## A Mathematics Lesson Starter Of The Day

Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid:

Teacher: Click on the dots above to show joining lines. Assume that the vertical and horizontal distances between adjacent dots is one unit.

A printable sheet for student use is available here.

• CB, Kent
•
• I can find 10 different quadrilaterals (if you're allowed to count Big Square and Small Square). Areas - two 1s, two 1.5s, four 2s, one 3, one 4. Can't find the 2.5 at all. Am I missing something really obvious?
• 8K3, Kettlethorpe High School
•
• We found 11 which included the area of 2.5. (top left to top right to middle right to bottom middle to top left).
• Snev, Holy Trinity, Crawley
•
• There are 14 different quadrilaterals and their total area is 31.5 cm2 assuming the dots are 1 cm apart. (2x1)(4x1.5)(5x2)(1x2.5)(1x3)(1x4). The 2.5 cm2 quadrilateral joins dots 1,2,6 and 7.
• Louise And Laura., Carnoustie High School
•
• The problem was very challenging and we all enjoyed it. It was more challenging than Friday's.
• Claire, Sam And Mr A, Alcester High School
•
• We found 16 quadrilaterals, (5x1)(5x2)(3x1.5)(1x2.5)(1x3)(1x4)
Only took us 3 minutes too (-ish!).
• Nairn Spink, 2AY2, High School Of Dundee
•
• We really enjoyed it and I thought it really got us thinking, we are really pleased to do all the staters of the day
thanks
:).
• Yr 8 Tops, Rego School
•
• There should be quite a lot. My class managed about 30 so far.
• Yr9 QTY, West Island School, Hong Kong
•
• We enjoyed this - it kept us occupied for over 15mins.
• Mrbeer, Essex
•
• Surely with a parallelogram that crosses over the diagonals, the area is root 5 = 2.23?
• Charles, Chelsea
•
• My class found about 167 wow.
• A And F, Dps
•
• Our team got 32 different ways.
• Jelissa, Massachusetts
•
• It would be great if each quadrilateral could keep its own individual color, for a visual.
•
• There are:
70 convex quadrilaterals (not including the triangles)
48 triangles with an extra vertex on the midpoint of one side
96 degenerate quadrilaterals where one edge overlays half of an adjacent edge
140 complex quadrilaterals where two opposite sides intersect each other in a fifth point that is not a vertex of the quadrilateral
The total number of quadrilaterals is 378, which is 126 ways to choose four vertices from nine possible points times three ways to arrange any of four vertices into a ring.
The possible areas for the convex quadrilaterals are 1, 1.5, 2, 2.5, 3 or 4.
The possible areas for the nonconvex quadrilaterals are 1 or 1.5.
The possible areas for the triangles are 1 or 2.
The possible areas for the degenerate quadrilaterals 0.5 or 1 (because it is half of the area of the corresponding triangle).
The area of a complex quadrilateral is defined as the difference between the areas of the two triangles that are created. The possible areas for the complex quadrilaterals are 0, 0.5 or 1.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

Previous Day | This starter is for 22 March | Next Day

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

## How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

## Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

## The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

## Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more...

## A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more...

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more...

Click the images above to see all the details of these gift ideas and to buy them online.

## Maths T-Shirts

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=pinBoard

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

For Students:

For All: