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

 

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
straws.png
coded_times_table_problem.png
calc_grid.png
digit_card_subtraction.png
Adding up to 200.png
Greater than 500.png
Tangram squares.png
digit_card_calc.png
digit_card_addition.png
twenty_divided_into_6.png
square_numbers.png
Bucket and beanbags.png
Join the dots.png
Roberta and Rodney.png
Pick three cards to make 12.png
Birthday presents.png
4 x 4 square puzzle.JPG
Number patterns.png
Bow tie number puzzle.JPG
Use only cards 4, 5, 6.png
Squares.png
Three cats.png
Rockets.png
Eight Triangles.png
Writing numbers from 300 to 400.JPG
Jumpers.png
Number square missing corner.png
Numbered triangles.png
Between 30 and 40.png
Sides total 12.png
Number stars.png
Sum and product.png
Prime numbers.png
Make 25.png
Five cards.png
Consecutive numbers.png
Can you find the odd one out.png
Three rings of 15.png
Three digit calculations.png
Mystery cards.png
H shaped puzzle.png
Snowflake shaped puzzle.png
Cross arrangement.png
Birthday cake.png
Half a shape.png
Four cubes.png
Fruit.png
Writing down numbers.png
Make 11.png
10 pound note.png
Lollies.png
Coloured Cube.png
stickers.png
Change.png
Number problem.png
stamps.png
bricks.png
Multiplication problems.png
Maths puzzle.png
Three rabbits.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.

 

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.

  1. Pick two (Year 1)

  2. Play pasta (Year 1)

  3. Coin challenge (Year 2)

  4. Four pin bowling (Year 2)

  5. Stick square (Year 3)

  6. Take ten cards (Year 3)

  7. Heads and tails (Year 3)

  8. At the sales (Year 3)

  9. Magic square (Year 4)

  10. Odds and evens (Year 4)

  11. Emma’s Jelly Babies (Year 5)

  12. Time for TV (Year 5)

  13. Carlo’s café (year 6)

  14. Money moves (Year 6)

  15. Think of a number (year 6)

© 2020 Liz Gibbs - The Busy Lizzie | Website by sohobs.co.uk

PRIVACY POLICY