Algebra Patterning and Graphs

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Algebra Patterning and Graphs. Exploring Patterns. e.g. Write the next two numbers in the following patterns and describe the pattern. a) 2, 5, 8, 11, 14,. 17, 20. b) 40, 34, 28, 22, 16,. 10, 4. Add 3. Subtract 6. c) 1, 3, 9, 27, 81,. 243, 729. d) 1, 4, 9, 16, 25,. - PowerPoint PPT Presentation

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Algebra Patterning and GraphsExploring Patternse.g. Write the next two numbers in the following patterns and describe the pattern.a) 2, 5, 8, 11, 14,b) 40, 34, 28, 22, 16,c) 1, 3, 9, 27, 81,d) 1, 4, 9, 16, 25,17, 2010, 4243, 72936, 49e.g. Draw the next shape in the pattern and add the number below 10631Add 3Subtract 6Multiply by 3Square NumbersFinding a Rule for Linear Patterns- Linear number patterns are sequences of numbers where the difference between terms is always the same (constant) Rule generating a linear pattern is: Difference n a constante.g. Write a rule (using n) to describe the following number patterns.nNumber of Squares (s)Number of Dots (d)11524937134101751321+ 3+ 3+ 3+ 3+ 4+ 4+ 4+ 4Rule: s =Rule: d =3n4n31= 33 = 1- 2- 241= 44 = 5+ 1+ 11. Find the difference between terms and if the same multiply by n2. Substitute to find constant3. Check if rule works34 2 44 + 1 e.g. To make these squares, the amount of matches below are needed.471013These results are shown on the table belowSquares (n)Matches (M)1427310410150a) Draw the next set of squaresb) Create a rule for the pattern and use it to help fill in the gaps in the table+ 3+ 3M = 3n31 = 33 = 4+ 1+ 1310 + 1133150 + 131451c) Write the rule in wordsThe number of matches equals three times the number of squares plus one.

34 + 1 = 13Simple Quadratic Patterns- Quadratic number patterns are sequences of numbers where the difference between terms is not the same - You need to look at the differences of the differences. If it is a 2, then the rule contains n2e.g. Write a rule for the following patternnTerm (T)14273124195281. Find the difference between terms+ 5+ 3+ 7+ 92. If difference is not the same, find the difference of the differences!+ 2+ 2+ 2Rule: T =3. If the 2nd difference is a 2, the rule contains n2 n24. Substitute to find constant12 = 11 = 4+ 342 + 3 = 195. Check if rule works+ 3Co-ordinates- Are two references used to identify places of interest- The horizontal reference is written first with the vertical second e.g. MapsMathematical Co-ordinates- Are used to describe positions of pointse.g. Plot the following points: A = (1, 3), B = (4, 2), C = (3, -4), D = (-5, 1)

1. Add in axes (if needed)2. Label and number axes x = horizontal, y = vertical xy123412345-3-2-1-4-5-1-2-3-43. Plot points using first number as the x co-ordinate and the second the y co-ordinate.4. Label pointsABCDCo-ordinate Patterns- Involves plotting rules that link the x co-ordinate to the y co-ordinatee.g. Complete the tables below and plot the following rulesa) y = 2x b) y = x 1 c) y = -3x + 2 xy = 2x y = x 1 -2-1012xy = -3x + 2 -2-1012

2 x -1 2 x -202-44-2 x -1 1 x -2 1-1- -20-1 -3 x -1 + 2 -3 x -2 + 22-18-45Scatterplots- Show relationships between two quantities- Has two axes, each showing a different quantity with its own scaleHeight (m)Age (years)BobJaneTomMarye.g.a) Who is the tallest?b) Who is the same age?c) Who is the oldest?TomBob and MaryJane

Line Graphs- Show how one quantity changes as another one does

e.g.a) What is the room temperature?b) How long does it take for the sweetcorn to cool down to room temperature?20C80 15 = 65 mins

e.g. Draw a graph to show how the water level may change in the following situation.- The sink is filled full of water- All of the dishes are put into the sink at once- The dishes are washed and removed separately- The water is then drained

10Distance/Time Graphs- Are line graphs with time on horizontal and distance on vertical axis.- If the line is horizontal the object is not moving- The steeper the line, the faster the movement

e.g.a) How far out from the harbour did the yacht travel?b) What happened while the graph was horizontal?c) Which part of the journey was quickest?5 kmThe yacht was stationarySteepestThe return journey

Applications- When using graphs to read off values and explain rulese.g. A student lends out his scooter for a fee of $3 and $2 for every km travelled. Complete the table and plot on graph below.Length of Journey (km)Charge ($)12345

a) What will be the charge for a journey of 2 km?1 2 + 352 2 + 3791113$8