KS3 Problems

KS2 - Problem Solving  Tasks - Click here        Solutions KS4 Problems
KS2 - Problems suitable for a Maths Fair - Click here Contextual Problems

I have a rectangle with an area of 200cm2

I make the length 20% longer and the width 20% shorter

What is the new area?


Assessing Problem Solving:               

Using and Applying Grid          
Mathematical 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 

Figure This Challenges for Families Set 1           Set 2           Set 3         Set 4

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

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

Superb Blog with lots of tried and tested ideas - Click here

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

A lovely set of short problems with an indication of difficulty - Click here

A useful collection of articles on the topic of rich tasks in mathematics. If you are new to rich tasks then we suggest that you begin by:

What do you notice and What are you wondering? -  Video Clip

Simply stated problems - ideal for starters: www.figurethis.org/index.html

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 tachers 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


Sets of 10 related Problems
These PowerPoints comprise sets of related problems which are designed to allow for a cohort or a 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

Maths Challenges from www.mathschallenge.net       1 Star Problems           2 Star problems         3 Star Problems       4 Star Problems
Problems presented as lovely Posters - Click here

A Teachers website with a wide range of investigations for Year 7 - Click here

Article and Problems involving Harmonic Mean such as Bill takes 6 hours to complete a task and Bob takes 5, how long does it take for them if they work together? - Click here

OCR Problem Solving Guide
An excellent guide to problem solving - Click here

A great website covering a wide range of puzzles - Click here

These problems have been used with Key Stage 3 pupils although many of them have also been used with Gifted Pupils in Years 6 and 7.

The mathematical ability needed ranges from Level 5 to Level 7

Problem 1   Number Based Problems
Problem 2 Coloring Problems 
Problem 3 Number Based Problems
Problem 4 Isaac Newton Research
Problem 5 Buying Flowers costing 100
Problem 6 Champion Dice
Problem 7 Pond Borders Investigation  
Problem 8 Max Box - PowerPoint Presentation
Problem 9 Soma Cube - Puzzle - Nets
Problem 10 Several short slightly harder problems 
30 Problems Teacher

Pupil Problems
Pentominoes 1 pdf
Pentominoes 2 pdf
A range of problems all using the 12 shapes that can be formed from 5 squares, commonly known as pentominoes
ilovemathsgames Series of short puzzles, starters and games
Shape Investigation A series of problems involving arrangements and counting numbers of shapes or outcomes
Dominoes Various number problems using a set of dominoes
Nrich  The NRICH site allows you to explore problems by selecting a topic and level of difficulty.
www.nzmaths.co.uk Graded topic related problems with guidance
www.mathforum.com/pow/ Mixture of problems
Galileo Educational Problems suitable for a Maths Fair

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