Links from Reflect, Expect, Check, Explain

Here you will find the links to all the sequences, diagrams and activities described in my book: Reflect, Expect, Check, Explain.

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If you have not yet read the book, then it is available from Amazon or John Catt Educational
My other books, including How I wish I’d taught maths, can be found here

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Contents

Key websiteskeyboard_arrow_up

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Variation Theory
Diagnostic Questions and Eedi
SSDD Problems
Maths Venns
Goal-free Problems

Researchkeyboard_arrow_up

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Many of the research papers quoted throughout the book and detailed in the References section can be accessed here

Mr Barton Maths Podcastkeyboard_arrow_up

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The easiest way to access the podcast episodes quoted in the text is to visit the Mr Barton Maths Podcast homepage

Clicker and timerkeyboard_arrow_up

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When running a workshop, the most common questions I am asked concern where I get my clicker and my PowerPoint egg-timer from. I am not sure what that says about the quality of my content. Anyway, here you go:

Logitech Spotlight clicker
PowerPoint egg timers

Chapter 1: Intelligent Practicekeyboard_arrow_up

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The five stage process for running Intelligent Practice sequences in the classroom:


The double-pause of questioning:


Student Prompts whilst they work on an Intelligent Practice sequence:

Two possible student templates for them to record their answers in:

Paired Discussion Prompts to support students working together on an Intelligent Practice sequence:

Discuss Relationships prompts for the teacher to use when going through the answers:

Prompts for Delving Deeper for the teacher to use after Discuss Relationships, or to challenge students who finish early:

• Sequence of questions on calculating an estimate of the mean from grouped data
• Take a Break #1: Subtracting decimals

Take a Break #2: Rounding to 1 decimal placekeyboard_arrow_up

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• You can find this sequence here

Chapter 2: Where does Intelligent Practice fit in?keyboard_arrow_up

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My model of a Learning Episode:


The Atomisation process:


The five stages of the Example-Problem Pair process:











Your Turn prompts:









Student prompt cards for each stage of the Example-Problem Pair process:

Suzanne Stoppard kindly created and shared a Word version of these Prompt cards where all the cards are the same size and editable here

My process for asking Diagnostic Questions:

My Extension Prompts for Diagnostic Questions:

• Julia Smith’s lovely Pythagoras hook
• Dan Anderson’s photo of the Pyramid of Pennies
• The etymology word tree is from the Unit Conversions edition of Jo’s wonderful Topic in Depth series
• White Rose Maths small steps are from their free schemes of work
• The inequality notation Diagnostic Question featuring Tom and Katie
• The inequality notation Diagnostic Question involving negative numbers
• The sequence of questions on finding the midpoint
• The rounding to 1 decimal place Diagnostic Question
• The discussion based Diagnostic Question on forming a sensible estimate for the mean
• Mr Taylor’s Increasingly Difficult Questions on fractions of an amount
• The sharing in a ratio Method Selection sequence
• The factorising quadratic expressions Method Selection sequence
• The percentage operation Method Selection sequence
• Take a Break #3: Reading Scales - decimals
• The first grouped data SSDD Problem
• The second grouped data SSDD Problem
• Martin’s driveway SSDD Problem
• The percentage pay rise SSDD Problem
• The grouped frequency table Goal-Free Problem
• The timetable Goal-Free Problem
• The concert ticket Goal-Free Problem
• The ratio Venn Diagram
• The UKMT questions on averages can be found in the Averages and Range Collections on Diagnostic Questions
• Jamie Frost’s questions on ratio 
• Kathryn Darwin on Twitter
• Dan Lewis (@4301maths) interleaved sequences questions
• MathByExamples materials
• AlgebraByExample materials
• The Diagnostic Question on which columns to include in the calculation of the estimate of the mean
• The Diagnostic Question on the weights of Easter eggs
• The Don Steward trapezium question
• Andy Lutwyche’s What was the question?
• Colin Foster’s Possible or Impossible, from Instant Maths Ideas, Statistical Calculations
• Colin Foster’s 17 / 5, from Instant Maths Ideas, Rounding

Chapter 3: Different features of Intelligent Practice sequenceskeyboard_arrow_up

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Prompts for student-generated sequences::

• The simplifying fractions sequence
• The straight line graphs tables of values sequence
• The expanding brackets sequence
• The direct proportion sequence involving rulers
• The mean from a list of data sequence
• The positive integer powers sequence
• The understanding inequality notation sequence
• The group width sequence
• The frequency density sequence
• Fill in the gaps - Histograms
• The reading scales with decimals sequence
• The probability without replacement sequence
• The one-step linear equations sequence
• The factorising double brackets with a purpose sequence
• Fill in the gaps - Quadratics
• Fill in the gaps - Linear sequences 

Take a Break #4: Carrying out rotationskeyboard_arrow_up

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• The carrying out rotations sequence
• Colin Foster’s Staying on the page task

Chapter 4: Intelligent Practice FAQskeyboard_arrow_up

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• The sharing in a ratio sequence
• The first UKMT question can be found in the percentages collections
• The second UKMT question can be found in the ratio collections
• The percentage of an amount sequence

Take a Break #6: Equation of a tangent to a circlekeyboard_arrow_up

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• This equation of a tangent to a circle sequence

Chapter 5: Rulekeyboard_arrow_up

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My process for running Rule sequences of examples:

Prompts for discussions with partner before the answer is revealed:

Prompts for discussions with partner after the answer is revealed:

Teacher prompts for Discuss Relationships:

Teacher prompts for Delving Deeper:

Frayer diagram template:

• The mode from a frequency table sequence

Chapter 6: Different uses of Rulekeyboard_arrow_up

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• What is a polygon sequence
• What is frequency sequence
• Is this number in standard form sequence
• Is this the subject of the formula sequence
• When can you use the multiplication law sequence 
• Number of significant figures sequence
• Factors sequence
• Prime factors sequence
• Factors from prime factors sequence
• Types of numbers from prime factors sequence
• Prime factor decomposition Fill in the gaps
• Product of prime factors - generalising
• Ordering decimals sequence
• Multiplying or dividing an integer by a fraction sequence
• Basic differentiation sequence

Take a Break #7: Averages and range from a list of data: Increase, decrease, same?keyboard_arrow_up

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• Averages and range from a list of data: Increase, decrease, same? sequence

Chapter 7: Patternkeyboard_arrow_up

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My process for running Pattern sequences of questions:

Student prompts for discussion:

Pattern prompts for delving deeper:

• Addition of negative numbers sequence
• Adding and subtracting negative numbers Intelligent Practice 
• Adding and subtracting negative numbers Fill in the gaps
• Addition Structured Variation Grid is available here and here
• Dividing with decimals sequence
• Power of zero sequence
• Expanding double brackets sequence
• The quadratic expressions Structured Variation Grid

Take a Break #8: Constructionskeyboard_arrow_up

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• The constructions sequence

Chapter 8: Demonstrationkeyboard_arrow_up

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My process for running Demonstration sequences of examples:

Prompts for discussions with partner before the answer is revealed:

Prompts for discussions with partner after the answer is revealed:

Teacher prompts for Discuss Relationships:

Teacher prompts for Delving Deeper:

• The straight line graphs Demonstration
• The straight line graphs Venn Diagrams activity
• The angle at the centre demonstration
• The area of a triangle demonstration

Chapter 9: Summary tablekeyboard_arrow_up

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A summary of the four types of sequences and where they fit into a Learning Episode:

Chapter 10: Teachers writing their own sequences of questions and exampleskeyboard_arrow_up

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A structure for teacher trying sequences:

A structure for teacher writing their own sequences: