# Lesson 7 Speed Back Assignment Definition

The CyberSquad tests out Wicked's brooms and determines how to calculate their speeds. In these Cyberchase activities, students explore their prior knowledge of rate and extend it to create tables of values coordinating time and distance. They learn how to examine distance-time graphs and how to calculate unit rates (that is, distance per one second).

1. Read the following to your students: "In this Cyberchase clip, Wicked the Witch decides to sell brooms. She uses the CyberSquad's pictures to endorse the quality of the brooms. To ensure truth in advertising, the kids decide to test the speed of the brooms. They decide to test which broom goes further after five seconds and then they figure out a way to describe this as a rate or speed."

2. Distribute Handout 1: Exploring Ideas of Rate .

3. Ask the students to complete handout 1 to test their knowledge of rate.

4. Play the The Fastest Broom QuickTime Video . Ask students to pay attention to how the CyberSquad tests the brooms to find out which one is the fastest.

5. Discuss the students' answers to question number 1 in handout 1 to see whether they chose Answer C, which includes both how far and in what amount of time something or someone can move. Discuss why the other answers to question number 1 do not fully describe rate or speed because they do not include both distance and time.

6. Discuss with the students their answers to question 2 and whether they distinguished the numbers (choices a and c) from the rates (b, d and e) and the fraction (g) and ratio (f).

7. Ask the students to predict what kind of measurements they need to make in order to figure out speed. Discuss what tools are necessary to make those measurements. Make a list of students' suggestions on the board.

8. Tell the students that they will now watch a video segment in which the CyberSquad is asked to figure out the speed or rate of their brooms.

9. Play the Calculating Speed QuickTime Video .

10. Discuss the tools and measurements the CyberSquad used in the video segment, and have students compare those with the suggestions the class made before watching the video.

11. Distribute Handout 2: Rate on the Coordinate Plane .

12. Ask the students to complete handout 2, and then discuss their answers.

Assessment: Level A (proficiency): Students determine relevant information from a graph charting the distance of two cars over time.

Assessment: Level B (above proficiency): Students determine the fittest person by calculating heart rates.

We asked six teachers to share their most successful functional maths lessons and here's what they came up with.

## Dance routines and symmetries of the square from Danny Brown, head of maths, Greenwich Free School

I wanted to teach inverses to my year 8s and thought why not throw in a bit of group theory and have a bit of fun at the same time (it's always fun to teach 12 year olds some degree-level maths). So we decided to create a dance routine based on the symmetries of the square.

Kids made up their own moves for rotations and reflections, such as 'windmill' for 90 degrees clockwise, and its inverse, 'anti-windmill'. Other names for these included 'righty-tighty' and 'lefty-loosey'! The reflections were given names like 'mirror-mirror'.

Armed with a collection of rotations and reflections, pupils got into dance troupes of four and created their own routines that took them from the starting position (known as the identity in proper maths speak), through a rather complex sequence of moves, and finally back to the start. We then analysed the routines and worked out why the sequence of moves took us back to the start using inverses.

As an added bonus, I even got the teacher and deputy head who were observing my lesson to accompany on the xylophone and bongo drums.

## Paper plane flight data from Mel Muldowney, a maths teacher at Trinity High School and co-founder of Just Maths

We've done this activity with our new intake (on transition days) for the past two years and it's been superb. The students work in teams and start by making their version of a paper plane. During the lesson they are introduced to more unconventional designs and then go on to build their choice. The teams then compete with each other based on which flies the farthest and they use the information from their flights to try to calculate its speed. It really is a great fun lesson and can be as structured or as freefall as you want it to be. I always win though, as I screw the paper up and throw it as a ball for the finale.

Find full details of this activity in the Guardian Teacher Network resource bank: Paper planes – practical maths lesson.

You may also be interested in the other type of practical maths that I use, topics that will be genuinely useful to them in their lives, but more importantly, things that they can relate to, and unsurprisingly these type of topics usually involve money or mobile phones. I have found the Personal Finance Education Group is invaluable for ideas – some of which I'll be using in tutor time, with my year 13s looking at the practicalities of money management as they go off into the big bad world so as a conversation starter I've put together this Always true, Sometimes true and Never true card that will trigger off all sorts of discussions about credit and money in general.

## Spaghetti trigonometry from Adrian Pumphrey, a British mathematics teacher, now teaching at Herron High School in Indianapolis, USA

One of my favourite activities is to use spaghetti to introduce trigonometric graphs. The aim is for students to understand the origin and characteristics of the graphs of sin(x) and cos(x). All students need to do spaghetti trigonometry is: a blank unit circle and trig graph, a glue stick, a protractor, a small pile of spaghetti noodles.

First ask students to label the unit circle axis (-1 and 1's) and the trig graph x-axis (0 degrees to 360 degrees). Now students use a piece of spaghetti to mark the unit distance from the origin at 15 degrees to the x-axis. They can stick it down and label the angle. Now they can take another piece of spaghetti and measure the y-coordinate (sin(x)) of the point on the circle. They can transfer this piece to lie on the trig graph vertically above the 15 degree mark. Repeat at 15 degree intervals all the way around the shape. When they have finished, they can draw a line going over the top of all their spaghetti sticks to show the graph. Finished all the way to 360 degrees? Try the same again but this time measure the x-coordinate (cos(x)) of each point on the unit circle (with a blank trig axis).

This activity is really good for students to make predictions about how they think the graph will continue past 15 degrees, at the start of the lesson. Students always ask me for more lessons like this, so do give it a try. More detailed info on my website.

## A swimming pool for Beyonce and Jay-Z from Fiona Stone, maths teacher, Deptford Green School

Perimeter can be a tricky concept for students to grasp. I tried putting students in the role of designers for 'Aqua', a high end swimming pool designer. I gave them a letter from Jay-Z and Beyonce asking for the most bling swimming pool possible, paved in gold so Jay-Z could exercise their dog around it while Beyonce swam. Students designed a swimming pool and measured the perimeter for the gold, which they then calculated the cost of (plus their design time, plus a profit margin) and wrote a quote back to the happy couple. You don't really need anything other than paper and a fake letter from Beyonce to the class to do this exercise. I also included a slide of extravagant pools. After this activity I found the silliness of the task made it easier to refer back to the gold path as a hook for perimeter. Can be done with loads of other things; from fencing round a farm to a security guard doing his rounds of a building to the framing of a picture.

## Visualised word problems from Valentina Castaldi, year 3 teacher at St John's and St Clement's Primary school

This is my first year of teaching after a long career as an accountant, so I'm really into real-world maths. Make maths relate to real life and the pupils' understanding and enthusiasm will be much increased.

So if you want to do word problems and divisions, make it real. We have 29 children in the class, plus myself and our teaching assistant. We want to go to the Science Museum. If each minibus sits six children, how many minibuses will we need to get there? Actually create the minibuses in class by putting six chairs in rows – get children to come and sit in the chairs in groups of six and then they can actually work out how many minibuses will we need. This helps children to visualise the idea of division and also to think of remainders (five minibuses will sit 30 people and we are 31 so we will need six to all fit in). It is also a fun activity, so children really want to take part.

My other tip is don't throw away your egg boxes with 10 holes. They are invaluable to visually reinforce number bonds. So put three blocks inside the empty egg boxes, how many more to get to 10?

## Coding calculations from David Benjamin, A-level maths teacher at Folkestone Academy

It goes without saying that all my students are obsessed by iPhones and other electronic devices. So what about investigating some maths on what happens behind the scenes every time they use them?

In everyday life we represent numbers which are created in base 10 (denary numbers). Students are fascinated to find out that electronic devices, like mobile phones, essentially use a binary system to move data around their internal circuits. The binary system uses only the two digits zero and one ['off' and 'on'].

In computer jargon, one binary digit is called a bit, two digits are called a crumb, four digits are called a nibble and eight digits are called a byte.

So challenge your A-level students:

The denary number 19 in base 2 is 10011 [16 + 2 + 1] – so what are the next two column headings after 16?

If A = 1, B = 2, C = 3 what is the definition of this word? 1 1100 111 1111 10010 1001 10100 1000 1101?

(The answer is ALGORITHM.)

Can your students to represent their name in a similar code?

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