PROBLEM SOLVING & REASONING
"Problem solving is the cornerstone of school mathematics. Without the ability to solve problems, the usefulness and power of mathematical ideas, knowledge and skills are severely limited. Students who can efficiently and accurately multiply but who cannot identify situations that call for multiplication are not well prepared. Students who can both develop and carry out a plan to solve a mathematical problem are exhibiting knowledge that is much deeper and more useful than simply carrying out a computation. Unless children can solve problems, the facts, concepts and procedures they know are of little use.
The goal of school mathematics should be for all students to become increasingly able and willing to engage with and solve problems.
Problem solving is also important because it can serve as a vehicle for learning new mathematical ideas and skills."
Schroeder and Lester 1989
New content has been added, please scroll down this page to find the number based problems
Copies of the 2016, 17, 18 and 19 SATs papers can be found in the Mathematical Publications Archive on this website. Click here to jump to the Mathematical Publications Archive
Problem solving can be divided into five types….
Finding all possibilities
Logic problems
Finding rules and describing patterns
Visual and diagram problems
Word problem
It is important to give children a balance of these problems.
Problem solving strategies include…
Working systematically
Sorting
Classifying information
Reasoning
Predicting
Testing hypotheses
Evaluating solutions
Working backwards
Using smaller numbers to find and establish a pattern
Making lists or tables
Drawing pictures
Using some classroom equipment to help
Trial and improvement
Using a tree diagram
Bar modelling
Working backwards
Able pupils often need support in developing skills to communicate their thinking, methods and solutions.
Here are some useful using and applying activities for you to try. They have all been tried and tested with children and teachers. Please note that some problems will fit into more that one category.
Suko puzzles published here with kind permission from Jai Kobayaashi Gomer:
Kobayaashi Studios www.kobayaashi.co.uk
Set 1 Puzzles 1 – 10 Click here to download
Set 2 Puzzles 11 – 20
Set 3 Puzzles 21 – 30
Set 4 Puzzles 31 – 40
Set 5 Puzzles 41 – 50
Sujiko puzzles pulished here with kind permission from
Jai Kobayaashi Gomer:Kobayaashi Studios
Set 1 Puzzles 1 – 10 Click here to download
Set 2 Puzzles 11 – 20 Click here to download
Set 3 Puzzles 21 – 30 Click here to download
Set 5 Puzzles 41 –
Calculation puzzles
Set 1 Puzzles 1 – 10 Click here to download
Set 2 Puzzles 11 –
Set 3 Puzzles 21 –
Set 4 Puzzles 31 –
Set 5 Puzzles 41 –
Multiplication square grid puzzles
Set 1 Puzzles 1 – 10 Click here to download
Set 2 Puzzles 11 –
Set 3 Puzzles 21 –
Set 4 Puzzles 31 –
Set 5 Puzzles 41 –
Yohaku puzzles
I found these YOHAKU puzzles online and in late 2017 I started
to introduce them to teachers starting with the international
teachers on our annual Asia maths tour in 2018 (check out
the courses and international pages for information about
our annual maths tour). There are a couple of small books
of puzzles and their solutions, available on Amazon for
approximately £3 each. Also check out the YOHAKU twitter
page here @yohakupuzzle and website here www.yohaku.ca
Multiplication Puzzles
Here are some missing number multiplication puzzles.
In the zipped folder you will find two PowerPoints, black line
masters and a pdf document of the PowerPoint Presentation.
There will be more puzzles to follow over the next few
months, so please revisit.
Number Challenges
Here are some number challenges written in PowerPoint.
There are two versions of PowerPoint in the zipped folder.
There will be more challenges to follow over the next few
months, so please revisit.
Click on the image below to open up a pdf version of the problem, possible way to solve and solution.
Bar modelling
Many thanks to Cassy Turner who has allowed me to convert her bar modelling videos from her Word Problem Wednesday into PowerPoint presentations.
Word problem Wednesday is available on her website www.singaporemathsource.com
These are available here as PowerPoints (pptx) or pdf downloads.
NNS Homework Activities
Here are some pdf copies of the old National Numeracy Strategy homework book.
Apologies in advance, as the quality isn’t great, but you can still use the ideas and activities.
Click on the linked text to open a pdf copy.