Numbers – Visualizations

A great vizualisation or diagram can make a very good starter…

Mathematics, Learning and Technology

I have several references in various places on this blog to some great visualizations.
Time to put them all together!

Jeffrey Ventrella’s Composite Number Tree Jeffrey Ventrella’s Composite Number Tree

From Jeffrey Ventrella this wonderful Composite Number Tree – I have used this successfully with many students. It makes a great starter. Students can work out themselves how the tree is being formed and comment on any patterns they notice.


Stephen Von Worley

Brent Yorgey Brent Yorgey

Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dance which tells the tale of the animation. Noting his reference to Brent Yorgey’s factorization diagrams led me to Brent’s own later post, More factorisation Diagrams. I love Brent’s use of colour here. If you want even more on these great diagrams he has more information and links on this page on his blog, The Math Less Traveled

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Happy New Year – 2017

New Year always provides us with January starters!
2017 – a prime year!

Mathematics, Learning and Technology

When 2017 starts around the world!

New Year Map – showing when cities round the world enter 2017.

2017-year-game 2017 Year Game from mathforum.org

It’s that time of year again and we can play the 2017 Year Game in our January lessons.


simon-jobs-mathsclass MathsClass

On Simon Job’s MathsClass, he suggests writing a number sentence under the date; as you can read on his blog he endeavoured to write the number sentence using the digits of the date in order in 2016. It strikes me this idea could be used as a starter, ask the students to come up with such a number sentence.


2017 is a prime number and as we see from the WolframAlpha properties below, in particular a Pythagorean prime, so another source of starters and investigations perhaps? The last time the Year was a Pythagorean prime was 1997.

2017-number-gossip

We can always turn to Number Gossip from Tanya Khovanova for information…

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Tools for Maths Teachers – MathsBot.com

Tools for Maths Teachers J Hall

JHall site

Jonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. 

J Hall Maths Tools

The illustration shows an example from Differentiated Questions; these have an oprional timer.

The GCSE questions bank is really useful; note the choices of topic. It is also possible to choose Foundation or Higher or both and Calculator or Non-Calculator. You have the option to show solutions.
j-hall-gcse-questions

j-hall-gcse-questions-solutions

This site has been added to the Collections and Revision pages.

Plenary Tweets

Mathematics, Learning and Technology

Discovering a novel idea for a plenary via Twitter recently, a UKEdChat resource by @grahamandre I thought I would try the idea with my very able Year 9 class (the same wonderful class I mentioned some time ago who gave their views on Good Maths Teachers).

I should mention that “Somewhere over the 2a” is part of some lyrics by one of my colleagues sung to the tune of “Somewhere Over the Rainbow!”

In the first part of this lesson I used one of my mini-tests to review the key points for solving quadratic equations. When we reviewed the solutions I also used Desmos to illustrate some of the answers and for these students, the first year who will tackle the new GCSE course made sure I used function notation! This time I told them that I was using the mini test to review the material we have been studying and…

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A perfect day…

What a perfect starter for 28th June – Perfect Numbers!

Mathematics for Students

28th June is a Perfect Day to enjoy some Mathematics!

perfect numberPerfect because 28 and 6 are both perfect numbers. You can easily check for properties of any number with Tanya Khovanova’s Number Gossip where we learn that 28 does not only have the rare property of being perfect, it is also composite, even, happy, odious, practical, triangular and Ulam! You can browse all the properties here.

28 is also happy! Happy Numbers – a favourite investigation, Dr Who knows about happy primes!

It’s also National Tau Day! Pi is wrong…..
This video provides a short version of the Tau Manifesto (14 minutes)

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Yohaku

These puzzles be good starters, note the Algebraic version.

Mathematics - Games

Yohauku

Additive Yohaku with rule

For a new kind of puzzle Yohakuu is a puzzle that will test your number sense and problem solving skills. Each Yohaku puzzle is either an additive or a multiplicative puzzle. You must fill in the empty cells such that they give the sum or product shown in each row and column as well as satisfying a rule if given.

Choose from 2×2, 3×3 or 4×4 puzzles.

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Multiplicative Yohaku with ruleThese could be used as Starters or perhaps in form time.

Follow Yohaku on Twitter. Checking the Twitter stream I noted this algebraic puzzle below, an excellent idea. Try a little logic, where must c be placed for example.

Algebraic Yohaku

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Mudd Math Fun Facts

Mathematics, Learning and Technology

mfunfacts

This searchable collection of Mathematics fun facts from Harvey Mudd College Math Department make ideal lesson starters or perhaps useful for those odd moments.
Note the search on the left, it is possible to search by topic, difficulty level and keywords.

For example, try:

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Mobile Puzzles – Algebra

For a wonderful Algebra starter – equations through Mobile Puzzles

Mathematics, Learning and Technology

Mobile Puzzles Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit solveme.edc.org to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.

Menu

Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:
Master Level

Note the menu in the corner of each puzzle page:
Play Menu

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

create equation
Note that you can then drag a heart to subtract a heart…

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