New Gcse: Ratio

I've only marked my Year xi mocks in addition to noticed that ratio continues to survive an expanse of difficulty. This isn't a surprise - nosotros realised a few years agone that ratio questions on the novel GCSE are much harder than they used to be. Here's an instance of a straightforward ratio enquiry - this is what ratio used to hold back similar at GCSE:

The ratio of boys to girls at a schoolhouse is 5:7

There are 600 children at the school.

How many boys are at that spot at the school?

But GCSE questions are to a greater extent than challenging now. We're seeing a lot of 'ratio change' questions - this example, from blog post are a goodness house to start for the basics. Your local Maths Hub may run a bar modelling course. If you lot know the basics but combat amongst the harder questions, depository fiscal establishment check out this Twitter thread to run into a bar model inwards activity for a trickier ratio problem. It's also worth watching this fantabulous video on solving harder ratio problems using bar models from Colin Hegarty.

Bar modelling surely is a clear in addition to accessible approach for unproblematic ratio questions. I would tell though that for some trickier ratio questions it's non ever quite every bit intuitive in addition to obvious every bit proficient bar modellers advise it is.

Let's conduct maintain a hold back at methods for some other 'ratio change' enquiry - this i is from Don Steward:

The algebra method I described inwards a higher house plant real quickly. Using equivalent fractions in addition to setting upwards an equation gives us 8(5x + 2) = 7(6x). The whole solution takes exclusively a few lines of working.

Scaling plant too:

5:6 gives 7:6 when January gains 2 marbles ✗

10:12 gives 12:12 when January gains 2 marbles ✗

15:18 gives 17:18 when January gains 2 marbles ✗

20: 24 gives 22:24 when January gains 2 marbles ✗

25: xxx gives 27:30 when January gains 2 marbles ✗

30: 36 gives 32:36 when January gains 2 marbles ✗

35: 42 gives 37:42 when January gains 2 marbles ✗

40: 48 gives 42:48 when January gains 2 marbles - this simplifies to 7:8 ✓

Again, nosotros tin larn at that spot to a greater extent than rapidly if nosotros mean value most multiples. We start amongst a multiple of xi in addition to terminate amongst a multiple of 15, but nosotros gained ii marbles along the way. So nosotros tin listing all multiples of xi in addition to all multiples of xv in addition to discovery a duo which are ii apart.

11, 22, 33, 44, 55, 66, 77, 88

15, 30, 45, 60, 75, 90

So nosotros started amongst 88 marbles.

Not all tricky ratio questions are inwards the cast of these 'ratio change' problems. We also straight off larn GCSE questions similar this:

If the ratio a:b is 4:7, write a inwards price of b

Though this may seem obvious to many of us (a is the smaller of the two, thus a is 4 sevenths of b), writing the ratios every bit equivalent fractions tin attention students larn their numbers the correct means circular (providing they are confident inwards rearranging equations).

Another type of enquiry is this:

If the ratio a:b is 2:5 in addition to the ratio b:c is 3:10, what is the ratio a:c?

Again, fractions mightiness help.

Influenza A virus subtype H5N1 quicker option is scaling here. We tin write a:b:c every bit i ratio if nosotros larn the b parts to match.

a: b tin survive written every bit 6:15

b:c tin survive written every bit 15:50

So a:b:c is 6:15:50

This shows that the ratio a:c is 6:50, which simplifies to 3:25

And here's some other type of question:

Punch is made my mixing orangish juice in addition to cranberry juice inwards the ratio 7:2. Mark has xxx litres of orangish juice in addition to 8 litres of cranberry juice. What is the maximum amount of punch that Mark tin make?

Again, I mean value that scaling is likely the quickest approach here. Multiplying the punch ratio yesteryear 4 gives us 28:8. This is the most punch nosotros tin brand because we're using all the cranberry juice. So inwards full we're making 36 litres of punch.

In summary, at that spot are a diversity of approaches for solving trickier ratio problems - most tin survive solved efficiently using algebra, scaling or bar modelling. If you're educational activity this topic for the showtime fourth dimension at GCSE it's worth spending some fourth dimension looking at the diverse methods. I mean value our students volition demand a lot of practise of numerous dissimilar types of ratio enquiry to gear upwards for their GCSE.


Resources
I've created a lesson to accompany this postal service - download it from TES here.

Here are some other resources that you lot mightiness discovery helpful:

• Mel from JustMaths collated ratio Higher GCSE questions from sample in addition to specimen papers here, in addition to has written upwards her solutions here. 
• If you lot subscribe to MathsPad thus you'll survive pleased to take away heed that they conduct maintain lovely resources for ratio including a laid of questions for Higher GCSE with loads of examples similar the problems I've featured inwards this post.  
• Don Steward has enough of ratio tasks including his laid of 'Harder Ratio Questions' in addition to a actually helpful collection of blog post are a goodness house to start for the basics. Your local Maths Hub may run a bar modelling course. If you lot know the basics but combat amongst the harder questions, depository fiscal establishment check out this Twitter thread to run into a bar model inwards activity for a trickier ratio problem. It's also worth watching this fantabulous video on solving harder ratio problems using bar models from Colin Hegarty.
  
  Bar modelling surely is a clear in addition to accessible approach for unproblematic ratio questions. I would tell though that for some trickier ratio questions it's non ever quite every bit intuitive in addition to obvious every bit proficient bar modellers advise it is.
  
  Let's conduct maintain a hold back at methods for some other 'ratio change' enquiry - this i is from Don Steward:
  
  
  The algebra method I described inwards a higher house plant real quickly. Using equivalent fractions in addition to setting upwards an equation gives us 8(5x + 2) = 7(6x). The whole solution takes exclusively a few lines of working.
  
  Scaling plant too:
  
  5:6 gives 7:6 when January gains 2 marbles ✗
  10:12 gives 12:12 when January gains 2 marbles ✗
  15:18 gives 17:18 when January gains 2 marbles ✗
  20: 24 gives 22:24 when January gains 2 marbles ✗
  25: xxx gives 27:30 when January gains 2 marbles ✗
  30: 36 gives 32:36 when January gains 2 marbles ✗
  35: 42 gives 37:42 when January gains 2 marbles ✗
  40: 48 gives 42:48 when January gains 2 marbles - this simplifies to 7:8 ✓
  
  Again, nosotros tin larn at that spot to a greater extent than rapidly if nosotros mean value most multiples. We start amongst a multiple of xi in addition to terminate amongst a multiple of 15, but nosotros gained ii marbles along the way. So nosotros tin listing all multiples of xi in addition to all multiples of xv in addition to discovery a duo which are ii apart.
  
  
  11, 22, 33, 44, 55, 66, 77, 88
  15, 30, 45, 60, 75, 90
  So nosotros started amongst 88 marbles.
  
  Not all tricky ratio questions are inwards the cast of these 'ratio change' problems. We also straight off larn GCSE questions similar this:
  
  
  
  
  
  If the ratio a:b is 4:7, write a inwards price of b
  
  
  
  
  Though this may seem obvious to many of us (a is the smaller of the two, thus a is 4 sevenths of b), writing the ratios every bit equivalent fractions tin attention students larn their numbers the correct means circular (providing they are confident inwards rearranging equations).
  

  

  
  Another type of enquiry is this:
  
  
  
  

  If the ratio a:b is 2:5 in addition to the ratio b:c is 3:10, what is the ratio a:c?

  
  

  
  

  
  Again, fractions mightiness help.
  

  

  
  Influenza A virus subtype H5N1 quicker option is scaling here. We tin write a:b:c every bit i ratio if nosotros larn the b parts to match.
  
  

  a: b tin survive written every bit 6:15

  b:c tin survive written every bit 15:50

  So a:b:c is 6:15:50

  This shows that the ratio a:c is 6:50, which simplifies to 3:25

  
  
  And here's some other type of question:
  
  
  

  Punch is made my mixing orangish juice in addition to cranberry juice inwards the ratio 7:2. Mark has xxx litres of orangish juice in addition to 8 litres of cranberry juice. What is the maximum amount of punch that Mark tin make?
  
  

  Again, I mean value that scaling is likely the quickest approach here. Multiplying the punch ratio yesteryear 4 gives us 28:8. This is the most punch nosotros tin brand because we're using all the cranberry juice. So inwards full we're making 36 litres of punch.
  
  In summary, at that spot are a diversity of approaches for solving trickier ratio problems - most tin survive solved efficiently using algebra, scaling or bar modelling. If you're educational activity this topic for the showtime fourth dimension at GCSE it's worth spending some fourth dimension looking at the diverse methods. I mean value our students volition demand a lot of practise of numerous dissimilar types of ratio enquiry to gear upwards for their GCSE.
  
  
  Resources
  I've created a lesson to accompany this postal service - download it from TES here.
  
  Here are some other resources that you lot mightiness discovery helpful:
  

  • Mel from JustMaths collated ratio Higher GCSE questions from sample in addition to specimen papers here, in addition to has written upwards her solutions here. 
  • If you lot subscribe to MathsPad thus you'll survive pleased to take away heed that they conduct maintain lovely resources for ratio including a laid of questions for Higher GCSE with loads of examples similar the problems I've featured inwards this post.  
  • Don Steward has enough of ratio tasks including his laid of 'GCSE ratio in addition to proportion questions.
  • On MathsBot you lot tin generate ratio questions, revision grids in addition to practise papers. Select 'ratio, proportion in addition to rates of change' at the top.
  • There are seek trend questions inwards this collection from Lucy Kilgariff on TES.
  • OCR has a 'Calculations amongst Ratio' Topic Check In and AQA has a Ratio in addition to Proportion Topic Test.
  • David Morse of Maths4Everyone has shared a laid of revision exercises in addition to ratio seek trend questions.

  There are loads to a greater extent than ratio resources inwards my number resources library.
  
  I promise this postal service volition survive helpful when you lot instruct ratio at GCSE. Do tweet me to permit me know what methods you lot purpose if I haven't mentioned them here.
  
  

  
  
  
  

New Gcse: Ratio

I've only marked my Year xi mocks in addition to noticed that ratio continues to survive an expanse of difficulty. This isn't a surprise - nosotros realised a few years agone that ratio questions on the novel GCSE are much harder than they used to be. Here's an instance of a straightforward ratio enquiry - this is what ratio used to hold back similar at GCSE:

The ratio of boys to girls at a schoolhouse is 5:7

There are 600 children at the school.

How many boys are at that spot at the school?

But GCSE questions are to a greater extent than challenging now. We're seeing a lot of 'ratio change' questions - this example, from blog post are a goodness house to start for the basics. Your local Maths Hub may run a bar modelling course. If you lot know the basics but combat amongst the harder questions, depository fiscal establishment check out this Twitter thread to run into a bar model inwards activity for a trickier ratio problem. It's also worth watching this fantabulous video on solving harder ratio problems using bar models from Colin Hegarty.

Bar modelling surely is a clear in addition to accessible approach for unproblematic ratio questions. I would tell though that for some trickier ratio questions it's non ever quite every bit intuitive in addition to obvious every bit proficient bar modellers advise it is.

Let's conduct maintain a hold back at methods for some other 'ratio change' enquiry - this i is from Don Steward:

The algebra method I described inwards a higher house plant real quickly. Using equivalent fractions in addition to setting upwards an equation gives us 8(5x + 2) = 7(6x). The whole solution takes exclusively a few lines of working.

Scaling plant too:

5:6 gives 7:6 when January gains 2 marbles ✗

10:12 gives 12:12 when January gains 2 marbles ✗

15:18 gives 17:18 when January gains 2 marbles ✗

20: 24 gives 22:24 when January gains 2 marbles ✗

25: xxx gives 27:30 when January gains 2 marbles ✗

30: 36 gives 32:36 when January gains 2 marbles ✗

35: 42 gives 37:42 when January gains 2 marbles ✗

40: 48 gives 42:48 when January gains 2 marbles - this simplifies to 7:8 ✓

Again, nosotros tin larn at that spot to a greater extent than rapidly if nosotros mean value most multiples. We start amongst a multiple of xi in addition to terminate amongst a multiple of 15, but nosotros gained ii marbles along the way. So nosotros tin listing all multiples of xi in addition to all multiples of xv in addition to discovery a duo which are ii apart.

11, 22, 33, 44, 55, 66, 77, 88

15, 30, 45, 60, 75, 90

So nosotros started amongst 88 marbles.

Not all tricky ratio questions are inwards the cast of these 'ratio change' problems. We also straight off larn GCSE questions similar this:

If the ratio a:b is 4:7, write a inwards price of b

Though this may seem obvious to many of us (a is the smaller of the two, thus a is 4 sevenths of b), writing the ratios every bit equivalent fractions tin attention students larn their numbers the correct means circular (providing they are confident inwards rearranging equations).

Another type of enquiry is this:

If the ratio a:b is 2:5 in addition to the ratio b:c is 3:10, what is the ratio a:c?

Again, fractions mightiness help.

Influenza A virus subtype H5N1 quicker option is scaling here. We tin write a:b:c every bit i ratio if nosotros larn the b parts to match.

a: b tin survive written every bit 6:15

b:c tin survive written every bit 15:50

So a:b:c is 6:15:50

This shows that the ratio a:c is 6:50, which simplifies to 3:25

And here's some other type of question:

Punch is made my mixing orangish juice in addition to cranberry juice inwards the ratio 7:2. Mark has xxx litres of orangish juice in addition to 8 litres of cranberry juice. What is the maximum amount of punch that Mark tin make?

Again, I mean value that scaling is likely the quickest approach here. Multiplying the punch ratio yesteryear 4 gives us 28:8. This is the most punch nosotros tin brand because we're using all the cranberry juice. So inwards full we're making 36 litres of punch.

In summary, at that spot are a diversity of approaches for solving trickier ratio problems - most tin survive solved efficiently using algebra, scaling or bar modelling. If you're educational activity this topic for the showtime fourth dimension at GCSE it's worth spending some fourth dimension looking at the diverse methods. I mean value our students volition demand a lot of practise of numerous dissimilar types of ratio enquiry to gear upwards for their GCSE.


Resources
I've created a lesson to accompany this postal service - download it from TES here.

Here are some other resources that you lot mightiness discovery helpful:

• Mel from JustMaths collated ratio Higher GCSE questions from sample in addition to specimen papers here, in addition to has written upwards her solutions here. 
• If you lot subscribe to MathsPad thus you'll survive pleased to take away heed that they conduct maintain lovely resources for ratio including a laid of questions for Higher GCSE with loads of examples similar the problems I've featured inwards this post.  
• Don Steward has enough of ratio tasks including his laid of 'Harder Ratio Questions' in addition to a actually helpful collection of blog post are a goodness house to start for the basics. Your local Maths Hub may run a bar modelling course. If you lot know the basics but combat amongst the harder questions, depository fiscal establishment check out this Twitter thread to run into a bar model inwards activity for a trickier ratio problem. It's also worth watching this fantabulous video on solving harder ratio problems using bar models from Colin Hegarty.
  
  Bar modelling surely is a clear in addition to accessible approach for unproblematic ratio questions. I would tell though that for some trickier ratio questions it's non ever quite every bit intuitive in addition to obvious every bit proficient bar modellers advise it is.
  
  Let's conduct maintain a hold back at methods for some other 'ratio change' enquiry - this i is from Don Steward:
  
  
  The algebra method I described inwards a higher house plant real quickly. Using equivalent fractions in addition to setting upwards an equation gives us 8(5x + 2) = 7(6x). The whole solution takes exclusively a few lines of working.
  
  Scaling plant too:
  
  5:6 gives 7:6 when January gains 2 marbles ✗
  10:12 gives 12:12 when January gains 2 marbles ✗
  15:18 gives 17:18 when January gains 2 marbles ✗
  20: 24 gives 22:24 when January gains 2 marbles ✗
  25: xxx gives 27:30 when January gains 2 marbles ✗
  30: 36 gives 32:36 when January gains 2 marbles ✗
  35: 42 gives 37:42 when January gains 2 marbles ✗
  40: 48 gives 42:48 when January gains 2 marbles - this simplifies to 7:8 ✓
  
  Again, nosotros tin larn at that spot to a greater extent than rapidly if nosotros mean value most multiples. We start amongst a multiple of xi in addition to terminate amongst a multiple of 15, but nosotros gained ii marbles along the way. So nosotros tin listing all multiples of xi in addition to all multiples of xv in addition to discovery a duo which are ii apart.
  
  
  11, 22, 33, 44, 55, 66, 77, 88
  15, 30, 45, 60, 75, 90
  So nosotros started amongst 88 marbles.
  
  Not all tricky ratio questions are inwards the cast of these 'ratio change' problems. We also straight off larn GCSE questions similar this:
  
  
  
  
  
  If the ratio a:b is 4:7, write a inwards price of b
  
  
  
  
  Though this may seem obvious to many of us (a is the smaller of the two, thus a is 4 sevenths of b), writing the ratios every bit equivalent fractions tin attention students larn their numbers the correct means circular (providing they are confident inwards rearranging equations).
  

  

  
  Another type of enquiry is this:
  
  
  
  

  If the ratio a:b is 2:5 in addition to the ratio b:c is 3:10, what is the ratio a:c?

  
  

  
  

  
  Again, fractions mightiness help.
  

  

  
  Influenza A virus subtype H5N1 quicker option is scaling here. We tin write a:b:c every bit i ratio if nosotros larn the b parts to match.
  
  

  a: b tin survive written every bit 6:15

  b:c tin survive written every bit 15:50

  So a:b:c is 6:15:50

  This shows that the ratio a:c is 6:50, which simplifies to 3:25

  
  
  And here's some other type of question:
  
  
  

  Punch is made my mixing orangish juice in addition to cranberry juice inwards the ratio 7:2. Mark has xxx litres of orangish juice in addition to 8 litres of cranberry juice. What is the maximum amount of punch that Mark tin make?
  
  

  Again, I mean value that scaling is likely the quickest approach here. Multiplying the punch ratio yesteryear 4 gives us 28:8. This is the most punch nosotros tin brand because we're using all the cranberry juice. So inwards full we're making 36 litres of punch.
  
  In summary, at that spot are a diversity of approaches for solving trickier ratio problems - most tin survive solved efficiently using algebra, scaling or bar modelling. If you're educational activity this topic for the showtime fourth dimension at GCSE it's worth spending some fourth dimension looking at the diverse methods. I mean value our students volition demand a lot of practise of numerous dissimilar types of ratio enquiry to gear upwards for their GCSE.
  
  
  Resources
  I've created a lesson to accompany this postal service - download it from TES here.
  
  Here are some other resources that you lot mightiness discovery helpful:
  

  • Mel from JustMaths collated ratio Higher GCSE questions from sample in addition to specimen papers here, in addition to has written upwards her solutions here. 
  • If you lot subscribe to MathsPad thus you'll survive pleased to take away heed that they conduct maintain lovely resources for ratio including a laid of questions for Higher GCSE with loads of examples similar the problems I've featured inwards this post.  
  • Don Steward has enough of ratio tasks including his laid of 'GCSE ratio in addition to proportion questions.
  • On MathsBot you lot tin generate ratio questions, revision grids in addition to practise papers. Select 'ratio, proportion in addition to rates of change' at the top.
  • There are seek trend questions inwards this collection from Lucy Kilgariff on TES.
  • OCR has a 'Calculations amongst Ratio' Topic Check In and AQA has a Ratio in addition to Proportion Topic Test.
  • David Morse of Maths4Everyone has shared a laid of revision exercises in addition to ratio seek trend questions.

  There are loads to a greater extent than ratio resources inwards my number resources library.
  
  I promise this postal service volition survive helpful when you lot instruct ratio at GCSE. Do tweet me to permit me know what methods you lot purpose if I haven't mentioned them here.
  
  

  
  
  
  

Stretching Practice

I currently instruct at a girls' grammer school. This way all of my students are on rails for an H5N1 or A* at GCSE. It's a fleck similar teaching exceed laid all the time, but without the confidence levels you lot would hold off from such brilliant students. They larn novel concepts real rapidly but are frequently unwilling to guide keep risks.

Finding suitable resources for such smart as well as hardworking students tin move difficult. If I select exercises that are also easy, they'll experience patronised as well as acquire bored alongside maths. Besides, it's non a proficient purpose of their fourth dimension to produce practise that's also easy. But if I select exercises that are also difficult, they'll move frustrated as well as it won't attention them railroad train fluency. So I pose a lot of effort into ensuring my resources are the appropriate aeroplane of challenge.

It tin move hard to find stretching practice questions. I frequently guide keep to brand my ain worksheets past times piecing together questions from a multifariousness of sources, which tin move actually time-consuming. In this post service I recommend proficient places to seem for challenging questions. I'm focussing on topic specific practice here, non full general employment solving questions similar those from UKMT.

Finding challenge inwards recap
Last calendar week I was planning a lesson on ratio for my Year 10s. My school's schemes of run are the real Definition of a 'spiral curriculum' (mastery people, seem away now!). My students written report ratio as well as proportion inwards Year 7, as well as 1 time to a greater extent than inwards Year 8, as well as 1 time to a greater extent than inwards Year 9. The Year 10 system of run includes 1 lesson recapping ratio. I demand to brand this lesson suitably challenging or it volition move a waste matter of time, but I can't abide by a unmarried GCSE enquiry on ratio that this shape would abide by inwards the slightest fleck difficult. Thankfully my subdivision has around copies of the textbooks from the serial 'Extension Mathematics' which comprise first-class stretching questions. Some examples of their ratio questions are shown below - they're harder than the measure ratio questions inwards other textbooks.

1. Paula finished a cross province race inwards twenty minutes. When Paula finished, Sonia had solely completed 5/8 of the total distance. Sonia’s average speed was 75 metres per infinitesimal less than Paula’s. Find the length of the race as well as Sonia’s speed (in metres per minute).

2. Two numbers are such that their difference, their amount as well as their production are inwards the ratio 1:4:15. What are the ii numbers?

3. Find x if  2 + x : 4 + x = 6 + x : 9 + x

Questions similar this volition likely move to a greater extent than commonplace over the adjacent few years equally nosotros laid upwards students for the 'new' GCSEs which volition guide keep a increased focus on employment solving.

Online sources of practise questions
1. CIMT - The Mathematics Enhancement Programme from CIMT offers an extensive collection of exercises for all Key Stages. I was using their website thus much inwards my NQT twelvemonth that I bought a laid of their textbooks to flick through (order shape here). Since then, Craig Barton has real helpfully provided links to CIMT's cloth on his website (via TES) - it's organised past times theme instead of past times book, making it easier to locate what you're looking for. For event if you're teaching angles as well as thus you lot tin access all the cloth through this link, including worksheets, activities as well as assessments.

2. Brilliant.org - I've mentioned this website earlier but it deserves around other recommendation because I'm right away using it on a daily reason to abide by extension questions. Two examples are shown below for the theme of linear graphs. The questions on brilliant.org are brilliant(!) as well as there's plenty to line together a challenging worksheet on virtually topics.

 

3. surds extension task.

4. Maths Malakiss - Written past times an experienced maths instructor based inwards Dubai, this website provides a hit of worksheets which include a proficient aeroplane of challenge. H5N1 circle theorem event is shown below.

I of late made a homework on angles for my exceed laid Year nine using questions from this website. I recommend the Windows snipping tool to brand the physical care for of collating questions equally quick as well as painless equally possible.

5. Exam Questions - If you're looking for GCSE practise questions as well as thus there's around first-class sources of questions past times topic, including:

• Bland.in - gratuitous booklets of past times newspaper questions past times theme for Edexcel as well as AQA (model answers are also available to buy).
• Corbett Maths - practice questions past times topic and GCSE practise papers
• KESH Maths Department -  collections of past times newspaper questions past times theme as well as grade.
• Maths Genie - a large option of GCSE as well as H5N1 aeroplane questions past times topic.

6. .com! I characteristic a hit of recommendations inwards my resources libraries (many - but non all - are aimed at 'high ability' students). In iii months I'm moving to a comprehensive schoolhouse thus I may instruct Foundation GCSE for the kickoff fourth dimension - hold off my resources libraries to grow accordingly.

Questions to brand students think
I desire to halt this post service alongside an event of a enquiry my exceed laid Year nine students of late encountered inwards a test. They'd studied indices (including fractional as well as negative indices) as well as virtually students constitute it pretty straightforward, thus it was hard to abide by a way to actually brand them think. The enquiry below worked good - the vast bulk of students got it wrong. In the event reply shown, at to the lowest degree the pupil attempted to evaluate each expression, although around clear misconceptions guide keep emerged. When I went through the enquiry inwards shape nosotros wrote the decimals equally fractions as well as it all became clear. It was definitely a enquiry worth looking at. This is the variety of affair I should ensure I include inwards my lessons - questions that require proper thinking rather than only next a measure procedure.

I'd dear to remove heed where you lot acquire your virtually challenging questions from - guide keep I missed whatever proficient sources? What produce you lot purpose to continue your best mathematicians on their toes? Please comment below or tweet me.

Stretching Practice

I currently instruct at a girls' grammer school. This way all of my students are on rails for an H5N1 or A* at GCSE. It's a fleck similar teaching exceed laid all the time, but without the confidence levels you lot would hold off from such brilliant students. They larn novel concepts real rapidly but are frequently unwilling to guide keep risks.

Finding suitable resources for such smart as well as hardworking students tin move difficult. If I select exercises that are also easy, they'll experience patronised as well as acquire bored alongside maths. Besides, it's non a proficient purpose of their fourth dimension to produce practise that's also easy. But if I select exercises that are also difficult, they'll move frustrated as well as it won't attention them railroad train fluency. So I pose a lot of effort into ensuring my resources are the appropriate aeroplane of challenge.

It tin move hard to find stretching practice questions. I frequently guide keep to brand my ain worksheets past times piecing together questions from a multifariousness of sources, which tin move actually time-consuming. In this post service I recommend proficient places to seem for challenging questions. I'm focussing on topic specific practice here, non full general employment solving questions similar those from UKMT.

Finding challenge inwards recap
Last calendar week I was planning a lesson on ratio for my Year 10s. My school's schemes of run are the real Definition of a 'spiral curriculum' (mastery people, seem away now!). My students written report ratio as well as proportion inwards Year 7, as well as 1 time to a greater extent than inwards Year 8, as well as 1 time to a greater extent than inwards Year 9. The Year 10 system of run includes 1 lesson recapping ratio. I demand to brand this lesson suitably challenging or it volition move a waste matter of time, but I can't abide by a unmarried GCSE enquiry on ratio that this shape would abide by inwards the slightest fleck difficult. Thankfully my subdivision has around copies of the textbooks from the serial 'Extension Mathematics' which comprise first-class stretching questions. Some examples of their ratio questions are shown below - they're harder than the measure ratio questions inwards other textbooks.

1. Paula finished a cross province race inwards twenty minutes. When Paula finished, Sonia had solely completed 5/8 of the total distance. Sonia’s average speed was 75 metres per infinitesimal less than Paula’s. Find the length of the race as well as Sonia’s speed (in metres per minute).

2. Two numbers are such that their difference, their amount as well as their production are inwards the ratio 1:4:15. What are the ii numbers?

3. Find x if  2 + x : 4 + x = 6 + x : 9 + x

Questions similar this volition likely move to a greater extent than commonplace over the adjacent few years equally nosotros laid upwards students for the 'new' GCSEs which volition guide keep a increased focus on employment solving.

Online sources of practise questions
1. CIMT - The Mathematics Enhancement Programme from CIMT offers an extensive collection of exercises for all Key Stages. I was using their website thus much inwards my NQT twelvemonth that I bought a laid of their textbooks to flick through (order shape here). Since then, Craig Barton has real helpfully provided links to CIMT's cloth on his website (via TES) - it's organised past times theme instead of past times book, making it easier to locate what you're looking for. For event if you're teaching angles as well as thus you lot tin access all the cloth through this link, including worksheets, activities as well as assessments.

2. Brilliant.org - I've mentioned this website earlier but it deserves around other recommendation because I'm right away using it on a daily reason to abide by extension questions. Two examples are shown below for the theme of linear graphs. The questions on brilliant.org are brilliant(!) as well as there's plenty to line together a challenging worksheet on virtually topics.

 

3. surds extension task.

4. Maths Malakiss - Written past times an experienced maths instructor based inwards Dubai, this website provides a hit of worksheets which include a proficient aeroplane of challenge. H5N1 circle theorem event is shown below.

I of late made a homework on angles for my exceed laid Year nine using questions from this website. I recommend the Windows snipping tool to brand the physical care for of collating questions equally quick as well as painless equally possible.

5. Exam Questions - If you're looking for GCSE practise questions as well as thus there's around first-class sources of questions past times topic, including:

• Bland.in - gratuitous booklets of past times newspaper questions past times theme for Edexcel as well as AQA (model answers are also available to buy).
• Corbett Maths - practice questions past times topic and GCSE practise papers
• KESH Maths Department -  collections of past times newspaper questions past times theme as well as grade.
• Maths Genie - a large option of GCSE as well as H5N1 aeroplane questions past times topic.

6. .com! I characteristic a hit of recommendations inwards my resources libraries (many - but non all - are aimed at 'high ability' students). In iii months I'm moving to a comprehensive schoolhouse thus I may instruct Foundation GCSE for the kickoff fourth dimension - hold off my resources libraries to grow accordingly.

Questions to brand students think
I desire to halt this post service alongside an event of a enquiry my exceed laid Year nine students of late encountered inwards a test. They'd studied indices (including fractional as well as negative indices) as well as virtually students constitute it pretty straightforward, thus it was hard to abide by a way to actually brand them think. The enquiry below worked good - the vast bulk of students got it wrong. In the event reply shown, at to the lowest degree the pupil attempted to evaluate each expression, although around clear misconceptions guide keep emerged. When I went through the enquiry inwards shape nosotros wrote the decimals equally fractions as well as it all became clear. It was definitely a enquiry worth looking at. This is the variety of affair I should ensure I include inwards my lessons - questions that require proper thinking rather than only next a measure procedure.

I'd dear to remove heed where you lot acquire your virtually challenging questions from - guide keep I missed whatever proficient sources? What produce you lot purpose to continue your best mathematicians on their toes? Please comment below or tweet me.

The Novel Gcse Debate

On Sabbatum I participated inwards an Institute of Ideas panel give-and-take on the novel maths GCSE. Here is the description of the session from the blogged previously almost using an entrance examination to assess algebra skills at the get-go of Year 12 - this wouldn't survive necessary if the GCSE was doing its project correctly. I know of a pupil who got cypher out of 15 on his entrance assessment - which consisted of pretty basic algebra questions - fifty-fifty though he got a Grade half-dozen at GCSE. This begs the question, what does a Grade half-dozen inwards maths genuinely mean? 

I'm non convinced that standards direct keep improved. I'd fighting that mistakes were made inwards designing the content of the novel GCSE specification. 

Over the final ii years, maths has gained extra teaching fourth dimension inwards most schools. This has oftentimes come upward at a damage to other subjects. Many schools direct keep gone from iii maths lessons a calendar week to four, or fifty-fifty more. But the extra fourth dimension inwards the classroom has non been spent improving fluency inwards algebra together with tackling key misconceptions - which would direct keep been the best agency to pass the extra time. Instead nosotros direct keep had to pass the extra fourth dimension teaching all the new, random, bitty topics that were added to GCSE - quadratic sequences, functions, iteration, frequency trees together with and then on. The breadth of the GCSE is vast - at that spot are 97 topics listed inwards the government's specification. Why precisely were all the novel topics added? 

It isn't a caput get-go on H5N1 flat at all - if our students pass a few lessons rushing through functions inwards Year 11, nosotros volition even together with then direct keep to instruct them functions from scratch inwards Year 13. Due to fourth dimension constraints, most students volition entirely attain a superficial agreement of the H5N1 flat topics that were added to GCSE.

What would direct keep been ameliorate - what would direct keep genuinely made a deviation to our H5N1 flat mathematicians - would direct keep been fewer topics on GCSE. I am pleased that Higher GCSE got harder, it used to survive likewise slowly for many students, just inwards my thought it got harder inwards the incorrect way. I would direct keep liked to direct keep seen the questions on the of import materials - algebra, number, trigonometry - made harder. I'd direct keep liked it if it was impossible to larn a high GCSE flat without truthful algebraic fluency together with understanding.

This increased flat of difficulty - just on fewer topics - would direct keep ameliorate equipped our students for the challenges of H5N1 level. Depth was the answer. And depth is the reply inwards many high performing jurisdictions. But our regime went for breadth.

It all comes downward to curriculum. It volition survive a few years until nosotros are able to get-go measure the comport on of GCSE reform inwards whatever meaningful agency - possibly fifty-fifty longer, equally nosotros await for the changes at Key Stages 1 together with 2 to filter through to Key Stage 4. But at the moment, whilst the specification remains together with then broad, it's hard for me to run into at that spot beingness whatever important comport on on our time to come generation of mathematicians". 

There were or together with then genuinely interesting points raised during the debate, together with I was frustrated that I couldn't address every betoken inwards equally much exceptional equally I'd direct keep liked (particularly points relating to the suitability of the Foundation specification together with the sense of students who struggle amongst maths). Apologies if yous were at the session together with raised something that nosotros didn't direct keep fourth dimension to properly explore - it would survive neat if nosotros (ie the maths teaching community) could proceed the conversation on Twitter or at a time to come conference. It's genuinely of import that teachers brand their vocalism heard inwards discussions almost qualifications together with curriculum.

Many thank yous to the Institute of Ideas Education Forum for organising the debate, together with to Tom Bennett together with all those involved inwards researchED for hosting an fantabulous conference.

The Novel Gcse Debate

On Sabbatum I participated inwards an Institute of Ideas panel give-and-take on the novel maths GCSE. Here is the description of the session from the blogged previously almost using an entrance examination to assess algebra skills at the get-go of Year 12 - this wouldn't survive necessary if the GCSE was doing its project correctly. I know of a pupil who got cypher out of 15 on his entrance assessment - which consisted of pretty basic algebra questions - fifty-fifty though he got a Grade half-dozen at GCSE. This begs the question, what does a Grade half-dozen inwards maths genuinely mean? 

I'm non convinced that standards direct keep improved. I'd fighting that mistakes were made inwards designing the content of the novel GCSE specification. 

Over the final ii years, maths has gained extra teaching fourth dimension inwards most schools. This has oftentimes come upward at a damage to other subjects. Many schools direct keep gone from iii maths lessons a calendar week to four, or fifty-fifty more. But the extra fourth dimension inwards the classroom has non been spent improving fluency inwards algebra together with tackling key misconceptions - which would direct keep been the best agency to pass the extra time. Instead nosotros direct keep had to pass the extra fourth dimension teaching all the new, random, bitty topics that were added to GCSE - quadratic sequences, functions, iteration, frequency trees together with and then on. The breadth of the GCSE is vast - at that spot are 97 topics listed inwards the government's specification. Why precisely were all the novel topics added? 

It isn't a caput get-go on H5N1 flat at all - if our students pass a few lessons rushing through functions inwards Year 11, nosotros volition even together with then direct keep to instruct them functions from scratch inwards Year 13. Due to fourth dimension constraints, most students volition entirely attain a superficial agreement of the H5N1 flat topics that were added to GCSE.

What would direct keep been ameliorate - what would direct keep genuinely made a deviation to our H5N1 flat mathematicians - would direct keep been fewer topics on GCSE. I am pleased that Higher GCSE got harder, it used to survive likewise slowly for many students, just inwards my thought it got harder inwards the incorrect way. I would direct keep liked to direct keep seen the questions on the of import materials - algebra, number, trigonometry - made harder. I'd direct keep liked it if it was impossible to larn a high GCSE flat without truthful algebraic fluency together with understanding.

This increased flat of difficulty - just on fewer topics - would direct keep ameliorate equipped our students for the challenges of H5N1 level. Depth was the answer. And depth is the reply inwards many high performing jurisdictions. But our regime went for breadth.

It all comes downward to curriculum. It volition survive a few years until nosotros are able to get-go measure the comport on of GCSE reform inwards whatever meaningful agency - possibly fifty-fifty longer, equally nosotros await for the changes at Key Stages 1 together with 2 to filter through to Key Stage 4. But at the moment, whilst the specification remains together with then broad, it's hard for me to run into at that spot beingness whatever important comport on on our time to come generation of mathematicians". 

There were or together with then genuinely interesting points raised during the debate, together with I was frustrated that I couldn't address every betoken inwards equally much exceptional equally I'd direct keep liked (particularly points relating to the suitability of the Foundation specification together with the sense of students who struggle amongst maths). Apologies if yous were at the session together with raised something that nosotros didn't direct keep fourth dimension to properly explore - it would survive neat if nosotros (ie the maths teaching community) could proceed the conversation on Twitter or at a time to come conference. It's genuinely of import that teachers brand their vocalism heard inwards discussions almost qualifications together with curriculum.

Many thank yous to the Institute of Ideas Education Forum for organising the debate, together with to Tom Bennett together with all those involved inwards researchED for hosting an fantabulous conference.

The Novel Gcse Debate

On Sabbatum I participated inwards an Institute of Ideas panel give-and-take on the novel maths GCSE. Here is the description of the session from the blogged previously almost using an entrance examination to assess algebra skills at the get-go of Year 12 - this wouldn't survive necessary if the GCSE was doing its project correctly. I know of a pupil who got cypher out of 15 on his entrance assessment - which consisted of pretty basic algebra questions - fifty-fifty though he got a Grade half-dozen at GCSE. This begs the question, what does a Grade half-dozen inwards maths genuinely mean? 

I'm non convinced that standards direct keep improved. I'd fighting that mistakes were made inwards designing the content of the novel GCSE specification. 

Over the final ii years, maths has gained extra teaching fourth dimension inwards most schools. This has oftentimes come upward at a damage to other subjects. Many schools direct keep gone from iii maths lessons a calendar week to four, or fifty-fifty more. But the extra fourth dimension inwards the classroom has non been spent improving fluency inwards algebra together with tackling key misconceptions - which would direct keep been the best agency to pass the extra time. Instead nosotros direct keep had to pass the extra fourth dimension teaching all the new, random, bitty topics that were added to GCSE - quadratic sequences, functions, iteration, frequency trees together with and then on. The breadth of the GCSE is vast - at that spot are 97 topics listed inwards the government's specification. Why precisely were all the novel topics added? 

It isn't a caput get-go on H5N1 flat at all - if our students pass a few lessons rushing through functions inwards Year 11, nosotros volition even together with then direct keep to instruct them functions from scratch inwards Year 13. Due to fourth dimension constraints, most students volition entirely attain a superficial agreement of the H5N1 flat topics that were added to GCSE.

What would direct keep been ameliorate - what would direct keep genuinely made a deviation to our H5N1 flat mathematicians - would direct keep been fewer topics on GCSE. I am pleased that Higher GCSE got harder, it used to survive likewise slowly for many students, just inwards my thought it got harder inwards the incorrect way. I would direct keep liked to direct keep seen the questions on the of import materials - algebra, number, trigonometry - made harder. I'd direct keep liked it if it was impossible to larn a high GCSE flat without truthful algebraic fluency together with understanding.

This increased flat of difficulty - just on fewer topics - would direct keep ameliorate equipped our students for the challenges of H5N1 level. Depth was the answer. And depth is the reply inwards many high performing jurisdictions. But our regime went for breadth.

It all comes downward to curriculum. It volition survive a few years until nosotros are able to get-go measure the comport on of GCSE reform inwards whatever meaningful agency - possibly fifty-fifty longer, equally nosotros await for the changes at Key Stages 1 together with 2 to filter through to Key Stage 4. But at the moment, whilst the specification remains together with then broad, it's hard for me to run into at that spot beingness whatever important comport on on our time to come generation of mathematicians". 

There were or together with then genuinely interesting points raised during the debate, together with I was frustrated that I couldn't address every betoken inwards equally much exceptional equally I'd direct keep liked (particularly points relating to the suitability of the Foundation specification together with the sense of students who struggle amongst maths). Apologies if yous were at the session together with raised something that nosotros didn't direct keep fourth dimension to properly explore - it would survive neat if nosotros (ie the maths teaching community) could proceed the conversation on Twitter or at a time to come conference. It's genuinely of import that teachers brand their vocalism heard inwards discussions almost qualifications together with curriculum.

Many thank yous to the Institute of Ideas Education Forum for organising the debate, together with to Tom Bennett together with all those involved inwards researchED for hosting an fantabulous conference.

Equations Exercises

I was looking at roughly of the one-time maths textbooks at my schoolhouse in addition to noticed than fifty-fifty equally latterly equally the 1980s, textbook exercises contained a lot to a greater extent than do questions than modern textbooks. Below is an instance comparison the same theme inward a 1980s textbook ('Negative Numbers in addition to Graphs' past times Heylings) in addition to a electrical flow GCSE textbook ('Edexcel GCSE Maths Higher' published past times Oxford University Press). The exercises encompass the same science only the root exercise is double the length of the second. I approximate modern textbooks convey to tally an entire GCSE course of didactics into a unmarried book, restricting the sum of do questions they tin include.

From 'Negative Numbers in addition to Graphs', root published 1984

From 'Edexcel GCSE Maths Higher', root published 2015

Last calendar month I wrote a post service virtually a 1950s algebra textbook called 'A Classbook of Algebra'. The questions inward this textbook are by in addition to large to a greater extent than challenging than questions inward most modern textbooks. In response to this post service a issue of rattling generous volunteers stepped forrad offering to type upward roughly of the exercises in addition to thence that teachers tin purpose them inward lessons. I am rattling grateful for the fourth dimension in addition to test that has gone into this. In this post service I convey provided links to all the exercises typed upward in addition to thence far which relate to the science of solving equations. I convey an additional xviii exercises on other topics which I volition collate over the side past times side few weeks.

These exercises are all rather long in addition to the thought is non necessarily to purpose them inward their entirety. Because they convey all been typed upward inward in Word, teachers volition easily endure able to edit the exercises or cutting in addition to glue item questions to purpose equally examples inward class.

Most exercises include answers. I volition edit this post service if anything is updated. For each exercise listed below I convey included a minor extract in addition to thence you lot tin preview the type of questions covered.

1. Very Easy Equations (four exercises) - alongside thank you lot to Caroline Beale (@cbealemaths)

2. Easy Equations I - alongside thank you lot to Claire Willis (@MissWillisMaths)

3. Easy Equations II - alongside thank you lot to Caroline Beale (@cbealemaths)

4. Equations Involving Fractions - alongside thank you lot to Michael Allan (@mrallanmaths)

5. Equations Involving Brackets - alongside thank you lot to Jane Appleton (@JaneAppleton24)

6. Equations alongside Brackets in addition to Harder Equations alongside Brackets - alongside thank you lot to Justin Thompson 

7. Equations Involving Directed Numbers - alongside thank you lot to Caroline Beale (@cbealemaths)

8. Easy Literal Equations - alongside thank you lot to Sandra Douglas (@mathsbox1)

9. Miscellaneous Simultaneous Equations - alongside thank you lot to Fee Wilson (@fionajw)

10. Miscellaneous Equations - alongside thank you lot to Dan Rodriguez-Clark (@InteractMaths). 

I promise this is useful. Thank you lot in 1 trial again to everyone who has worked on this. And of course of didactics total credit to Sidney Trustram, the master writer of these exercises which, lxx years on, are all the same making us think. Look out for my side past times side posts inward which I'll percentage exercises on simplifying algebra, expanding, factorising, writing algebraically in addition to working alongside directed numbers.