TickTockMaths

Tag: algebra

  • Writing Expressions

    Download the PowerPoint here

    I think one of the reasons students struggle so much when facing this topic is the amount of ways we can phrase things. x multiplied by y. x times y. x lots of y. x items costing y each.

    I’ve tried to collect some of these here, but I’m sure there are loads more!

    This lesson is whiteboard heavy. It’s the best way, I think.

    Students still found it hard. Sometimes with a topic like this, it’s hard to see why. We muddled through, but it didn’t flow as gracefully as it could have. I’d love some feedback/thoughts on this.

    @ticktockmaths on twitter if you wanna chat, although I don’t know how much longer I can justify having a Twitter. All my audience is there. But it’s not a great place. I think I’m moving to BlueSky sooner rather than later.

    Maybe FDP next. Maybe not for a while.

  • Substitution with positive integers

    Download the resource here

    Sometimes a resource benefits from you deleting stuff, not adding stuff.

    I’ve got a much better understanding of what I want these resources to be, and how they’re helpful these days.

    Case in point. This used to be a massive PowerPoint stuff with activities, just for the sake of doing activities. But there’s way better stuff on resourceaholic.com if you want nice worksheets.

    I’ve cut right down on that. Now I know what I want. An example problem pair, some good questions and a base to build from. Other people have made interesting and fun substitutions tasks. I don’t need to put bad approximations of them in my slides. These are the bones of a lesson.

    One thing I DO need is lots of feedback opportunities. Thus I’ve added in loads of mini whiteboard work.

    These don’t move as quick as the gif 🙂 Clicking controls the speed.

    And some questions whose progression makes sense

    And that’s pretty much it. There’s some exam questions and a plenary, but I genuinely think that by deleting loads of stuff I’ve got much closer to the actual inquisition of the skill.

    Sometimes, less is more.

  • Solving equations with unknowns on both sides

    Download the lesson here.

    It’s a double bill today. Not mind blowing stuff, but my old slides were in desperate need of an update. I think that’s most of solving linear equations done now (bar working with fractions which is going to be a biiiiiiiiiiig job).

    I wasn’t sure about what to add to this resource. I couldn’t find many ways to jazz up the topic. If anyone has some really nice questions for this topic, hit me up at @ticktockmaths and I’ll add some stuff for this.

    I took the exercise format from a book called Maths with Pizzazz, which is a 1990s Australian textbook that’s full of codebreakers and nice exercises. I think the drawings and style have a really nice, friendly look.

  • Solving Equations with brackets

    Download the lesson here.

    I only did ‘one side’ here. I figured it would be better to leave the two sides until later.

    Contains a lot of discussion slides.

    And some ‘correct the work’ slides. I don’t normally do ‘correct the work’ because I’ve had limited success with it in the past, but I’ve always asked students to work out which are wrong, rather than telling them that work is definately wrong and asking them to find the mistake. When I did this, the task went much better than it has before.

  • Vary and twist: Collecting like terms

    Download the worksheet here

    Not sure how I feel about some of the decisions here. I’ve introduced a bit of index laws towards the end of the sheet. Is this madness? I thought I would add it to reinforce the difference between simplifying powers and simplifying regular expressions. Maybe it’s too much.

    As usual here’s my little justification for the first 10 questions.

    1. A simple one to start
    2. If you change the letter, it’s the same process
    3. You can have multiples of terms
    4. And it doesn’t matter where in the expression they occur
    5. You can have 3 terms
    6. And it doesn’t matter where in the expression they occur
    7. Introducing a negative for the first time. At the end to make it easier
    8. But the negative can occur anywhere! Here it actually makes you use negatives unless you collect the terms first
    9. Introducing terms like bc. It’s not the same as b + c
    10. We can do some division

    Later questions cover stuff like ab being the same as ba.

    I quite like the last question

    How often do we present students with expressions that can’t be simplified?

    If you use it or adapt it, please comment here.

  • The UK's cheapest mortgage?

    HSBC launches Britain’s first fixed-rate mortgage below 1% [The Guardian]

    The bank is offering customers the chance to lock in for two years at an interest rate of 0.99%, but they need a deposit of at least 35% and will pay a product fee of £1,499.

    The question then is, is this cheaper that most people can currently get? How much cheaper.

    Untitled-1

    It seems like a lot! I’ve done a quick graph in DUDAMATH here comparing debt after 2 years between the new mortgage and a typical no-fee 1.89% mortgage. I’ve used x to represent the amount that you’re borrowing.

    Stuff like this is good.

    1. It’s nice to demonstrate that the maths we do has real world applications. Solving equations links to mortgages.
    2. It’s nice to show all the different maths I’ve used here. Forming equations is useful when plotting graphs and comparing data. You can also see why I’ve plotted the graph. It gives a much nicer and easier to read handle on the financials when compared to the article.
    3. Teaching this in a lesson I could vary the interest rate using DUDAMATH. We could investigate at which point the 0.99% deal is better than a y% deal.

  • Balancing Equations vs Sign Change

     

    I was showing a fellow teacher DUDAMATH on Friday. It was all going well until this teacher, who I respect greatly, recoiled in horror.

    When you drag a term in an equation in DUDAMATH, and drop it on the other side, it changes the sign of the term. 4x becomes -4x.

    ‘Next you’ll be moving the decimal point!’ came the agonised voice of this fellow teacher. This fellow teacher also happens to be a member of our teaching and learning team. She knows her stuff.

    This sparked a lively debated in the maths office. I’ve always been told to show students balancing equations. Another teacher pointed out that in his view balancing equations was essential, as it preserves the shows the fundamentals of the equals sign. This is something that is not explicit when using inverse operations.

    Another teacher pointed out that when students who are taught inverse operations come across equations with unknowns on both sides, they struggle.

    I’m undecided. I get that balancing is good, but I like maths because I enjoy using a variety of methods to get to the same answer.

    Maybe students need a plurality of methods in order to learn. Maybe the best method depends on context. I ran a Twitter survey on this, but no one replied. I’m bad at Twitter.

    Add your thoughts below the line.