Powers and Roots (Part 1)

I am always fascinated to see the way other countries write their maths curriculum. Some are very prescriptive and others are quite open.

Below are the outcomes in the Scottish Curriculum for Powers and Roots. These outcomes are aimed at students aged between 11 and 14.

“Having explored the notation and vocabulary associated with whole number powers and the advantages of writing numbers in this form, I can evaluate powers of whole numbers mentally or using technology”

“I have developed my understanding of the relationship between powers and roots and can carry out calculations mentally or using technology to evaluate whole number powers and roots, of any appropriate number”

“Within real-life contexts, I can use scientific notation to express large or small numbers in a more efficient way and can understand and work with numbers written in this form”

Powers and Roots is the first topic for me starting back with my S2 class (age 12/13).

My plan is to teach:

  • square numbers
  • square roots
  • cube numbers
  • powers
  • scientific notation

Here are a few of the ideas that I want to use when teaching these topics.

Square Numbers – I want to introduce the idea of a square number visually then have my students work out the first 20 square numbers. I am hoping that they will know some of them (up to 12) and will use their knowledge of multiplication to work out the others. I would them like my students to learn these numbers. I am hoping to do some old fashioned rote learning to practice first (i.e. 1 squared is, 2 squared is, 3 squared is, …) then use mini whiteboards to practice these square numbers in a mixed up order.

Square Roots – I’d like to start by having some empty sums like  square root sumthen introduce the square root symbol. I want to make sure I show my students that square root symbol

so that they understand that other roots do exist. Hopefully this will help them later on when then study surds and indices. Then I want my class to make a square root clock. These can be as simple as the one shown below or can use more complicated calculations.

square root clock.jpg

For cube numbers I wanted to find a game to play that would help my students learn their cube numbers. So once they have worked out the first 10 cube numbers, here is a game of Connect 4 to play.

cube numbers game

These will be laminated so the students can mark on them with whiteboard pens and they can be reused. In order to use the 10 sided dice, 0 will have to count as 10. I think it is a fun game, hopefully the class will too.



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