This is a level (2+ to 3+) mathematics in science contexts activity from the Figure It Out series.

A PDF of the student activity is included.

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Students will:

- use the language of geometry to describe position, direction, and angle
- relate angle of lean to radius.

Students should discover that:

- turning circle is proportional to angle of lean
- cone spacing is proportional to turning circle.

a reel tape measure

a large protractor

strong string

a skateboard

chalk

a classmate

FIO, Forces, Levels 2+-3+, Skateboarding Theory, pages 12 - 13

**Activity One**

**Preparation**

Establish or reinforce appropriate rules for safe, non-disruptive skateboarding and how best to share

skateboard time. As with any group activity, carefully consider the needs of individual students.

**Points of entry: Mathematics**

Encourage the students to think about shapes. Although they will set up the cones in a straight line, when they lean on the skateboard, the board describes **arcs*** of circles. Ask them to sketch (on paper or in the air with their hands) the shapes they make as they decrease the distance between cones.

Encourage the students to look for the relationship between the **radius** of the circle and the position of the deck of the skateboard. For example, ask: *Does a sharper angle of the deck produce a smaller or larger circle? How does the shortest distance relate to the geometry of the skateboard – that is, how steeply can you lean the board?*

Ask the students what other relationships they notice. Prompt them to compare different groups and different boards: *Are wider boards easier to turn? Why?*

Have the students record more than one **variable**, for example, distance between cones, rider, angle of lean, and time. Ask them to think about which variables are important and which probably don’t affect cone distance, and then to test their thinking.

**Points of entry: Science**

Students need to have opportunities to explore how to use their **weight** to change direction and to discuss, consider, and attempt to explain why this happens. Give the students opportunities to closely examine the truck and have them use drawings and diagrams, both their own and those of others, to make sense of how it transmits **forces**. All this encourages reflection and evaluation, which are aspects of the key competency thinking.

Encourage the students to use scientific vocabulary. Ask: *What forces are acting on the skateboard? What forces are acting on the rider so that they keep their balance? How do these forces affect the motion of the truck?*

**Answers**

**Activity One****1. a. **Rameka bends his knees and moves his chest and arms forwards and backwards to shift his weight. When your weight shifts, the heavier side of the board starts to tilt down, like a see-saw.

**b. i.** As your weight shifts, that side of the truck moves backwards with respect to the deck (board) and turns slightly inwards to the centre. The skateboard turns towards the “down” side of the board.

**ii. **Your speed should be about the same, but direction will change.

**2. a.** Practical activity. The shortest distance between the cones will depend on your skill and the quality or other features of the board.

**b. **The tighter you can turn, the closer the cones can be. (Loose trucks that lean at a hard angle will turn better than stiff trucks that keep the deck relatively level.) The faster you travel, the more difficult it will be to turn in time to go around the cones.

**Activity Two**

**Preparation and points to note**

Circles with a radius of 4 metres take up a lot of space. You may want to have the groups overlap their circles.

Students may not think about recording their data in a systematic way. For them to comment meaningfully on what they have observed in question **1**, they will need to fi nd an effi cient way to record this data. Consider providing a chart for recording angle of lean, radius, truck turn angle, and radius for each circle. (Large wooden protractors will allow students to measure angle easily.)

**Points of entry: Mathematics**

When the students have recorded angle of lean, truck turning angle, and radius for each circle, challenge them to make predictions based on their data. For example, they could estimate the “smallest circle” instead of fi nding it by experimentation. See if they can estimate what angle will produce a given radius or vice versa. They could also plot angle versus radius.

To get the most out of this activity, students will need to work co-operatively, initially in pairs. This gives them an opportunity to develop the key competency *participating and contributing*.

Have the students compare and contrast the circles and the line of cones. For example, for different circles, they could put two cones just outside and one just inside the circle. Ask* How does the distance between the cones relate to radius?*

**Points of entry: Science**

Discuss why modelling is not always an accurate refl ection of real life. Ask: *Why are you able to navigate a tighter circle pushing the board than standing on the board? Why is it more difficult to ride a skateboard around a small circle than to push it with your hands?*

Have the students compare how a skateboard steers with how other vehicles steer. Ask: *Instead of a truck, what if the front wheel was connected to handles, like the front wheel of a scooter or bicycle? What really determines how large a circle a skateboard can make?* (It’s the turn-in of the wheels, not the lean of the board.)

**Answers**

**Activity Two****1. a–b. **Practical activity. Your observations will be most useful if you record your data in a systematic way.

**2. a.** The size of the smallest circle will depend on the skateboard, but it will be when the board is tilted the most.

**b. **You could ride a skateboard in circles around the line of cones in Activity One. The closer the cones, the smaller the radius of the circle.

**3. a.** The wheels move forwards and backwards because the vertical axle in the truck converts the tilt of the board into a rotation of the wheel axle.

**b.** A skateboard truck is like a see-saw because it contains levers that rotate around fulcrums. For example, the deck or board is like a see-saw, with the middle of the truck as a fulcrum. Shifting your weight to one side is like putting more weight on one side of a skateboard – the other side tilts up.

A skateboard truck is different from a see-saw because it contains more than one lever, fulcrum, and axle and it changes the direction of the force from up-and-down to side-to-side.