Differentiated investigation lesson aimed KS3. Particularly suitable for a mixed-ability class. In this lesson, less-confident students are given lots of opportunity to practice 2-digit multiplication, whilst stronger students are asked to generalise a rule for when “reverse-digit” multiplication gives the same product as the original multiplciation. Can easily be extended into two lessons, by extending the investigation to 3-digit numbers and beyond.

This 1 or 2 lesson investigation, is aimed at KS3 classes and is particularly suitable for mixed ability classes. The lesson uses the theme of “How many different ways are there to cross a river, given an increasing number of stepping stones” Students begin by working methodically to find exhaustive lists of all the different ways to cross the river. Students are then encouraged to spot patterns and predict future outcomes, before testing their predictions, with the resulting pattern being a Fibonacci Sequence. This lesson works particularly well when taught after the sequences topic in year 7 or 8.

This 1 or 2 lesson investigation is aimed at higher ability classes in KS3 or KS4. The lesson is self-differentiating, as less confident students are given the opportunity to practice conpound area and pattern-spotting, whilst the more confident mathematicians are given the opportunity to derive general formulae for the area of shapes with different properties. The lesson begins by asking students to find compound area using the method of subtracting smaller areas from the whole. The investigation progresses to exploring the properties of polygons drawn on dotted paper and deriving rules for the areas of shapes with different numbers of dots on their interior and their perimeter. Finally, students are asked to generalise a formula for the area of any shape drawn on dotted paper.