It was 2010!

If the answer's 2010, what could the question be?

Age

5 to 11

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

At the start of a new year teachers often like to use the number of that year.

Well I know that some teachers often use an idea like,

The pupils would get things like:

$16 \div 2$

$20 - 4 - 4 - 4$

$6 + 2$

$\sqrt{64}$

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So here's a challenge to make an answer of $2010$

You could try things like:

$$2000 + 10 \quad\quad 201 \times 10\quad\quad 500 + 1000 + 500 + 5 + 5$$

even this

$$19^2 +25^2 + 32^2$$

Don't forget you might like to use calculators or computers!

See what different questions you can find and compare yours with others.

Perhaps you can make up one that is easy, one that is harder and one that is very hard.

Now that $2010$ has passed try the same for the year we have now!

Well we certainly had a lot of solutions sent in THANK YOU! Here are just a selection.

On the $1$st of January we had this idea from Nebal from Al khor school in Qatar:

$4$ times $5$ then times $100$ then add to the product of $2$ times $5$

which could be written as $(4\times5\times100)+(2\times5)$

Priyanha from North Haringay said - quite amusingly - that the question was

"What is the year?"

Priya from Edgbaston High School gave an example using four different actions,

$2000 + 20 - 10$ squared add $10$ minus $5$ and $4 - 9$ square rooted!

which of course would have been difficult to write just using symbols.

Anabel from the Convent of Jesus and Mary wrote

The squared root of four million forty thousand and one hundred.

Kiran from Brooke Weston Academy produced ideas as follows:

$2\times3\times5\times67$ (Prime Factor Decomposition)

$11111011010$ in binary

MM+X in Roman addition to give MMX

A good combination of different operations came from Hannah at Rawdon Littlemoor School:

$4$ squared $\times 100 + 25 $ squared $ - 215$

James from Queen Victoria School (who sent in many solutions) sent in:

$8\times6=48 +2=50\times25=1250+50=1300+710=2010$

We have to be a little bit careful of where we put an equals sign when we're writing out a calculation like that one, but we understand what you mean, James.

Qize Jaic from Brook Street sent in

$201000000000000000 \div 100000000000000$

These from Tudhoe Grange Lower School (Lucy, Brianna, Jordan and Hannah Louise):

"What year will be the reggae singer Bob Marley's $65$th birthday?"

"What is this word ... net-dna-dnasuoht-owt?"

Two thousand and ten 1s , added together.

$211-25-22-2 =2010$

These from Aycliffe Drive School, (Omotayu, Callum and Jonathan):

Using just $1$'s and zeros:

$1000$ divided by $1$add $10$ add $1000$

Good use of brackets:

$((((610\times2)-200)-20)+5)\times2$

James from Eskdale sent in his good idea:

$6950428-6940423+1005$

Samuel from Scisset School also had a good idea:

$30$ squared $ + 35$ squared $ - 11$

Krystof sent in these two which were both well thought-out:

$16^3 - 2000 - 96 + 10$

$12^3 +5^3+5^3+4^3-5^2-2^3+1$

Well done all of you I am very pleased that so much good work came from you all who sent ideas in.

It Was 2010!

At the start of a new year teachers often like to use the number of that year.

Well I know that some teachers often use an idea like,

The pupils would get things like:

$16 \div 2$

$20 - 4 - 4 - 4$

$6 + 2$

$\sqrt{64}$

----------

So here's a challenge to make an answer of $2010$

You could try things like:

$$2000 + 10 \quad\quad 201 \times 10\quad\quad 500 + 1000 + 500 + 5 + 5$$

even this

$$19^2 +25^2 + 32^2$$

Why do this problem?

This activity is very useful when you have a very wide attainment range within your class. It enables pupils to use whatever knowledge and skills they have, and it can inspire them to try to get to grips with new calculations that they may well not have come across before. It therefore provides a fantastic assessment opportunity for you.

Possible approach

This activity needs little introduction. You can simply ask the question orally, or have it written on the board at the start of the day/lesson. You may like to give a few minutes and then ask children to think of a harder example than the one/s they have already devised. After a few more minutes, ask them to make an even harder example.

You may want to give the group time to share what they have done with a partner as talking with someone else may well inspire individuals to try something different.

Use the time that they are working to walk around the room and observe. You may be surprised by the inventiveness of some children and equally by the 'safeness' of others. You could use the opportunity to engage in conversation with some learners, perhaps because you notice a pattern in the way they are working.

Key questions

Tell me about the ones you found.

How are you finding new questions?

Could you use more/fewer numbers?

Have you thought about decimals/fractions/square numbers/negative numbers?

Possible extension

Encourage pupils to try other ways of getting that answer.

Alternatively, you could try "The answer's $1$, what's the question?" and/or "The answer's $0$, what's the question?".

Possible support

Some children might find it useful to start with the I'm Eight activity, possibly using counters as well as calculators.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics