Blog: Vicki Robinson, Communications Officer

# #MondayMaths – Six houses and one garden

Posted: 22/08/16

**This week, we’ve combined a lovely bit of logic with landscape design in our #MondayMaths challenge.**

The hexagonal puzzle – made up of six houses and one garden – is a great visual activity to start or end a lesson with. It also encourages pupils to build their problem-solving skills when faced with a relatively small amount of information.

**A puzzling perimeter**

To crack the conundrum, we’re asking how the length of the blue houses can be calculated by using information about the other shapes (in a very sociable group of houses!)

In our mastery curriculum, pupils should have gained confidence in working with perimeters of rectangles and composite rectilinear shapes by the end of Autumn 2 of Year 5. This perimeter puzzle is great practice for applying this learning.

When working it out, learners should spot that the red outer perimeter is composed only from the sides of rectangles* and so students can then start piecing together what they know about the side lengths of these rectangles.

**Tips for tackling **

**The garden is a regular hexagon**– identifying this enables pupils to calculate the length of each side of the garden from its perimeter**The grey houses are square**s – knowing this informs pupils that all their sides are equal in length and are the same length as the sides of the hexagon**The opposite sides of a rectangle are equal**– this helps pupils spot that the widths of the blue houses are equal to the side lengths of the hexagon

Once they reach this point, the only unknown parts of the outer perimeter are the longer sides of the blue houses.

**Using the Concrete Pictorial Abstract (CPA) approach**

If some pupils are finding this method tricky, how about using a pictorial representation and suggesting that they construct the perimeter as a bar model?

**We’re keen to find out what the most popular approach to cracking this problem is. Do let us know on Twitter so we can share your insights.**

**Don’t forget a square is a special type of rectangle!*