Year 7 Algebra And Graphs Unit Plan For Scribd

Draft Unit Plan for Year 7 Coordinates and Graphs Unit: Delivered: Time to deliver:

Coordinates and Graphs

MPA map for this unit:

From Year 7 Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise straight-line graphs parallel to the x-axis or y-axis Plot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphs

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From Year 8 Express simple functions algebraically and represent them in mappings or on a spreadsheet Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise that equations of the form y = mx + c correspond to straight-line graphs Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distance–time graphs

Audit of Personal Learning and Thinking Skills in this unit: Pupils plan what to do, selecting the most appropriate methods, tools and models when representing situations or problems

Work collaboratively as well as independently.

Combine understanding, experiences, imagination and reasoning to construct new knowledge. Think creatively, drawing on their knowledge and understanding of mathematics and identifying the mathematical features that are important. They will make decisions autonomously while working towards goals, showing initiative, confidence, commitment and perseverance.

Evaluate their own and others' work and respond constructively. Value feedback and learn from mistakes.

Develop convincing arguments to influence others and take part in discussions. Working on problems that arise in other subjects and outside school helps pupils understand how mathematics is relevant in all areas of life.

Where does all this fit in terms of attainment? Click here to see level by level descriptions for this work. Description of content: Content Phase A: This is about ensuring that students can read and plot coordinates in the first quadrant. Please look at the following resources and choose those which are suitable for your ability set, you are not expected to use them all.

http://nrich.maths.org/public/viewer.php?obj_id=6280 gets students to identify the vertices of squares in the first quadrant. They do not need to be able to read coordinates to identify the squares so students could be working on a printed version of this whilst you are wandering and asking them to tell you the location of some of the vertices – use this to assess how good they already are at using the correct convention. You could make your own version of this in 4 quadrants if that was more appropriate. Take the opportunity to use key shape vocabulary like vertex, side, etc. Connect 4 activity, basically use your desk layout as a grid, establish where (0,0) is, probably best as bottom left hand corner and then just check that a few of the students in their places can tell you their coordinates. Play connect 4 as boys v girls, originally all standing at the front of the class with a mini whiteboard or sheet of paper, select a boy or girl, they write the coordinates of where they are going to sit on their board and then go there. If correct, they can sit down. Alternate boy, girl until one team has successfully made a continuous line of 4. Establish convention of x direction first then y and writing in brackets separated by a comma. The following activity can now be used to assess ability to read and plot in first quadrant, it links nicely to the

Further points

first task of finding squares on a grid and to previous work on properties of shape. http://nrich.maths.org/public/viewer.php?obj_id=1110 it requires them to plot three vertices of a quadrilateral and then identify the fourth vertex of a symmetrical shape. You will need to print versions of this for them. The eight corners plotted then make the vertices of an eight sided shape which is also symmetrical. http://nrich.maths.org/public/viewer.php?obj_id=6288 is a cops and robbers game which could be used as a plenary (or starter for next lesson) which requires students to identify coordinates of robber and then make a better guess after being told how far away they are. Harder levels in this game extend the task to all four quadrants which then takes you into Phase B of this unit. A good extension task in Phase A is http://nrich.maths.org/public/viewer.php?obj_id=2667 which could be done as plenary or starter on the board, you drag two adjacent corners to new positions and students have to come up and position the remaining vertices to make a tilted square (not a rhombus). Then in small groups, students are to work through the tasks on the sheet, trying to establish a general description of how to position the remaining two corners if they are told two, and how to test if four given pairs of coordinates form a square. Test ability and understanding by moving two vertices to new places, all groups then write down where the remaining coordinates will be, pick a group to come up and move to their places to test if correct.

Phase B: This extends coordinates into four quadrants. See the Cops and Robbers reference at the end of Phase A content - possible use as extended starter activity. Students may already be confident in plotting in all four quadrants Levels 2 and 3 both use grids in all four quadrants, Level 3 is more restrictive about where you are allowed to guess. Even for lower ability sets the idea of four coordinates can be practiced by using the connect 4 game using someone in the centre of the class as the origin. For any class for whom you have tackled all four quadrants you can assess their ability in this by using a resource such as Flippy Neck from MyMaths (class versus computer or boys v girls) found at http://www.mymaths.co.uk/gold/flippy/flippyNeck.html or by a paper activity such as the Riddles worksheet.

Phase C: This phase is about understanding and plotting straight line graphs, in all quadrants if possible but possibly restricted to first quadrant if other quadrants are still causing difficulties. Ideas for establishing and practicing “seeing” straight lines as the result of being given a rule as to how x and y coordinates relate are as follows: Position the origin at the near left corner (as viewed from the BACK of the classroom) so that the grid or visual representation of the desks that you are all looking at on the SmartBoard is oriented the same way. Teacher reads out a connection between the x and y values e.g. “Stand up if your x value is 2x your y value” etc to establish idea that these rules will generate straight lines. Include horizontal and vertical lines. At some point, get a student to mark the coordinates of the students standing on your SmartBoard version to demonstrate the straight line connection. An alternative idea is to have post it notes prepared with things like “My x coordinate is 2” and “My y coordinate is double my x coordinate plus 3” to hand out as students come in and they stick these to your SmartBoard grid (make sure only one rule is being stuck up at a time, possibly use different colour post it notes? Idea still is to establish that a given rule relating x and y produces a straight line.

Using your class to plot these points can then be extended to all 4 quadrants by putting the origin near the centre of your room, could use this to establish that as you already know that it will produce a straight line, start with the easy x values (i.e. the positives) and then continue the straight line into the negative quadrants. Refer to this idea later when completing tables of results and plotting on paper. This same idea of positioning the easy ones first and then continuing the line can be used with positioning the post it notes in all quadrants too. Use the last tasks to change wordy explanations like “my y value is twice my x value” into “Maths Speak” such as y=2x – probably could just practice this task. You should find a card sort activity. Move from this confidence to being able to complete a table of results using a given rule, remind to start from the easy x values and then just use the pattern in the differences to complete the section where the x values are negative, to generate coordinate pairs. Plot these pairs to form straight lines, highlighting that they can spot obvious errors if the line is not straight. Good practice on this can be found here, it even starts to get students to notice similarities and differences in the straight lines – e.g. steepness. Core and extension groups now need to appreciate that the variables might not always be called x and y but in real life we might have cost and minutes (mobile phone tariffs), pounds and euros, centigrade and Fahrenheit etc and they should be able to use equations given in these contexts to plot and interpret. See the linked SmartBoard screens for progressing from finding the midpoints of two numbers to finding the midpoints of a line segment given just the coordinates of both ends of the line.