed ability group to tackle similar problems.  The problems begin with the easiest and become more difficult as you progress through the PowerPoint.
 

Task Title Content NC Levels   Task Title Content NC Levels
Click here to DOWNLOAD ALL THE FILES in a zipped folder (Select right click and save as)
Number Tasks   Number - Algebra Tasks
Bunch of Pens Money 3-7   3Rex Straight Lines plus 5-7
NumProps Number Properties 4-7   Magic Magic Squares 3-8
Seesaw Percentages 3-8   Number Grid nth term & (n+2)(n+4) 5-8
Side by Side Fractions & Percentages 4-7   Flowing Numbers Equations 4-Exp
Digits Place Value 3-6   Towerism Simultaneous Equations 4-8
Dice Ordering Numbers 3-6   Consecutive Consecutive Numbers 4-Exp
Bouncy Percentages 5-7   Lines Straight Lines 6-Exp
Fraction Patterns Fractions of Shapes 3-6   Line Up Sequences 3-7
Fruit Fraction Calculations 3-6   Quad Form Quadratics 8
Moussey Unitary Method 4-6   Pyramids Adding Numbers & Expressions 3-6
Paint Ratios 6-7   Shape Tasks
Squares Square Numbers 4-8   Points Properties of Shapes 4-7
Data Tasks   Surfaces Surface Ares 8-Exp
Mean Street Averages 4-6   Bugs Eye Perimeter 4-7
DGame Fair Probability Games 3-8   Pinboard Angles and Shapes 3-8
Mad Bags Probability 5-8   Mixed Tasks
        Mazy Problems on a 4 by 4 Grid 4-7

This set of 8 booklets comprise short questions which I have nominally assigned a National Curriculum Level, not in terms of pure content but in terms of problem solving skills.

Booklet 1 - Level 5- Booklet 2 - Level 5 Booklet 3 - Level 6 Booklet 4 - Level 6
Booklet 5 - Level 7 Booklet 6 - Level 8 Booklet 7 - Level 9 Booklet 8 - Level 10

 

Mix of Problem Solving Tasks - Click here


Problem Solving Websites

Maths Challenges from www.mathschallenge.net       1 Star Problems           2 Star problems         3 Star Problems       4 Star Problems

The Further Maths Support Programme have put together 20 varied problems with Teacher Prompts and worked Solutions - Click here     Dropbox Folder

Problems suitable for a Maths Fair - Galileo Educational

A+ Click Superb site with a wide range of categorised and levelled problems - Click here

NRICH - Must be one of the first you look at - Click here

180 Problems to encourage discussion with more able pupils - Click here

Simply stated problems - ideal for starters - Click here

KS5 Problems

Random Selection of Problems from the Senior Maths Challenge - Click here

www.risps.co.uk
Imaginative ideas to explore A level Core Mathematics topics