Mathematical Miscellany #75

A collection of impressive resources…

Jake Gordon has been rather busy! Have a look at his “monster of a PowerPoint”. These detailed worked examples are based on the book Teaching math with examples by Michael Pershan.

Also inspired by Michael Pershan’s book and her research on self-explanation, have a look at Karen Hancock‘s journey into worked examples.

From Nathan Day – a brilliant collection of resources on Distributivity: Partitioning, Grid Method, and Expanding Brackets The 15 tasks increase in demand. Note the complete thread.

Also from Nathan Day – a wonderful collection of Starters – again, note the complete thread.
I have added this collection to my Starters page, a collection that includes Advanced Level Starters.

Andy Lutwyche’s collection of Erica’s Errors where students must identify errors in solutions can be an ideal starter for either retrieval practice for an earlier topic or to consolidate learning for a current topic.

Added to my Primary page – curriculum mappings from NCETM

Also added to the Primary page:

On DrFrostMaths there is a growing collection of Key Skills for Primary students.

I have mentioned DrFrostMaths more than once recently, a new instruction manual for teachers is now available.

From the GCSE/IGCSE/L2 Further Maths page, the pages for individual topic areas all include Sites with clear resources by topic, see the Algebra page for example. These resources by topic include links to the relevant DrFrostMaths key skills.

Algebraic Notation

From the KS3 National Curriculum we see the above on algebraic notation, see also pages 56-66 of the Teaching mathematics at key stage 3 guidance. The guidance covers the entire KS3 curriculum and includes common difficulties and misconceptions, examples for use in lessons, and suggested questioning and other strategies for teachers to use.

The following slideshow includes several resources you can use with students for practice in writing algebraic notation.

Included you can see Jonathan Hall’s Worded Expressions, as always with MathsBot resources we have lots of choices – for example, hide either the sentences or expressions. With the ability to generate new expressions we have an endless supply; also from Jonathan Hall, see his Forming Expressions, these resources are ideal for self-study as well as for use in class.

From Don Steward, we have translating English to algebra, expressions, see also translating English to algebra, relationships. Also included here is an activity, A1 from the Standards Unit on Interpreting algebraic expressions. This includes 4 card sets to match, ideal for looking at multiple representations, students match algebraic expressions, explanations in words, tables of numbers and areas of shapes. One of the goals of the activity is to help learners to translate between words, symbols, tables, and area representations of algebraic shapes. The Standards Unit resources can all be accessed without a login from the very clear to navigate University of Nottingham site linked to in the Standards Unit post.

One of Chris McGrane’s Starting Points MathsCurriculum Booklets – Algebra 1 from Phase 3 features some great activities for writing algebraic statements, featured on the slides you can see a Smile activity, and Jo Morgan’s lovely Introduction to Writing Algebraically – this is such a good idea, as Jo says in the resource description if they know how to do it with numbers, then they just do the same thing with the algebra.

Further excellent resources on this skill are available on Maths4Everyone.

On Transum, Writing Expressions is an exercise with a difference, listen to the audio then type in the expression.

From Corbett Maths
Algebra: expressions – forming     Video 16    Practice Questions    Textbook Exercise

From Andy Lutwyche – Algebraic Expressions Spiders

Here’s an interesting query type on WolframAlpha – simple word problems. See more examples of Word Problems (and All Examples by Topic).

From my post on Bar Modelling see The Mathenæum from Ken Wessen which includes Modelling Word Problems.

Mathematical Miscellany #55

Featuring:

In Mathematical Miscellany #54 I featured two excellent resources from Curriculum for Wales; a third is now available, “The Foundations of Algebra” is suitable for progression step 3 of the new #CurriculumForWales (age 11). The workbook contains chapters on patterns, commutativity, distributivity & associativity.

I do like the above exercise which as the Teacher’s Guide acknowledges is based on Don Steward’s work, directed number arithmetic speed up and Chris McGrane’s Alternative representation of integers. A further useful resource for such an exercise is Jonathan Hall’s Directed Number MCQ Generator on MathsBot with which you can generate all the addition and subtraction multiple-choice questions you want; choose between Counters on or off.

As with the other two resources, a very comprehensive teacher’s guide is also available. You can see the contents here, this resource with its carefully chosen and varied activities and exercises will help students with the foundations of Algebra.

On the subject of negative numbers, from PhET simulations we have another excellent resource in their latest addition to the Mathematics collection. To use the number line as a model for ordering real numbers and also to illustrate operations with negative numbers we can use the excellent, Number Line: Distance. Also available are Number Line: Integers, and Number Line: Operations. All are excellent for students to explore.

This resource has been added to my post on Negative Numbers which looks at some resources to develop understanding of operations with positive and negative integers and exercises for practice.

A popular post on this blog is on Venn Diagrams, first written in 2016 this has recently been checked and updated with some new resources including always excellent resources from Amanda Austin on Dr Austin Maths. Included in her Probability resources you will find an excellent section on Set Notation and Venns.

GeoGebra retweeted this from Javier Cayetano Rod

…the translation:

“Adding some leaves to the stem of a flower can be the perfect excuse to talk about translations and turns in space @debora_pereiro . Added to the flower generator in @geogebrahttps://geogebra.org/m/duqthjva

Which in turn led me to this amazing GeoGebra collection, Flowers 3D, Author: Deborah Pereiro Carbajo.

Have look at Flowers from Curves, simply brilliant!

Explore the collection – you could be a while!

Complete Maths has made Robert Smith’s session “Web Autograph, a First Look” freely available

I wrote earlier this year on the excellent Math Whiteboard. This is completely free to use; If you create a whiteboard you can then get a link for that whiteboard which you can share. When I have created a whiteboard I then save a second copy so I can always return to the original.

With an individual subscription ( currently \$15 for a year) it is possible to access all the features of Fluid Math including as an authoring tool for creating Math Whiteboard activities. It is also possible to save your activities.

A new feature is available – the ability to create answer boxes to check for correct answers. You can see examples using this feature here.

By Colleen Young

Coordinate Geometry – Underground Maths

Exploring Algebra Review Questions from Underground Mathematics I came across some Coordinate Geometry questions I really like and yesterday spending a day with the very talented writing team and my fellow Underground Mathematics Champions we explored Straight Line Pairs, a question with much scope for exploration and possible methods of solution.

The image above has been created from the Printable/supporting materials.

My Year 11s will be looking at Coordinate Geometry this week and I have some other questions I would like them to try. It is possible to create pdf files for a collection of questions, see Saving Favourite Resources, one of Underground Mathematics’ How To Videos. (See the tutorials page I have in the Underground Maths series of pages – a work in progress).

You will find a whole collection of such questions if you look at Geometry of Equations. This includes many resources including Review questions. Note the Building Blocks resources. I think I’ll be using Underground Mathematics resources with ever younger students – Year 9 can try Lots of Lines! You will see from the the supporting materials that this has come from the brilliant Standards Unit (A10) collection. Students must sort the lines into six pairs, each pair matching one of the given descriptions.

Staying with the Building Blocks I do like Straight Lines where students must decide which of 17 equations are equations of a straight line.
Look at the list – a wonderful lesson in not jumping to conclusions here! Both my Year 9 and my Year 11 are going to be trying these this week!

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Straight Lines reminded me of Line Pairs, I feel an extension for Year 11 coming on!

By Colleen Young

Underground Mathematics Algebra Review Questions

Underground Mathematics provides such an outstanding collection of resources that I have begun to create a series of pages on the site. The resources are not only good for Advanced Level but for GCSE students too, particularly for students aiming at the very highest grades. This series of pages is very much a work in progress which I will be updating regularly.

I have used many of the Review questions for my able GCSE students. As you can see from the descriptions of  resorce types, the review questions are ideal for the new GCSE specifications as they have been selected to test students’ understanding of one or more topics and to exercise their problem-solving skills. The questions which have been chosen require non-routine thinking. You can browse all the Review questions or narrow your search by question type; note the O/AO-level questions which are questions from old papers. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.

If you create an account you can easily save and organise your favourite resources. This list of favourites can be easily downloaded as a csv file. To further organise your favourites you can create subcollections.

This too is a work in progress, I will create a collection of resources I believe are particularly useful for GCSE. I have several Algebra favourites so far. This Excel file has hyperlinks to all the resources shown here. algebra-gcse-9-1. Alternatively this pdf file also has the relevant hyperlinks. algebra-gcse-9-1