Module 12  Numbers Properties & Indices  
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Module  Grade  Topic 
Description 

12 
2 
1 
Understand the concepts and vocabulary of factor (divisor), multiple and common factor and prime number. Recognise and use multiples, factors (divisors), common factor, highest common factor and lowest common multiple in simple cases, and primes (less than 100); use simple tests of divisibility. 




Prime Numbers 









Factors and Multiples 






HCF By Listing 




LCM By Listing 

12 
3 
2 
Use and understand the terms reciprocal, highest common factor, lowest common multiple, prime number; find the prime number decomposition of positive integers. 




Prime Factor Decomposition 









HCF & LCM By Using Prime Factors 
















12 
3 
3 
Use the term squares, square roots, cube and cube roots; recall the cubes of 2, 3, 4, 5, and 10; use index notation for simple integer powers. 




Square and Cube Numbers and Square and Cube Roots 









12 
5 
4 
Understand ‘reciprocal’ as multiplicative inverse, knowing that any nonzero number multiplied by its reciprocal is 1 and that zero has no reciprocal because division by zero is not defined. 











12 
5 
5 
Use index laws with numerical and algebraic expressions involving multiplication and division of positive integer powers. Substitute positive and negative numbers into expressions such as 4x – 2, 3x^{2} + 4 and 2x^{3}. Derive a formula and in simple cases, change its subject. 




Simplify Algebraic Expressions involving Multiplication 







Index Notation 






Rules of Indices 
















12 
5 
6 
Use standard index form expressed in conventional notation and on a calculator display; convert between ordinary and standard index form representations. 




Standard Form Large 





Standard Form Small 





12 
5 
7 
Use a calculator effectively and efficiently, including using the memory and bracket keys, and function keys for reciprocals, squares and powers; enter a range of measures including ‘time’; interpret the display; round off a final answer to a reasonable degree of accuracy. Use Inequality notation to specify errors intervals due to rounding. 




Calculator Methods 1 








Calculator Methods 2 





12 
5 
8 
Understand, recall and use Pythagoras’ theorem. Find the length AB given the points A and B in 2D 




Midpoint and Line Length 

















Pythagoras' Theorem 












12 
5 
9 
Solve problems involving calculating with powers, roots and numbers expressed in standard form, checking for correct order of magnitude and using a calculator as appropriate 




Standard Form Large 








Standard Form Small 








Standard Form Using a Calculator 





12 
5 
10 
Solve problems involving repeated proportional or percentage changes, including compound interest; represent repeated proportional change using a multiplier raised to a power. 




Compound Interest 





Depreciation 


12 
6 
11 
Use fractional, negative and zero powers in simplifying numerical expressions, including using inverse operations. 




Indices Introduction 






Indices Negatives and Fractions 









12 
8 
12 
Shortest distance from a point to a straight line 











12 
8 
13 
Use Pythagoras’ theorem in 3D contexts, including using 3D coordinates and Pythagoras’ theorem to find the length AB given the points A and B in 3D. 




Pythagoras in 3D 


12 
9 
14 
Set up solve and interpret Growth and Decay Problems. Use calculators to explore exponential growth and decay and work with general iterative processes. 










