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Gradient of a line

Adapted a Don Steward diagram for a Year 8 lesson on the Gradient. Started with this, and asked students to put the staircases in order of steepness. Students were talking in pairs initially (Think-Pair-Share) before coming back to a whole class discussion. We discussed how they were deciding on what steepness is and what the key features were. We came to the conclusion that more information was needed.   I asked students what measurements would they like to have.  Student: "Can you tell us the angles?" Me: "Sorry guys, I don't have my protractor on me!" Instead I added these values and allowed students to discuss further.  The variation in the numbers allowed for comparisons and a 'discovery' of how we can calculate the gradient. This was a really nice 'hook' into the lesson and helped students understand the concept of the gradient better.  Following this we formalised our method for finding the gradient as rise over run. I went through one fu...

Curriculum Progression

There are more and more conversations around the curriculum happening now but are we talking about the right things? I would argue not completely, let me explain: Vertical Progression of a topic Quite often we talk about how we can progress a topic vertically e.g. how percentages develops from finding a percentage, to increasing and decreasing, compound growth and decay, reverse percentages etc. This is often taught and learnt over a number of years and we look at where that fits in our Year 7 SOW and where it leads in Year 8,9,10 and so on. I love this from  @SarahFarrellKS2  about how she progresses times tables in her Primary school over a number of years.  https://mrsfclassroom.wordpress.com/2022/01/19/times-tables-understanding-and-applying-them/ Horizontal Progression of a topic We discuss horizontal progression less than vertically e.g. how percentages links across the curriculum. If we continue with the example of percentages, I am sure lots of maths teachers make...

📝 Weekly Report #33

This week I listened to a really good podcast episode from Greg McKeown called Where am I wrong? In it he talks about a really effective method to have deeper discussions on what is important.  Write down/say the 3-5 issues/priorities you think there are as well as the cost/consequence of them. Then just simply ask where am I wrong? It starts the conversation off with the other person talking and getting their points across. You can then get that shared understanding about what needs to be done and why.  It got me thinking about other areas this could be useful for e.g. dealing with conflicts, leading departments/teams, pitching a new initiative. I am going to start doing this in some of these scenarios as I think we can have more productive conversations from it.  Have a listen to the episode here .  🔊 Listen: Alan Stein Jr on the Modern Wisdom podcast discussing high performance and overcoming stress. He talks about thinking like an athlete with your work and impr...

📝 Weekly report #32

I've been thinking this week about CPD and more specifically how we deliver it to teachers. As teachers, we are trained on the best ways of explicitly teaching new knowledge to students however quite often we don't use the same techniques when teaching teachers. Why? Most, if not all of the techniques we use with students should also be used with teachers: retrieval of knowledge, teacher led instruction, opportunities for formative assessment. The difficulty with delivering CPD to teachers though is that there group you are delivering to is often very diverse in their understanding but will also be using the knowledge in different subjects and in different ways. It is a difficult task for anyone delivering CPD.  As part of my PD Lead course, I am being trained up to deliver effective CPD to teachers. Within the course we have spoken about having a common starting point, e.g. it could be a Maths question based on the topic I want to deliver to the Maths team, it could be asking ...

Drip feeding topics into your teaching

It's no wonder students struggle with Trigonometry, Pythagoras, Quadratic Formula etc. We overload them with too much new information all at once. Instead, drip feed these topics into the time before these lessons to reduce cognitive load and give students time to learn to a greater depth. Here's how I have done it: Drip feeding future content is an untapped gold mine that we can exploit further in our teaching. Why drip feed the content when we have dedicated time to teach it? - Reduces cognitive load - Can explore the topic to a greater depth - Ensure students have the relevant prior knowledge to be successful - Reduces the need for constantly reteaching In starters in the lead up to the topic and during lessons on substitution I use the relevant formulae students will use later in their Maths journey. My Yr 10s are about to learn about the Sine Rule and Cosine Rule, last term they were answering questions like this in the starter. They have no previous knowledge of these for...

📝 Weekly Report #31

It's been a bit of a mad first week back this term. Stress levels are high with the year 11s and 13s very close to their exams. For them lessons have been revising the advance information topics.  One of the issues I've found with the A level Maths is that students are often unsure what the questions are actually asking them to do.  A strategy I have been using is goal free problems. If you're unsure what they are take a look at the following website . The basic idea is that I'm giving students just the description and perhaps a diagram and ask them to just work stuff out. I find it particularly effective for topics within Mechanics especially.  Initially students struggled with what to do as to they wanted a target to aim for. After doing it for a little while now they are finding it really useful and are often calculating values to hat is beyond what the question actually was. They are making generalities with topics and styles of questions and have massively improved...

Prime Factor Decomposition

I have stopped using a Prime factor tree when teaching Prime Factor Decomposition and so should you! Here's why: 1. Students mix up Frequency trees and Prime Factor trees.  2. Students don't always realise that the prime numbers are the 'building blocks' of the number and they just need to complete the tree to get the mark. 3. Incorrectly writing their final answer. What I now do: It still looks very similar but I have a big focus on rewriting the original number each time and using a line for each step of their workings. For some students I have used little arrows to show which numbers need to be split further and underlined the prime numbers so they can more clearly identify what their next step is. I explicitly teach about using the numbers to 'go backwards' and find other factors e.g. 3 x 2 x 2 = 12 which is a factor of 72. I show students how no matter the starting point, we still end up with the same building blocks e.g. if we started with 2 x 36 we would...