The learning objective: To be able to multiply and divide decimals by 10 and 100

Big Ideas and Connections::

Big Ideas and Connections: The subject knowledge needed: The decimal place never moves. The numbers move to the left along the place values when you are multiplying. When multiplying numbers by 10 and 100 we are making them 10 or 100 times bigger

Big Ideas and Connections::

Big Ideas and Connections: The numbers shift to the right along the place values when dividing. When dividing numbers by 10 and 100 we are making them 10 or 100 times smaller. That 0 is used as a place holder.

Dynamic Representations:

Dynamic Representations

Essential:

Essential A common misconception is that the decimal moves. Children are also told that when multiplying by 10 or 100, that we ‘add’ 0s. However, the decimal stays in the same place. The numbers move to the right or the left depending on whether we are multiplying or dividing. The numbers will jump the same number of times there are zeros, so x and 10 jumps once, x and 100 jumps twice.

Essential:

Essential When introducing the concept, try to give calculations with numbers with 2 decimal places: 2.35 as opposed to 2.3 This can be introduced when the concept of 0 as a place holder is introduced.

PowerPoint Presentation:

U H T H T T 2 3 5 2 Multiplying by 10:

PowerPoint Presentation:

9.65 x 10 = Calculations

PowerPoint Presentation:

9.65 x 100 = Calculations

PowerPoint Presentation:

9.65 10 = Calculations

PowerPoint Presentation:

9.65 100 = Calculations

PowerPoint Presentation:

Calculations 0 as a place holder 2.1 x 100= 21 0

Wider:

Wider Another way to look at multiplying decimals is to put it in to terms of money. This is useful as most children will have some understanding of money as decimals. The pupils can be given a ‘slider’ with a pound sign on it. They can then answer money questions using this as a visual aid. It is important to point out that in money, there will always be 2 decimal places.

Deeper:

Deeper The investigation would allow the children to apply their knowledge to a real life scenario. The children would again use decimals in the form of money. They will work on two ‘real life’ problems.

Deeper:

Deeper Investigation: Task one: We are planning a special school trip for 10 prize winning pupils. We have a budget of £50. Using the brochure, can you work out if we can afford to take all the pupils on the trip? Look at the deals, will these work out cheaper per person?

Deeper:

Deeper Investigation: Task two We are planning a special school trip for 100 pupils. We have a budget of £500. Using the brochure, can you work out if we can afford to take all the pupils on the trip? Look at the deals, will these work out cheaper per person?

Deeper:

Deeper The first investigation will look at multiplying and dividing by 10 and the second by 100. This can then be extended to look at taking a 1000 children on a trip. Can the children apply their learning to work out how to figure out the cost of a trip for 1000 pupils? The pupils could then present their findings to the class and explain how they have come to that conclusion.

References:

References Hopkins C, Gifford S & Pepperell S (1999) Mathematics in the Primary School: a sense of progression Second edition (London, David Fulton Publishers). Victoria Neumark (1996) Actively numerate TES Newspaper, 8 March, 1996 Steve Abbott (2004)Playing for real, TES Newspaper, 17 September, 2004

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