The Math Doctor Tutoring Service

A Day Without Sunshine Is Like, You Know, Night.

Avis | Contractor's License School Porto - Responsive HTML5 Template

Taking part in a research engages students in science, and raises awareness about environmental issues. Photograph: Alamy.

From the outside, the scientific community may seem impenetrable – an exclusive club where they check your PhD at the door. But many scientists owe more to the general public than you might imagine, and boffins are increasingly doing research based on data collected by school students.

The rise of citizen science in education is turning classrooms into labs and pupils into pioneers, with projects investigating humanity's impact on the planet among the most accessible for schools.

Sixth form students from Wymondham High Academy in Norfolk were among amateur researchers from six schools in the area conducting experiments to see how plants resist a major wheat disease called Take-all.

Dr Paul Nicholson of the Norwich-based John Innis Centre sent the students seeds of Brachypodium, a plant used to study wheat. They learned how to grow the seeds in the classroom and then recorded the extent of root blackening caused by the infection with the aim of identifying resistant varieties.

Wymondham teacher Sara Caine, who led the initiative catchily named the Super model fights famine project, says the real hook for her and the students was that the work had never been done before. Pupils were motivated by the fact that they "weren't churning out yet another experiment on page 80 of the textbook."

The data students gathered proved valuable for scientists, and the students also got something out of it, many discovering a new-found love of an "unsexy" field of biology.

One student described the experiment as the most exciting one he'd ever done, while others said it had influenced their choice of degree subject. Caine explains that while children are interested in the animal sciences, the study of plants is crucial and neglecting plant diseases in the future will lead to major problems with food security. The project plays an important role in raising awareness of the issues.

Caine says the best way to start a similar project is to first find a scientist who is interested in working with the school, and will put in the time required. Funding may be another issue as materials can be costly. Partnership grants are available from the British Society for Plant Pathology, from whom Wymondham secured their funding.

For many children, learning about nature is fun because it involves going outside and getting your hands dirty. The Open Air Laboratories (Opal) project encourages people of all ages to do just that. The science initiative runs surveys across the UK with the aim of learning more about the state of our environment, and schools are encouraged to get involved.

Opal also provides easy-to-follow instructions for teaching students about their local environment, including the health of soil, the quality of air and how our actions affect our climate.

Students at La Sainte Union Catholic School, Highgate, London, took part in Opal surveys investigating the area's air quality and the health of local trees. Through their hands-on experiments they identified different species of trees for the first time and discovered how to keep their leafy streets green and free from damaging insect infestations and diseases. Their teacher, Dr Pari Collis, says that while citizen science projects hit the bulls-eye in terms of engaging students in the subject, the benefits go beyond meeting the demands of the curriculum.

"Projects such as these make science relevant to students and it's so important for them to take an interest in their surroundings," she says, adding that it is very empowering. "Although you are helping them with the ideas, it does become their project in the end."

But how useful are student observations to professional researchers? According to Opal project manager Roger Fradera, there will always be a trade-off between the research value and the educational value of the project. The challenge of balancing the two can be overcome by the design of the surveys which should avoid getting pupils to observe anything too obscure or specialised.

The evidence gathered by students may also help inform not only scientists, but also policy makers exploring how to tackle Britain's changing climate. Opal director David Slawson hopes that by getting students excited about science, the projects will inspire more people to choose a career in an industry which faces a worrying shortage of talent in the future.

"School children are vital to citizen science," says Fradera. "In terms of finding people who have a genuine enthusiasm, and love of nature, you can't really do better than going to a school where there are 30 kids screaming with excitement at what they are going to do."
The Live Better Challenge is funded by Unilever. All content is editorially independent except for pieces labelled advertisement feature. Find out more here. http://www.theguardian.com/teacher-network/teacher-blog/2014/jul/29/citizen-science-school-pupil-engagement-environment

Are fractions your nightmare? Turn the nightmare to fun with fraction games.

Once they get the hang of them, kids like fractions! The problem is that many students don't build a solid foundation with fractions. Then, as they move through school without the basics, fractions become a source of fear. Fraction games for kids can help change that!

Give a child you know the benefit of using these games to start off on the right foot, or to sort out the trouble of the past. Need to review fractions before going to the fraction activities?

Fraction Number Line Concentration: "New" game cards. Using fraction number line activities really help give students a visual of what's going on with fractions let's them seem how fractions relate to each other. That way they can have that "Oh, I see" moment and .

"New" Fraction-Rectangles Multiplication: Visualize multiplying and dividing fractions with fraction rectangles.

Fraction Strips: Are you using fraction strips for teaching fractions yet? They're great for helping students visualize and get a better understanding of hoe fractions work.

Fraction Flip It: Grab a deck of cards, print off the Fraction Flip It game sheet, grab a pencil and paper, and you're ready to have fun multiplying fractions.

Fraction Fiasco: Students will love getting practice adding and subtracting fractions with Fraction Fiasco. Our new printable fraction board game that again!

Basketball: Ready for some basketball? Paper basketball that is. What kid hasn't tossed the crumpled up paper into the waste cam at one time or another? Well, here's a fun activity that let's them do just that and get some fractions in at the same tome!

Fraction Rings: In Fraction Rings, students will students get practice adding fractions by first finding a common denominator.

Online Games: There are plenty exciting online fraction activities to improve your child's math ability. Kids enjoy playing the games and the cool thing is they're building math skills! We provide some of our own and give links to others already on the Internet.

Four-Sums Fractions: Four-Sums Fractions is a fun activity for kids that are beginning to learn about adding fractions with common denominators. You can just print off the game boards and fraction cards right from your computer.

Hands-On Activities

Hands-on fraction activities are a great way to give students a chance to touch and feel fractions. Often times if they can visualize fractions, it makes this sometimes difficult math concept a lot easier to understand.
Fraction Strips
Fraction strips are a hands-on way for demonstrating how fractions work! Teachers and parents find may find this to be a good teaching tool when it comes to getting their students to feel comfortable with the concept of fractions. Kids enjoy it because of the game-like and its hands-on!

Fraction Card GamesComparing and Ordering: Comparing fractions can be a little tricky for some kids. Especially when fractions have different denominators! Click the link above for card games that focus on comparing fractions. Learning Video

Here's a collection of fraction videos that will make fractions easier to understand.
Visualize Multiplying and Dividing
Get a visual picture of how multiplication and division of fractions works. Sometimes a picture is worth a thousand words.

There are loads of free fraction games on this site so you won’t need to spend tons of money. When you do have to spend, you’ll love our helpful reviews. And we promise not to tell if you overcome your own fraction phobia as you help a child.

Go to Elementary Math Games page

Go to Middle School Math Activities page

Return from Fraction Games to Learn With Math Games Home http://www.learn-with-math-games.com/fraction-games.html

There’s a new geometry tool in town and it goes by the name of Robocompass.com. It’s a tool that shows geometrical constructions in a 3D environment, rather than the 2D plan view used by Geogebra, Geometer’s Sketchpad etc. In addition to a wealth of common construction examples, you can program Robocompass to make your own constructions using an easy to learn language.

Here’s the video tour:
[embedded content] http://www.greatmathsteachingideas.com/2014/05/05/robocompass-com/

How about using a multiplication games printable like this one to help make learning how to multiply fun for your students. Math can be pretty intimidating for many kids. But we want to change that notion!

Have You Tried

Multiplication Boxes

Students will enjoy solving these Multiplication Box Printables! And they will be building their multiplication skills at the same time.

You'll notice in the three rows of multiplication box shown, the two factors multiplied by each other equal the product. For example. 3 x 4 = 12. And finally, 6 x 24 = 144.

Likewise in the three columns, it works the same way. In the first column you'll see 3 x 2 = 6. The second column, 4 x 6 = 24. And finally, 12 x 12 = 144.
Multiplication Games Printable (Easy)
You can print off Multiplication Box #1 here and have them work on them individually or in groups. The first multiplication printable is one of the easier ones.

This first sheet is good for students needing to build skills on their multiplication facts and also one-digit by two-digit multiplication. Solutions
Multiplication Games Printable (Medium)
Are you ready to take it up a notch? These multiplication boxes are a bit tougher. Print off the Multiplication Box #2 here.

Good for students building skills on their two-digit by two-digit multiplication. Solutions
Multiplication Games Printable (Hard)
Now for the harder ones. Hopefully you've already tried the multiplication boxes above and got the hang of them. These are a bit tougher. Multiplication Box -3

Now for two-digit by two-digit, and two-digit by three-digit multiplication. Solutions

Go to main Multiplication Games page

Return from Multiplication Games Printable to Learn With Math Games Home http://www.learn-with-math-games.com/multiplication-games-printable.html

Retired assistant headteacher Dave Tucker reflects on his career and shares some advice for NQTs. Photograph: Dave Tucker.

Dave Tucker recently retired as assistant headteacher at Darlington School of Mathematics and Science.

By the time I was 25 I was in charge of one of the top seven pig herds in the country. I'd left school at 16 and followed in my dad's footsteps, becoming a farm manager on a north Yorkshire estate. I quickly reached the top of my game and before long I was exporting pigs all over the world.

It was then that the work stopped being as satisfying because I realised there was nothing for me to improve on. I needed a change, so nine years into my career as a farmer I decided to train as a teacher.

I went to Northumberland college of higher education and was one of the last people to do the teacher's certificate – this was before teaching became a degree-level qualification. Training was very different back then; it was all theory and, although we visited schools, we didn't get put in front of a class until our third year.

At that time, teaching appealed to me because I loved sport and my first job was as a PE teacher. I immediately loved the job, and working with children. The biggest challenge was getting the youngsters to accept me, and realise that I wasn't going anywhere. Children often don't treat supply and cover teachers right because they know they're going to leave.

Young people need stability in their lives, especially the low- to middle-ability ones or children from broken homes. I retired this summer, and the relationship I had with the kids at school was phenomenal, in part, because they knew that I wasn't going anywhere. During the past decade I've only had seven days off sick.

Although I became head of my PE department and eventually assistant headteacher, I never had any ambition to be a headteacher because that takes you away from the kids. My strength was in the pastoral and behaviour management side of things, through which I could have a major effect on the young people and our staff.

By the end of my career I was basically the head of pastoral care, dealing with all sorts of things – from young people who had problems at home to students who'd split up with their girlfriends or boyfriends.

As a teacher it's easy to just think, "Oh come on!", but to lots of 12-13 year olds falling out with the best friend they've had since year 5 can be the biggest thing in the world. These problems matter because they affect behaviour.

Sanctions such as detentions or exclusions can be used by schools, but there are other things to try first and building a relationship with students is important.

I call all new teachers "baby teachers" and I always tell them the same thing: when you get to school it's not just about teaching. If there's a trip, go on it. If you can go out with the youngsters for a walk on a Sunday (we have a walking club), do it. These things let children see that there's more to you than simply being their maths or English teacher. Teachers who have the best relationships with students are the most successful.

Exam results are important there's no doubt about that, but my school's ethos was to turn out rounded children who believe in themselves and go on to do great things. I do worry that we're going back to the bad old days where everything depends on final end-of-year tests. We have lots of former students in their early twenties doing really good jobs, which they wouldn't have if they hadn't had the chance to resit exams.

I taught for 35 years in total. The thing that kept me going was watching the kids do well. We as teachers get to see young people scrub up well for the prom, in their big dresses and suits. Lads who I couldn't get to wear a tie throughout school dress up. Then in August we're there for them during results day if they need a shoulder to cry on.

I was at my last school for 20 years and saw it through special measures, when we were given notice to improve, to coming through it all and getting a good rating from Ofsted.

Of course, I'll miss teaching a lot but even though I have retired I will still go back to help with fundraising, and to see how everyone's getting on. http://www.theguardian.com/teacher-network/teacher-blog/2014/jul/27/new-teachers-school-not-just-about-teaching

This week's Secret Student gives their verdict on peer assessment. Photograph: Alamy.
Student: "Can you repeat the answer?"
Teacher: "Well if you were paying attention, I wouldn't have to repeat myself would I?"
It might just be me, but this has to be one of the most annoying sentences ever to leave a teacher's lips. Most students aren't machines and at times we'll will zone out, sorry. But getting you to repeat the answer should not be too much of an ask. Yet some teachers seem to hate it when this happens. I can understand it is annoying but even so, just repeating what you said because a student didn't hear you shouldn't really cause such a contemptuous response.
Teachers who forget to teach
Most teachers are great, but there's the odd one that spoils it. I remember spending a whole term going through physics papers and being told to look up the answers for something we hadn't been taught for homework. I learned nothing in that term except that Google is a better teacher than Mr Physics.
Ridiculous sanctions
My school is part of a federation of other academies and because of this, it's not unusual for teachers from another branch to come in to do a "teacher swap". With the rules being different at every academy, it can take a while for teachers to adjust, which is fine as long as students aren't worse-off because of it.

But there have been countless times where my peers and I have been sanctioned for writing in blue pen. The fact that in my school you're allowed to indulge in a little blue ink means that when teachers pick us up on it we just find it amusing – even more so when a friend's parents received a letter informing them of his terrible doing in school.
Placing the naughty kid next to you because you're a good student
All classes have well-behaved students and less well-behaved students and I accept that some students are difficult to deal with. I would like to think that I'm rather well behaved but while placing the tricky students next to me might help the teacher, I don't learn as well and often find myself in trouble for being at the scene of a crime. Finding yourself in hot water for not having enough equipment even though you donated half your pencil case to the injudicious juvenile on your right who was lumped on you by your teacher is not fair.
Extended deadlines
It's a constant dilemma: at the weekend, playing your favourite video game will earn you double points, but you have homework to do. You take the sensible decision of doing your homework – and doing it well – only to find that when you get to school your teacher decides to extend your deadline.
Peer marking
On the theme of marking, I would much prefer to get my work marked by a teacher than Joseph Barker who has been picking his nose for the last half an hour.

• Have you ever experienced some student feedback that's really made you stop and think about certain techniques or tasks you do? Share your experience with us below. http://www.theguardian.com/teacher-network/teacher-blog/2014/jul/26/secret-student-six-things-never-tell-teacher

Visible Learning is John Hattie’s mantra. I’ve written previously about being a big fan of Hattie’s work about what affects achievement. He’s collected just about every piece of academic research and collated a ranked taxonomy of factors that affect achievement. Visible Learning is his suggested approach to teaching in a way that incorporates many of the significant drivers of achievement.

He sums up what Visible Learning looks like using the analogy of teaching someone to abseil. The main features of the learning being:
The success criteria is explicit. The learners not only know what they’re trying to achieve, but also what success looks like. Giving learning objectives isn’t enough, they need to see what success looks like. The tasks are challenging. Trusting in the rope to support your weight requires real trust. Learners find it extremely challenging, but when they complete it the first time they get a real sense of satisfaction and have the hunger to repeat it again. Student expectations. Ask students to state how they think they will do before they start a task. Human nature is for them to play safe in their prediction. When they exceed their forecast, their belief in themselves as a learner increases. This ratchets up over time and their expectations of themselves rise. This has by far the highest ranking effect size in all of Hattie’s findings.
Know thy impact is another of his mantras. He argues that formative assessment is vital in quality teaching and teachers should constantly be using evidence to reflect on the impact their practice had on their learners. Hattie says assessments are more for teachers than students; they are for you to find out what you taught well and to whom. This reflective, evidence-based mindset, he argues captures the essence of what educational research concludes has a high-impact on achievement. Teaching is to D.I.E for, says Hattie: Diagnose what they do/don’t know, Intervene, Evaluate your impact. Repeat.

I’ve been experimenting with an approach to teaching maths that meets the Visible Learning criteria and allows me to systematically know my impact by using the D.I.E philosophy. This has been the biggest step forward in my practice this year and the learners really like it. The problem is, I can’t see a way of embedding it permanently in my practice. Let me explain…

At the beginning of a topic students are given this sheet that gives the learning objectives.



The students then make a prediction of how many questions they will get right on the pre-learning assessment and enter this number into the table.

The students then sit the pre-learning assessment:



This is class-marked and the students then highlight the appropriate smileys on the tracker sheet (after the pre-learning assessment, not before it) to record their success against each learning objective on the pre-learning assessment. They update the score in the table with what they actually got. Finally a grid is passed round with the students’ names vs the learning objectives. They tick and cross the grid so I then have a record of how each student did on each question.

I plan my lessons based on this pre-learning assessment feedback. I structure my lessons based on who knows what. I know exactly where to pick up from to avoid teaching things they really already know.

After the series of lessons student predict how they will do on the post-learning assessment, sit it, record their actual score, update the smileys and set targets about anything they still haven’t mastered.

The students love it. Comments include: “It really helps me understand what I’ve got to learn”, “It makes me realise that I am actually making progress in maths even when my grade on the exams isn’t going up every time”, “It makes the things I’ve got to learn a lot clearer” and “the assessments help you figure out what you do and don’t know. Stuff I thought I knew, I found out I didn’t and the other way round too. It’s been really useful”.

There are other things I really like:
Using formative feedback from assessments has allowed me to be much more diagnostic and really impacted on my lesson planning. Rather than making assumptions about where to pick up from, I know without any doubt now. Things I would have spent whole lessons on before are now little-and-often starters. The pitch of my activities has changed. When I can see they have visited things before I set deeper learning activities much earlier than I would have previously. What was a chatty class are suddenly much more focussed and on task more regularly. I’m pitching work much better than ever because of the better than ever information I have on what students already know. I’ve never been a fan of giving students a list of learning objectives and asking them to RAG (red/amber/green) how good they think they are at them. RAG-ing doesn’t account for student ignorance! The conscientious, high attaining students underestimate what they can do and the overly-confident, lazy ones overestimate. By doing the RAG-ing based on what they can do on an actual assessment, the results are much more accurate. This is confirmed by the score students predicting they will get prior to the pre-learning assessment and the actual score they get being different; significantly so in many cases. I think the approach captures the spirit of the forthcoming assessing without levels reforms. The pre and post learning assessments document progress in a formative portfolio. Targets can be set based on accurate diagnostic assessment of their weaknesses. Progress is very clear to external observers, me the teacher and to the students. Supplying the learning objectives in conjunction with the pre-learning assessment really gives students focus from the start. They see the learning journey and buy into it. “I can’t wait until we get to the trapezium lesson”, was one student’s comment after the pre-learning assessment. I’ve never had students consistently looking forward along their learning journey like this before.
All sorted then, the world is fixed! No. I just can’t see a way of making it work all the time. I’m not trying to be defeatist. It’s not the preparation involved, it’s simply the time required to run it. There are 30 modules on the scheme of work, 352 learning objectives and it is already a struggle to cover the course content within the allotted time. Two extra lessons for the pre and post learning assessments mean 60 more lessons needed over the KS4 course. It’s simply not possible to sacrifice 60 lessons to this and still cover the course content. Do you agree?

This has been an issue causing me great frustration recently. The learning is so good with this system. It encapsulates so much of what Hattie says really boosts achievement and I have seen at first-hand why. Visible Learning is really, really good learning.

I want this to be something that is practical. I can’t see where the 60 lessons are going to come from. Schools just can’t do it. In theory, because you don’t need to teach everything (some topics students already know are identified on the pre-learning assessment) there are some savings here, but it’s not enough. Perhaps set the pre and post learning assessments as homeworks? That would have pitfalls! Where’s the time going to come from?!

I’m out of ideas currently. Do you have any? How could I make this work? Please make any suggestions you have in the comments section.
Related articles John Hattie- Why are so many of our teachers and schools so successful? A Grand Day Out With Hattie & Waters http://www.greatmathsteachingideas.com/2014/06/13/how-do-we-make-john-hatties-visible-learning-work-in-maths/

Boosts Math Skills

Ready for some more magic triangle fun? If you've already tried the easier ones, these are a little bit tougher. Great way for students to build critical thinking skills while they're having fun.

Just in case you don't know how a magic triangle works, all of the numbers in each row of the triangle must add up to the same number (Magic Number). See picture below.

Here's a magic triangle pictured on the left that's already been worked out. The Magic Number for this triangle is 9.

Notice that the sum of each of the three sides of the triangle is 9.


So now let's try to do some triangles that are just a bit tougher. These magic triangles have four numbers on each side instead of three. But they're still worked out the same way.

So you can see we've filled out a few of the numbers for you already to make it a little easier. The magic number for this one is 19. The student's task is to fill in the missing numbers so that the sum of each side totals 19. Print the triangles here.

Make sure your students try to work it out first before giving them the answers. Print the solutions.

The Benefits of doing math puzzles
Math puzzles help students who hate or are frightened of math, to have fun while developing thinking skills at the same time.Help increase numeracy skills and logical thinking.Help students with developing concentration as well as perseverance.
By the way if you haven't checked out the magic squares page, you might want to try those too.

Go to main Math Puzzles page

Return from magic Triangle to Learn With Math games Home http://www.learn-with-math-games.com/magic-triangle.html

So how about a nice handy fraction to decimal chart to spice up your lessons on decimals and fractions! Got it for you here. Also be sure to check out the printable fraction to decimal worksheets further down the page.

Comparing Fractions and Decimals


Students need to know how decimal numbers and fractions are related. The fraction to decimal chart gives students a good idea of how the place values to the right of the decimal point can be represented by the fractions one-tenth (1/10), one-hundredth (1/100), and one-thousandth (1/1000) respectively.

You can print a copy of the chart above so your students can use it as a reference. It also explains step-by-step how to change a mixed number to a decimal.


They should be comfortable converting fractions to decimals and visa-versa. They need to combine their knowledge of place value, whole numbers, and fractions, in order to have a thorough understanding of how decimals fit into the picture.

We've provided some fraction to decimal worksheets below for your students to get some practice. You'll find the solution sheet as well.


Another good teaching tip for helping students master this area is getting them familiar with some of the more recognizable fraction - decimal equivalents. For example, one-half is the same as .5.

Another example is one-fourth in decimal form is .25.

Go to Decimal Games page

Return from Fraction To Decimal Chart to learn With Math Games Home http://www.learn-with-math-games.com/fraction-to-decimal-chart.html

Pappus Chain (Photo credit: fdecomite)

Ever heard of Circle Inversion? It’s a bit like a combination of enlargement and reflection, but using circle radii as projection lines. What is it useful for? Pappus Chains… Watch and find out:

Epic Circles- Numberphile
[embedded content] http://www.greatmathsteachingideas.com/2014/04/15/epic-circles-numberphile/