Higher Level Mathematics

Sets and Set Notation L.O. All pupils recognise set notation and sets of numbers All pupils can use set notation and Venn Diagrams to represent sets of numbers Most pupils can write all rational numbers as fractions

Main 1: set notation and sets of numbers

Main 1: set notation and sets of numbers

Main 1: set notation and sets of numbers

Main 1: set notation and sets of numbers

Draw a Venn Diagram to show the relationships between these sets Main 1: set notation and sets of numbers Draw a Venn Diagram to show the relationships between these sets

Main 1: set notation and sets of numbers

Main 1: Use set notation to describe these sets: set notation and sets of numbers Use set notation to describe these sets: The set of all integers between -8 and 6, not including -8 and 6 (i.e. exclusive) The set of all integer multiples of ∏/4 greater than zero and less than or equal to 2∏ The set of positive odd integers *which of these sets are finite and which are infinite?

Sets and Set Notation L.O. All pupils recognise set notation and sets of numbers All pupils can use set notation and Venn Diagrams to represent sets of numbers Most pupils can write all rational numbers as fractions

use set notation and Venn Diagrams to represent sets of numbers Main 2: use set notation and Venn Diagrams to represent sets of numbers

use set notation and Venn Diagrams to represent sets of numbers Main 2: use set notation and Venn Diagrams to represent sets of numbers

Sets and Set Notation L.O. All pupils recognise set notation and sets of numbers All pupils can use set notation and Venn Diagrams to represent sets of numbers Most pupils can write all rational numbers as fractions

Write each of these recurring decimals as a fraction. Main 3: write all rational numbers as fractions If irrational numbers are none repeating decimals then all other decimals must be able to be written as a fraction. Write each of these recurring decimals as a fraction. E.g. 1.4115454545454……

Where do the recurring digits start? Main 3: write all rational numbers as fractions 1.4115454545454…… Where do the recurring digits start? So to make the green part a whole number (in order to make it a fraction) we need to multiply by: 1.135454545454…… 10000

write all rational numbers as fractions Main 3: write all rational numbers as fractions 1.135454545454…… x 10000 = 11354.545454… If 1.135454545454…… = N Then 11354.545454… = N 10000

How many digits are recurring? Main 3: write all rational numbers as fractions If 1.135454545454…… = N Then 11354.545454… = 10000 N How many digits are recurring? 2 digits are recurring 10000N

write all rational numbers as fractions Main 3: write all rational numbers as fractions If 1.135454545454…… = N Then 11354.545454… = 10000 N 10000N 11354.545454… = 100 N

write all rational numbers as fractions Main 3: write all rational numbers as fractions 11354.545454… = 10000 N 113.545454… = 100 N 10000 N – 100 N = 9900 N 11354.545454… 113.545454… 11241.000000…

write all rational numbers as fractions Main 3: write all rational numbers as fractions 11241 = 9900 N 11241 = N 9900

Write each of these rational numbers as fractions: Main 3: write all rational numbers as fractions Write each of these rational numbers as fractions:

Sets and Set Notation L.O. All pupils recognise set notation and sets of numbers All pupils can use set notation and Venn Diagrams to represent sets of numbers Most pupils can write all rational numbers as fractions