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.

 

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…

 

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

www.kobayaashi.co.uk

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.

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

months, so please revisit.

Number Challenges 1 - 10

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.

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…

 

  • 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.

 

Finding all possibilities

Abacus make three digit numbers.pdf

Buttons.pdf

Digit cards greater than 500.pdf

Prime numbers.pdf

Roll two dice.pdf

Stamps.pdf

Logic Problems

NNS Logic problems.pdf

Fifteen digit cards.pdf

Panda, dog & cat pan balance.pdf

Picture playing cards.pdf

Rabbits pan balance problem.pdf

Squares & circles pan balance.pdf

Three egg baskets.pdf

​​

Finding rules and patterns

Birthday presents.pdf

Dominoes make 7 small squares.pdf

Dominoes Make 100.pdf

Make 100.pdf

Twenty divided into six.pdf

Two-digit numbers.pdf

 

Visual and diagram problems

Birthday cake.pdf

How many squares.pdf

Join the dots print version 2.pdf

Matchstick squares.pdf

Six counters.pdf

Straw squares.pdf

Word problems

Cans of soup.pdf

CD collection.pdf

Egg boxes.pdf

Game.pdf

Reading book.pdf

Sweets.pdf

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)

Click on the image below to open up a pdf version of the problem, possible way to solve and solution.

stacking coloured cubes.png
five squares.png
six counters.png
find the difference.png
towers of coloured cubes.png
spotty_puzzle.png
my_mystery_number.png
domino_lineup.png
domino_addition_square.png
shape_calculation.png

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.

 

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