Here you will find a collection of tasks and commentary on how the Isles of What if…? approach is used in them.

**Most recent Isles:**

## 3-2-1 Totals

A triangular grid contains the numbers one, two and three. Combine them into regions with unique totals. What is the lowest possible value of the region with the highest total?…

## Add the Ones, Double or Halve

Explore chains of numbers by adding the ones digit and then doubling or halving. Do all numbers loop? Do they follow similar loops?…

## Addition Digit Swap

Start with a three-digit addition. What digits are produced in the answer? Swap one of the digits for a new one to create a new addition. How many swaps are…

## Addition Wheels

Arrange the digits 0-9 in three rings going clockwise. Using different diameter lines that go through the different digits, how many of the five additions total over 1000?…

## All the Angles Inside

Draw angles from each corner of a square to the midpoint of the side opposite. Can you determine each missing angle?…

## Area Twice, not Thrice

Drawing ‘L-shaped’ lines in a square, how many shapes can be created without having the same area more than twice at any one time?…

## Balancing Act

Using consecutive numbers, can equations be created where both sides are balanced?…

## Christmas Tree Tinsel

Each day of December, tinsel is placed between the baubles showing 1-9 in such a way that each set of numbers can form an equation that equals the day of…

## Circular Number Constructions

Create the greatest number possible by going around a number circle. Lots of thinking on place value required….

## Consecutives with Common Multiples

Using 1 to 6 as digits exactly once, can we make multiples of 1, 2, 3 and 4. What if we were able to share common multiples across numbers? What…

## Denominator Dilemma

With two number lines showing halves and quarters, children try and add and subtract fractions to reach as many values as possible across them both….

## Detached Dots

Using a dotted square with numbers, join lines between dots so that a line is only ever intersected at most once. What is the lowest total possible from unjoined dots?…

## Difference Daisies

Find the differences between sets of three numbers repetitively as layers of a flower. The repeating of numbers in lines builds a sense of awe….

## Digital Root Chains

Find the digital root of the product of two numbers – one of which should be a single-digit number. Using the digital root, adjust the number and try again until…

## Digital Shape Sequences

Create chains by adding single-digit numbers. Each number is inside either a triangle, a square or a hexagon. In each polygon, the number must include a digit that is the…

## Digital Shape Sequences – Multiplication

Use times tables within a repeating shape sequence. Each number is inside either a triangle, a square or a hexagon. In each polygon, the number must include a digit that…

## Distinct Digits to 5555

This island focuses on the use of column addition and even though it focuses on only four digits, it promotes a trial and improvement approach that requires a lot of…

## Don’t Pull Out Right Angles

This island involves starting with shapes made with elastic bands on Geoboards and ‘pulling’ the sides out over the nearest peg – trying to avoid making right angles for as…

## Dot-to-Dot Acute Angles

Join dots with acute angles to try and create as many polygons as possible. What if we had to place the dots on a spiral? So many possibilities!…

## Formed From Three

Using three similar shapes, surround an area that forms a triangle. Then using three more the same, form a quadrilateral, then a pentagon etc. How far can you go?…

## Money Bags

This island focuses on adding money and involves strategy in placing coins to ensure the greatest amount is obtained. What is nice is that they have to continually think about…

## Multiples Ping Pong

In a 3×3 grid, digits are added to make numbers horizontally and vertically. Each time a digit is added, it must create numbers that are either not a multiple of…

## One Intersection

With a hexagon of dots, draw lines between them. After the first line is drawn, each new line must intersect exactly one line. Explore further with curved lines or different…

## Opposite Digit Circles

With this island on addition, it takes a little bit to set it up but once you have done so, it’s fairly easy to follow and the patterns are quite…

## Overhanging Squares

How many possibilities of shapes of each area are there without overhanging squares?…

## Partitioning Polygons

Partition polygons to create shapes with different numbers of sides. Using ‘what if…?’ questions, we can come up with some really creative solutions….

## Pentagonal Rounding

Place digits around one or two pentagons that share a side so that each number rounds to a different integer….

## Polygons of Many Multiples

This shares similarities with Triangular Threes but focuses on constructing multiples instead. I used squares as that worked well with my Year 4 class when I came up with the…

## Powers of Ten Cycles

By only multiplying or dividing by powers of ten, can complete cycles be created? Through this, inverse operations and the associative law is emphasised….

## Product Parting

Starting with a three-digit number and a one-digit number, find the product. Split the final digit from the answer to create two new numbers and go again. How many multiplications…

## Time to Win

A game where each player advances a clock by selecting an interval. The winner is the player that makes a time of ‘quarter to…’…

## Top-Three-Digit Times Tables

Create sets of five times tables thoughtfully using links between each one. From each of these, total the highest three digits in the multipliers and product to create a score….

## Totals Turned to Ten

Starting with four dice, we rotate them so that the number facing us is now on top. However, we must avoid any number of dice in a row, whether two,…

## Triangular Threes

Numbers are arranged in triangular grid starting with 1, 2 and 3. Each time a new triangle is made, its numbers must be used in a calculation to equal 3….