Number Problems Extension                                               

To view the problem statement, double click on the problem title. This will open up the problem in a new window. From there, you can download the full problem-and-solution Word document.

Examples Page Ref  Problem Title Objectives Ref Description Key Words
91, 97 Sisterly Squares Multiplication Strategies,  (a+b)(a-b), Factorizing 25 and 36 are both squares, and 2+1=3, 5+1=6... when's the next pair ?!  Factorize
57, 91, 133 Power Twins Index Laws, Powers, Trial + Improvement 2 4 = 4 2 - find some more examples ! Exponent, Index, Reciprocal, Trial + Improvement
59, 105 Large Perfect Squares Algebraic expressions, Refine written methods This is based on the idea of squaring a bracket and would follow on from practice in for example squaring 13 as (10+3) or 28 as (20+8). Factorize, Power, Brackets, Quadratic expansion
59 Friendly Surds Index Laws Using factorization of surds to find why   Surds, Factorize
 57, 63  Factor Fractions Indices, Powers, Cancelling Fractions

Can you find three different whole numbers a, b and c, which will make the value of      a whole number itself?

Index, Factorize, Common Factors
109  PC Plod... Complex Calculator methods How many ways can a policeman patrol a grid of streets ?  Factorial, Pascal's triangle