All About Maths

Gradients and rate of change (8300 - Higher - Ratio, proportion and rates of change)

Topic:Gradients and rate of change

Route Map

Specification references (in recommended teaching order)

Specification content Specification notes
R15
  • Interpret the gradient at a point on a curve as the instantaneous rate of change
  • Apply the concepts of average and instantaneous rates of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts

R14
  • Interpret the gradient of a straight-line graph as a rate of change


The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

Teaching resources

Gradients and rates of change - all resources for 3 year route map - zip folder
Downloadable resource in zip format. 19/10/2015
8.1 MB
Related resources: Gradients and rate of change
Topic overview and lesson plans
Downloadable resource in doc format. 19/10/2015
236 KB
Related resources: Gradients and rate of change

Lesson 1 Activity 1
Downloadable resource in ppt format. 19/10/2015
1.4 MB
Related resources: Gradients and rate of change
Lesson 2 Activity 1
Downloadable resource in ppt format. 19/10/2015
1.4 MB
Related resources: Gradients and rate of change
Lesson 3 Activity 2
Downloadable resource in ppt format. 19/10/2015
1.6 MB
Related resources: Gradients and rate of change
Lesson 3 Activity 1
Downloadable resource in ppt format. 19/10/2015
1.4 MB
Related resources: Gradients and rate of change
Lesson 4 Activity 1
Downloadable resource in ppt format. 19/10/2015
1.5 MB
Related resources: Gradients and rate of change
Lesson 5 Activity 1
Downloadable resource in ppt format. 19/10/2015
1.4 MB
Related resources: Gradients and rate of change

Lesson 1 Worksheet 1
Downloadable resource in doc format. 19/10/2015
213 KB
Related resources: Gradients and rate of change
Lesson 1 Worksheet 2
Downloadable resource in doc format. 19/10/2015
318 KB
Related resources: Gradients and rate of change
Lesson 2 Worksheet 1
Downloadable resource in doc format. 19/10/2015
218 KB
Related resources: Gradients and rate of change
Lesson 3 Worksheet 1
Downloadable resource in doc format. 19/10/2015
2.0 MB
Related resources: Gradients and rate of change
Lesson 4 Worksheet 1
Downloadable resource in doc format. 19/10/2015
587 KB
Related resources: Gradients and rate of change
Lesson 5 Worksheet 1
Downloadable resource in doc format. 19/10/2015
10.4 MB
Related resources: Gradients and rate of change
Lesson 6 Worksheet 1
Downloadable resource in doc format. 19/10/2015
8.5 MB
Related resources: Gradients and rate of change
Lesson 6 Worksheet 2
Downloadable resource in doc format. 19/10/2015
303 KB
Related resources: Gradients and rate of change

Lesson 1 Homework sheet 1
Downloadable resource in doc format. 19/10/2015
202 KB
Related resources: Gradients and rate of change
Lesson 2 Homework sheet 1
Downloadable resource in doc format. 19/10/2015
203 KB
Related resources: Gradients and rate of change
Lesson 3 Homework sheet 1
Downloadable resource in doc format. 19/10/2015
2.6 MB
Related resources: Gradients and rate of change
Lesson 4 Homework sheet 1
Downloadable resource in doc format. 19/10/2015
317 KB
Related resources: Gradients and rate of change
Lesson 5 Homework sheet 1
Downloadable resource in doc format. 19/10/2015
238 KB
Related resources: Gradients and rate of change
Lesson 6 Homework sheet 1
Downloadable resource in doc format. 19/10/2015
395 KB
Related resources: Gradients and rate of change

Diagnostic Questions - gradients and rates of change 1
AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017
E-library
Type(s): Diagnostic Questions (e-library)
Diagnostic Questions - gradients and rates of change 2
AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017
E-library
Type(s): Diagnostic Questions (e-library)
Diagnostic Questions - gradients and rates of change 3
AQA have teamed up with Craig Barton's Diagnostic Questions website to share free diagnostic questions assessment for our new 2017 GCSE Maths specification.21/07/2017
E-library
Type(s): Diagnostic Questions (e-library)

Curves and Gradients
Powerpoint and associated worksheet which introduces the ideas of average and instantaneous rates of change. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015
E-library
Type(s): Overview (e-library) | Worksheets (e-library)
Gradients and area under a curve
An overview of how to find the gradient of a curve and how this could be used in a real life context to find acceleration from a velocity time graph.21/08/2015
E-library
Type(s): Overview (e-library)
Gradients at points and area under curves
A straightforward powerpoint which introduces the idea of finding the instantaneous rate of change of a curve through drawing tangents. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015
E-library
Type(s): Overview (e-library) | Activities (e-library)
Gradients on a curved graph
A powerpoint and associated worksheet in which students learn how to find the gradient of a curve at a point by drawing a tangent. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015
E-library
Type(s): Overview (e-library) | Worksheets (e-library)

Average and Instantaneous rate of change
A dynamic geogebra file which illustrates average and instantaneous rates of change in a model of the height of a hot air balloon. 21/08/2015
E-library
Type(s): Activities (e-library)
Geogebra: Average rate of change
A Geogebra file which shows dynamically how the average rate of change varies as a point is moved along a curve.21/08/2015
E-library
Type(s): Activities (e-library)
Geogebra: Instantaneous rate of change
A Geogebra file which shows dynamically how the average rate of change becomes the instantaneous rate of change when the gradient of the chord approaches the gradient of the tangent.21/08/2015
E-library
Type(s): Activities (e-library)
Gradients at points and area under curves
A straightforward powerpoint which introduces the idea of finding the instantaneous rate of change of a curve through drawing tangents. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015
E-library
Type(s): Overview (e-library) | Activities (e-library)

Curves and Gradients
Powerpoint and associated worksheet which introduces the ideas of average and instantaneous rates of change. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015
E-library
Type(s): Overview (e-library) | Worksheets (e-library)
Gradients on a curved graph
A powerpoint and associated worksheet in which students learn how to find the gradient of a curve at a point by drawing a tangent. You will need to register for a TES account to access this resource, this is free of charge. 21/08/2015
E-library
Type(s): Overview (e-library) | Worksheets (e-library)

Topic Tests

8300 GCSE Higher Kinematic graphs Mark Scheme
Downloadable resource in pdf format. 30/06/2023
321 KB
Related resources: Gradients and rate of change
8300 GCSE Higher Kinematic graphs Topic Test
Downloadable resource in pdf format. 30/06/2023
380 KB
Related resources: Gradients and rate of change
Exampro

Access thousands of exam questions with Exampro Mathematics

Sign up to All About Maths

Create, edit, and share assessments quickly and easily with Exampro Mathematics

Quick links