Y9 Mathematics - Welcome

Spot the mistake - Collecting like terms and expanding brackets Walk around in pairs and answer as many of the 5 questions as possible Venn diagram - Expressions vs. Equations 1. What are they? 2. What do they both have in common? 3. How are they different? 4. What can you d...

Spot the mistake - Collecting like terms and expanding brackets Walk around in pairs and answer as many of the 5 questions as possible Venn diagram - Expressions vs. Equations 1. What are they? 2. What do they both have in common? 3. How are they different? 4. What can you do to one that you can not do to the other? 5. What is a common mistake students make with expressions? What are algebraic Expressions? (copy these important defs) What are algebraic expressions? Coefficient: The number attached to a variable. Constant: A number without any variable attached to it. SOLVING EQUATIONS L.O. Prior knowledge review One Step Solving – Keep it balanced… X =2 Can you Justify Your answer? 1x 111 Two Step Solving – Keep it balanced… X =1 Can you Justify Your x 1x answer? 111 Two Step Solving – Keep it balanced… X=2 Can you Justify Your x 1 1 answer? x1 1x 11 1111 Whiteboards - Either answer Q1 or Q2 - Show working Independent study - Solving equations - Choose your challenge Answers Exit ticket SOLVING EQUATIONS WITH UNKNOWNS ON BOTH SIDES L.O. Prior knowledge review  Date:_______________________ Equations with an unknown on both sides Starter: in your notebooks, write the date and title, then find out how many cubes weigh the same as one ball. You must justify your answer. How can you turn this Into an equation? Where was the mistake made? What should the answer be? Think, pair, share Where was the mistake made? What should the answer be? Think, pair, share Blue - Watch video and answer questions online https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:s olve-equations-inequalities/x2f8bb11595b61c86:linear-equatio ns-variables-both-sides/v/equations-3 Yellow - Answer Q1 and Q4 https://corbettmaths.com/wp-content/uploads/2013/02/equation s-letters-both-sides-pdf.pdf Magenta - 1. Answer Q1 to Q5 from the ‘Apply’ section - https://corbettmaths.com/wp-content/uploads/2013/02/equat ions-letters-both-sides-pdf.pdf 2. https://www.ixl.com/math/grade-8/solve-equations-with-var iables-on-both-sides-word-problems 3. SOLVING EQUATIONS WITH Fractions L.O. To know how to solve equations involving fractions. Starter In groups of 3, look at the worked examples of the first two questions. Discuss the method(s) and check you understand what the process is. Then, answer the remaining questions in the set TOGETHER. Method 1 Method 1 WORKED EXAMPLES Method 2 Method 2 Think, pair, share 1. What if you had to solve the equation ½ x + 4 = 10? (HINT: How could you rewrite this to make solving easier) 2. How about ¾ x - 2 = 5? Question 2  WORKED EXAMPLES Question 5  WORKED EXAMPLES Question 6  WORKED EXAMPLES Question 8 Answers https://corbettmaths.com/wp-content/uploads/2018/09/Fraction al-Equations-pdf.pdf  Coordinates and Lines L.O. To review coordinates and use this to find the equations of lines (rules). (-9,9) (5,8) (2,9) (-5, -8) (3, -3) (-6,3)(3,-3)(3,-3)(-8,-7) (2,1) (0,0) (2,1)(9,5)(6,4)(6,4)(3,-3)(2,1)(2,1)(-6,-3)(9,5)(-5,8) (2,1) (3,-3)(-5,8)(-5,8)(-9,9)(-8,-7)(-4,-5) (-6,3)(0,0)(2,9)(-2,1)(2,1) (-9,9)(-8,-7) (9,9) (-7,10) (2,9)(-2,1)(-2,1)(-9,9)(6.4)....(2,1)(2,9)(-9,9)(-5,8)(2,1) (2,9)(-3,5)(3,-3) (-2,1)(5,8)(-3,5)(0,0)(9,5)(-4,-5)(5,8) (-2,1)(5,8)(3,-3) (-3,5)(0,0(0,0)(-6,-3) Desmos Go through this Desmos activity. Make notes throughout. Then summarise your understanding in writing at the end. Discuss this with your group and teacher. https://teacher.desmos.com/activitybuilder/custom/64f99587da 73464b6477a551  Drawing straight line/Linear graphs L.O. To be able to draw straight line graphs through substitution and plotting. Starter - Substitution and drawing lines 1. Work out the value of y=7x-2 when a) x=2 b)x=-1 c) work out the value of x when y=5. 2. Plot the lines y=2, y=-4, x=1 3. Would the point (4, 10) lie on the line y = 3x + 1? 4. Identify if the point (3, 5) or (1, 4) would be on the line y = x + 2. Looking at the Table of values - Why are they all Straight lines/ linear? Complete all questions from worksheets When finished, come and get the challenge questions from me. Equation of a straight line graph L.O. To begin exploring what y=mx+c represents starter The equations of straight lines are generally written as y=mx+c Looking at the straight lines you have drawn today, discuss what m could represent and what c could represent? Use sliders on desmos graph for m and c - https://www.desmos.com/calculator/krg4bkfvg9  We have drawn some lines where the equation is in this form y = mx + c You will need to As a group present your visual you will Draw graphs exploration on the explore this poster template form of Complete tables of values with ONE summary equation in sentence of what one of three Follow directions to explore coordinates you observed. ways: Group 1 Draw the lines y=x, y=2x, y=3x, y=4x. What happens to the line as the coefficient of x increases? y = 4x+1 x 0 1 2 3 4 y y = 3x-2 x 0 1 2 3 4 y y = -2x+5 x 0 1 2 3 4 y Group 2 Fill in the table of values for the given equations. How does the coefficient of x link to the table of values? Group 3 Drawn are the lines y=4x+6 (green), y=2x-5 (blue) and y=3x-1 (red). Pick a point on a line (a corner of a square would be easiest). Draw a horizontal line (a run) of a few squares to the right. Then draw a line up (your rise) until you meet the diagonal line again. How many squares did you “rise”? Divide this by how many squares you "ran". Do this for each line. What do you notice? Group 4 Draw the lines y=2x+4, y=3x-5, y=x+1. What do you notice about where they cross the y-axis (the y-intercept)? Group 5 Draw the lines y=x, y=-2x, y=3x, y=-4x. What do you notice about the line when the coefficient of x is negative or positive? Group 6 Drawn are the lines y=4x+6 (green), y=2x-5 (blue) and y=3x-1 (red). Pick two points from one line, call one a and one b. Do the following calculation. the y-coordinate of a - the y-coordinate of b the x-coordinate of a - the x-coordinate of b. Do this for each line. How does the resulting number link to your equations? Which words can you define? m represents the rate of change between x and y As m gets larger, the slope gets steeper When m is negative it forms a downwards slope, when m is positive it forms an upwards slope From the graph, we can calculate m by drawing a right angle triangle and calculating “rise” over “run” With two points from the line we can calculate gradient change in y/change in x When drawing a graph we can use the gradient - as x increases by 1, y increases by m. c represents the y-intercept. This is where the line crosses the y-axis and also the y value when x is 0.  Finding the gradient L.O. To understand that the rate of change of a graph is the same as the gradient and to know how to calculate it. Starter Rate of Change Reflect and Discuss Finding the gradient given two points Do it yourself We have drawn lines where the equation is in this form y = mx + c Finding the gradient from a straight line Go to desmos graphing Independent study https://corbettmaths.com/wp-content/uploads/2018/12/Gradient -pdf.pdf BLUE - Q1, Q3, Q5 YELLOW - Q2, Q5, Q6 (half) and Q7 (half) MAGENTA - Q3, Q4, Q6 (half), Q7 (half) and from the ‘APPLY’ section Q2 onwards https://www.transum.org/Software/GraphMatch/Default.asp  Identifying the equation of a straight line - y=mx+c L.O. To know how to find the gradient and the y-intercept of a graph and express it as an equation. Recap from last lesson - finding the gradient and y=mx+c 1. How to graph vertical and horizontal lines - y=1, x=4 2. What y=mx+c is and what m and c represents? 3. Finding the gradient from a line - 4. Finding the gradient when only given two points - (-1, 3) and (4, -2) Linear equation Starter - Find the gradient - Rally Coach (Partner A/Partner B) 1. 1. 2. (2 , 4) and (6, -10) 2. (-3, 2) and (-1, 0) Draw a line with a gradient of 2 and y-intercept 3. What will be the equation of this line? Finding the gradient WHY??? (Hint: Think of the gradient formula) Independent work -strengthen your knowledge - 10 minutes https://mmerevise.co.uk/app/uploads/2019/04/Gradients-of-Straight-Line-Grap hs-Questions.pdf We will then mark it together. Give yourself a mark out of 18. Reflect and Discuss What does a linear equation look like? What is the gradient and y-intercept from the equation? y= 3x + 2 y= 5 - x Clumsy Clive Gradient and y-intercept from the equation Plenary - People maths Treasure hunt! Complete Practice 2 (p.116) Q1 and Q2 Q5 a) b) and d) (FIND M AND C ONLY) Q6 a) and b) only Criteria B Revision - Formative 1 L.O. Revision, revision, revision Starter - why do we need to verify using two methods? And practice drawing graphs Just another formative to make you feel like YOU GOT THIS on Thursday 1. x y x y x y 2 1 3 1 4 1 4 2 6 2 8 2 6 3 9 3 12 3 y=½ x y=⅓ x ? Patterns and rule (L3/4) 2. Describe any patterns that you notice 3. Write down a general rule of the form y=ax+b Verify (L5) 4. Verify your general rule is valid using one example in Q1. Verify (L6) 5. Verify your general rule is correct using a different example not given in Q1. Justify (L7/8) 6. Justify that your general rule is valid for  rearranging formulae/equations L.O. To be confident in using the balancing method to solve equations and also rearrange formulae/equations. Starter Examples - How can we use the balancing method when rearranging equations? Whiteboards! Ms Aksinoglu’s Answers Ms Aksinoglu’s Answers Ms Aksinoglu’s Answers BLUE Worksheet - Q1 to Q7 - https://corbettmaths.com/wp-content/uploads/2013/02/changing-the-subject-p df.pdf Answers - https://corbettmaths.com/wp-content/uploads/2015/03/changing-the-subject-an swers.pdf YELLOW Worksheet - Q5 to Q12 - https://corbettmaths.com/wp-content/uploads/2013/02/changing-the-subject-p df.pdf Answers - https://corbettmaths.com/wp-content/uploads/2015/03/changing-the-subject-an swers.pdf MAGENTA Worksheet - Q5 to Q12 - https://corbettmaths.com/wp-content/uploads/2013/02/changing-the-subject-pdf.pdf And https://docs.google.com/document/d/17jTDXv3OxvU4lttDFex5sVoAS0z6d8ly/edit?usp=s haring&ouid=114666561463993371950&rtpof=true&sd=true Answers - https://corbettmaths.com/wp-content/uploads/2015/03/changing-the-subject-answers. pdf Treasure hunt WILT - How can we use what we have learnt today with rearranging into y=mx+c BLUE MAGENTA YELLOW WILT - Answers BLUE MAGENTA YELLOW  Finding the equation of a straight line L.O. To know how to find the equation of a straight line from a graph and when given two points. Starter BLUE YELLOW MAGENTA Answers Determining the equation of a line Do it yourself Do it yourself If you are still stuck on Q2, watch this video: 1) https://www.youtube.com/watch?v =AqONrrPhJvk 2) Do it yourself https://corbettmaths.com/wp-content/uploads/2013/02/equation-of-a-line-pdf.p df Q1 to Q7 Q8, Q9, Q11, Q12, Q13, Q14 Q15 to Q17 What are intercepts?  Parallel and Perpendicular Lines L.O. To understand the relationship between parallel and perpendicular lines, and to find the equations of those lines. Going through plotting graphs Starter: On grids in front of you, plot these straight line graphs 1) Y = 2x + 1 2) Y = 3x - 2 3) Y=-½x+3 4) 3y = 9x - 3 5) 6y - 2x = 0 6) 3/2 x - 2y = 4 If still stuck, watch this video - https://corbettmaths.com/2013/04/20/drawing-graphs-using-gradient-and-interc ept/ Complete both tarsias based on what we have studied so far 1) Make sure to cut the triangles first! 2) Then, match the sides of the triangles. 3) Once finished matching, you should end up with one large shape! Criterion B Investigation: Parallel and Perpendicular Lines Task 1: Plot using DESMOS Task 2: Plot using DESMOS Nd y= 3x + 1 y=2x + 3 y= -1/3x - 2 y= -1/2x - 4 What do you notice when you plot the blue lines? Then, what do you notice when plotting the purple lines?  Parallel Lines Parallel lines never meet, even if they carried on FOREVER! Parallel lines have the same GRADIENT (m) but different Y INTERCEPTS (C) Here are some lines which are parallel to y=2x+5 y=2x + 6 y=2x + 7 y=2x + 16 y=2x + 1 y=2x+5 y=2x + 3 y=2x + 12 y=2x - 6 y=2x -2 y=2x y=2x + 0.2 y=2x - 11 y=2x + 60 y=2x -10  Perpendicular Lines Perpendicular lines meet at right angles If you multiply gradients of perpendicular lines you will always get -1 Gradient 1 x Gradient 2 = -1 for perpendicular lines y=-1/3x+6 y=3x-8 y=-1/3x+7 y=-1/3x-11 3 times -1/3 gives -1 So any line with a gradient of -1/3 will be perpendicular to y=3x-8 Example 1: Parallel Lines Example 2: Perpendicular Lines Find the equation of the line which is perpendicular y=5x + 8 at the point (5,33) Gradient will be -1/5 Equation so far is y=-1/5x + c We know it passes through (5,33) so put these values in 33=-1+ c c must be 34 y=-2x + 34 Do it yourself Do it yourself: Choose your level of difficulty (Blue, Yellow or Magenta) https://drive.google.com/file/d/1uZ4nSwfMd3ALC54RXtd_Ps-9VKrbhj1f/view?usp =sharing Independent study 1) Finish worksheet on parallel/perpendicular lines if you haven’t done so. 2) Practice 3 (p.122): Q2 only (correct when finished) 3) Practice 4 (p.128): Q4 (a to f) only (correct when finished) 4) Practice 6 (p.138): Q2 to Q7 (correct when finished)