# Ward309's Shop

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I am a full time secondary teacher and head of department who started teaching in 2004. I love to teach mathematics and try to create interesting and dynamic visual resources to enhance the delivery of my subject. I hope you find my resources useful.

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I am a full time secondary teacher and head of department who started teaching in 2004. I love to teach mathematics and try to create interesting and dynamic visual resources to enhance the delivery of my subject. I hope you find my resources useful.

#### Investigating time graph rates of change (filling containers)

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An interactive PowerPoint that models how the rate of change changes over time in the context of filling containers with water. Select the container set and fill them up using the control buttons to show their corresponding graphs.

#### Area of a Trapezium

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An interactive PowerPoint that models how to calculate the area of a trapezium by dynamically converting it into a parallelogram.

#### Graphical linear programming

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An interactive geogebra applet that enables the user to input their own inequalities and objective functions in any linear programming problem and solve it graphically. Add an inequality/objective function using the controls and drag the points to the desired co-ordinates to create the boundary line then click up/down to shade the desired inequality. Find all points of intersections via the click of a button and drag the objective function to leave a trace and revel the optimum vertex (i.e. the ruler method referred to in many A level texts). Auto zoom and fitting for easy class use and to model a clear solution. Some pre-defined questions are included if you want to use them to model with. I have also attached a worksheet i have used with my own A-level students to practice using this technique. The geogebra applet is attached but if you don’t have it installed then the web link is also attached so you can use the applet in a web browser.

#### Forming quadratic equations from probability trees (as seen in Edexcel GCSE 1MA1)

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Fully interactive question generator and solver. Use this to model how to set up and solve worded quadratic equations in the context of a probability tree. Randomly generate questions or specify with/without replacement and same/different colours (see image. Model the solutions line by line by using the controls to reveal each step. This is an interactive geogebra applet but if you don’t have geogebra installed (free) i have also included the web link so that you can use this applet in a web browser.

#### Angles in circles (circle theorems)

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A fully interactive geogebra presentation. Generates examples of all circle theorems that can be manipulated dynamically to reinforce that the relationships are always maintained despite how each theorem can appear visually. Modeling of all proofs are also included and differentiated questions can be generated for whole class participation or to create a worksheet of your own. See the attached images for examples and how the controls work. This is an interactive geogebra applet but, if you don’t have geogebra installed (free), I have also included the web link so that you can use this applet in any web browser. I have also included some worksheets I made.

#### Solving by iteration (trial and improvement). Fully dynamic and interactive.

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An interactive PowerPoint to model solving quadratic and cubic equations using trial and improvement. Use the +/- buttons on each row to change the input and click on the x number shown to watch it dynamically substitute. Click on the blank parts of the table to reveal the substituted parts evaluated. Using the +/- button on the next row, modify the input and substitute again by clicking on the number shown and repeat the process. If more table is needed, click clear.

#### Adding and subtracting fractions visually

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An interactive and dynamic PowerPoint that models how to add and subtract fractions using pictures. Use the 'fraction' buttons to show the visual representation of each fraction and click on each sector to shade it in. Click on 'add/subtract' once to reveal the common denominator shape and again to visually see the fractions adding together.

#### Pythagoras and trig in three dimensions

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Generates a 3D co-ordinate axes by adding an extra dimension onto a 2D gird. Demonstrates how to plot 2 co-ordinates in three dimensions and considers this as the diagonal of a cuboid. Hover the mouse over the pink and orange triangles and press 'play' to see them in two dimensions. Click the covers to reveal the lengths. Extends to generalising the longest diagonal of a cuboid and includes some exam style questions.

#### Placing probabilities and fractions on a probability scale (Interactive)

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Scroll through the examples and press 'start' to start the event scrolling up and down the probability scale. Invite students to the board to click the screen to stop the even in the correct position. Revel the fraction using the buttons and split the probability scale into fractions using the 'fraction' button to see if the even it accurately placed. Includes student activity worksheet.

#### Balancing Equations with subtraction (interactive balancing)

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I've always struggles to show students how subtraction works as a balance as it can't be visulaised, until now!Keep the balance of the scales by adding or subtracting content from both sides. Do this by clicking on the 1's or x's at the top to add on and on each side of the balance to remove them. Pop the balloons by adding weights to both sides (sound effects included!)

#### Lowest common multiple and highest common factor (LCM and HCF)

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An interactive PowerPoint that uses prime factor trees and Venn diagrams to model how to calculate the LCM and HCF. Uncover the end branches by clicking on the covers, click on the end branches to select the prime factors, show the Venn diagram and click on the selected factors to place them in the Venn diagram.

#### 2D views of 3D objects

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An interactive PowerPoint that models the three views of a 3D object. Use the navigation buttons to scroll through the examples and use the plan, side and front buttons to show the object rotate into the correct position. Before revealing, invite students to the board and ask them what the views might look like by clicking on the square grid. I have attached some questions also.

#### Shape transformations (rotations, reflections, enlargements (inc. negative) and translations)

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A big PowerPoint that is fully interactive and models both doing and describing all transformations. I have also added in a lesson plan for instruction how to use. Fully interactive with dynamic examples.

#### Constructing triangles SAS

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A PowerPoint modelling how to construct a triangle given two side lengths and one angle. Includes non-unique triangles (SSA).

#### Area of a Parallelogram

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Models how to find the area of a parallelogram by linking it to the area of a rectangle. Fully dynamic and interactive examples.

#### Area of a Triangle

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Models how to find the area of a triangle by converting it into a parallelogram. Fully interactive and dynamic examples.

#### Creating designs with rotation symmetry

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An interactive PowerPoint and worksheets that model how to complete/create patterns with rotation symmetry using tracing paper. Using the navigation buttons...1)Select the example, 2)Show the tracing paper, 3)Trace the design, 4)Rotate the tracing paper to find the missing parts of the design.

#### Expanding two linear brackets

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An interactive PowerPoint that uses partitioning (as with numerical multiplication) to expand the product of two linear brackets. Also includes some simple factorising where you can drag-and-drop the correct factors (must enable macros). Click on show/hide to reveal the grid, click on the factors in the brackets in input these into the grid and unhide the expansion by clicking on the covers.

#### Constructing triangles (ASA)

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A PowerPoint modelling how to construct a triangle given two angles and a side length.

#### Lowest common multiple and highest common factor using prime factors (interactive PowerPoint)

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Starts by finding LCMs and HCFs by listing and extends to using prime factors and Venn diagrams to calculate LCMs and HCFs. Scroll through the PowerPoint using the navigation buttons. Reveal the covered factor trees by clicking on the covers and click the end branches of each tree to select the prime factors. Once all end (prime) numbers have been found use the show/hide button to reveal the Venn diagram. Click on the prime factors again to place them into the Venn diagram. Click on the LCM or HCF to reveal the answers.