Mathematical Starter / Plenary Activities
Teaching Guidance
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/ Activity 1 – nth Term
This is a Powerpoint File and an Excel document which I have used when I have been teaching the nth Term Formula.
I have already introduced the concept of the nth term and have done several exercises from the text book looking at patterns and number sequences. These two resources are used 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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/ Activity 2 – Simultaneous Equations
This is a Powerpoint File and an Excel document which I have used when I have been teaching Simultaneous Equations.
This PowerPoint file I have used as a plenary session, where down the right hand side of the slide is the solution to a simultaneous equation question. It is up to the students to drag the solution into the correct order to achieve the desired outcome. You must enable macros when using this PowerPoint as it utilises the drag and drop macro. This allows you to pick up an object e.g. a shape/ text box and move it around on screen 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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/ Activity 3 – Probability Scale
This is a Powerpoint I have used to ascertain the students concept of probability and how to represent this on a probability scale. Again it uses the drag and drop macro to allow myself or the students to drag the relevant statement to the correct position on a probability scale.
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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/ Activity 4 – Scatter Diagrams and Correlation
This is a resource I use to allow the students to discuss various statements and if there would be any relationship (correlation) between the statements. I encourage the 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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/ Activity 5 – Number Blockbusters
This is an Excel multiplication game based on the old T.v. series. The idea of the game is for two teams to compete (boys v’s girls) to either get across the board or down the board.
By multiplying two of the white numbers across the top of the game board they should get 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!
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/ Activity 6 – Number Magic and Solving Equations
This is a resource I use when looking at algebra to represent number.
I introduce this work by doing some Number Magic ! This allows the students to practice non calculator arithmetic work and also gains the students attention with a kind of WOW factor – how did you do that. This works particularly well with KS3 students.
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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/ Activity 6 – Number Magic and Solving Equations
Building on the previous slides this activity then goes on to look at equations, but I have approached this slightly different.
I first of all use the knowledge the students have acquired from the Number Magic work to look at building equations rather than solving them. This gets the concept of balance across to the students so that they realise to maintain balance what happens to one side of the equation must happen o the other top maintain balance.
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).
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/ Activity 7 – Transformations
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.
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/ Slide 2 begins to introduce reflection. Early in KS3 this tends to be just in the y or x axis but as the work progresses it may be a reflection in the line x=2 or y=-3 etc. The red and blue line on the border of the graph has the drag and drop macro enabled and 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.
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/ Slide 4 is looking at rotation. Again it uses the drag and drop macro to allow me or the student’s to drag the correct orange triangle to the correct position give the question. The red dot at (0,0) is also drag and drop enabled which 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
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/ Slide 6 is just an extension to the refection work on a previous slide using more complex shapes.
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/ Slide 7 and 8 are just templates I have used to create classroom white boards I can use when doing graph work. These I have printed off back to back and then laminated the sheet to create the white board.
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/ Activity 8 – What am I?
This game is linked to shape properties and by providing clues the students have to identify the shape as early as possible.
By clicking on the question mark next to the Clue 1 a description within the game board turns white e.g. ‘I have three sides’ in the screen shot opposite. I then encourage the 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!