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  • Number
    • Arithmetic >
      • The Four Operations >
        • The Four Operations (QQI)
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      • Order of Operations >
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      • Powers of Ten >
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      • Decimal Operations >
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      • Rounding >
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      • Products and Sums (QQI)
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    • Fractions >
      • Cancelling Fractions >
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      • Mixed Numbers and Improper Fractions >
        • Mixed Numbers and Improper Fractions (QQI)
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      • Fractions of Amounts >
        • Fractions of Amounts (QQI)
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      • Fraction Arithmetic >
        • Fraction Arithmetic (QQI)
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    • FDP >
      • Fraction Decimal Conversions Drill
    • Percentages >
      • Percentages of Amounts >
        • Percentages of Amounts (QQI)
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        • Percentage of Amounts (Video)
      • Writing Numbers as a Percentage >
        • Writing Numbers as a Percentage (QQI)
        • Writing Numbers as a Percentage (10QQI)
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        • Writing Numbers as a Percentage (Video)
      • Percentage Change >
        • Percentage Change (QQI)
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      • Increase and Decrease by a Percentage >
        • Increase and Decrease by a Percentage (QQI)
        • Increase and Decrease by a Percentage (10QQI)
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        • Increase and Decrease by a Percentage (Video)
      • Compound Interest and Simple Interest >
        • Compound Interest and Simple Interest (QQI)
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        • Compound Interest and Simple Interest (Video)
      • Overall Percentage Change >
        • Overall Percentage Change (QQI)
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      • Reverse Percentages >
        • Reverse Percentages (QQI)
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        • Reverse Percentages (Video)
      • Mixed Percentages >
        • Mixed Percentages (QQI)
        • Mixed Percentages (10QQI)
        • Mixed Percentages (QQI Count Down)
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    • Factors and Multiples >
      • Number Properties (QQI)
      • Product of Primes >
        • Product of Primes (QQI)
        • Product of Primes (10QQI)
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      • HCF and LCM >
        • HCF and LCM (QQI)
        • HCF and LCM (10QQI)
        • HCF and LCM (QQI Count Down)
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        • HCF and LCM (QQI Worksheets)
        • HCF and LCM (Video)
      • 100 Square Multiples (QQI)
      • 100 Square Types of Numbers (QQI)
    • Standard Form >
      • Standard Form Conversions >
        • Standard Form Conversions (QQI)
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        • Standard Form Conversions 2 (QQI BINGO)
        • Standard Form Conversions (QQI Worksheets)
      • Standard Form Arithmetic >
        • Standard Form Arithmetic (QQI)
        • Standard Form Arithmetic (10QQI)
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    • Ratio and Proportion >
      • Ratio (Video)
    • Surds >
      • Surds Activities >
        • Surds (QQI)
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        • Surds (QQI Worksheets)
  • Algebra
    • Algebraic Manipulation >
      • Collecting Like Terms >
        • Collecting Like Terms (QQI)
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      • Expanding Single Brackets >
        • Expanding Single Brackets (QQI)
        • Expanding Single Brackets (10QQI)
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      • Factorising >
        • Factorising (QQI)
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        • Factorising (QQI Worksheets)
      • Expanding Quadratic Brackets >
        • Expanding Quadratic Brackets (QQI)
        • Expanding Quadratic Brackets (10QQI)
        • Expanding Quadratic Brackets (QQI Count Down)
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        • Expanding Quadratic Brackets (QQI BINGO)
        • Expanding Quadratic Brackets (QQI Worksheets)
      • Factorising Quadratics >
        • Factorising Quadratics (QQI)
        • Factorising Quadratics (10QQI)
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        • Factorising Quadratic Expressions (Video)
        • Factorising Four Term Expressions (Video)
      • Indices >
        • Indices (QQI)
        • Indices (10QQI)
        • Indices (QQI Count Down)
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        • Indices (QQI Worksheets)
      • Completing the Square >
        • Completing the Square (QQI)
        • Completing the Square (10QQI)
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        • Completing the Square (QQI BINGO)
        • Completing the Square 2 (QQI BINGO)
        • Completing the Square (QQI Worksheets)
      • Algebraic Fractions >
        • Simplifying Algebraic Fractions (Video)
        • Adding and Subtracting Algebraic Fractions (Video)
        • Multiplying and Dividing Algebraic Fractions (Video)
    • Coordinates >
      • Coordinates (GGB)
      • Coordinate Battleship First Quadrant (GGB)
      • Coordinate Battleship All Four Quadrants (GGB)
      • 3D Coordinates (AGG)
    • Equations >
      • Linear Equations >
        • Solving Linear Equations >
          • Solving Linear Equations (QQI)
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        • Solving Equations with Algebraic Fractions (Video)
      • Quadratic Equations >
        • Solving Quadratic Equations >
          • Solving Quadratic Equations (QQI)
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        • Solving Quadratic Equations by Factorising (Video)
        • The Quadratic Formula (Video)
        • Problems Involving Quadratic Equations (Video)
      • Simultaneous Equations >
        • Solving Simultaneous Equations >
          • Solving Simultaneous Equations (QQI)
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          • Solving Simultaneous Equations (QQI BINGO)
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        • Solving Simultaneous Equations Graphically (Video)
        • Simultaneous Equations by Substitution (Video)
        • Simultaneous Equations by Elimination (Video)
        • Simultaneous Equations - One Non-Linear (Video)
    • Sequences >
      • Sequences Activity (QQI)
      • Sequences Activities >
        • Sequences (QQI)
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      • Generating Sequences (Video)
      • General Term for Linear Sequences (Video)
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      • General Term for Quadratic Sequences (Video)
      • General Term for Cubic Sequences (Video)
      • Geometric Sequences (Video)
      • Common Differences (QQI)
    • Graphs >
      • Straight Line Graphs >
        • Drawing Straight Line Graphs (GGB)
        • Gradient of a Line (GGB)
        • Gradient of a Line 2 (GGB)
        • Parallel Lines (GGB)
        • Perpendicular Lines (GGB)
        • y = mx + c Activity (GGB)
        • Battleships 1 (AGG)
        • Battleships 2 (AGG)
        • Battleships 3 (AGG)
        • Find the Lines 1 (AGG)
        • Regions in Graphs (Video)
      • Non-Linear Graphs >
        • Drawing Curves (GGB)
        • Quadratic Graphs Activity (GGB)
        • Finding Quadratic Functions (Video)
      • Graphs with a Casio GDC (Video)
    • Graph Transformations >
      • Graph Transformations 1 (GGB)
      • Graph Transformations 2 (GGB)
      • Graph Transformations 3 (GGB)
      • Graph Transformations 4 (GGB)
      • Graph Transformations 5 (GGB)
      • Graph Transformations 6 (GGB)
    • Functions >
      • Functions Introductions (Video)
      • Function Graphs and Important Points (Video)
      • Solving Unfamiliar Equations Using Functions (Video)
      • Function Notation Revision (Video)
      • Composite Functions (Video)
      • Inverse Functions (Video)
  • Shape
    • Symmetry >
      • Reflection Symmetry >
        • Reflection Symmetry in Quadrilaterals (GGB)
        • Reflection Symmetry in Triangles (GGB)
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      • Rotational Symmetry >
        • Rotational Symmetry in Quadrilaterals (GGB)
        • Rotational Symmetry in Triangles (GGB)
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    • Area and Perimeter >
      • Polygons >
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      • Circles >
        • Discovering Pi (GGB)
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      • Area (QQI)
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    • Volume and Surface Area >
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    • Angles >
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    • Transformations >
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    • Pythagoras Theorem >
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      • Finding the Hypotenuse Example (Video)
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    • Trigonometry >
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        • Discovering Trig Ratios (GGB)
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        • Finding Missing Lengths (Video)
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      • Sine Rule (Video)
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    • Circle Theorems >
      • Angle in the Centre vs Angle at the Circumference (GGB)
      • Angle at the Centre vs Angle at the Circumference (Video)
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      • Tangents (GGB)
      • Tangents (Video)
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    • Vectors >
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    • Miscellaneous >
      • Squares (GGB)
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  • Statistics
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    • Statistical Diagrams >
      • Cumulative Frequency (Video)
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      • Scatter Graphs and Linear Regression on a GDC (Video)
      • Correlation and the Correlation Coefficient on a GDC (Video)
  • Post 16 Topics
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      • Binomial Expansion (Video)
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      • Folding Paper (Video)
      • Nature by Numbers (Video)
      • Inspirations (Video)

Introducing Logarithms

5/7/2018

1 Comment

 
I started logarithms with my (second to bottom) S4 class this week, and I think I managed to introduce it in a way that really helped the students to understand what a logarithm is. First I started the lesson with this recap set of questions on indices.
Picture
​As the students were completing it I realised my error in including 4^(1/2) as this can lead to misconceptions that an index of 1/2 is the same as halving. I probed this after the class completed the questions by asking what 9^(1/2) is, and most of them correctly recalled that it was 3.
Next I used the idea from James Tanton's Take on Logs where I wrote some on the board like this
power2(8) = 3
power5(25) = 2
Your turn!
power3(27) = ___
power10(100) = ___
I didn't use the examples from his essay, but rather used ones that linked to the questions from the starter (the answers were still projected), and wrote them from scratch on the whiteboard. Students could easily see the link between the two. As they grew confident I started to use some that were not from the starter. Towards the end I threw in a couple of impossible situations such as power1(73) = ? and power5(-1) = ?. As James suggests, I then made a big deal out of changing power to log, and explaining that we just use a different name for the function. As we went through these examples I stuck to a particular routine. So, for example, for the question power3(27) = the back and forth went like this:​

Me: "Maria, what is the actual question being asked?"
Maria: "3 to the power of what is 27"
Me: "And the answer is?"
Maria: "3"
​I used cold call from Teach Like a Champion 2.0 throughout this process, writing a question up and asking a student. The class came to the phrase "3 to the power of what is 27" as a group rather than me telling them.
​At this point a student asked "Why do we need logs". Fortunately I had this slide from Dr Frost Maths ready, and launched in to talking about how logarithms are the inverse of exponentials and that we need them to solve equations where the unknown is in an index.
Picture
​We then did an example problem pair, just to reiterate the process, and again I asked what the question was saying.
Picture
Then I set them this exercise that I put together in the style of the ones from the amazing variationtheory.com by Craig Barton. I designed it to try to get students thinking about the connections between each question, though I admit that I still need to work on this aspect of running an exercise like this. However, the questions did bring out some interesting ideas, and many of them were able to spot the impossible ones.
Picture
Picture
​In going through the answers we once again used Cold Call, and rattled through them pretty quickly, again following the same dialogue as above. That was the end of the first lesson.
In the second lesson I started with a few simple questions as retrieval from the previous day, and then students filled in this stickable from Sarah Hagan, with the slide with information given below.
Picture
Picture
We then did these excellent place the log on the number line activities from the Mathematics Vision Project.
Picture
And finished with students writing their own set of Two Truths and a Lie cards (again from Sarah Hagan) based on logarithms. I collected these in, and in the next lesson we started using these, which I projected through the visualiser. Students then used this ordering activity from Susan Wall.
Picture
After this I will be going on to teach the laws of logarithms and solving simple exponential equations using logs.
You can find my folder of resources on this topic here. It includes a work booklet for students, the powerpoints I used, along with some other activities.
1 Comment
Aisha Abid
16/5/2022 09:56:15 am

This is a fantastic way of introducing logs to my year 9's as an enrichment lesson. Thank you for taking the time to put this together.

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    Dan Rodriguez-Clark

    I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.

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