Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Numbers as Shapes

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

How Odd

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Largest Even

Stage: 1 Challenge Level:

Well done for giving clear solutions to this problem.  Many of you were able to explain a general strategy.  Tom and Jeevan from Devonshire Primary School said:

If you are trying to make the largest even number using an odd number you put the odd number in the tens column and in the units column you put $8$.
But if you're doing it with an even number then you put $9$ in the tens column and then put the even number in the units column.

Peter, Henry, Charlie, Lulu and Samuel at Weald C of E Primary School assumed that you could also get a zero.  They went on to think about how you would make the smallest even number:

Largest Even
1.If you get an odd number, put an eight in the units column.
2.If you get an even number, put a nine in the tens column.
3.If you get a zero, put a nine in the tens column.

Smallest even
1.If you get an odd number, add a zero in the units column.
2.If you get an even number, add a one in the tens column
3.If you get a zero, put a one in the tens column.

Homeroom 7 at Kororoit Creek Primary School, Australia looked at a strategy for making the largest odd number too:

The largest two-digit odd number we could make is $97$. We could not make $99$ because we only have one $9$.
If you pulled out an odd number first this should always go in the 'ones' column. Unless you pull out a number $9$. The $9$ will always go first because $97$ is the biggest number we can make. e.g. $97$, $79$, $59$, $39$, $19$.
If you pull out an even number first it should always go in the 'tens' columns, otherwise your two-digit number will not be odd. You should still always choose the number $9$ as your second card to make the largest number possible. e.g. $89$, $69$, $49$, $29$.

Well done too to Robert from West Hoathly and Sophie from Greenacre who also sent very full responses.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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