TGHS Maths
Algebra
| Linear Equations | |||
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| Lesson | Content | Notes | |
| 1-2 | Real Life Equations | The emphasis in this unit is on forming rather than solving equatons. The lesson structure is described in the document, and the philosophy etc of the lessons is described in this brief teacher guide. Use only the section headed Suggested Lesson Outline. |
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| 3 | Solving equations. Formal Methods Beta Text Book (old version) |
Largely revision from year 9, when they were intially introduced to solving equations in a 'balance' model (doing the same to both sides). Most solving techniques should be taught in a problem-based context. |
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| 4-5 | Word problems Beta Text Book (old version) 10Ticks L6 P1 p. 9-10 |
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| Lesson 6 | Weighing Time | These 2 problem-solving lessons can be used anywhere during this unit of work. | |
| Lesson 7 | Tricky Rectangles | ||
| Linear Graphs | ||||||
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| These lessons will require a Chromebook between 2 students for each activity. | ||||||
| Lesson | Content | Notes | ||||
| 1 | Desmos |
Requires an even number of 'pairs'. The teacher needs to summarise this lesson well, so that it is not just playing a game! |
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| 2 | Desmos |
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| 3 | Desmos Put the Point on the Line |
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| 4 | Desmos Match My Line |
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| 5 | Desmos Land the Plane |
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| 6 | Desmos Card Sort: Linear Functions |
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| 7 | Desmos Marblesides: Lines |
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| 8 | Desmos Lego Prices |
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| 9 | Formalizes the methods from the Desmos Activities | |||||
| 10 - 11 | Interpreting Linear Graphs |
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| 12 | Worksheet: Equation from graph | Drawing and describing linear graphs. This lesson is to make sure that students can draw graphs from equations without the computer and understand y=mx+c. First put up a few equations to plot (eg y=2x + 1) and asking about gradient/y-intercept). Include some negative gradients/intercepts. |
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| Simultaneous Equations | |||
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At the end of this unit students should be able to form simultaneous equations, and solve them graphically and by substitution (only). |
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| Lesson | Content | Notes | |
| 1 | Picture: what story could go with this graph? Worksheet: Martian Football |
Part of the "posing questions" theme. Think/Pair/Share (before talking about simultaneous equations). Solving Martian Football should be left to the students - trial and improvement is an obvious strategy. Clearly it work better for the Martian than the Jupitian problem (which is a discussion point). |
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| 2 | Worksheet: Simultaneous Equations |
Solve by Graph and by Substitution. Make the links back to previous work on graphing and solving linear equations. |
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| 3- 4 | Solving Linear Equations | Use the Suggested Lesson Outline section only | |
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| 6 | Desmos |
There are more activities in the Linear Systems Bundle. However, time will probably be short at this point. Teachers may like to show students a solution (or two) to the Martian Football problem. | |
| Plotting Quadratics | |||
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Intended as a brief introduction only. The emphasis is on plotting by using a table. |
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| Lesson | Content | Notes | |
| 1-2 | Worksheet: Plotting Quadratics | ||
| 3 | What questions can we ask here? |
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| Expanding and Factorizing | |||||||||||||||||||||
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| Lesson | Content | Notes | |||||||||||||||||||
| 1 | Draw a picture to show that... |
Don't do any rote practice at this stage! Emphasise the picture drawing (area model). The Challenge is quite hard! Make so that NO calculations are done (not even 10 x 10). |
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| 2-3 | These are the key lessons in this sequence. Students should be encouraged that the extension is a matter of course in questions like this (and should find their own). Students who are finding maths hard should be encouraged that the entry point allows them multiplication pratice. |
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| 4 | Straight practice exercises. There's no need to complete all of these, but make sure that students encounter examples with negative numbers. Any 'rules' for expanding definitely should not be taught! |
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| 5 | These exercises form a link between expanding and factorizing. | ||||||||||||||||||||
| 6 | Factorising by removing common factors | Beta text book (old version) p. 327-329 Ex. 24.5-24.8 Encourage students to check by (at least mentally) re-expanding their answers. |
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| 7-8 | Factorising quadratics
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Mix-and-Match can be used in both directions. Some students will stick in the x2+bx+c version, and find the factorized version. Other students will still be praticising expanding by going the other way. Beta (old version) p352-355 Ex. 26.8 - Ex. 26.12 I recommend teaching this as reverse , using the "table" method: So to factorize x2 + 5x + 6
Then check. Perfect squares and difference of two squares can also be done by this method. The extension problems are for students who need less practice with factorising. The first two are not as hard as they look. Obviously, the second should (ideally) be done WITHOUT computation! |
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| Introduction to Indices | |||
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| Lesson | Content | Notes | |
| 1 | Exploring Indices |
A (re-)introduction of powers. NOT intended as extension! However, exploring further and (especially) justifying require higher level thinking skills. | |
| 2-3 | Properties of Exponents | The lesson structure is described in the document, and the philosophy etc of the lessons is described in this brief teacher guide. Use only the section headed Suggested Lesson Outline. The Laws of Indices are not formalized at this stage. |
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| Simplifying Expressions | |||
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| Lesson | Content | Notes | |
| 1-4 | Beta (old version) Chapter 23 Beta (2nd Edition) Chapter 8 | This section is intended to summarise many of the notational aspects of algebra which have been covered in passing in year 9 and 10. Some of these aspects (such as the rules of indices) are formalized for the first time. |
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| 5-6 | Magic E (open-ended) Magic E (guided) |
An investigation using (simple) simplifying. The challenge is in the open nature of the task. In line with the theme for this year, the first version has little guidance ("Investigate"), the second is the same task but with more guidance. Don't be in a hurry to present the hints contained in the second version. |
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| Solving Quadratic Equations | |||
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| Lesson | Content | Notes | |
| 1 | Solving factorized quadratics 10 Ticks Level 7/8 Pack 3 Page 10 |
It is worth making the link with graphs (parabolas) here. It also gives an opprtunity to revise those. |
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| 2 - 3 | Solving by factorizing 10 Ticks Level 7/8 Pack 3 Page 10 |
For some students, this will constitute more practice with factorizing quadratic expressions. | |
| 4-5 | Parabolic Investigation | A simplified version of the "max tray" investigation. Differentiated (by task) versions are given. | |
| Revision | |||
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| Lesson | Content | Notes | |
| 1-5 | Revison worksheets | An external link to a multitude of worksheets. Does not match exactly with our scheme, but is quite close. | |
