Teaching Guidance - Mathematical Starter and Plenary ...



Mathematical Starter / Plenary Activities

Teaching Guidance

|1. |Activity 1 – nth Term |

|[pic] |This is a Powerpoint File and an Excel document which I have used when I have been |

|2. |teaching the nth Term Formula. |

|[pic] |I have already introduced the concept of the nth term and have done several exercises |

|3. |from the text book looking at patterns and number sequences. These two resources are used|

|[pic] |to test understanding and recall of method when solving an nth term question. |

| |The nth Term Jigsaw Powerpoint require that you have Macros enabled (see help slide |

| |within Powerpoint) as it uses the drag and drop macro. This allows you to pick up an |

| |object e.g. a shape and move it around on screen whilst running a Powerpoint show. |

| |When you run the Powerpoint show you will see that on the left hand side of the slide you|

| |have a column of green cards with nth term formula on them and a stack of yellow cards |

| |below them with the first three terms of a sequence. You then need to find a yellow card |

| |that matches an nth Term formula on the green card. You are able to drag the yellow card |

| |to match up with the green card above. |

| |It is the same principle on the right hand side of the screen but visa versa. The first |

| |three terms of a sequence are given (yellow card) and you need to drag the relevant green|

| |card with the nth Term formula to match. |

| |If you want to adapt the jigsaw pieces just enter different questions into the text box |

| |when Powerpoint is in design mode. |

| |The Excel File is a random question generator. You have a question sheet with 5 questions|

| |and then 5 more sheets which are the answers to the 5 questions. This enables me to |

| |quickly go over answers and reinforce the methods that have been taught during the topic.|

| |When you press F9 a new set of questions and answers are generated. |

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|[pic] |Activity 2 – Simultaneous Equations |

|1. |This is a Powerpoint File and an Excel document which I have used when I have been |

|[pic] |teaching Simultaneous Equations. |

|2. |This PowerPoint file I have used as a plenary session, where down the right hand side of|

|[pic] |the slide is the solution to a simultaneous equation question. It is up to the students |

|3. |to drag the solution into the correct order to achieve the desired outcome. You must |

|[pic] |enable macros when using this PowerPoint as it utilises the drag and drop macro. This |

|4. |allows you to pick up an object e.g. a shape/ text box and move it around on screen |

|[pic] |whilst running a Powerpoint show. These slides can be adapted to meet your own |

| |particular needs, I have used this resource with KS4 students. |

| |The Excel File is a random question generator. I have designed this to practice the |

| |process of solving a simultaneous equation which the students find a very long and |

| |difficult task. There are various levels of difficulty on several sheets within the |

| |Excel file. |

| |My own particular teaching method is to get the coefficient of y the same, thus if you |

| |teach by getting the coefficient of x the same you will get strange things happening!! |

| |In screen shot 1 the question is given. This can be changed by pressing New button |

| |(macros must be enabled). You can also get the question to Fit Screen. Down the left |

| |hand side of the screen there are empty cells which I ask the student what is required |

| |to solve the pair of equations. |

| |In screen shot 2 I have told the computer to times equation 1 by 2. This makes a new |

| |equation 3 which now has the same y coefficient as equation 2. |

| |In screen shot 3 I now need to decide whether to add or subtract the equations. Because |

| |there is a positive and a negative coefficient of y I tell the computer to add the |

| |equations. This eliminates the y variable from the equation. |

| |Screen shot 4. All I now need to do is to tell the computer to divide by 21 to find the |

| |value of x. The computer then goes on to substitute this value and find the correct |

| |value of y. It then shows good practice by checking the values of x and y in the |

| |equation it hasn’t used in the previous part. |

| |This is not a perfect teaching tool by all means, but allows me to assess the students |

| |understanding and concept of the process of solving simultaneous equations. It allows me|

| |quickly to generate questions and focus on the method involved when solving simultaneous|

| |equations without the laborious task of writing out each question again and again. I can|

| |also use this as a starter to a lesson where I get students to solve the equation and |

| |then lead me through the process which they have done allowing the whole class to see a |

| |text book solution. |

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|1. |Activity 3 – Probability Scale |

|[pic] |This is a Powerpoint I have used to ascertain the students concept of probability and |

|2. |how to represent this on a probability scale. Again it uses the drag and drop macro to |

|[pic] |allow myself or the students to drag the relevant statement to the correct position on a|

|3. |probability scale. |

|[pic] |Slide 1 is a slide I use just to store statements I may or may not use. |

| |I have then used various scales e.g. Slide 2 and 3 to set up a probability scale which |

| |may be useful to represent some of the statements on. It is up to the students to |

| |discuss and reason whether or not the statement can be displayed accurately on a |

| |particular scale. |

| |I also get the students to use their white boards (back of their organiser) to show a |

| |scale which may be used to represent statement I have chosen e.g. linked to a deck of |

| |cards and how this scale may alter if I change the probability events to be linked to |

| |the outcomes on a dice. |

| |By using the Change button on the top left hand of the slide you can cycle through the |

| |probability scales without affecting drag and drops you have already done. This has been|

| |done by just assigning a hyperlink to the next slide in the document and the last |

| |probability scale slide just links back to the first probability scale slide which |

| |creates a loop. |

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|1. |Activity 4 – Scatter Diagrams and Correlation |

|[pic] |This is a resource I use to allow the students to discuss various statements and if |

|2. |there would be any relationship (correlation) between the statements. I encourage the |

|[pic] |students to use their white boards (back of organiser) to plot points of what they think|

| |certain relationships would look like, either statements I have given or statements they|

| |have chosen. |

| |I will then pick pairs of students to model there scatter diagram on the board, again |

| |using the drag and drop macro or the students coming out to the board and plotting |

| |points with a board pen. |

| |I can quickly change the activity by just altering the statements on the x and y axis, |

| |and by using the buttons at the bottom of the left hand side of the slide I can quickly |

| |add a trend line to represent the relationship we would expect. |

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|1. |Activity 5 – Number Blockbusters |

|[pic] |This is an Excel multiplication game based on the old T.v. series. The idea of the game |

|2. |is for two teams to compete (boys v’s girls) to either get across the board or down the |

|[pic] |board. |

|3. |By multiplying two of the white numbers across the top of the game board they should get|

|[pic] |an answer in the yellow game board. I say should because the answer board can only hold |

| |20 answers and therefore there are some multiplication combinations which the answer |

| |board cannot hold. If a student finds one of these combinations I offer a merit point |

| |etc. |

| |I use a calculator to see if the students are correct and if they are I change the cell |

| |colour to their team colour by pressing the red or blue button within the answer cell |

| |(Slide 3). In this particular game the blue team have won by creating a continuous link |

| |of blue cells from the top of the board to the bottom, thus stopping the reds from |

| |getting across the board. |

| |To stop the students randomly guessing answers at the start I allow the students 5 min |

| |preparation time. To do this I use the picture stored on the Methods worksheet to cover |

| |the answer board, this stops the students from randomly guessing answers (Slide 2). This|

| |also provides examples of the three main methods of multiplication to help the weaker |

| |students within the group. |

| |The game board can quickly be altered by changing the white numbers at the top of the |

| |board. This game is about multiplication but other methods/ strategies can be involved |

| |like: estimation (over or under), concepts of even and odd number multiplication what |

| |will the answer be even or odd, what will the number be in units column of the answer if|

| |two particular numbers are multiplied together. To allow the above to happen, as a |

| |teacher you have to put a little bit of thought into the white numbers you chose. |

| |To reset the game board back to all yellow, at the moment you have to click the yellow |

| |button in each answer cell. Further development of this resource will hopefully contain |

| |a button to do this in one click! |

|1. |Activity 6 – Number Magic and Solving Equations |

|[pic] |This is a resource I use when looking at algebra to represent number. |

|2. |I introduce this work by doing some Number Magic ! This allows the students to practice |

|[pic] |non calculator arithmetic work and also gains the students attention with a kind of WOW |

|3. |factor – how did you do that. This works particularly well with KS3 students. |

|[pic] |Using the PowerPoint slide or by just reading out instructions I get the students to do |

| |some non calculator arithmetic work, which ends by the whole class having a particular |

| |number or by the whole class having a value which is + or – a value from their starting |

| |number. |

| |By clicking the previous instruction the next instruction appears finally finishing with|

| |a general rule (Slide 1 and 2). This then goes on to explain by generalising the |

| |instructions using algebra instead of a number to start with (Slide 3) |

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|1. |Activity 6 – Number Magic and Solving Equations |

|[pic] |Building on the previous slides this activity then goes on to look at equations, but I |

|2. |have approached this slightly different. |

|[pic] [pic] |I first of all use the knowledge the students have acquired from the Number Magic work |

|3. |to look at building equations rather than solving them. This gets the concept of balance|

|[pic] |across to the students so that they realise to maintain balance what happens to one side|

|4. |of the equation must happen o the other top maintain balance. |

|[pic] |First of all click on Build it and the instructions opposite (Slide 1) appear. What |

| |happens that in effect I am starting with the answer of x = 3, and then by applying |

| |knowledge from Number Magic I begin to build an equation with the students. I stress |

| |that what I do to one side of the equation must be done to the other and at each stage |

| |it is important to emphasise that when x is substituted with 3 the equation remains |

| |balanced (Slide 2). What I actually end up with is a quiet complicated equation but by |

| |substituting x with 3 into 3x + 6 = x + 12 I can show that balance is maintained. |

| |By clicking on Destroy It I now look at the method of solving this equation. |

| |Again by clicking the boxes on the right hand side I begin to solve the equation. At |

| |each point I am stressing balance and what happens to one side of the equation must |

| |happen to the other and also because it is the same equation which we built, and we know|

| |that x should equal 3 we can check at each stage of the solving process that balance is |

| |maintained when we substitute x with 3 (Slide 3 and 4). |

|1. |Activity 7 – Transformations |

|[pic] |This is a resource I use when doing graph work. Slide 1 is just a set of axis, but the |

| |coloured lines which boarder the graph have the drag and drop macro enabled. This means |

| |I can quickly discuss/ revisit the equations that produce a horizontal or a vertical |

| |line as this is something that the majority of students get confused with. |

|2. |Slide 2 begins to introduce reflection. Early in KS3 this tends to be just in the y or x|

|[pic] |axis but as the work progresses it may be a reflection in the line x=2 or y=-3 etc. The |

|3. |red and blue line on the border of the graph has the drag and drop macro enabled and |

|[pic] |also the triangle to the right hand side of the screen. This easily enables me or the |

| |students to set up a question to be answered as in Slide 3. With the aid of the wireless|

| |mouse students can drag the correct triangle to create the correct reflected image. |

|4. |Slide 4 is looking at rotation. Again it uses the drag and drop macro to allow |

|[pic] |me or the student’s to drag the correct orange triangle to the correct position |

|5. |give the question. The red dot at (0,0) is also drag and drop enabled which |

|[pic] |allows me to alter the centre of rotation. |

| |The boxes to the right hand side of the screen allow me to show what the |

| |triangle would look like given a degree of turn (multiples of 90°) by clicking |

| |on clockwise or anti clockwise, e.g. Rotate triangle A through 90° clockwise |

| |about (0,0), Slide 5 |

|6. |Slide 6 is just an extension to the refection work on a previous slide using |

|[pic] |more complex shapes. |

|7. |Slide 7 and 8 are just templates I have used to create classroom white boards I |

|[pic] |can use when doing graph work. These I have printed off back to back and then |

|8. |laminated the sheet to create the white board. |

|[pic] | |

|1. |Activity 8 – What am I? |

|[pic] |This game is linked to shape properties and by providing clues the students have to |

|2. |identify the shape as early as possible. |

|[pic] |By clicking on the question mark next to the Clue 1 a description within the game board |

|3. |turns white e.g. ‘I have three sides’ in the screen shot opposite. I then encourage the |

|[pic] |students to draw possible shapes that could match that description either on their white|

| |boards or in the back of their work book. I then go on to reveal further clues by |

| |clicking the question mark next to Clue 2 and Clue 3. Each clue revealed should make it |

| |easier for the student to identify the shape being described. I play a game with the |

| |students that they stand up when they think they can identify the correct shape and I |

| |award points to correct answers e.g. correctly identify the shape on Clue 1, 3 points |

| |etc. but once they stand up I do not allow them to sit back down if they change their |

| |mind! |

| |Finally by clicking on Reveal Question 1 the shape will be identified. I discuss |

| |notation to be used with the diagram like parallel lines or lines of equal length so |

| |that the diagram does not have to be drawn accurately and the notation used with the |

| |diagram defines the shape. |

| |I also use the game board to allow the students to pick descriptions to describe a shape|

| |which they have chosen. This leads to valuable discussion on shape properties and why a |

| |certain shape is a certain shape! |

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