You may also like

problem icon

Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

problem icon

Number Detective

Follow the clues to find the mystery number.

problem icon

Six Is the Sum

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Two and Two

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two and Two

How many solutions can you find to this word-arithmetic challenge? 

Each of the different letters stands for a different number.
 


 
Click here for a poster of this problem.

Why do this problem?


This problem
offers an opportunity to practise addition in a more interesting and challenging context than is usual. It requires students to work systematically, record their progress efficiently and apply their understanding of place value.


Possible approach


Write the following sum on the board and ask students to complete it.

    8 6 1
+   ? ? ?

  1 4 2 7
   
Expect justifications for any suggestions.
This should be unproblematic so move onto a more challenging problem.

If each letter stands for a distinct digit what are the values of $a$, $b$ and $c$?

  b b
+ c b

a c c
 
"How can we approach this?"
Expect fairly random suggestions to start with but aim to use the discussion as an opportunity to model working systematically.
"What happens if $b$ is $1, 2, 3, \ldots$ ?" - rejecting values as soon as it is apparent they do not work and discussing how you know.
"How can we be sure we have all the solutions?"

Set the students off in pairs to work on the problem TWO + TWO = FOUR.
Establish that you are not going to announce how many solutions there are and that you will expect students to work systematically and be able to justify that they have all the possible solutions.

To finish off, students could present their approach to the rest of the class, with emphasis on explaining clearly why they are convinced that they have found all the possible solutions.

Key questions


Are we certain we have considered all the possibilities?

Possible extension


Suggest students find other word sums that work.

Here are some possibilities that they might consider:
 
ONE + ONE = TWO
ONE + TWO = THREE
ONE + THREE = FOUR
FOUR + FIVE = NINE
 
Why are some impossible?

Can they make a word subtraction?

Students could also try Fly Fly Away and Alphabet Soup

Possible support


Suggest students start with Spell by Numbers