Inventing Decimals/Place Value

It can be challenging for students to understand decimals, and they may try to memorise a set of rules to deal with them rather than developing a deeper understanding. These slides walk them through a (fictional) historical story that motivates the invention of decimals and prompts them to invent the rules for adding and multiplying decimals, with the secondary goal of explaining why the number 10 has the magical property of moving the decimal point around.

I put the lesson together for a class with some deep misconceptions about place value and decimals, e.g. thinking that multiplying by 10 always adds a zero and therefore 3.2 x 10 = 30.2, which these slides cleared up. The standard form and bounds topics right at the end are a great test of understanding for older students, but the other slides should be fine soon after introducing decimals for the first time!