The 1 to 5 problem 

Introduction

I am not sure where I first met this problem, however, John Bradshaw and I included in a publication of the Lancaster Joint Branch of the MA-ATM titled "5-Minute Fillers" In the introduction we wrote that a 5-minute filler for one teacher could be a more extensive piece of work for another. This is certainly the case with this problem. Since using it in InSET a number of interesting extension ideas have emerged and I offer them for use in classrooms.

Once again the 'beauty' of this problem is that it is simple and accessible, only requiring students, in the first instance, to carry out single figure subtractions and additons, however, possible extension ideas can be developed with students throughout KS2, KS3 and KS4. As such it is highly suitable for using with mixed-ability classes.

The following areas of the curriculum can be developed or consolidated:

taking differences

addition

multiplication

converting fractions to decimals

adding decimals

adding fractions

plotting co-ordinates

working out Area

producing algebraic generalisations (linear, quadratic, cubic...) 

Section 1: Starting points and extension tasks:

Summing differences (or "takes and adders") (KS2, KS3 and KS4)

Summing products (KS2, KS3 and KS4)

Summing fractions and/or decimals (KS2, KS3 and KS4)

Plotting co-ordinates & shapes (KS2, KS3 and KS4)