Desk Calendar Problem

So, I saw this on a colleague's desk. It got me thinking: "These are six-sided cubes. So, how can twelve digits split as a six and a six represent all thirty-one days of a month?"

It's a problem that makes use of trial and error, make a model and test and thinking logically. I made a sheet to introduce the problem:

The sheet, with differentiated support and my answer can be found here.

I wonder how many combinations of answer there are...

Advent Maths

So, this year (2018), 1st December was on a Saturday. Doors opened on Advent calendars all around the land. Go to church on 2nd December and they're lighting their candle and saying that it was the first day of Advent.

So,

There are four Sundays in Advent. The four Sundays leading up to Christmas Day.

What's the earliest date the First Sunday of Advent can be in a given year.

And,

What the latest date the First Sunday of Advent can be in a given year?

Part Part Whole, Bar Model & Perimeter

Earlier this year, we were calculating perimeter of compound shapes with some missing measurements. Some children were struggling to work out which measurements were missing. 

So, we took to using the bar model to offer some support.

1. Count the sides of the shape
2. Colour horizontal sides one colour and vertical sides another colour
3. Identify which sides have an unknown length
4. Use 'Part Part Whole' bar model (one for horizontal and one for vertical) to help find missing lengths
4a. The bar models can also be colour coded the same as the sides
5. Check the number of lengths found matches number of sides and looks sensible 
6. Add them up...

It worked well for us. Of course, as always with the bar model, it will help work towards an answer, but not give an answer. 

The Piano Key Problem

I was watching a program about how a piano works earlier with my daughter. One of the facts was about the number of white and black keys. Wonder if children can use their reasoning skills (drawing a picture, making a model or looking for a pattern) to solve this:

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On an 88 key piano, there are 52 white keys. How many are black? 

The lowest key (first note) is an A. The last note is C.How many A, B, C, D, E, F & G notes are there?

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A copy of this can be found here.

Here's the answer with a picture from Piano-Keyboard-Guide.com:

Supermarket Maths

It's a quick one...

Supermarkets are full of maths, well everywhere is. You're probably walking around with your phone in your pocket. Snap some maths starters or additions to your lessons. they'll be a real life link. We've started here.

Maths Reasoning - Was Peter right? What did he mean?

On Thursday 16th November, Peter Kay was on the radio with Chris Evans. Here's a conversation they had. Available for 30 days (listen at 41:15)... 

Peter Kay (PK): You're lying in bed now thinking, I'll get up after this song. Round it up... What is it now? 7 what?
Chris Evans (CE): 7:12.
PK: Wait until 7:15.
CE: Yes, yes...
PK: Don't get up on an odd number.
CE: Go crazy.
PK: Wait until 7:15. When it's 7:17, wait until 20 past. 
CE: Is that what you do?
PK: You gotta round it up. You can't just get up mid numbers. 

So, Peter said to not get up at 07:12 and wait until 07:15 as he doesn't like to get up on an odd number. What's wrong? What was he intending to say? How can that be re-worded, but more mathematically accurate?