New Gcse: Existent Life Graphs

I guide keep a feeling that I nonetheless haven't identified all the novel GCSE content. This makes me nervous. I glanced through a textbook concluding calendar week as well as spotted a few topics that aren't on my quadratic graphs, but I didn't know that students volition likewise survive required to position the roots of cubic graphs (see instance inquiry below). The specification but says 'recognise, sketch as well as translate graphs of ... unproblematic cubic functions'. Previously students guide keep exclusively been required to recognise the shape of cubics - roots didn't come upward up until H5N1 level. Now I've spotted this content inwards the textbook, I'll demand to adjust my plans to ensure I guide keep fourth dimension to encompass this at some indicate inwards the side yesteryear side eighteen months. The fourth dimension pressure level is increasing.

A inquiry from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

Real Life Graphs
I've just taught linear graphs to my Year 10s. My system of piece of job tells me that I straight off guide keep to learn 'real life graphs'. But what does that mean? In this postal service I volition endeavour to clarify what comes nether this title.

The previous GCSE specification said that students had to 'construct linear, quadratic as well as other functions from real-life problems as well as plot their corresponding graphs'. Examples included conversion graphs, 'ready reckoners' (whatever they are...) as well as distance fourth dimension graphs.

Here's the relevant extract from the novel specification:

The wording is unlike to the previous specification but it's broadly the same content, alongside perchance to a greater extent than emphasis on interpreting contextual graphs. AQA's first-class Teaching Guidance gives us a to a greater extent than detailed description:

There's a lot here! The commencement 4 points follow on from linear graphs - for instance students volition guide keep to translate a y-intercept equally a fixed charge. AQA gives this instance question:

There's some swell novel resources for this variety of graph inwards AQA's Bridging Unit: Resource Pocket 3. The back upward provided yesteryear AQA is fantastic.

Modelling

The most mutual examples of 'graphs showing real-life situations inwards geometry' are those that model H2O flow. In AQA's sample assessment materials (Question 23 inwards Higher Paper 3) students are shown a graph representing the depth of H2O inwards a container over time. They are asked to position the corresponding container from a alternative (shown below). They are thence asked to gauge a charge per unit of measurement of change, requiring them to calculate the slope of a tangent to the curve.

It's worth spending a distich of lessons developing the skills required for the commencement component of this inquiry (ie identifying the right container). Thankfully there's plenty of practiced resources for this topic.

In previous years I've used a 'filling upward a bath' card sort (I adapted this from a treasure hunt I institute on TES). I don't oft exercise carte du jour sorts but I cry upward this 1 working well. There's likewise a practiced existent life graph card sort from Nuffield.

I'm actually keen to exercise Desmos Water Line - this is an online lesson inwards which students graph the charge per unit of measurement at which containers create total alongside water. They likewise create their ain containers to graph. Desmos lessons are absolutely bright thence if y'all guide keep access to tablets or computers thence do give it a try. For me it volition survive a rare but worthwhile view to the information technology Room.

The classic Red Box is total of first-class graphing activities - it's a shame that the ikon character isn't great.

Kinematics Graphs
Although I'm education existent life graphs side yesteryear side week, I'm planning to leave kinematic graphs until I learn chemical compound measures. This volition thence Pb onto rates of alter as well as surface area nether a graph, which I've already blogged about. It doesn't brand sense to do kinematic graphs earlier education speed.

We guide keep plenty of resources for distance fourth dimension graphs. AQA's Bridging Unit has some practiced questions (extract above). Interpreting Distance-Time Graphs from the Mathematics Assessment Project is excellent. I likewise similar this commentary activeness from Transum - The Hurdles Race.

I don't guide keep much on speed fourth dimension graphs, apart from those listed inwards my post close finding the surface area nether a graph as well as those available from Toticity's Mind the Gap Maths Toolbox.

Exponential Graphs
The Higher Tier specification includes contextual exponential graphs. An instance inquiry from my Edexcel textbook is shown below. I invention to encompass this variety of graph when I learn increment as well as decay (eg chemical compound interest) side yesteryear side year.

My Plan
Next calendar week I'm education 'real life graphs', but what precisely volition I teach? Having looked through the novel GCSE specification, the sample assessment materials, AQA's Teacher Guidance as well as a distich of novel GCSE textbooks, I straight off guide keep a clearer stance of what I demand to cover. It's taken a lot of travail to decide that I demand to do a lesson or ii on contextual linear graphs as well as a distich of lessons on modelling. I'll come upward dorsum to kinematic graphs, rates of alter as well as areas nether graphs afterwards I've done chemical compound measures. I just promise I'll guide keep plenty fourth dimension to encompass everything.

Proportional graphs also seem to come upward up a lot inwards the novel GCSE. Often a context is given inwards the question. I'll teach these inwards Jan when I encompass ratio as well as proportion. here.

New Gcse: Existent Life Graphs

I guide keep a feeling that I nonetheless haven't identified all the novel GCSE content. This makes me nervous. I glanced through a textbook concluding calendar week as well as spotted a few topics that aren't on my quadratic graphs, but I didn't know that students volition likewise survive required to position the roots of cubic graphs (see instance inquiry below). The specification but says 'recognise, sketch as well as translate graphs of ... unproblematic cubic functions'. Previously students guide keep exclusively been required to recognise the shape of cubics - roots didn't come upward up until H5N1 level. Now I've spotted this content inwards the textbook, I'll demand to adjust my plans to ensure I guide keep fourth dimension to encompass this at some indicate inwards the side yesteryear side eighteen months. The fourth dimension pressure level is increasing.

A inquiry from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

Real Life Graphs
I've just taught linear graphs to my Year 10s. My system of piece of job tells me that I straight off guide keep to learn 'real life graphs'. But what does that mean? In this postal service I volition endeavour to clarify what comes nether this title.

The previous GCSE specification said that students had to 'construct linear, quadratic as well as other functions from real-life problems as well as plot their corresponding graphs'. Examples included conversion graphs, 'ready reckoners' (whatever they are...) as well as distance fourth dimension graphs.

Here's the relevant extract from the novel specification:

The wording is unlike to the previous specification but it's broadly the same content, alongside perchance to a greater extent than emphasis on interpreting contextual graphs. AQA's first-class Teaching Guidance gives us a to a greater extent than detailed description:

There's a lot here! The commencement 4 points follow on from linear graphs - for instance students volition guide keep to translate a y-intercept equally a fixed charge. AQA gives this instance question:

There's some swell novel resources for this variety of graph inwards AQA's Bridging Unit: Resource Pocket 3. The back upward provided yesteryear AQA is fantastic.

Modelling

The most mutual examples of 'graphs showing real-life situations inwards geometry' are those that model H2O flow. In AQA's sample assessment materials (Question 23 inwards Higher Paper 3) students are shown a graph representing the depth of H2O inwards a container over time. They are asked to position the corresponding container from a alternative (shown below). They are thence asked to gauge a charge per unit of measurement of change, requiring them to calculate the slope of a tangent to the curve.

It's worth spending a distich of lessons developing the skills required for the commencement component of this inquiry (ie identifying the right container). Thankfully there's plenty of practiced resources for this topic.

In previous years I've used a 'filling upward a bath' card sort (I adapted this from a treasure hunt I institute on TES). I don't oft exercise carte du jour sorts but I cry upward this 1 working well. There's likewise a practiced existent life graph card sort from Nuffield.

I'm actually keen to exercise Desmos Water Line - this is an online lesson inwards which students graph the charge per unit of measurement at which containers create total alongside water. They likewise create their ain containers to graph. Desmos lessons are absolutely bright thence if y'all guide keep access to tablets or computers thence do give it a try. For me it volition survive a rare but worthwhile view to the information technology Room.

The classic Red Box is total of first-class graphing activities - it's a shame that the ikon character isn't great.

Kinematics Graphs
Although I'm education existent life graphs side yesteryear side week, I'm planning to leave kinematic graphs until I learn chemical compound measures. This volition thence Pb onto rates of alter as well as surface area nether a graph, which I've already blogged about. It doesn't brand sense to do kinematic graphs earlier education speed.

We guide keep plenty of resources for distance fourth dimension graphs. AQA's Bridging Unit has some practiced questions (extract above). Interpreting Distance-Time Graphs from the Mathematics Assessment Project is excellent. I likewise similar this commentary activeness from Transum - The Hurdles Race.

I don't guide keep much on speed fourth dimension graphs, apart from those listed inwards my post close finding the surface area nether a graph as well as those available from Toticity's Mind the Gap Maths Toolbox.

Exponential Graphs
The Higher Tier specification includes contextual exponential graphs. An instance inquiry from my Edexcel textbook is shown below. I invention to encompass this variety of graph when I learn increment as well as decay (eg chemical compound interest) side yesteryear side year.

My Plan
Next calendar week I'm education 'real life graphs', but what precisely volition I teach? Having looked through the novel GCSE specification, the sample assessment materials, AQA's Teacher Guidance as well as a distich of novel GCSE textbooks, I straight off guide keep a clearer stance of what I demand to cover. It's taken a lot of travail to decide that I demand to do a lesson or ii on contextual linear graphs as well as a distich of lessons on modelling. I'll come upward dorsum to kinematic graphs, rates of alter as well as areas nether graphs afterwards I've done chemical compound measures. I just promise I'll guide keep plenty fourth dimension to encompass everything.

Proportional graphs also seem to come upward up a lot inwards the novel GCSE. Often a context is given inwards the question. I'll teach these inwards Jan when I encompass ratio as well as proportion. here.

New Gcse: Tangents In Addition To Areas

At commencement glance it appears that calculus features inwards the novel GCSE specification. On closer inspection it turns out that our students volition detect the slope of a plication past times drawing a suitable tangent rather than past times differentiating. And instead of integrating, students volition use the trapezium rule (or similar) to detect the expanse nether a curve. So calculus remains reserved for Key Stage 5, merely our students volition straightaway go amend prepared for calculus when they commencement regard it. GCSE volition create got given them a conceptual agreement of charge per unit of measurement of modify together with an powerfulness to translate this contextually.

This postal service talks you lot through this novel GCSE topic - it tells you lot what you lot demand to learn together with provides links to resources.

Specification together with Exam Questions
Here's the relevant extracts from the novel GCSE specification:

This all becomes clearer when nosotros await at example examination questions. Huge thank you lot to Tom Bennison (@DrBennison) for doing the difficult operate for me hither - he's been through the sample assessment materials for all examination boards together with collated the relevant questions inwards this Subject Knowledge Check. In a typical question, students are given a velocity-time graph together with asked to detect the amount distance travelled and/or the acceleration at a specific time.

AQA helpfully provides additional clarification nigh the specification inwards their instructor guide. The extract below is from GCSE Mathematics (8300) Teaching Guidance (available to All About Maths members) which provides a release of additional example questions.

Methods
The diagrams below are taken from this extract from a novel GCSE textbook which sets out the criterion methods that our students volition use.

Students volition already know how to detect the slope of a direct business (ie 'rise over run' or equivalent). To guess the slope of a plication they volition create got to pull a tangent, every bit shown here:

They'll also demand to create upward one's hear whether the slope is positive or negative.

To guess the expanse nether a graph, students volition create got to dissever the expanse into sections. The AQA Teaching Guidance says 'the trapezium dominion demand non go known merely it is recommended every bit the most efficient way of calculating the expanse nether a curve'. Unlike at Influenza A virus subtype H5N1 level, they won't go given the formula inwards the exam.

The option to using the trapezium dominion is to dissever the expanse into a release of triangles together with rectangles.

Motion Graphs

The methods described to a higher house are fairly straightforward. I recall interpretation powerfulness examine trickier (eg agreement what motion graphs are showing). Students volition demand to know that speed, acceleration together with deceleration are rates of change, together with that the expanse nether a velocity-time graph represents distance. There's a lot of novel concepts together with vocabulary here.

Bear inwards hear that motion graphs come upward up inwards Physics GCSE too. As shown inwards this extract from the AQA Physics GCSE Specification, it's precisely the same content:

Other Contexts
I was initially confused past times the cite of 'graphs inwards fiscal contexts' inwards this department of the specification - I've seen questions inwards which students create got to interpret fiscal graphs merely cypher involving tangents or areas. Thanks to @DJUdall for sharing the moving painting below (taken from this novel GCSE textbook) which shows an example of estimating a charge per unit of measurement of modify inwards a fiscal context.

Could examination questions encompass other contexts, also motion together with finance? It's possible. In the example below from CIMT students are asked to detect the majority of H2O represented past times the shaded area. To empathise why the expanse nether the graph represents majority nosotros tin dismiss consider the units - the units on the horizontal axis are seconds, together with the units on the vertical axis are m³/s, then when nosotros multiply the 2 together nosotros larn m³.

Instantaneous Rate of Change

Students volition demand to empathise the divergence betwixt an average charge per unit of measurement of modify over a menstruum of fourth dimension together with an instantaneous charge per unit of measurement of change. In my postal service 'Introducing Differentiation' I talked nigh how to give students an intuitive agreement of the slope of a plication at a point. It's worth reading the department entitled 'An Instantaneous Rate of Change' for ideas, videos together with resources (including my worksheet 'Thinking About Gradient' which was designed for Influenza A virus subtype H5N1 degree merely is straightaway suitable for GCSE).

Resources
Resources for this topic are listed below. I'll add together these to my library together with volition go along to add together novel resources every bit I detect them.

• @DJUdall has produced this first-class graphing activity which covers both tangents together with areas nether graphs. 
• @jase_wanner has written this super hero activity on distance-time together with speed-time graphs to prepare students' agreement of how to translate these graphs.
• Gradient on a curved graph by Owen134866 on TES gives students the chance to practice drawing graphs together with tangents. My worksheet Finding the slope of a plication using a tangent is similar, merely students aren't required to pull the graphs themselves.
• Using Graphs from CIMT covers a broad arrive at of graph topics. Section 17.2 covers areas nether graphs using the trapezium dominion together with Section 17.3 covers tangents to curves. The amount arrive at of resources for this module are available on TES.
• Nuffield Mathematics provides a Free-Standing Mathematics Activity 'Speed together with Distance' which is nigh finding the expanse nether a speed-distance graph. Resources include slides, a student sheet and teacher notes.

'Graphing' by @DJUdall

I promise this postal service has been useful inwards helping you lot fix to learn this novel GCSE topic. Please permit me know if you lot create got whatever resources to share.

You powerfulness also detect my other posts nigh novel GCSE topics helpful: Sequences, Inequalities together with Quadratic Graphs.

See my New GCSE Support Page for resources together with links for all novel GCSE content. 

'Drawing a Tangent Line' past times NCTM

New Gcse: Tangents In Addition To Areas

At commencement glance it appears that calculus features inwards the novel GCSE specification. On closer inspection it turns out that our students volition detect the slope of a plication past times drawing a suitable tangent rather than past times differentiating. And instead of integrating, students volition use the trapezium rule (or similar) to detect the expanse nether a curve. So calculus remains reserved for Key Stage 5, merely our students volition straightaway go amend prepared for calculus when they commencement regard it. GCSE volition create got given them a conceptual agreement of charge per unit of measurement of modify together with an powerfulness to translate this contextually.

This postal service talks you lot through this novel GCSE topic - it tells you lot what you lot demand to learn together with provides links to resources.

Specification together with Exam Questions
Here's the relevant extracts from the novel GCSE specification:

This all becomes clearer when nosotros await at example examination questions. Huge thank you lot to Tom Bennison (@DrBennison) for doing the difficult operate for me hither - he's been through the sample assessment materials for all examination boards together with collated the relevant questions inwards this Subject Knowledge Check. In a typical question, students are given a velocity-time graph together with asked to detect the amount distance travelled and/or the acceleration at a specific time.

AQA helpfully provides additional clarification nigh the specification inwards their instructor guide. The extract below is from GCSE Mathematics (8300) Teaching Guidance (available to All About Maths members) which provides a release of additional example questions.

Methods
The diagrams below are taken from this extract from a novel GCSE textbook which sets out the criterion methods that our students volition use.

Students volition already know how to detect the slope of a direct business (ie 'rise over run' or equivalent). To guess the slope of a plication they volition create got to pull a tangent, every bit shown here:

They'll also demand to create upward one's hear whether the slope is positive or negative.

To guess the expanse nether a graph, students volition create got to dissever the expanse into sections. The AQA Teaching Guidance says 'the trapezium dominion demand non go known merely it is recommended every bit the most efficient way of calculating the expanse nether a curve'. Unlike at Influenza A virus subtype H5N1 level, they won't go given the formula inwards the exam.

The option to using the trapezium dominion is to dissever the expanse into a release of triangles together with rectangles.

Motion Graphs

The methods described to a higher house are fairly straightforward. I recall interpretation powerfulness examine trickier (eg agreement what motion graphs are showing). Students volition demand to know that speed, acceleration together with deceleration are rates of change, together with that the expanse nether a velocity-time graph represents distance. There's a lot of novel concepts together with vocabulary here.

Bear inwards hear that motion graphs come upward up inwards Physics GCSE too. As shown inwards this extract from the AQA Physics GCSE Specification, it's precisely the same content:

Other Contexts
I was initially confused past times the cite of 'graphs inwards fiscal contexts' inwards this department of the specification - I've seen questions inwards which students create got to interpret fiscal graphs merely cypher involving tangents or areas. Thanks to @DJUdall for sharing the moving painting below (taken from this novel GCSE textbook) which shows an example of estimating a charge per unit of measurement of modify inwards a fiscal context.

Could examination questions encompass other contexts, also motion together with finance? It's possible. In the example below from CIMT students are asked to detect the majority of H2O represented past times the shaded area. To empathise why the expanse nether the graph represents majority nosotros tin dismiss consider the units - the units on the horizontal axis are seconds, together with the units on the vertical axis are m³/s, then when nosotros multiply the 2 together nosotros larn m³.

Instantaneous Rate of Change

Students volition demand to empathise the divergence betwixt an average charge per unit of measurement of modify over a menstruum of fourth dimension together with an instantaneous charge per unit of measurement of change. In my postal service 'Introducing Differentiation' I talked nigh how to give students an intuitive agreement of the slope of a plication at a point. It's worth reading the department entitled 'An Instantaneous Rate of Change' for ideas, videos together with resources (including my worksheet 'Thinking About Gradient' which was designed for Influenza A virus subtype H5N1 degree merely is straightaway suitable for GCSE).

Resources
Resources for this topic are listed below. I'll add together these to my library together with volition go along to add together novel resources every bit I detect them.

• @DJUdall has produced this first-class graphing activity which covers both tangents together with areas nether graphs. 
• @jase_wanner has written this super hero activity on distance-time together with speed-time graphs to prepare students' agreement of how to translate these graphs.
• Gradient on a curved graph by Owen134866 on TES gives students the chance to practice drawing graphs together with tangents. My worksheet Finding the slope of a plication using a tangent is similar, merely students aren't required to pull the graphs themselves.
• Using Graphs from CIMT covers a broad arrive at of graph topics. Section 17.2 covers areas nether graphs using the trapezium dominion together with Section 17.3 covers tangents to curves. The amount arrive at of resources for this module are available on TES.
• Nuffield Mathematics provides a Free-Standing Mathematics Activity 'Speed together with Distance' which is nigh finding the expanse nether a speed-distance graph. Resources include slides, a student sheet and teacher notes.

'Graphing' by @DJUdall

I promise this postal service has been useful inwards helping you lot fix to learn this novel GCSE topic. Please permit me know if you lot create got whatever resources to share.

You powerfulness also detect my other posts nigh novel GCSE topics helpful: Sequences, Inequalities together with Quadratic Graphs.

See my New GCSE Support Page for resources together with links for all novel GCSE content. 

'Drawing a Tangent Line' past times NCTM

Linear Graphs

One of the topics that my pupils fighting amongst the most, from Key Stage iii correct through to Year 12, is linear graphs.

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't operate out how to respond a GCSE interrogation similar this:

Strangely, I learn this differently at GCSE too Influenza A virus subtype H5N1 level.  At GCSE my pupils write down

y = mx + c

too substitute values for y, thousand too x, too thus solve for c.  Whereas at Influenza A virus subtype H5N1 marker my pupils utilization the equation

y - y₁ = m(x - x₁)

Essentially the same method but a slightly dissimilar approach. Perhaps I should hold out to a greater extent than consistent too innovate the 'A marker method' at GCSE. I'd similar to remove heed what other teachers do.

In this postal service I’ll advise closed to ideas too resources for didactics linear graphs.

Key words

Let's showtime amongst the basics. There's a lot of novel vocabulary inward coordinate geometry, closed to of which pupils volition accept encountered at primary school. This is a overnice vocabulary noesis survey every bit suggested inward my earlier post. 

Here's a overnice play a trick on for remembering the words parallel too perpendicular (this could hold out helpful for spellings - parallel is oftentimes misspelt): 

too this activity is suitable for Year six or 7. 

Introducing the shape y = mx + c
I'd unremarkably showtime this topic inward Year seven or 8 amongst plotting conduct work graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This topic provides an splendid chance for pupil investigation using Desmos. Use a worksheet to guide pupils through the lesson:

• Investigating Straight Lines amongst Desmos (by Tristan Jones on TES)
• Straight Line Graphs inward Desmos (by me!)

Once pupils are able to translate the values of thousand too c too thus they tin endeavour this exercise or this true/false activity (both from rogradymaths.blogspot.co.uk). Teachit Maths also has a overnice 'Understanding y = mx+c' worksheet and two activities on horizontal too vertical lines.

My weblog postal service 'All nigh gradient' features ideas too resources for didactics slope (the postal service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets too activities).

Understanding parallel too perpendicular gradients

So here's the primal data that pupils demand to understand:

(source)

If they know how to operate out a slope every bit 'rise over run' (or equivalent) too thus pupils should hold out able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this ane from MathsPad.

Here's a few activities for a lesson on perpendicular lines:

• Finding Equations of Parallel too Perpendicular Lines past times Mathematics Assessment Project
• Perpendicular Lines Worksheet (by me!)
• AS marker Parallel too Perpendicular Lines  (suitable for GCSE extension)
• Perpendicular lines: equations past times toticity.co.uk

Bringing it all together
When students written report linear graphs at AS level, they don't actually acquire anything novel - my GCSE pupils should accept the necessary skills too noesis to respond C1 coordinate geometry questions. I gave my Year xi pupils questions 5 - seven from this AS worksheet final twelvemonth - it took them ages to respond each question, but they were for sure capable. Essentially it's merely the wording of the questions that throws them.

Here's closed to to a greater extent than recommended resources suitable for GCSE students:

• Foundation: Linear Graphs 'I Can' from Mathsbox
• Mathattack Linear Graphs homework sheet
• Topic checklist
• MathsPad Linear Graphs Problems
• Rich activities from Five Triangles
• Rich activities from Median Don Steward

Finally, fun for puzzle-lovers in linear relationships sudoku and a overnice Key Stage iii Christmas activeness on plotting linear graphs from Teachit Maths - Mistletoe too Lines.

Finally, always wondered which countries utilization y = mx + c annotation too which countries utilization something different? Check out this map.

Linear Graphs

One of the topics that my pupils fighting amongst the most, from Key Stage iii correct through to Year 12, is linear graphs.

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't operate out how to respond a GCSE interrogation similar this:

Strangely, I learn this differently at GCSE too Influenza A virus subtype H5N1 level.  At GCSE my pupils write down

y = mx + c

too substitute values for y, thousand too x, too thus solve for c.  Whereas at Influenza A virus subtype H5N1 marker my pupils utilization the equation

y - y₁ = m(x - x₁)

Essentially the same method but a slightly dissimilar approach. Perhaps I should hold out to a greater extent than consistent too innovate the 'A marker method' at GCSE. I'd similar to remove heed what other teachers do.

In this postal service I’ll advise closed to ideas too resources for didactics linear graphs.

Key words

Let's showtime amongst the basics. There's a lot of novel vocabulary inward coordinate geometry, closed to of which pupils volition accept encountered at primary school. This is a overnice vocabulary noesis survey every bit suggested inward my earlier post. 

Here's a overnice play a trick on for remembering the words parallel too perpendicular (this could hold out helpful for spellings - parallel is oftentimes misspelt): 

too this activity is suitable for Year six or 7. 

Introducing the shape y = mx + c
I'd unremarkably showtime this topic inward Year seven or 8 amongst plotting conduct work graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This topic provides an splendid chance for pupil investigation using Desmos. Use a worksheet to guide pupils through the lesson:

• Investigating Straight Lines amongst Desmos (by Tristan Jones on TES)
• Straight Line Graphs inward Desmos (by me!)

Once pupils are able to translate the values of thousand too c too thus they tin endeavour this exercise or this true/false activity (both from rogradymaths.blogspot.co.uk). Teachit Maths also has a overnice 'Understanding y = mx+c' worksheet and two activities on horizontal too vertical lines.

My weblog postal service 'All nigh gradient' features ideas too resources for didactics slope (the postal service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets too activities).

Understanding parallel too perpendicular gradients

So here's the primal data that pupils demand to understand:

(source)

If they know how to operate out a slope every bit 'rise over run' (or equivalent) too thus pupils should hold out able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this ane from MathsPad.

Here's a few activities for a lesson on perpendicular lines:

• Finding Equations of Parallel too Perpendicular Lines past times Mathematics Assessment Project
• Perpendicular Lines Worksheet (by me!)
• AS marker Parallel too Perpendicular Lines  (suitable for GCSE extension)
• Perpendicular lines: equations past times toticity.co.uk

Bringing it all together
When students written report linear graphs at AS level, they don't actually acquire anything novel - my GCSE pupils should accept the necessary skills too noesis to respond C1 coordinate geometry questions. I gave my Year xi pupils questions 5 - seven from this AS worksheet final twelvemonth - it took them ages to respond each question, but they were for sure capable. Essentially it's merely the wording of the questions that throws them.

Here's closed to to a greater extent than recommended resources suitable for GCSE students:

• Foundation: Linear Graphs 'I Can' from Mathsbox
• Mathattack Linear Graphs homework sheet
• Topic checklist
• MathsPad Linear Graphs Problems
• Rich activities from Five Triangles
• Rich activities from Median Don Steward

Finally, fun for puzzle-lovers in linear relationships sudoku and a overnice Key Stage iii Christmas activeness on plotting linear graphs from Teachit Maths - Mistletoe too Lines.

Finally, always wondered which countries utilization y = mx + c annotation too which countries utilization something different? Check out this map.