Here we focus on rounding numbers. The examples focus on decimal numbers but it could just as easily be rounding to the nearest hundred. Careful placement of digits and to be successful with children being thoughtful on when they will need to round up and down.

What if we had a pentagon that can contain five decimal numbers? Each number will be less than ten. To build the numbers, we can use the digits 0-9 only once.

What if we rounded each number to the nearest whole number? Can they all be different? What sets of numbers could we create? Here is one possibility:

I have managed to make a set of five different numbers when rounded to the nearest whole number:

Number | Rounded to the nearest whole number |

8.12 | 8 |

2.95 | 3 |

8.76 | 9 |

5.34 | 5 |

6.04 | 6 |

There are many different ideas that we could explore with this but equally, there is another, more challenging problem ahead of us by extending further.

- Can they be consecutive?
- What is the largest group of numbers?
- Can I construct only even numbers?
- Can I construct only odd numbers?

**What if we had two pentagons that shared a side?**

With this, in each pentagon, we are required to have the digits 0-9 only once still. This means that three digits are used once, in the vertical middle line and seven others are used twice (once in each pentagon). The challenge I envisaged was to try and arrange the digits in such a way that when the numbers are rounded, each still makes a different number. A good focus could be to try and make the numbers one to nine. How many solutions are possible?

**What if we used hundreds instead of decimals?**

I’ve provided some template images here in case this is something you might want to focus on.

**What if we used different shapes?**

In this one, there are three shapes, two shared sides and ten sides total. Is it possible?

**What if we we used different sets of digits?**

Rather than allowing all of zero to nine, we could have a different set of digits. The children could set goals in terms of what they are trying to accomplish (consecutive numbers, all numbers the same etc.) and then think about the set of digits that might lead to them working.

**Children’s possible use of reasoning skills:**

## Search

The children will have to consider the placement of the digits carefully after the initial roaming. Some digits matter more than others. Some places matter more than others. These are all things they can use as a basis for choosing their placements.

Digit cards will really help them with this.

## Organise

It will help the children to keep a track of which digits they have used and which rounded numbers they have constructed.

## Discover

There is lots of uncertainty here and so that means there is a lot of scope for conjectures. What is possible? What is not possible? Lots to explore.

## Investigate

The entire problem is investigating what is and what is not possible. How many solutions are there?

## Argue

Working in pairs, the children can discuss the merits of placing different digits in different positions.

## Explore

There is a lot of scope for ‘what if…?’ questions, particularly with different shapes. Although the construction of those shapes could prove a little tricky for the children with the considerations of how many numbers should be created and the number of digits used in each shape.

## Leave a Reply