Move it one space to the left?

me: OK, what is 0.54 x 1000?

student: Blank face...

me: Let's draw a place value table.

student: Blank face...

me: See, when we multiply a number by ten, we move each digit one space to the left.

student: Blank face...

This Y11 student is doing her GCSEs in less than 10 months! How do I help her?

By going back to basics and explaining how our number system works, using one, ten and hundred blocks (Dienes). Have you ever thought about why we write 5437 and not 5000400307? To you it makes sense, to her it didn't. Using a one block, making it ten times as big and putting the tens rod in the tens column, showing her that ten of the tens rods make a hundred square which goes in the next column (hundreds) and then writing it as a number and explaining that yes it is 1 ten, and 1 hundred, but we need 0 as a place holder in the units column to show that a 1 in the second place actually mean 10 and not 1. She got it!!!!! she realised that when we move a number to the left it is ten times as big!!!

We then wrote other one-digit numbers in the place value table, showed her what they looked like in Dienes, and recorded in the table that the digit actually moves one place to the left when the value is multiplied by 10. She got it!!!! We ended with 0.54x1000... she got it right!!!! Very proud tutor moment!!!

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