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24 x 21 = 42 x 12

For detailed notes and resources on this prompt see the main inquiry maths page.
These are the questions and comments of Amanda Klahn's grade 4 (year 5) class at the Western Academy of Beijing (China). The Academy is an international Primary Years Programme (PYP) school with an inquiry-driven curriculum. Amanda reports that she has been trying to get more inquiry into maths lessons: "As an introduction to using prompts I worked with my more able mathematical thinkers. There was a lot of excitement as they discovered new patterns and then went on to write some great 'What if ...' questions. There was true inquiry, collaboration and challenging of each other's thinking." The board above shows a very rich set of questions and observations with which to launch an inquiry.

is an IB teacher in Beijing and blogs about the activities of her class here. You can be follow Amanda on twitter @KlahnAmanda.
Alternative prompt
24 + 21 = 45
42 + 12 = 54
This prompt has developed out of students' changes to the 24 x 21 = 42 x 12 prompt. If you reverse the digits of two two-digit numbers, are the digits in the sum always reversed? Under what conditions does this occur? Is it linked to the multiples of nine? 

Learning path
David Aaron's year 6 class in Blackpool (UK) posed the questions and made the observations above, which represent a very impressive start to the pupils' first inquiry! David reports that one of his pupils commented: "I like this inquiry because I'm planning my own learning path." As the inquiry developed, another found 31 x 21 = 651 and 13 x 12 = 156, which is a novel result and could form the basis for another inquiry. David was pleased that the class enjoyed its first taste of inquiry.