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## 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

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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 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

www.kobayaashi.co.uk

Set 5 Puzzles 41 –

Calculation puzzles

Set 2 Puzzles 11 –

Set 3 Puzzles 21 –

Set 4 Puzzles 31 –

Set 5 Puzzles 41 –

Multiplication square grid puzzles

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

Multiplication Puzzles 1 - 10

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

Number Challenges 1 - 10

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