Stage 5 -Number – Indices

Describe numbers written in index form; translate numbers into index form; understand the meaning of zero index and negative indices; calculate with numbers written in index form; use scientific notation to write large and small numbers

Strategy

Students can:

  • describe numbers written in index form
  • translate numbers into index form
  • understand the meaning of zero index and negative indices
  • calculate with numbers written in index form
  • use scientific notation to write large and small numbers

Activities to support the strategy

Activity 1: power and exponent

1. Introduce students to the terms power, index, indices and exponent. A power is the product of multiplying a number by itself. A power usually has a base number (what number is being multiplied) and an exponent, which tells how many times the base number is being multiplied. For example, 56 is said as "five to the sixth power" and 5 is the base, while 6 is the exponent.

Complete this table of common powers.

View/print (PDF 102.74KB)

2. Use the cards cut from the worksheet to play concentration.

View/print (PDF 83.91KB)

Activity 2 – index form

1. Use The scale of the universe2 website as an engaging way to introduce scientific notation as means of dynamically comparing dimensions associated with very small and very large objects in our universe.

2. Have students investigate the history of very large numbers and very small numbers and some of the methods mathematicians and scientists use to write those numbers. Students could investigate these examples: nanotechnology, the distance between planets and solar systems, googol, googolplex, sexdecilliard, size of electrons, marine diatoms, and wavelength of blue light.

3. Use calculators or formulas in a spreadsheet to calculate these values:

View/print (PDF 102.74KB)

References

Australian curriculum

ACMNA209: Apply index laws to numerical expressions with integer indices

NSW syllabus

MA5.1 – 5NA: Operates with algebraic expressions involving positive – integer and zero indices, and establishes the meaning of negative indices for numerical bases.

Teacher resources

Lesson plans and activities

Understanding exponents, exponents and powers, exponent expressions

Student resources

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