# 361. Routes, Reindeer & Reasoning

Well, we are nearly at the end of a very crazy year. Congratulations on surviving it!

So, it’s been a while since the last blog post. Apologies for that. At the moment I am involved in Mixed Attainment teaching with Year 8. To finish off the term, I thought we deserved a bit of fun. We have a week of lessons left so I’m going for a mini project each lesson.

Lesson 1: Santa’s Route
I found this fab task on the Maths Drill website. There is a real chance for extension in this task, which is great for the mixed attainment classroom.

Lesson 2: Reindeer Ratios (Updated 13th Dec)
We have been following the White Rose Maths scheme for Year 8, which covers a lot of proportion and reasoning through ratio, multiplicative change and fractions. This task tries to cover some of these skills. The answers will be uploaded soon.

Lesson 3: Elf Box Packing Problem (Updated 14th Dec) Elf Box Packing Problem Solutions
This task involves using multiplicative change and fractional multiplication and division, with a dash of unit conversion. There is some work on shapes, but formulae are given where necessary. The first four pages print nicely into a folded A4 (A5) booklet. There is a help sheet for the box packing problem; this would be better printed on A4.

# 293. Boxing Bounds

I thought this would make a nice little starter – address a few different topics, bit of problem solving, all over in 15 minutes. How wrong I was!

The Question: A company packs toys into boxes which measure 12cm by 8cm by 10cm (to the nearest centimetre). The boxes are packed into crates which measure 1m by 0.75m by 0.8m (to the nearest centimetre).
(a) Basic question – How many boxes fit into the crate?
(b) What is the maximum volume of a toy box?
(c) What is the minimum volume of the crate?

It was a simple question about fitting toy boxes into a shipping crate. It extended to looking at upper and lower bounds, then recalculating given this extra information. Simple? No chance!

Problem One
Not changing to the same units

Problem Two
Working out the two volumes and dividing to find the number of toys. When challenged on this, it took a while to get through to the basics of how many toys actually fit – mangled toys and split up boxes don’t sell well.

Problem Three
Maximising the arrangement of boxes – remainders mean empty space

Problem Four
Using the information from Problem Three to find the total number of toys

Problem Five
Working out the dimensions and volume of the empty space in the box

Problem Six
Trying to convert centimetres cubed into metres cubed. I don’t even know why they wanted too!

Problem Seven/Eight
What’s an upper/lower bound?

Problem Nine
What do you mean that the original answer changes when the box size alters?

Problem Ten
All those who weren’t paying attention when you went over Problem Two and don’t ‘get’ why the answer isn’t 625!

# 291. Elves and Trees

Image credit: www.clipartpanda.com

Here is a quick festive probability resource for you covering elves, outcomes and tree diagrams. The task starts with logically listing outcomes, before looking at working with tree diagrams in the extension.

# 290. Alcoholic Percentages

The season of gratuitous excess is upon us and the reminders about safely consuming alcohol are popping up in supermarkets … usually next to the massive bottle of brandy, which are on special offer! We educators are counting the days to the holiday break.

But wait!

Keep your eyes peeled for all the alcohol awareness promotions. My local supermarket had information leaflets and these goodies:

Forget doing percentages about sale prices. How about working out the volume of alcohol in different beverages? Finding out how easy it could be to exceed the recommended intake? A bit of education of the effects of alcohol in a cross curricular lesson?

Now how much brandy soaked Christmas cake is equivalent to one unit of alcohol?

# 246. ChrisMaths Cheer

Hey … it’s that time of year again! Baubles and cheesy jumpers are creeping into the most mundane of places. How about a more mathematical festive season?

Image credit: http://technabob.com/blog/

Here is a round up of the Sandpit’s Christmas resources:

Twelve Days of ChrisMaths

# 228. Toblerone Tessellation

Christmas has come early to my local Co-Op. I was intrigued enough to buy and eat the new Christmas chocolate, but not before marvelling at the mathematical elegance of it’s structure:

Image credit: http://www.distinctiveconfectionery.com/personalised-christmas-triangular-toblerone-box.html

The slab of equilateral chocolate breaks up into 9 smaller equilateral triangles. Or you could tessellate more of the big triangle.

Break off the corners and you get a hexagon.

Break off one corner and you get a trapezium.

Two triangles together makes a parallelogram … or it a rhombus? Good discussion point there!

The bar weighs 60g – how much does each triangle weigh? What about the weights of the other shapes you could make?

The dimensions are listed as 180x180x10mm. Where would these measurements fit on the triangle? Is it the length, width and height? Why? Can you calculate the dimensions of the other possible shapes?

Once you start thinking about it, there are lots of activities you could do … and there is the potential to eat your work! As usual, if you are going to do this, make sure you are aware of food allegeries.