Interactive Maths - The Interactive Way to Teach Mathematics
  • Interactive Maths
    • Activities Index
    • 50 Great Activities for Any Classroom
    • QQI Activity Descriptions
    • About Me
    • Contact Me
    • Links
    • Legal & Fees
    • Privacy Policy
  • Blog
  • Number
    • Arithmetic >
      • The Four Operations >
        • The Four Operations (QQI)
        • The Four Operations (10QQI)
        • The Four Operations (QQI Count Down)
        • The Four Operations (QQI Relay)
        • The Four Operations (QQI BINGO)
        • The Four Operations (QQI Worksheets)
        • The Four Operations (Video)
        • Timestables Square (QQI)
        • Grid Multiplication (QQI)
      • Missing Numbers >
        • Missing Numbers (QQI)
        • Missing Numbers (10QQI)
        • Missing Numbers (QQI Count Down)
        • Missing Numbers (QQI Relay)
        • Missing Numbers (QQI BINGO)
        • Missing Numbers (QQI Worksheets)
      • Order of Operations >
        • Order of Operations (QQI)
        • Order of Operations (10QQI)
        • Order of Operations (QQI Count Down)
        • Order of Operations (QQI Relay)
        • Order of Operations (QQI BINGO)
        • Order of Operations (QQI Worksheets)
      • Powers of Ten >
        • Powers of Ten (QQI)
        • Powers of Ten (10QQI)
        • Powers of Ten (QQI Count Down)
        • Powers of Ten (QQI Relay)
        • Powers of Ten (QQI BINGO)
        • Powers of Ten (QQI Worksheets)
      • Decimal Operations >
        • Decimal Operations (QQI)
        • Decimal Operations (10QQI)
        • Decimal Operations (QQI Count Down)
        • Decimal Operations (QQI Relay)
        • Decimal Operations (QQI BINGO)
        • Decimal Operations (QQI Worksheets)
      • Rounding >
        • Rounding (QQI)
        • Rounding (10QQI)
        • Rounding (QQI Count Down)
        • Rounding (QQI Relay)
        • Rounding (QQI BINGO)
        • Rounding (QQI Worksheets)
      • Products and Sums (QQI)
      • Products and Sums (10QQI)
    • Fractions >
      • Cancelling Fractions >
        • Cancelling Fractions (QQI)
        • Cancelling Fractions (10QQI)
        • Cancelling Fractions (QQI Count Down)
        • Cancelling Fractions (QQI Relay)
        • Cancelling Fractions (QQI BINGO)
        • Cancelling Fractions (QQI Worksheets)
      • Mixed Numbers and Improper Fractions >
        • Mixed Numbers and Improper Fractions (QQI)
        • Mixed Numbers and Improper Fractions (10QQI)
        • Mixed Numbers and Improper Fractions (QQI Count Down)
        • Mixed Numbers and Improper Fractions (QQI Relay)
        • Mixed Numbers and Improper Fractions (QQI BINGO)
        • Mixed Numbers and Improper Fractions (QQI Worksheets)
      • Fractions of Amounts >
        • Fractions of Amounts (QQI)
        • Fractions of Amounts (10QQI)
        • Fractions of Amounts (QQI Count Down)
        • Fractions of Amounts (QQI Relay)
        • Fractions of Amounts (QQI BINGO)
        • Fractions of Amounts (QQI Worksheets)
      • Fraction Arithmetic >
        • Fraction Arithmetic (QQI)
        • Fraction Arithmetic (10QQI)
        • Fraction Arithmetic (QQI Count Down)
        • Fraction Arithmetic (QQI Relay)
        • Fraction Arithmetic (QQI BINGO)
        • Fraction Arithmetic (QQI Worksheets)
    • FDP >
      • Fraction Decimal Conversions Drill
    • Percentages >
      • Percentages of Amounts >
        • Percentages of Amounts (QQI)
        • Percentages of Amounts (10QQI)
        • Percentages of Amounts (QQI Count Down)
        • Percentages of Amounts (QQI Relay)
        • Percentages of Amounts (QQI BINGO)
        • Percentages of Amounts (QQI Worksheets)
        • Percentage of Amounts (Video)
      • Writing Numbers as a Percentage >
        • Writing Numbers as a Percentage (QQI)
        • Writing Numbers as a Percentage (10QQI)
        • Writing Numbers as a Percentage (QQI Count Down)
        • Writing Numbers as a Percentage (QQI Relay)
        • Writing Numbers as a Percentage (QQI BINGO)
        • Writing Numbers as a Percentage (QQI Worksheets)
        • Writing Numbers as a Percentage (Video)
      • Percentage Change >
        • Percentage Change (QQI)
        • Percentage Change (10QQI)
        • Percentage Change (QQI Count Down)
        • Percentage Change (QQI Relay)
        • Percentage Change (QQI Worksheets)
        • Percentage Change (Video)
      • Increase and Decrease by a Percentage >
        • Increase and Decrease by a Percentage (QQI)
        • Increase and Decrease by a Percentage (10QQI)
        • Increase and Decrease by a Percentage (QQI Count Down)
        • Increase and Decrease by a Percentage (QQI Relay)
        • Increase and Decrease by a Percentage (QQI BINGO)
        • Increase and Decrease by a Percentage (QQI Worksheets)
        • Increase and Decrease by a Percentage (Video)
      • Compound Interest and Simple Interest >
        • Compound Interest and Simple Interest (QQI)
        • Compound Interest and Simple Interest (10QQI)
        • Compound Interest and Simple Interest (QQI Count Down)
        • Compound Interest and Simple Interest (QQI Relay)
        • Compound Interest and Simple Interest (QQI BINGO)
        • Compound Interest and Simple Interest (QQI Worksheets)
        • Compound Interest and Simple Interest (Video)
      • Overall Percentage Change >
        • Overall Percentage Change (QQI)
        • Overall Percentage Change (10QQI)
        • Overall Percentage Change (QQI Count Down)
        • Overall Percentage Change (QQI Relay)
        • Overall Percentage Change (QQI BINGO)
        • Overall Percentage Change (QQI Worksheets)
      • Reverse Percentages >
        • Reverse Percentages (QQI)
        • Reverse Percentages (10QQI)
        • Reverse Percentages (QQI Count Down)
        • Reverse Percentages (QQI Relay)
        • Reverse Percentages (QQI BINGO)
        • Reverse Percentages (QQI Worksheets)
        • Reverse Percentages (Video)
      • Mixed Percentages >
        • Mixed Percentages (QQI)
        • Mixed Percentages (10QQI)
        • Mixed Percentages (QQI Count Down)
        • Mixed Percentages (QQI Relay)
        • Mixed Percentages (QQI BINGO)
        • Mixed Percentages (QQI Worksheets)
    • Factors and Multiples >
      • Number Properties (QQI)
      • Product of Primes >
        • Product of Primes (QQI)
        • Product of Primes (10QQI)
        • Product of Primes (QQI Count Down)
        • Product of Primes (QQI Relay)
        • Product of Primes (QQI BINGO)
        • Product of Primes (QQI Worksheets)
      • HCF and LCM >
        • HCF and LCM (QQI)
        • HCF and LCM (10QQI)
        • HCF and LCM (QQI Count Down)
        • HCF and LCM (QQI Relay)
        • HCF and LCM (QQI BINGO)
        • 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)
        • Standard Form Conversions (10QQI)
        • Standard Form Conversions (QQI Count Down)
        • Standard Form Conversions (QQI Relay)
        • Standard Form Conversions (QQI BINGO)
        • Standard Form Conversions 2 (QQI BINGO)
        • Standard Form Conversions (QQI Worksheets)
      • Standard Form Arithmetic >
        • Standard Form Arithmetic (QQI)
        • Standard Form Arithmetic (10QQI)
        • Standard Form Arithmetic (QQI Count Down)
        • Standard Form Arithmetic (QQI Relay)
        • Standard Form Arithmetic (QQI BINGO)
        • Standard Form Arithmetic (QQI Worksheets)
    • Ratio and Proportion >
      • Ratio (Video)
    • Surds >
      • Surds Activities >
        • Surds (QQI)
        • Surds (10QQI)
        • Surds (QQI Count Down)
        • Surds (QQI Relay)
        • Surds (QQI BINGO)
        • Surds (QQI Worksheets)
  • Algebra
    • Algebraic Manipulation >
      • Collecting Like Terms >
        • Collecting Like Terms (QQI)
        • Collecting Like Terms (10QQI)
        • Collecting Like Terms (QQI Count Down)
        • Collecting Like Terms (QQI Relay)
        • Collecting Like Terms (QQI BINGO)
        • Collecting Like Terms (QQI Worksheets)
      • Expanding Single Brackets >
        • Expanding Single Brackets (QQI)
        • Expanding Single Brackets (10QQI)
        • Expanding Single Brackets (QQI Count Down)
        • Expanding Single Brackets (QQI Relay)
        • Expanding Single Brackets (QQI BINGO)
        • Expanding Single Brackets (QQI Worksheets)
      • Factorising >
        • Factorising (QQI)
        • Factorising (10QQI)
        • Factorising (QQI Count Down)
        • Factorising (QQI Relay)
        • Factorising (QQI BINGO)
        • Factorising (QQI Worksheets)
      • Expanding Quadratic Brackets >
        • Expanding Quadratic Brackets (QQI)
        • Expanding Quadratic Brackets (10QQI)
        • Expanding Quadratic Brackets (QQI Count Down)
        • Expanding Quadratic Brackets (QQI Relay)
        • Expanding Quadratic Brackets (QQI BINGO)
        • Expanding Quadratic Brackets (QQI Worksheets)
      • Factorising Quadratics >
        • Factorising Quadratics (QQI)
        • Factorising Quadratics (10QQI)
        • Factorising Quadratics (QQI Count Down)
        • Factorising Quadratics (QQI Relay)
        • Factorising Quadratics (QQI BINGO)
        • Factorising Quadratics (QQI Worksheets)
        • Factorising Quadratic Expressions (Video)
        • Factorising Four Term Expressions (Video)
      • Indices >
        • Indices (QQI)
        • Indices (10QQI)
        • Indices (QQI Count Down)
        • Indices (QQI Relay)
        • Indices (QQI BINGO)
        • Indices (QQI Worksheets)
      • Completing the Square >
        • Completing the Square (QQI)
        • Completing the Square (10QQI)
        • Completing the Square (QQI Count Down)
        • Completing the Square (QQI Relay)
        • 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)
          • Solving Linear Equations (10QQI)
          • Solving Linear Equations (QQI Count Down)
          • Solving Linear Equations (QQI Relay)
          • Solving Linear Equations (QQI BINGO)
          • Solving Linear Equations (QQI Worksheets)
        • Solving Equations with Algebraic Fractions (Video)
      • Quadratic Equations >
        • Solving Quadratic Equations >
          • Solving Quadratic Equations (QQI)
          • Solving Quadratic Equations (10QQI)
          • Solving Quadratic Equations (QQI Count Down)
          • Solving Quadratic Equations (QQI Relay)
          • Solving Quadratic Equations (QQI BINGO)
          • Solving Quadratic Equations (QQI Worksheets)
        • Solving Quadratic Equations by Factorising (Video)
        • The Quadratic Formula (Video)
        • Problems Involving Quadratic Equations (Video)
      • Simultaneous Equations >
        • Solving Simultaneous Equations >
          • Solving Simultaneous Equations (QQI)
          • Solving Simultaneous Equations (10QQI)
          • Solving Simultaneous Equations (QQI Count Down)
          • Solving Simultaneous Equations (QQI Relay)
          • Solving Simultaneous Equations (QQI Relay Fixed)
          • Solving Simultaneous Equations (QQI BINGO)
          • Solving Simultaneous Equations (QQI Worksheets)
        • 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)
        • Sequences (10QQI)
        • Sequences (QQI Count Down)
        • Sequences (QQI Relay)
        • Sequences (QQI BINGO)
        • Sequences (QQI Worksheets)
      • Generating Sequences (Video)
      • General Term for Linear Sequences (Video)
      • Simple Quadratic Sequences (Video)
      • 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)
        • Reflection Symmetry in Other Shapes (GGB)
      • Rotational Symmetry >
        • Rotational Symmetry in Quadrilaterals (GGB)
        • Rotational Symmetry in Triangles (GGB)
        • Rotational Symmetry in Other Shapes (GGB)
    • Area and Perimeter >
      • Polygons >
        • Perimeters (GGB)
        • Area of a Triangle (GGB)
        • Area of a Parallelogram (GGB)
        • Area of a Trapezium (GGB)
        • Area of Compound Shapes (GGB)
        • Perimeter and Area (GGB)
      • Circles >
        • Discovering Pi (GGB)
        • Circumference of a Circle (GGB)
        • Area of a Circle (GGB)
        • Running Tracks (GGB)
        • Circle Area Problem (GGB)
        • Circles and Squares (GGB)
      • Area (QQI)
      • Area (10QQI)
      • Tilted Squares (GGB)
      • Difference Between Two Squares (GGB)
    • Volume and Surface Area >
      • Volumes and Surface Areas (QQI)
      • Volumes and Surface Areas (10QQI)
    • Angles >
      • Guess the Angle (GGB)
      • Angles on a Straight Line (GGB)
      • Angles around a Point (GGB)
      • Angles in a Triangle (GGB)
      • Angles in a Quadrilateral (GGB)
      • Angles in a Regular Polygon (GGB)
      • Angles on Parallel Lines (GGB)
      • Striping Angles (GGB)
    • Transformations >
      • Reflection >
        • Reflections (GGB)
        • Reflection Challenge (GGB)
      • Rotation >
        • Rotations (GGB)
        • Rotation Challenge (GGB)
      • Translation >
        • Translations (GGB)
        • Translation Challenge (GGB)
      • Enlargement >
        • Enlargements (GGB)
        • Enlargement Challenge (GGB)
        • Other Scale Factors (GGB)
      • Challenges >
        • Which Transformation (GGB)
        • How Many Transformations (GGB)
        • Find Them All (AGG)
        • Ultimate Challenge (GGB)
      • Matrix Transformations (AGG)
    • Pythagoras Theorem >
      • Pythagoras Theorem Activities >
        • Pythagoras Theorem (QQI)
        • Pythagoras Theorem (10QQI)
        • Pythagoras Theorem (QQI Count Down)
        • Pythagoras Theorem (QQI Relay)
        • Pythagoras Theorem (QQI BINGO)
        • Pythagoras Theorem (QQI Worksheets)
      • Pythagoras Theorem (GGB)
      • Pythagorean Triples (GGB)
      • Pythagoras Proof (GGB)
      • Ladders up Walls (GGB)
      • Pythagoras in 3D (GGB)
      • Finding the Hypotenuse Example (Video)
      • Finding a Shorter Side Example (Video)
    • Trigonometry >
      • Right Angled Trigonometry >
        • Right Angled Trigonometry (QQI)
        • Right Angled Trigonometry (10QQI)
        • Right Angled Trigonometry (QQI Count Down)
        • Right Angled Trigonometry (QQI Relay)
        • Right Angled Trigonometry (QQI BINGO)
        • Right Angled Trigonometry (QQI Worksheets)
        • Discovering Trig Ratios (GGB)
        • Finding Lengths (GGB)
        • Finding Missing Lengths (Video)
        • Finding Missing Angles (Video)
      • Sine Rule (Video)
      • Cosine Rule (Video)
      • Sine and Cosine Rules (Video)
    • Circle Theorems >
      • Angle in the Centre vs Angle at the Circumference (GGB)
      • Angle at the Centre vs Angle at the Circumference (Video)
      • Angles in a Semicircle (GGB)
      • Angle in a Semicircle (Video)
      • Angles in Cyclic Quadrilaterals (GGB)
      • Angles in a Cyclic Quadrilateral (Video)
      • Angles in the Same Segment (GGB)
      • Angles in the Same Segment (Video)
      • Tangents (GGB)
      • Tangents (Video)
      • Alternate Segment Theorem (GGB)
      • Intersecting Tangents (GGB)
      • Intersecting Tangents (Video)
      • Intersecting Chords (GGB)
    • Vectors >
      • Vectors and Scalars (Video)
      • Vector Notation (Video)
      • Resultant Vectors (Video)
      • Resultants of Column Vectors (Video)
      • Scalar Multiplication (Video)
      • Magnitude of a Vector (Video)
    • Miscellaneous >
      • Squares (GGB)
      • Tangrams (GGB)
      • Euler Line (GGB)
      • Geoboards
  • Statistics
    • Probability >
      • Probability (QQI)
      • Probability (10QQI)
      • Probability Tools (Flash)
    • Averages >
      • Averages Activity (QQI)
      • Listed Averages >
        • Listed Averages (QQI)
        • Listed Averages (10QQI)
        • Listed Averages (QQI Count Down)
        • Listed Averages (QQI Relay)
        • Listed Averages (QQI BINGO)
        • Listed Averages (QQI Worksheets)
        • Averages From Lists of Data (Video)
        • Quartiles and Interquartile Range (Video)
      • Averages from Frequency Tables >
        • Averages from Frequency Tables (QQI)
        • Averages from Frequency Tables (10QQI)
        • Averages from Frequency Tables (QQI Count Down)
        • Averages from Frequency Tables (QQI Relay)
        • Averages from Frequency Tables (QQI BINGO)
        • Averages from Frequency Tables (QQI Worksheets)
        • Averages From Frequency Tables (Video)
        • Averages From Grouped Frequency Tables (Video)
      • Averages With A GDC (Video)
    • Statistical Diagrams >
      • Cumulative Frequency (Video)
      • Scatter Graphs and the Mean Point (Video)
      • Scatter Graphs and Linear Regression on a GDC (Video)
      • Correlation and the Correlation Coefficient on a GDC (Video)
  • Post 16 Topics
    • Binomial Expansion >
      • Binomial Expansion (Video)
      • Binomial Theorem (Video)
      • Binomial Coefficients (Video)
      • Binomial Applications (Video)
    • Coordinate Geometry >
      • Coordinate Geometry (QQI)
      • Coordinate Geometry (10QQI)
      • Equation of a Circle (AGG)
    • Differentiation >
      • Differentiating Polynomials >
        • Differentiating Polynomials (QQI)
        • Differentiating Polynomials (10QQI)
        • Differentiating Polynomials (QQI Count Down)
        • Differentiating Polynomials (QQI Relay)
        • Differentiating Polynomials (QQI BINGO)
        • Differentiating Polynomials (QQI Worksheets)
      • Finding Gradients of Curves (QQI)
      • Finding Gradients of Curves (10QQI)
      • Finding Turning Points of Curves (QQI)
      • Finding Turning Points of Curves (10QQI)
    • Trigonometry >
      • Radian and Degree Conversions >
        • Radian and Degree Conversions (QQI)
        • Radian and Degree Conversions (10QQI)
        • Radian and Degree Conversions (QQI Count Down)
        • Radian and Degree Conversions (QQI Relay)
        • Radian and Degree Conversions (QQI BINGO)
        • Radian and Degree Conversions (QQI Worksheets)
      • Trigonometric Exact Values >
        • Trigonometric Exact Values (QQI)
        • Trigonometric Exact Values (10QQI)
        • Trigonometric Exact Values (QQI Count Down)
        • Trigonometric Exact Values (QQI Relay)
        • Trigonometric Exact Values (QQI BINGO)
        • Trigonometric Exact Values (QQI Worksheets)
      • Graphs of Trig Functions (GGB)
  • Starters, Puzzles and Enrichment
    • UKMT Random Question Generator
    • @mathschallenge Random Questions
    • School of Hard Sums Random Questions
    • Random Starter of the Day
    • Mathematically Possible (QQI Starter)
    • Adding Challenge (QQI Starter)
    • Date Starter (QQI Starter)
    • Name That Number (QQI Starter)
    • Matchstick Random Questions
    • Choose 3 Numbers (QQI Starter)
    • What's The Question (QQI Starter)
    • Mathematical Words (QQI Starter)
    • Number of the Day (QQI Starter)
    • Anagrams and Missing Vowels (QQI Starter)
    • Missing Vowels and Word Jumbles (QQI) >
      • Missing Vowels and Word Jumbles Simple Numbers (QQI)
    • Tables (QQI)
    • Target Boards (QQI)
    • Missing Signs (QQI)
    • Random Activities >
      • Exploding Dots
      • Easter Date
      • Easter Tangrams (GGB)
      • Zeller's Algorithm
      • Batman Equation (AGG)
      • Templates
    • Mathematical Videos >
      • Fermat's Last Theorem (Video)
      • Pi Song (Video)
      • Monty Hall Problem (Video)
      • Symmetry, Reality's Riddle (Video)
      • Music of the Primes (Video)
      • Folding Paper (Video)
      • Nature by Numbers (Video)
      • Inspirations (Video)

How I Teach

5/2/2018

0 Comments

 
In this post I am going to share some of the ideas I use in my day to day lessons. These aren't lessons that I have prepared specifically for an observation, or those one-off lessons designed to engage/challenge students beyond the curriculum. These are the bread and butter of my teaching. The things I do every day and every unit. Some of these are things I have been doing for a while, some are relatively new, and a few are actually brand new (I have started them in the last few weeks). This post was inspired by this post (https://teachinnovatereflectblog.wordpress.com/2017/12/29/just-me-doing-what-i-do/) by Ben Gordon.

Planning the unit

First off, I think it important to acknowledge the bigger picture for any lesson, and begin by planning the unit as a whole. Before anything else, I identify the different objectives I need to explicitly teach, as well as the prior knowledge students should have to be successful in this topic. Identifying all the individual items that will need to be covered in a given unit helps me clarify exactly what it is I need to do, and what I want the students to be able to do by the end of the unit. This is something I have always done, but the process has become much more rigorous since reading this excellent blog post (https://tothereal.wordpress.com/2017/08/12/my-best-planning-part-1/) by Kris Boulton. Below is an example for our first unit of Year 10 on Percentages. 
Picture
Prior Knowledge and Initial Assessments

This produces two lists of objectives for student learning: one list of things they should already know; and one list of things I will teach them during this unit. The importance of prior knowledge on learning new content is well established and I have come to believe that checking for prior knowledge and addressing any issues is key to any good instructional sequence. My approach to checking prior knowledge previously has been largely down to asking questions of the class, and perhaps the use of starters in each lesson. Although these certainly served to activate prior existing prior knowledge, they were not always successful in identifying if there was a small problem for some students. I recently read this interesting post (https://misscotterillmaths.wordpress.com/2017/12/24/give-them-a-test/) which discusses in depth the use of Initial Assessments. I really like this idea, and will be using this to start all units this year, giving each class a test in the first lesson which covers the prior knowledge they are expected to know, and some aspects of the new content too. I will include aspects of the new content due to something known as the "pretesting effect" which seems to suggest that testing on unknown content before teaching it can improve later retention after teaching (see http://learninglab.uchicago.edu/Pre-Testing_files/RichlandKornellKao.pdf and https://bjorklab.psych.ucla.edu/wp-content/uploads/sites/13/2016/07/Kornell_Hays_Bjork_2009_JEP-LMC.pdf).

Students will self mark this quiz, and I will quickly check understanding by getting students to raise their hands if they got a question right, and taking a note of how many did for each question on a copy of the unit plan. This will then allow me to plan the following lessons accordingly, if I need to cover any of the prior knowledge material in more depth, or indeed skip over some of the new content they have actually seen before.
Picture
https://drive.google.com/file/d/1VGWsKXEh-BfW7p4HMfrPlEHQFxp5n3Dc/view?usp=sharing

Types of Lesson

In developing the learning of students I use two types of lesson: teaching new content; and practicing the skills. I am a firm believer that humans need enough time to practice a certain skill in order to learn it (by which I mean commit it to long term memory), but that they also need very clear instruction when in the initial stages of learning (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/05/24/Why-Minimal-Guidance-Instruction-Does-Not-Work).

Teaching New Content
For each of the objectives I have identified I would separate a time to follow this process. For some this will be no more than 10 minutes, and for others it will run over more than a single period.

Retrieval Starters
Each lesson begins with a retrieval or fluency starter. This is slightly different for different age groups, but they are all designed to last between 5 and 10 minutes.

With Middle School classes, I use a fluency developing programme called Numeracy Ninjas (http://www.numeracyninjas.org/), which is designed to develop their mathematical fluency in the basic skills required for the subject (number bonds, timestables, rounding, etc).

Previously, with IGCSE classes I used a similar set of resources called the Corbett Maths 5-a-day (https://corbettmaths.com/5-a-day/) which covers the basic skills required for IGCSE Maths. However recently I have started to make use of daily retrieval challenge grids (as described here https://lovetoteach87.com/2018/01/12/retrieval-practice-challenge-grids-for-the-classroom/, with links to templates here https://ictevangelist.com/retrieval-practice-challenge-grid-templates/). I do not run them in quite this way, as I want all students to answer all questions rather than choose, but the concept is the same (see below).

Picture
With IB classes I use a single exam question on a topic we have covered at some point during the course.

These are designed to make the most of the idea of retrieval practice (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/11/07/Retrieval-Practice), and also build in some spaced practice. The important part of these is that they are done individually and without looking up how to do it (thus making use of the strength of retrieval to improve learning). They are always self-marked, and in a similar approach to the initial assessments, I asked students to identify if they got each question correct, which informs my future use of questions.

I spend some time explaining the importance of retrieval with my students in the hope that they will use this opportunity to improve their learning. It has been shown that actively developing student metacognitive strategies can improve learning outcomes significantly (https://educationendowmentfoundation.org.uk/evidence-summaries/teaching-learning-toolkit/meta-cognition-and-self-regulation/).

Introducing New Content
When introducing the new content I will teach it explicitly, mainly using example problem pairs (https://gregashman.wordpress.com/2016/02/09/example-problem-pairs/) where I do one example and then students do a very similar example. These are presented side by side so that students can refer back to the example whilst completing their question, thus lowering the extraneous cognitive load (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/09/25/Cognitive-Load-Theory-Research-that-teachers-really-need-to-understand). I do the example on the board without asking for ideas from the students. Most of the time I will narrate my thoughts as I do the example, though recently I have started to like the idea of the silent example, where students focus all their attention on the example without the split-attention required to listen to me at the same time. I will then go through the important points afterwards. All students are expected to do the second question, and after recently listening to the Mr Barton Podcast with Doug Lemov (http://www.mrbartonmaths.com/blog/doug-lemov-teach-like-a-champion-and-top-tips-for-delivering-training/), I am planning to make use of Show Call, where I will take a photo of a student's work and project it on the board (as I explained in this post http://markhamtl.wixsite.com/teaching-learning/single-post/2017/11/01/A-simple-but-effective-use-for-Google-Docs-in-class), either as an example of an excellent answer or to identify a misconception.
Picture
Test Your Understanding
After teaching the content, it is vitally important for me to know if students have successfully acquired the information or skill, and this is where AFL comes into play. I call this section of the lesson "Test Your Understanding" and this will usually entail between 4 and 10 questions (depending on the complexity) where students will answer them one at a time on mini-whiteboards. These questions are designed to check if students have grasped the concept I have been teaching, and are usually similar to the examples presented. Once they have had enough time to answer the question, all students raise their mini-whiteboard, and I pick up on any misconceptions. An alternative option at this stage is to use well designed multiple choice diagnostic questions (https://diagnosticquestions.com/), where each incorrect answer reveals a specific misconception. If using these, I will usually ask students to vote for their chosen answer using 1 finger for A, 2 fingers for B etc. In both cases, students do not answer until I ask them to raise their board, or make their choice, so that they are not persuaded by other members of the class.

During this stage of the lesson I am asking lots of questions to delve into why students have written certain things, and to get students to explain their reasoning. If different students have got different answers, we will discuss this as a class. If I have used a diagnostic question, we will discuss what misconceptions have been made to reach the incorrect answers.

This is the one part of the lesson where I allow students to discuss with the person next to them, which gives them a chance to clarify the ideas in their head, and further develop their understanding. Sometimes I will only give them a single mini-whiteboard between the pair to encourage this dialogue. Through this process I get a pretty good idea of how well the students have understood my explanations, and can intervene if necessary.

Independent Practice
The final part of the lesson entails a small amount of independent practice, where students will do some questions on their own to embed the skill/knowledge they have just learned. This does not necessarily mean a long boring exercise from the textbook (though I have no issue using the textbook). This will usually include some form of purposeful practice, and will be more involved than the test your understanding questions, getting students to apply their new knowledge in some way. One particularly amazing resource I have come across recently which I will be making use of in this part of the lesson is Increasingly Difficult Questions (http://taylorda01.weebly.com/increasingly-difficult-questions.html) where each question is slightly more challenging than the previous.

One of the most important aspects of these lessons for me is that all students can be successful. As I have mentioned before, I am coming to believe that success is one of the biggest motivators for students (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/10/18/Motivation-in-class). This approach has been tweaked over the last two years as I have come to learn about cognitive load theory, and my interpretation is that breaking the learning into small chunks and teaching them explicitly will lead to the best understanding. My recent personal experience backs this up.

Practising the Skills
After teaching the individual skills there is usually a need to put them all together in some way. These lessons are made up of different tasks, such as:
  1. A simple exercise with questions involving all the different skills. This builds in some interleaving, and as it is a few days after initial teaching, provides another opportunity for simple retrieval. I make use of treasure hunt and tarsia activities quite a lot at this stage. Another popular choice at this stage is doing an exam question relay, where there are 10 questions, and students have to answer one to move on to the next, in a race to be the first to finish.
  2. A rich task (or low-entry high-ceiling task) which all students can access, but gives plenty of scope for challenge. My go to sites for these types of activities are Don Stewards excellent blog (donsteward.blogspot.com) and nrich (https://nrich.maths.org/​).
  3. A modelling task where students have to apply their new found knowledge to model some situation.

Resources/Class Website

This year I have set up a class website (http://classes.interactive-maths.com/) which contains the objectives for each unit, with links to videos, the pdf versions of lessons and any other resources used in class. The image below shows a unit from the IB Mathematical Studies course.
Picture
I use a mixture of SMART Notebook and PowerPoint for my presentations, generally using Notebook for IB classes, and PPTs for other classes. When I finish the lesson for IB, I export the whole lesson, with all my handwritten examples, as a PDF, which is what the "Lesson" links to. For IGCSE and lower, I upload the whole PowerPoint. Sometimes these include the worked examples, but I am much more "on top of" the younger classes to get them to copy examples in class. The presentations themselves are fairly plain, with no flashy images or animations (due to the Redundancy Effect described by cognitive load theory).

Last year I started creating work booklets for my IGCSE class. These booklets include everything they need for the unit, including links to revision videos, the notes (with important information left out for them to copy from my explanation) and the examples with space for them to copy the worked solution. Last year I included the Test Your Understanding in the booklet as well, but for next year I am going to remove these, as some students would jump ahead which made it hard for them to fit the purpose described above. I also include either the exercise/activity for independent practice, or the textbook page number, but expect these to be answered in their exercise books.

For an example of the unit on percentages I have just planned see here: https://drive.google.com/drive/folders/1qr5E5iBn_2RuuuS4WVEVrGpmy0oRstJr?usp=sharing

Fortnightly Quizzes
I have read a lot of research on retrieval practice (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/11/07/Retrieval-Practice) lately, and I am starting to believe it is one of the best ways we can help our students achieve their best. Due to this I have started to do fortnightly quizzes covering the topics we have previously covered. Ideally I would do these weekly, but do not feel I have that much time available to set aside. Currently I have only been doing them with my IGCSE classes, but I am thinking of extending this to IB a well.

These run in a very similar way to the initial assessments, in that I take a lesson to administer, self mark and review any areas of weakness. They are zero stakes quizzes, and the students marks do not count towards their grades at all. The questions in these quizzes are usually very knowledge/skills based, and do not require students to apply their knowledge to difficult new ideas. I have read a few blogs recently who approach this in a much more structured way than I currently do, including 2 questions from the current work, 2 from a month ago, 2 from last term and things like this. I like these ideas, and will be building more structure into the way I prepare these retrieval quizzes in the future.

Homework
In the last few years I have used homework as a retrieval strategy, giving a mixed topic homework. However, I have found that these do not work the way they are intended, as students would use their books and hence not actually engage in active retrieval, which is why I have switched to retrieval quizzes in class. This year I will be using homework for independent practice to consolidate key skills. These tasks will be aimed largely at developing fluency in the skill or skills currently being learnt.

Final Comments
I don't think any of these ideas are my own, they have all come from a variety of sources over the last few years. This approach is very different to how I was teaching before I came across the amazing world of education research (mainly through the Mr Barton Podcast http://www.mrbartonmaths.com/podcast/), and I don't know if it will stay like this forever, but I would need a pretty strong argument to convince me that the ideas of CLT and Retrieval Practice were things to drop from my teaching! One of the most influential pieces on my teaching, that I think all teachers should read, is the Principles of Instruction (http://markhamtl.wixsite.com/teaching-learning/single-post/2017/09/11/Principles-of-Instruction) by Barak Rosenshine, and I based a lot of this system of teaching on those ideas.

0 Comments

Your comment will be posted after it is approved.


Leave a Reply.

    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.

    Categories

    All
    Coaching
    Displays
    General
    Leadership
    Personal
    Planning
    Projects
    Reading Review
    Reflections
    Research Based
    Resources
    Teaching Ideas
    Tech Ideas

    Archives

    August 2021
    April 2021
    January 2021
    December 2020
    October 2020
    August 2020
    July 2020
    June 2020
    May 2020
    April 2020
    March 2020
    February 2020
    January 2020
    December 2019
    November 2019
    October 2019
    September 2019
    August 2019
    July 2019
    June 2019
    May 2019
    April 2019
    March 2019
    January 2019
    December 2018
    November 2018
    October 2018
    September 2018
    August 2018
    July 2018
    June 2018
    May 2018
    April 2018
    February 2018
    December 2017
    November 2017
    October 2017
    May 2017
    May 2016
    February 2016
    January 2016
    September 2015
    July 2015
    April 2015
    March 2015
    February 2015
    April 2014
    March 2014
    February 2014
    January 2014
    December 2013
    November 2013
    September 2013
    July 2013
    June 2013
    May 2013
    April 2013
    March 2013
    February 2013
    January 2013
    December 2012

    RSS Feed

Information
  • About Me
  • Contact Me
  • Links
  • Legal and Fees
  • Privacy Policy
Indices and Activities
  • QQI Activity Descriptions
  • Activity Index
  • Video Index
Sister Sites
  • The blog
  • Generators
  • Crypto Corner
  • ​Mr R-Cs Classes
©2012-2023 Daniel Rodriguez-Clark
All rights reserved
Picture