Negative Indices and Half-life in Mathematics
Explore the concept of negative indices and half-life in mathematics as presented by the NSW Department of Education. Learn how to write numbers with indices, decipher patterns in index values, and delve into the implications of negative indices in different scenarios.
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Presentation Transcript
Negative indices Explicit teaching NSW Department of Education
Half-life plutonium How can you write these numbers with indices? 4 8 2 1 2
Half-life plutonium (2) What would come next? What is happening to the index value in each step? What pattern is happening as the solution changes in each step? 22= 4 23= 8 21= 2 20= 1 3
Half-life plutonium (3) Negative index 2 1=1 22= 4 23= 8 21= 2 20= 1 2 4
Half-life plutonium (4) What if we kept going further? ?? ?? ?? ?? ? ? ? ? ? ? ? ? ? ? ? ? 8 4 2 ? 5
Half-life plutonium (5) What do you notice? ?? ?? ?? ?? ? ? ? ? ? ? ? ? ? ? ? ? 8 4 2 ? What do the denominators have in common with other answers in the table? How else could we write these denominators? 6
Half-life plutonium (6) What do you notice? ?? ?? ?? ?? ? ? ? ? 1 21 ? ? ? ? 1 22 ? ? ? ? 1 23 8 4 2 ? What is the connection between the first and third rows of the table? 7
Negative indices your turn Does this work for other bases? ?? ?? ?? ?? ? ? ? ? ? ? ? ??? ??? ? 8
Negative indices your turn solutions Base 5 ?? ?? ?? ?? ? ? ? ? 1 51 ? ? ? ?? 1 52 ? ? ? ??? 1 53 ??? ?? ? ? 9
Negative indices rule 1 ? ?= ?? 10
