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Zühlke Project Management Model

GetAbstract

This presentation explores the intersection of business and technology, featuring discussions on topics such as product, business models, and implementation. It also includes insights from industry experts and opportunities for audience engagement.

Avoidable Losses in the Food Supply-Chain

RemNote Math Map: JayTeach.me Site Plan

I want to use RemNote for building my teaching site. Part 1: How to embed RemNote Queues into static Jekyll site or in iFrames? Part 2: Use RemNote as a back-end to export .md files, which Jeykll will statically render as my blog, to build an interactive Math Map

S2 Bearings

N5 Trig Intro

Online Teaching Tools

Looks like our teaching is going digital, by choice or by virus. Transition more easily to Flipped Learning and Online Teaching by using these tools.

S1 Pythagoras

S3 Gothic Geometry

S2 Quadrilaterals

S4 Graphing Transformations Sin Cos

S5 Calculus Curve Table Min Max

·Understand the relation between the shape of \(f’(x)\) and \(f(x)\), how one connects with the other. · ·Can plot Curve Tables of functions to identify their shape, and can use these to plot the graph of \(f’(x)\) for a given \(f(x)\). ·S5 Class, 2x40min period, end of day, 3 days in a row, usually quite tired. · ·Heinemann Higher Mathematics textbook Chapter6 pg105–111. https://is.gd/ea_21 ·Slides: https://slides.com/jayteach/s5_calc_min_max/fullscreen/ Desmos:https://www.desmos.com/calculator/fxglkpqt4p · · ·# Review yesterday’s content and feedback: · ·# Every value of \(a\) that makes \(f’(a)=0\) is called a “stationary point” · ·When \(f’(x)\) is negative, \(f(x)\) is decreasing. ·When \(f’(x)\) is \(0, f(x)\) is stationary. ·When \(f’(x)\) is positive, \(f(x)\) is increasing. · ·Minimum: - 0 + “min” for “minus” Maximum: + 0 - “max” has ‘x’→ ‘+’ · \ _ / / ‾ \ · ·Steps for Constructing ‘Curve Tables” to Analyze Graphs using the Derivative Graph: ·1. Differentiate ·2. Solve for Zeroes ·3. Assign sign of zones (by plugging-in values, visually from the graph, or from patterns) ·4. Identify as either minimum, maximum, or turning point. ·Use DESMOS to help visualize things · ·# ·pg104 Exercises 6L 2–8 finding where functions are positive/negative · ·The parabola \(f(x)=x^2-5x\) differentiates to \(f’(x)=2x-5\), with maximum at \(x=\frac{5}{2}\). ·The parabola \(f(x)=-\frac{1}{4}(x+2)(x-4)\) differentiates to \(f’(x)=-\frac{1}{2}x+\frac{1}{8}\), with maximum at \(x=1\). [Annotate Printout side 1] · ·# ·To sketch the graph of \(f’(x)\) from \(f(x)\): ·1. Find the stationary and turning points, ·2. Assign the sign for each zone, and ·3. Connect-up all the details. [Annotate Printout side 2] · ·pg110 Exercises 6P sketching graph of derivatives · ·# Same feedback questions as yesterday: Assess self-reported confidence in: ·●Pairing up a particular graph with its derivative graph. ·●Identifying where f’(x) is +,-,0 just by looking at f(x). ·●Sketching f'(x) just by looking at f(x). ·●Using f(x) to explain what happens in f’(x). ·●Using f'(x) to explain what happens in f(x). ·●Using the equation for f'(x) to calculate the rate of change of f(x) at different places.

S5 Calculus Tangents and Stationary Points

·# Assess (using https://www.menti.com/5fteqn32yx ) their understanding of gradients by pairing equations of straight lines with their graphs, (graphs available at https://www.desmos.com/calculator/pmqizkrhxq ): ·●y=2(x+3.5) ●y=-1/4(5x-24) ●y=4(x+1)-1 ●y=-1/2x-2 · ·# Assess self-reported confidence in: [If not confident, do them.] ·Differentiating ●x⁻², ●1/(2x), ●3x²-5x+1, ●3/sqrt(x³), ●(x+2)(2x-1) · · ·# Recap: Basic Differentiation Rules ·d/dx( f(x) ) = f’(x) = df/dx The derivative of a function is the instantaneous rate of change of that function at each point. · ·d/dx( x^n ) = nx^(n-1) To differentiate: by the old power, decrease the power by one. · ·d/dx( a ) = 0 The derivative of a constant is zero. · ·d/dx( ax^n ) = a d/dx(x^n) = a nx^(n-1) When differentiating a constant times a power of x, extract the constant and multiply it from the outside. · ·d/dx( f(x)+g(x) ) = f’(x)+g’(x) The derivative of a sum of functions is the sum of their derivatives. · · ·# Recap: Finding the equation of a line between two points ·●Find m = Δy/Δx ●Put this into y=mx+c ●Put a coordinate-pair into the equation to solve for c ●Re-write y=mx+c with values for m and c ·Example Ex.: Find the equation of the line passing through (2,4) , (3,9) · · ·# Differentiating from First Principles ·We construct a crude tangent line between two points on f(x) ·The first point has coordinates (a, f(a) ) ·The second point is shifted-over by ‘h’, with coordinates (a+h, f(a+h) ) ·●y = mx+c ●m = (f(a+h)-f(a))/((a+h)-(a)) ●c = f(a)-ma · ·# What is the pattern as we zoom in and make ‘h’ shrink? (Discuss in pairs) ·Experiment with some real numbers: a=2 and h=1, decreasing ‘h’ to 0.5, 0.25, 0.1 etc. ·Conclusion: shrinking h gives a better-and-better fit to the f(x) graph. ·[Differentiation: canned answer for potential hard question: We aren’t ‘dividing by zero’ because 1. h cancels-out from the top and bottom, and 2. we never actually go to h=0, we just go near it → problem dodged 👌! · ·# The slope of the tangent line (m) at any point on f(x) EQUALS the value of f’(x) for that point ·This expression for ‘m’ is the DEFINITION of ‘Differentiating’. [Write eq] ·(If you’re keen, ask me after for the proof for how it works for x^n) · · ·# We can now use f’(x) to gain knowledge about changes in f(x) ·Task: sketch f(x)=x² , on another pair of axes below it sketch f’(x), below this sketch a table horizontally of f’(-2),f’(-1),f’(0),f’(1),f’(2), evaluate f’(x) at those points. ·If the result is positive/negative/zero, below it write +/-/0 ·What’s the pattern (Discuss): When f’(x) is -, f(x) is decreasing, when f’(x) is +, f(x) is increasing, when f’(x) is 0, f(x) is stationary. · ·# Exercise: For f(x)=x²-4x, 1. find f’(x) 2. Sketch the graph of f(x) 3. When does f’(x)=0 ? 4. Sketch the graph of f’(x) (solutions: https://ssddproblems.com/differentiate-y-fx/ ) · ·# Every value of ‘a’ that makes f’(a)=0 is called a “stationary point” ·Does the stationary point always line up with the minimum/maximum of the parabola? Re-write these parabolas in point-intercept form to investigate! ·In the form y=a(x+b)²+h ●f(x)=x²+4x+4 ●p(x)=-x²-8x ●s(x)=x²+6x-3 ·After doing it by hand, you can check your results by typing them into today’s Desmos graph. · ·# Extra Exercises: page 102 Ex. 2,3,4 Page103-104 Examples16–18, 6L2 · ·Plenary: Assess self-reported confidence in: ·●Pairing up a particular graph with its derivative graph. ●Identifying where f’(x) is +,-,0 just by looking at f(x). ●Sketching f'(x) just by looking at f(x). ●Using f(x) to explain what happens in f’(x). ●Using f'(x) to explain what happens in f(x). ●Using the equation for f'(x) to calculate the rate of change of f(x) at different places.

S3 Circle Sectors and Perimeters

·# Competition: Which cone will give the best area to height ratio? · ·Calculate the missing values for each shape. (First scaffold with solving a simpler variant) · ·Separate the paper into its 8 quadrants. Pick one quadrant to complete first. Find the sector area and the arc length. Contribute those results to the class before repeating it for more quadrants. · ·Calculate all sector areas. Sort the papers from smallest to largest and record your number as a sequence (e.g. “12 345 876”). [28 651 473] ·Do the same for arc length. [85 671 234] ·Calculate the height of the cone this area wold make if rolled up in 3D. [24 316 758] ·Calculate the ‘best’ ratio of area to height. [85 671 234] ·Here we must be careful to interpret ‘best ratio’ as meaning “the least area for the greatest height” · ·Triangle r /cm ϴ /° Area /cm² L /cm H /cm Area per Height / cm ·1 1.000 90.00 0.785 1.571 0.968 0.811 ·2 0.500 180.00 0.393 1.571 0.433 0.907 ·3 1.000 114.47 0.999 1.998 0.948 1.054 ·4 0.707 180.00 0.785 2.221 0.612 1.283 ·5 1.414 41.41 0.723 1.022 1.405 0.514 ·6 1.000 60.00 0.524 1.047 0.986 0.531 ·7 1.414 45.00 0.785 1.111 1.403 0.560 ·8 1.414 22.50 0.393 0.555 1.411 0.278

S1 Statistics Probability

·# Probability Number Line [Drawn on Board] (Exciting Vegas Cover Picture) · ·impossible unlikely even 50/50 likely certain ·0 0.5 1 ·A B C D E F G · ·# Describing Probability with Words (Qualitative) ·An event's probability is a prediction of how LIKELY it is to occur e.g. ·impossible unlikely even 50/50 likely certain · ·# Estimate the Likleyhood of Different Events ·https://www.menti.com/hpippc1cdf ·1. P(A bus stops in George Street within 10mins) ·2. P(you see a bright pink Lamborghini in a car park) ·3. P(an equilateral triangle has a 60° angle) ·4. P(the next baby born in a family is a girl) ·5. P(Saturday is 3 days after Tuesday) ·6. P(it rains on at least 1 day in April) ·7. P(a wife is taller than her husband) ·Answers: 1. E 2. B 3. G 4. D 5. A 6. F 7. C ·Invent your own events. Locate their probability on the scale using words, numbers, and labels · ·# Describing Probability with Numbers (Quantitative) ·It is a number between 0–1, with no units. ·It can be written as a percentage, or more commonly as fraction or decimal. ·Express probabilities as 1/2 (0.5) rather than "1 in 2", because a probability is always a number in-between or equal to 0 or 1 ·This is a fraction, we should always simplify fractions (e.g. the probability 6/15 = 2/5) · ·# Calculate Probabilities Using Frequency ·To compare probabilities, we need a fair way to measure them (to put numbers on them). ·Probability = P(number of the events we want) / P(number of all the possible events) · ·# Examples of Counting the Number of Possible Cases (Quickly with Show-Me Boards) ·Coin flip / Dice / Egg Cartons / Truck Wheels / Different Spinners · ·# How to Write Probability Equations ·We can write a probability in an equation: ·"The probability of event 'X' happening is 1." ·becomes: "P(event 'X') = 1" ·Or even shorter: P(X)=1 · ·# Probability of Rolling a 6 on a Cube ·There is only one '6' out of the 6 sides of a dice, there is only one 'blue' side on a fully-solved Rubik's cube. [Roll a cube around as an example of a large dice]. · ·# Exercise 2 page 161 Questions 1-6 · ·# Easier vs. Harder Dice Games ·Take a dice game where you win if you roll 5 or 6, and lose otherwise. Is it more likely to win this game or to lose it? [2 cases / 6 possible] ·Compare this probability to a game where you only win if you roll a 6. · 2/6 > 1/6 · 1/3 > 1/6 ·33.3% > 16.67% · ·# Opposite Probabilities ·If P(A) is the probability that A happens, the opposite probability (the probability that A does NOT happen) is calculated using 1-P(A) . ·Page 161 Question 6: 4 marbles, 1 blue 3 red. P(red)+P(blue)=1 so P(blue)=1-P(red)=1-3/4=1/4 · ·# Probability Kahoot https://create.kahoot.it/details/probability/cab63a54-cac7-41d1-9e46-72f5235e800d

S3 Equations and Fractions Review

·# Pushing Past Your Limits Takes Lots of Practice and Confidence · ·Be brave like Alex Honnold and keep practicing Maths to get past your blocks! He had a training plan and focused on every part of his skills to be completely confident at every step. ·https://www.youtube.com/embed/urRVZ4SW7WU?start=5&end=57 · · ·# Today’s Goal ·Work through questions 10.3 to 10.6 (they took me 40min to complete) · ·# 10.3 Dealing with Negative Coefficients · ·# 10.4 Dividing by Coefficients · ·Challenge: ·There are two consecutive questions who’s answers in the book are wrong, find them! [10.4 5b&c] · ·# 10.5 Expanding and Re-arranging Both Sides · ·# 10.6 Combining Fractions with Different Denominators · ·# You can use “PhotoMath” to remind yourself of Algebra Steps ·On your device you can install this app (at break time). Use it to scan an equation, and it will solve it, showing all the algebra steps. ·But remember, the goal isn’t the numbers (answers), it’s developing the SKILLS to reliably GET the numbers. So if you use it to ‘cheat’ you’re only cheating yourself of the skills you want to learn. (The whole point of “Free Solo” was that he climbed *without* a safety rope!) · ·# Persistent Focused Practice ·Unlock the next level of maths! ·[Picture of ‘game progression’ unlockable sequence, emphasizing that further maths mastery is only available once the basic algebra steps are completely

Statistics Pie Charts

·# Introduction ·The first ever pie chart was invented in 1805 by William Playfair, a Scotsman born near Dundee. ·He also lead a successful 1793 plot to bankrupt the French Government and cause their civil war (by counterfeiting their currency). ·https://link.springer.com/content/pdf/10.1007/s00180-009-0170-z.pdf · ·# What’s the point? ·Different charts aim to tell different stories. ·Pie charts are useful to compare different numbers as a *ratio* of the whole. They use *angle* and *area* (not *length*, and not so much *numbers* or *position*). · ·# How to Read A Pie Chart? ·Pie charts can either be labeled with a “Key” (a.k.a. a “Legend”), or directly on the diagram · ·# Real Life Example 1: World Population (2017) ·This area map of world population stretches land size to tell us the size of the country's population ·https://ourworldindata.org/uploads/2018/09/Population-cartogram_World-2.png · ·The same information presented in a pie chart gives a much clearer *comparison* of the numbers, although it makes the individual values harder to read. ·https://en.wikipedia.org/wiki/World_population#/media/File:World_population_percentage.png · ·# Real Life Example 2: CO₂ Emissions (2016) ·Be careful! Avoid thinking “pretty = informative”. This graph is artistic, but it doesn’t tell a clear story. · ·# Pie chart showing the top CO₂ Emitting Countries of 2016 ·Instead, using a pie ch

Starting Slides.com for Maths Teachers

An overview of the different levels of interactivity unlocked by using Slides.com : Video, Timers, Desmos, GeoGebra, whiteboards, any web-page, mathsbot, polls ... anything that is a website can be effortlessly embedded in your shared presentation.

Statistics Bar Graphs & Histograms

·# Starter: ·Video of a Galton board (physical simulation of Normal Distribution histogram) ·Task: Write down in your own opinion a description of what is happening. Try to use mathematical language. · ·# Bar Graph: Categorical (Discrete) Data ·Interactive example of coin toss bar graph https://seeing-theory.brown.edu/basic-probability/index.html ·An example of a very simple Bar Graph. ·This one only has two categories: Heads OR Tails. The Category is shown below the bars and the bars are separate. · · ·# Interactive worksheet to input tally data, which will be automatically plotted. https://www.desmos.com/calculator/g1khyxce0d · ·Demonstrate a simple live tally: class’s number of Girls vs. number of Boys ·Demonstrate refreshing the page to reset the table · ·Demonstrate more tallies: favorite food (pick from a few options), number of siblings, enjoyment of maths class (1-5), etc. · ·Task: input numbers between 1-6 to recreate the shape at the beginning of the lesson (a “bell curve”) · · ·# Worksheet: Reading info from Tables and Plotting a Bar Graph · ·# Worksheet 2: Plot a Bar Graph, interpret Tally Table · ·Exercises from the Book (summarizing data tallies, plotting bar graphs, and interpreting bar graphs) · · ·# Histogram: Numerical (Continuous) Data ·Revisit the Desmos activity, but set the histogram bin width to “1”. · ·Use real-life examples of continuous data: hand length (they can measure with rulers), height, favorite day of the week (1-7), month of year born (1-12), etc. · ·Exercises from the Book (plotting Histograms, interpreting Histograms) · · ·# Plenary: Examine “Scotland’s Population is Ageing” Histogram ·Identify it as a Histogram ·Compare 2008 with 2018 results.

Bearings3

·# Identifying and Writing Bearings ·## Starter: ·pg60 Ex.4 Q3to5 when finished, draw a sketch of a Compass into jotter with labels and 3 digit bearings for N, NNE, NE, ENE, E etc. · ·## Assess: ·Question 4 is more tricky. If you aren’t sure how to do it; try it, raise your hand to tell me, and then move on to Question 5. · ·## Demonstrate: ·### Algebra for Question 4. ·360° = 50° + 310° ·360° = 50° + 180° + 130° · ·50° is that bearing measured counter-clockwise (which is incorrect) ·310° is the same bearing, but measured clockwise (which is correct) · ·This is to prevent us from getting our directions mixed up. · ·# Measuring angles and converting them into bearings ·## Complete pg62 Ex.5 Q1to4 ·Be careful when the angle is larger than 180° · ·## Worksheet: Labeling Bearings ·Start and end points are given, you need to construct the ‘North’ lines, then follow the arrow to measure bearing FROM the start TO the end. Apply cardinal direction labels (when appropriate) for N,S,E,W,NE,SE,SW,NW Bonus: Do the same thing but FROM the end TO the start. · ·# Outdoor Bearings Activity ·1. Orient towards North, and draw a ‘North’ line ·2. In pairs, accurately chalk a large (1m²) compass rose of N,S,E,W,NE,SE,SW,NW. Then also draw large squares, triangles. Challenge: draw a 6-pointed star ·3. Work out bearings FROM any A TO any B ·4. Give instructions in your pairs to navigate all t

Bearings2

·# Starter: Labeling bearings from one big circle ·Next to the objects, write down the 3 digit bearing from the center to the different objects. · ·# Measuring angles and converting them into bearings ·## TeeJay pg62,63 Ex.5 Q2 a,b,c,d & Q4 a,b,c,d · ·# Recap what we learned from our experience in the Outdoor Activity · ·# Bearing “from” vs. Bearing “of” (draw diagram example) ·"to": from to ·"of": of from · ·# Complete Dr. Brookman’s 1993 bearings worksheet (finish for prep) · ·You started by reading and interpreting bearings. · ·Now you need to write and explain using bearings. · ·And if we have a scaled map, we can measure it (and do scale-drawing calculations) to calculate real-life distances!

Bearings