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 and 18 SATs papers can be found in the Mathematical Publications Archive on this website. Click here to jump to the Mathematical Publications Archive.
New content for 2019
Here are some number based puzzles for primary children to solve.
There are currently four types of puzzles.
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Suko puzzles
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Sujiko puzzles
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Calculation puzzles
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Multiplication number grid puzzles
In each of the puzzle downloads you will find the following contents.
A PowerPoint presentation written in PowerPoint presentation (*.pptx) and PowerPoint 97 – 2003 (*.ppt) which includes:
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A how to use page
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Suggestions about on how to give easy to slightly harder clues, so that young children can solve the puzzles (Sujiko only)
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Ten puzzles, one per page and their answers, one per page
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A 12 page PDF file which is a copy of the PowerPoint presentation, where you can view two slides per page.
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Black line masters
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5 PDF copies of the puzzles, two puzzles per page to copy and give to children.
Suko puzzles published here with kind permission from Jai Kobayaashi Gomer:
Kobayaashi Studios
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
Sudoko
Are available everywhere. If you want a selection of easy colour based (not number based puzzles) then go to the ATM website and check out a book called
“It Makes You Think!” Check out the ATM shop page via the
ATM site by clicking here www.atm.org.uk
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.
Problem solving can be divided into five types….
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Finding all possibilities
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Logic problems
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Finding rules and describing patterns
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Visual and diagram problems
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Word problem
It is important to give children a balance of these problems.
Click here to download a useful sheet outlining the skills and strategies for each of the problem solving types. pdf file (115kb)
Problem solving strategies include…
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Working systematically
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Sorting
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Classifying information
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Reasoning
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Predicting
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Testing hypotheses
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Evaluating solutions
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Working backwards
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Using smaller numbers to find and establish a pattern
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Making lists or tables
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Drawing pictures
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Using some classroom equipment to help
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Trial and improvement
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Using a tree diagram
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Bar modelling
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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.
Finding all possibilities
Abacus make three digit numbers.pdf
Digit cards greater than 500.pdf
Logic Problems
Panda, dog & cat pan balance.pdf
Rabbits pan balance problem.pdf
Squares & circles pan balance.pdf
Finding rules and patterns
Dominoes make 7 small squares.pdf
Visual and diagram problems
Join the dots print version 2.pdf
Word problems
Here are a the NNS PDMs (Professional Development Meetings) documents
Finding rules and describing problems
NNS Finding rules & describing patterns.pdf
Finding all possibilities
NNS Finding all possibilities.pdf
Good Looking Dinosaurs
This is a well tested activity across the UK, British schools overseas
and across all year groups from Year 1 to Year 6. The value of the
dinosaur and multilink pieces means that the act of constructing
of the dinosaur does not take over from the mathematical focus
of the activity. The dinosaurs and the children’s calculations make
a marvelous classroom display.
Please read these instructions before downloading (word doc 381kb)
Good looking dinosaur teacher notes (pdf 51kb)
Good looking dinosaur decimals (pdf 55kb)
Good looking dinosaur fractions (pdf 64kb)
Good looking dinosaur measures (pdf 55kb)
Good looking dinosaur whole numbers (pdf 55kb)
KS 1 problem solving cards, two problems per card.
Apples and purse problem for year 2 (pdf 246kb)
Buttons and Dice (pdf 195kb)
Chocolate and Number square (pdf 238kb)
Difference and Number problem (pdf 225kb)
KS 2 problem solving cards, two problems per card.
Coins 1 and coins 2 (pdf 305kb)
Roly Poly 1 and Roly Poly 2 (pdf 242kb)
Sum and Product and Number (pdf 231kb)
Single sheet problems.
Building arches (pdf 31kb)
Building chimneys (pdf 35kb)
