Karen Chow

1. Practical Activities to Use in the Classroom Karen Chow

2. Like Terms We can replace a number with a letter. This letter is called an unknown. We can only add or subtract like terms. Like terms have the exact same unknown. 6a – 10b – 3a + 2 + 2a + 5b – 5 6a – 3a + 2a – 10b + 5b +2 – 5 = = = – 5b – 3 5a Final Solution: 5a – 5b – 3

3. Algebraic Conventions • y + y + y + y = 4y or 4 × y “4 lots of y” If there is no symbol between letters or a number and a letter, it means “×” • y means 1y. The “1” is not included • If there is more than one letter, they should be written alphabetically. e.g. ab not ba

4. Welcome to Burger Nation! Hi, and welcome to Burger Nation! Listen in, as a young man makes his order with Burger Nation. Your goal is to see if you can get his order right while he speaks during the video. You can work in small groups to compare your solutions. At the end of the video, we will compare and see if we can somehow make his order work somehow! • https://www.youtube.com/watch?v=US95J1g6iY4

5. The Burger Nation Order Two more junior fries A hamburger with everything Two more hamburgers with everything Two more hamburgers with everything Four large cokes One large sprite Two large cokes Five large cokes One large coke A small coke Three small cokes A small coke A small coke Two hamburgers with just pickles Four more hamburgers with everything A cheeseburger with no pickles Cheeseburger with nothing but pickles Two more hamburgers with everything but onions on one and one with everything but pickles mustard and tomatoes on the other Three large fries Six medium fries One large fries A junior fry Two junior fries Three more cheeseburgers with extra cheese and bacon

6. Climbing to 100 What patterns can you see here? There are lots of different patterns, write down as many as you can in pairs.

7. Your Group Mission… In your groups, you should each have a different coloured pen. Each person completes one of the sheets they have been given using a coloured pen. You are revising the same skill, so if you can see someone in your group struggling, make sure you help them, but do not tell them the answer! When each person in your group is ready, pass the paper you have been working onto someone else in your group to check. You should either mark it correct, or you should change the answer if you think it is incorrect and talk to the person about why you think your answer is correct. One person brings up all the sheets to me. I will mark it and give you your next set of questions. If you have more than two incorrect answers, you will be sent back to your group to correct it. There are four sets of questions. The aim of this mini-relay is to revise with other people so you can learn new ideas and also finish all the questions as accurately as you can!

8. Let’s Pass the Equation! The aim of the game is to solve your equation as a group and check to make sure your answer is correct. The first person in your group does the first line of working before passing the equation on to the next person. Each line of working must be done by a new person in your group. Each person in your group should also have a different coloured pen. Once the judge has ticked off your solution, you will be given another problem. There are a total of 12 questions and a bonus round. Not on a team? You must be a judge here to help…

9. Algebra Assessment You have three different options on how to present this assessment: • Create a test including all the algebraic skills with model solutions • Create a worksheet like Are You Kitten Me with your own joke and questions • Create a murder mystery where algebra is used to solve and find the murderer. You will be assessed on the originality of your assessment and the level of difficulty in the questions you write.

10. Algebra Criteria

11. Aoife and Isla! Isla’s full name has letters The girls have been living with me for almost months! Last week, I spent dollars on tinned food for Aoife and Isla! The girls were born in January 2017 on day Aoife’s nickname has letters

12. Different Types of Slopes… The gradient tells you how steep your line is. It also tells you whether your linear graph is positive or negative! Negative graph The gradient is also negative! Positive graph The gradient is also positive!

13. Miss Chow’s First Skiing Experience… Going DOWN the hill, I spent more time on my behind than on my skis and my friends made fun of me, I cried, and the snot froze to my face. It was a very NEGATIVE experience.  Going UP the chair lift, I had a very POSITIVE attitude – skiing was going to be great! I had a new outfit and felt like a snow bunny.

14. Miss Chow’s First Skiing Experience… I failed to see the very steep cliff and skied right off the edge – words could not describe that feeling – it was UNDEFINED. By the time I got to the bottom of the hill, I was having ZERO fun, was exhausted, and closed my eyes

15. Miss Chow’s First Skiing Experience… The gradient of this graph is zero, because there is no RISE This means the equation of this graph is y = – 3

16. Miss Chow’s First Skiing Experience… The gradient of this graph is undefined, because the RUN is zero…and you cannot divide by zero! This means the equation of this graph is x = 6

17. Bouncy, Bouncy! Zookeepers at Wellington Zoo are always trying to find new ways to entertain and educate the animals in their care. An idea the zookeepers have come up with for the tigers in their care is a game involving a bouncy ball. They want to be able to drop a bouncy ball from a platform above the tiger enclosure and have them jump on it after the first bounce. Before the zoo invests in a large bouncy ball, they want to see if the ball will at least bounce 2m high on the first bounce Based on this scenario, write down some questions you would like to ask or information you would like to find out.

18. Bouncy, Bouncy! Are we dropping the ball straight down? How high can tigers jump? How bouncy is the ball? What are the dangers here? How high is the platform? How could we test this? Will the tigers enjoy this?

19. Bouncy, Bouncy! A set of small bouncy balls that has a similar bounce to the ones the zoo is looking into are purchased. We need to find out… What is the relationship between the height the ball is dropped and the height of the first bounce? We need to do some pattern-seeking experimenting to find out how high the ball needs to bounce if we know that: • The platform is 5.8m above the enclosure • Tigers can jump 4m

20. Bouncy, Bouncy! Let’s create a plan together… • We need a dependent variable – this is the thing we measure that we have control over • We need an independent variable – this is the thing we measure that we don’t have control over The problem is bouncing the ball from a certain height and seeing how high it bounces. What are some things that could affect this experiment? The things that could affect this experiment are called sources of variation.

21. Bouncing Next Session… In groups of three or four, you need to see if there is a pattern when you bounce a ball and see how high it bounces. • Hold the ball next to a metre ruler 10cm off the ground and drop it without bouncing • Record how high the first bounce is. • Do this five times. Take the median bounce as the result • Repeat steps 1 – 4 for 20cm, 30cm, 40cm, 50cm and 60cm.

22. Introduction to Your Assessment Barbie is feeling very adventuresome these days, and with the opening of our new building wants to go bungee jumpingfrom the first floor of our new building to the ground floor. With the help of some elastic bands, Barbie wants to feel the thrill of a big jump. Let’s talk a little about this though… • What are some consequences of selecting the wrong number of elastics for Barbie? • How could we test this before Barbie does her big jump (and don’t worry, she will!) • What information might be useful to know in this situation? Brainstorm your ideas as a group on the A3 paper you’ve been given!

23. Guess the Age! You have been given a sheet with the names of 20 celebrities: 10 males and 10 females. You will be shown a photo of this celebrity and you have to guess how old they were when the photo was taken. No checking with another person, the guess must be your own!

24. Guess the Age! Beyonce Jennifer Lawrence

25. Guess the Age! Jennifer Lopez Margot Robbie

26. Guess the Age! Ellen DeGeneres Kendell Jenner

27. Guess the Age! Goldie Hawn Taylor Swift

28. Guess the Age! Miley Cyrus Adele

29. Guess the Age! Pharell Johnny Depp

30. Guess the Age! Leonardo DiCaprio Harrison Ford

31. Guess the Age! Robert Downey Jr Adam Lambert

32. Guess the Age! Harry Styles Phil Lester

33. Guess the Age! Chris Hemsworth Benedict Cumberbatch

34. Guess the Age!

35. Graph These… On a fresh page, draw a set of axes. On the x-axis, label it Actual Ages On the y-axis, label it Estimated Ages For each celebrity, plot the point for their actual age and estimated. Colour males and females differently Complete the gaps and answer all questions fully on your worksheet. Comment on any other information that your graph may also tell you about your ability to estimate celebrity ages.

36. Let’s Discuss… A scatter graph shows a relationship or correlation between two measurements. Here’s a scatter graph showing the relationship between the actual age and estimated age of actual celebrities. The red line is the line of best fit and helps us identify the type and strength of relationship. • What does the strength of the relationship indicate about our ability to estimate celebrity ages? • Why might estimating the ages of celebrities be harder than for non-celebrities? • The older a celebrity gets, do you think guessing their ages gets easier or harder?

37. The Language of Scatter Graphs Scatter graphs show the relationship or correlation between two variables (measures). We can determine the strength of the correlation, by the distance the points are from the line of best fit. Positive linear correlation Values go upwards Negative linear correlation Values go downwards No correlation

38. Test score Time spent doing homework (minutes) What Type of Relationship? MODERATE STRONG WEAK POSITIVE NEGATIVE LINEAR

39. Outdoor temperature (ºC) Electricity used (kWh) What Type of Relationship? MODERATE STRONG WEAK POSITIVE NEGATIVE LINEAR

40. Science score Maths score What Type of Relationship? MODERATE STRONG WEAK POSITIVE NEGATIVE LINEAR

41. IQ House number What Type of Relationship? MODERATE STRONG WEAK POSITIVE NEGATIVE LINEAR

42. What Type of Relationship? Describe the relationship you think would exist between these variables: • The number of firemen in attendance vs. how big a fire is • The amount of people showing symptoms of hayfever vs. the amount of pollen in the air • The length of someone’s hair vs. the length of someone’s shoe size • The number of ice creams sold vs. number of bees MODERATE STRONG WEAK POSITIVE NEGATIVE LINEAR As [variable x] increases, [variable y] will tend to increase or decrease

43. What Do We Know About Scatter Graphs? Sort the statements into two groups: “agree” or “disagree”. Listen to other people and discuss your answers. You may like to add a “don't know” group. It is more important to be able to explain some of your answers than to finish sorting all of the statements. You can use the examples to help support your argument.

44. What Do We Know About Scatter Graphs? • The line of best fit should go through all of the points on the graph. • It is always easy to see where the line of best fit should go. • The line of best fit must go from bottom left to top right. • There should be about the same number of points above the line of best fit as below it. • There is always only one correct line of best fit for each graph. • The line of best fit should go through as many points as possible. • The line of best fit must go through zero. • The less 'scatter' there is about the line of best fit, the stronger the correlation is between the two sets of data. • A line of best fit going up (from left to right) shows that as one quantity increases, so does the other. • If there are more points on the graph it is harder to tell whether or not there is a correlation.

45. Reviewing Statistical Calculations Averages tell us about the majority of people: • Median: The middle number • Mean: Add all the numbers and then divide by the total number of people • Mode: The most popular The lower quartile is the median of the lower 50% of data values. The upper quartile is the median of the upper 50% of data values. Other statistical measures are: • Range: Maximum number – minimum number • Interquartile range: UQ – LQ

46. Line It Up! A certain number of students will be chosen from the class and asked one of the questions below. They will write their answers on a whiteboard. You need to calculate the median, lower quartile, upper quartile, median and mode for each group of students. • The number of siblings they have • The number of different names they are known by • The longest streak they have on snapchat • The number of friends they have on FB • The number of followers on Instagram • The number of people they follow on Instagram

47. Let’s Go Flying (Again!) You might remember this exercise from last year… This year, how we analyse the data we get will be a little more sophisticated! The instructions for this activity are still the same: Using the A4 piece of paper provided, you must fold a paper plane. You may use your device to help you, but you MUST fold your own paper plane. Make sure you have written your name clearly on your paper plane.