“It doesn’t work” claimed a pupil to me in class last week. “Of course it does” I replied. “Yeah ok, I suppose it does but it’s not a proper answer” replied the pupil.

This is a discussion about solving equations where the answer was not a whole number. It really made me think. Why is it that pupils don’t accept fractions (or decimals) as a solution to an equation? It’s not that my pupils aren’t familiar with fractions and decimals.

The problem is the type of questions I ask my pupils. It is fairly typical when first learning to solve equations to have “nice” whole number solutions. Maybe non-whole number solutions should be introduced right from the start.
Then I thought about some other areas of maths. Angles, area, perimeter, volume, Pythagoras, statistics, algebra, … do I focus on “nice” solutions too often in these areas too?

The positive is that I’ve already started planning to correct this. I’m currently writing a new S1 course in which this will be a focus. I wrote calculating new angles worksheets which contain decimals and algebra as well as whole numbers. Hopefully my pupils in the future won’t be so confused or bothered by answers that are not whole numbers.

# Solving Trig Equations Red Amber Green

A while back I blogged about one of my favourite tasks Red Amber Green. This is a task structure that I used to use regularly but recently I have not. I have no idea why not as it is a perfect task for any year group and perfect for mixed ability groups. I am hoping that by refreshing my memory of Red Amber Green tasks I will start to use again in class.

# New Homework Plans

I’ve been teaching for quite a while now and homework is an area I still feel I’m not getting right. Whether it be forgetting to set homework, not setting homework that doesn’t impact learning or poor feedback on homework handed in. Recently I read a blog post about 2-4-2 homework. This homework sets 2 questions on the current topic, 4 questions on previously covered topics and 2 extension questions.

Instantly I was intrigued by this format. So often I complain about my pupils poor retention of previous topics. This 2-4-2 format would provide spaced and interleaved practice giving pupils to revisit and review topics throughout the year.

My aim is to write a collection of these homeworks for National 5 maths that will be ready to use at the start of the next session. Hopefully having a set of homeworks prepared in advance with proper planning put into them will help pupils next session.

My other consideration for homework is feedback. I have seen a lot around Twitter about Marking Crib Sheets. These are used to provide whole class feedback. Here is an example of one that I’m considering of adapting.

I would love to hear other opinions on setting homework.

# My Favourites

Over the last few months I have been blogging less and less. Partly due to starting a new job and partly due to lack of inspiration.

Then I saw this on twitter:

This got me excited about the new year and a chance to renew my blogging.

# Sharing: 5 Favourites

The power of Twitter still amazes me. On Friday at 4.43pm I tweeted these two tweets about a starter I had used with my S2 class on Friday morning:

Then at 9.21pm, these tweets appeared:

A link that I had shared as part of #mathsrockedtoday had allowed another teacher to find a new resource and use it within a lesson that same day. So cool! Continue reading

# Maths Teachers At Play Blog Carnival 102

Here is the 102nd edition of the Maths Teachers At Play Blog Carnival (MTaP). It is a collection of blogs submitted by teachers. If you’ve never heard about MTaP then check this out from Denise Gaskins.

The last carnival was hosted by Arithmophobia No More – do take a look.

I am very pleased to host the 102nd edition. So here it is!

Here are some interesting facts about the number 102:

• it is the sum of four consecutive prime numbers (19, 23, 29 and 31)
• 102 is the smallest number with three different digits
• 102 is a Harshad number – a Harshad number is an integer which is divisible by the sum of its digit

Let’s start the carnival. Thanks for all your submissions.

Robot Function: First up is a great post by Nora Oswald. This post describes a game Nora has created for her Algebra classes. It teaches the concept of Composition of Functions. The game objective is to collect the most victory tokens by winning bot fights. I don’t think I’ve ever quite seen a game like it. Can’t wait to try it.

AP Calculus Curve Sketching Tips & Tricks: This is a collection of strategies for AP Calculus about Curve Sketching by Caitlyn Gironda. In the post Caitlyn describes some of her favourite conversations to have with students about curve sketching.

I’s so confused!!! Lovely post here from Lori Martensen. In it Lori describes how she uses learning menus to help planning for purposeful differentiation. These menus are used for scaffolding learning and enriching learning in order to make learning accessible to all. Really useful tool to use when planning to consider the needs of all.

Doodling With: heading now to the artistic side of mathematics. In this post Dan M explains all about nineteenth century Froebelian textbooks. Take a look at what you can do when faced with a blank piece of paper.

Coin Counting: here Erick Lee describes a situation when he tried to take coins to the bank to be counted and the machines had been removed. Interesting look at if a coin counting machine can ever really be 100% accurate.

Midsegments in Triangles Paper Folding Activity: in this post Mrs E. shows how she uses paper folding to help student understanding of midsegments in triangles in a clear visual way. I love anything visual and involves a bit of folding!  And if singing is more your thing, check out this post by Mrs E. which talks about a lesson using songs to learn about functions.

Holes: Simon Gregg explores the use of pattern blocks. Some fascinating diagrams looking at area of shapes and holes. Excellent for discussions about geometry and patterns. Here’s a little peek – “A dodecagon like this

can be made a lot of different ways (try it!) but they will all have an area equivalent to six squares and twelve triangles.”
There seems to be some problem in Table of 15…. : this blog post by Rupesh Gesota details a problem that a pupil had multiplying by 15 and the type of questioning used to fix the error. Really great to read about how a teacher can, through proper facilitation, not steal away the pupil’s credit of finding and correcting his mistake,… thus enabling him to be an independent problem solver…

I come before you: Joshua Greene sent a link to a blog by A.O. Fradkin talking about a simple and fun activity involving organised thinking. Take a read about using building blocks to discover why order matters.

And finally, a post from Denise Gaskins entitled Prof. Triangleman’s Abbreviated List of Standards for Mathematical Practice. As Denise says herself “I loved Christopher Danielson’s list when he first published it, so I asked to quote it in my Multiplication & Fractions book. To my joy, he offered this expanded version, with permission to post it on my blog as well.” Make sure you have a look to see how can we help children learn to think mathematically.

Well that’s all from me. Hope you have enjoyed this selection of blog posts. Thanks for reading.

# #loveteaching

It’s the middle of the school holidays but I am writing this post in response to the article today by the Secret Teacher in the Guardian. I read a great post by Miss B Lilley about spreading the positive message of teaching instead of all the negativity. Here’s the invitation:

I invite you to become the Not So Secret Teacher, send me through your positive experiences of teaching, just focus on one particular thing that you love about teaching, or that makes your day, or that reminds you of how lucky you are to spend your days teaching young people, let’s inspire people to take on (and keep) a career that is more rewarding than so many others.

missblilley

Before I write about why I love teaching I want to share three things:

1. there is a lovely website One Good Thing where teachers all over the world share one good thing from their day. Make sure to check it out here.
2. teaching is a challenging profession but through debate, discussion, sharing and support it can be the most wonderful job.
3. Some maths teachers back in August started using the hashtag #mathsrockedtoday as a way to highlight positivity in the classroom. I would love to see others joining in.