TGHS Maths
Algebra
| Growing Patterns | |||
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| Lesson | Content | Notes | |
| 1 | Starter: Dot Cards (use Card 1)
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Dot cards where originally designed to encourage “subitizing” is the ability to recognize dot arrangements in different patterns. In this context, we can use them to look at multiple representations of number, helping with aspects of arithmetic, and also, by way of grouping begin to look at the link between number and an algebraic generalization. In every case, the question is, how can/could we “count up” the number of dots, without counting every individual dot. See: https://www.youtube.com/watch?v=cy3UCaAiXQE (about 5 minutes in) for a video clip of dot charts in use in the high school class room. The Coloured Border is an introduction to the concept of a variable. This video is teacher Cathy Humphries teaching the lesson. |
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| 2-5 | Starter: Dot Cards (use Card 2-5) |
Using Pattern Tasks to Develop Mathematical Understandings and Set Classroom Norms The sequence of lessons "Growing Patterns" can be used as worksheets or projected. The current lessons make no use of graphs, but they might be used as an important link with the next topic. If so, they should be plotted as discrete graphs (in preparation for AS91028 in year 11). This unit of work requires students to communicate their answer verbally and in writing (with diagrams), which may (should?) be in poster format. This is a similar unit of work from the website youcubed.org |
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| 6-7 | Starter: Dot Cards (use Cards 6-7) Ten Ticks Level 5 Pack 5 pages 36-37 "Practical Number Patterns" |
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| Distance-Time Graphs | |||
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| Lesson | Content | Notes | |
| 1-2 | Starter: Dot-Cards (use Cards 8-9) |
Use the lesson from the section Suggested Lesson Outline. | |
| The Language of Graphs | |||
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| Lesson | Content | Notes | |
| 1-2 | Starter: Dot-Cards (use Card 10) Worksheet: Ten Ticks Level 4 Pack 7 p. 19 Worksheet: Ten Ticks Level 5 Pack 4 p. 23 Desmos activity: Mini Golf Marbleslides |
Plotting Coordinates in 4-quadrants. Students can also design their own pictures. |
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| 3 | Worksheet: Graphs A Worksheet: Graphs B Instructions: Cooperative Learning Strategies |
Back-to back pairs. Class discusses strategies which were useful for describing their graphs. Encourage: x-intercept, y-intercept, slope (gradient), origin, coordinates. If some students see rules, then bring that out too, but giving gradient a numerical value comes in the next section. |
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| 4 | Worksheet: Plotting Linear Functions |
Students should know that the routine for plotting functions involves making a table, then plotting points. |
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| 5-7 | Activity: Set up a 50m. tape measure, and time a walker/jogger/runner at 5m. intervals. Graph (take care to graph distance-time in the correct order!). Teachers will need to give some guidance with the scale, and also introduce "line of best fit". The exercise provides a good opportunity to revise rounding in context. Worksheet: Graphs mix-and-match cards with answers |
The meaning of gradient. An experiment which links steepness (on a distance-time graph) with speed. Gradient is not (yet) formalized.
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| 8-12 | Worksheet: Linking Rules Worksheet: Using Graphs to Investigate Worksheet: Equations from Graphs Extension Worksheet: Equations from Lines Worksheet: Lots of Graphs Desmos activity: Card Sort: Linear Functions (part of the ‘Linear’ Bundle) |
Formalizing y=mx+c. Students should understand gradient as y-increase as x-increase is 1 and as rise/run, and should understand the link between gradient and sequences. Some explicit teaching is needed between these lessons. |
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| Simplifying Expressions and Expanding Brackets | |||||
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| Lesson | Content | Notes | |||
| 1-3 | Interpreting Algebraic Expressions | Just use the Suggested Lesson Outline section in this series of lessons |
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| 4 |
Alpha Text p. 221 - 222 |
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| 5 | Crossed Ends | This investigation provides opportunities to discuss gtting stuck and extended abstract thinking. It has a low levl entry point, but a sophisticated approach to solving it will require some organized thinking. | |||
| 6-8 | Expanding Brackets Both multiplying by a factor, and quadratics. It is not necessary (as usual) to cover all of these questions. About 2 lessons should be spent of quadratic expansion. The basis for this was covered when we covered 2-digit multiplication in Number. |
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| Solving Linear Equations | |||
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| Lesson | Content | Notes | |
| 1 | What's my Number? | The first lesson gives an opportunity for students to develop informal methods (including guess-and-check). THINK-PAIR the worksheet. |
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| 2 | Equations | The key idea is to view an equation as a BALANCE: always keeping the equation balanced by DOING THE SAME TO BOTH SIDES. Teacher demonstrates the Balance model, and students complete worksheet by drawing balances, and developing the algebraic notation alongside. | |
| 3-6 | Starter: BTS Equations
Text book equations
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From Transum. Can be used before any lesson. Perfect LTHC task.
Alpha Text (Second Edition) p. 201 Ex. 14.07 |
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| 6-9 | Steps to Solving Equations | ||