Students will:

• (Science) Identify plants and animals that are endangered or even extinct, investigating the reasons that led to this situation.

• (Mathematics) Measure lengths using appropriate measuring instruments, expressing measurements in metres and centimetres, represented using decimals.

• (Science and mathematics) Understand how mathematics can be mobilized to identify characteristics of dinosaurs

Materials

Dinosaur (theropod) footprints (Appendix 1)

Equipment

Laptop and projector or interactive board

Digital resources

Preparation for the lesson

1. You should create a dinosaur footprint track before the lesson. The track can be made up of 6 to 8 (or more) footprints. Consecutive footprints must be at the same distance from each other, as shown in the diagram below (Figure 1).

Figure 1. Dinosaur footprint track.

If you prefer to organize the activity in an indoor setting, like a corridor, a hall or a porch, you can use footprints printed on paper (see annex I). As an outdoor alternative, you can adapt the footprint by turn it into to a template and use it to paint them on the floor.

2. The foot length, pace length and stride length must be identifiable in order to be measured by the students on the track (Figure 2). 

Figure 2. Foot length, pace length and stride length.

For a footprint length of between 22 and 24 cm (don’t exceed 25 cm) use a stride length of about 2,50 m.

Watch this video to learn more about dinosaur footprints: https://youtu.be/RTMAe9TSdZQ

Dinosaurs are among the main focuses of young students’ conceptual interest. Studying dinosaur footprints and tracks can raise their awareness of ancient animals and the causes of their extinction. Although the approach to the study of dinosaur tracks proposed in this work is simple, it must be done with great rigor, bearing in mind that measuring correctly the footprints is needed.

5 min

Inquiry-Based learning

Collaborative learning

Mathematics: reasoning and measuring skills

Arts: drawing dinosaur footprints

Almost all the steps of the lesson are comprehensible to most special needs students who have well-preserved cognitive abilities. The lesson does not comprise long written explanations. The role of the special needs teacher or the assistant teacher is to help target group students in case they are not able to cope with some of the tasks or steps.

Dinosaur

Footprints

Tracks

Part I | Dinosaur extinction

Start the lesson asking students what they know about dinosaur extinction.

Ask them to explore the following online pages:

• “Death of the dinosaurs (Credits: European Space Agency)” 

• “Dinosaur – Kids” (Credits: Britannica Kids).

Then, ask students to identify if they initial ideas are similar to the reason for dinosaur extinction proposed by science. To promote discussion, the teacher can ask students some of the following questions: 

• How long have dinosaurs been extinct?

• Which is the man cause proposed for dinosaur extinction?

• How do you think the world changed after the dinosaurs went extinct?

• Why is it important for us to learn about dinosaur extinction?

• How do you think the extinction of dinosaurs affected other animals and plants?

• If dinosaurs were still alive today, how do you think our world would be different?

• Do you think it's possible for another mass extinction to happen? Why or why not?

Part II | Dinosaur size and dynamics

Step 1: Get to know the footprint track - Appendix 1

The students are taken to the school site where the footprint track was created. The students are told that the trackway is a record of dinosaur's activity in the distant past and that we can extract information from it about the dinosaur's characteristics and behaviour. The simulated track is similar to many that can be found around the world (Figure 4).

Figure 4. Dinosaur footprint in Alcanede, Portugal.

The tridactyl footprints indicate that they were produced by a theropod dinosaur. 

At this stage it makes sense to ask the students what additional information this track can provide. What characteristics of the track can be measured?

For example, the length of the footprint, which give us information about the size of the animal, can be measured.

Students are asked to organise themselves in pairs to measure and record the length of the footprint. These are aspects to take into consideration:

• the fact that all the footprints should be the same length, considering that they come from the same individual (invariance).

• Students should carefully measure the length of the footprint, consisting of the distance between the heel and the end of the big toe, as shown in the diagram below (Figure 5). 

Figure 5. Foot length.

Students can use a ruler to measure, as it is a short length. They can also use a tape measure, which they will need later to measure the other parameters of the track.

• Measurements taken by different students may vary slightly. The measurement process, being rigorous, is never exact, due to errors arising from different factors that cannot be eliminated, such as the limitations of the measuring instrument or the operator himself. The teacher should supervise the implementation of the measurement process done by the students to ensure rigour but should also allow each group to work with their own measurement if they don't vary too much between them (the difference should not exceed 1 cm). These differences, and what will result from them, can be explored didactically during the final discussion at the end of the activity.

• the length of the footprint can be recorded using different levels of accuracy, ranging from a measurement to the nearest centimetre or millimetre, expressed in metres (standard unit) or centimetres, using integers or decimals. For example, the length of a footprint 23 cm and 5 mm long can also be represented as 23.5 cm, 0.235 m or 235 mm.

After measuring and recording the foot length, the working pairs should recognise two other parameters of the track, namely the pace length and the stride length, according to the following diagram (Figure 6). 

Figure 6. Foot length, pace length and stride length.

Students are also required to measure and record these two elements of track data. The pace length should be understood as the distance between two consecutive footprints, measured from heel to heel; stride length as the distance between two consecutive footsteps of the same foot, also measured between two corresponding points (as before, for example, from heel to heel).

Again, it’s important to realise that: 

• the pace length is approximately, but not exactly, half the size of the stride length. 

• The stride length, which is related to the pace length, is an indicator of how fast the dinosaur was moving – The longer the stride, the faster it moved.

• The considerations outlined above for the foot length are equally valid now for the pace length and the stride length.

Step 2: Interpreting the data to understand size and type of locomotion

At this stage of the work, students will have the opportunity to obtain simple but relevant additional information about the theropod dinosaur from the data collected, just by using simple mathematical models.

The size of the footprint gives us an idea of the size of the dinosaur that produced it. An important parameter is the size of the leg, usually referred to as the hip height, is an indicator of the size of the dinosaur (Figure 7)

Figure 7. Hip height (H).

For a small theropod (with a foot length of less than 25 cm), the hip height can be estimated by multiplying the footprint length by 4.5. Students must now multiply their measurement for the foot length by 4.5 to determine the hip height of the dinosaur. 

Stride length tells us whether the dinosaur moved faster or slower: the longer the stride, the faster it moved. However, this is relative, depending on the size of the leg, which in this context we call hip height. This means that a certain stride length could mean faster displacement for a dinosaur with shorter legs, or a slower locomotion for a dinosaur with longer legs. For this reason, discovering the type of dinosaur locomotion responsible for the trackway involves assessing the stride length in relation to the hip height. So, students must divide the value of the stride length (measured on the track) by the hip height (determined in the previous step). If this ratio is found to be:

• Less than 2, then the dinosaur was walking

• Greater than 2.9, then the dinosaur was running

• Is between 2 and 2.9 (including this values), then the dinosaur was trotting.

In this case, as a reference with a stride length of 250 cm, for a footprint of 24 cm, the hip height would be:

Hip height=4,5 × foot lenght=4,5×24=108 cm

After obtaining this value, the students can use a tape measure to represent what this dinosaur's hip height would be. Students can imagine how tall was the dinosaur.

Then, they should calculate the dinosaur locomotion, as in the following example:

Dinosaur locomotion=Stride length : Hip height= 250 : 108=2.3 (Dinosaur was trotting)

To carry out the division, the teacher can authorise students, if considered appropriate, to use a calculator or, alternatively, engage in “pencil and paper” calculation (algorithm) or use any other calculation strategies, according to the level of the students. It is not important to achieve an exact result, but only an approximation that allows the ratio to be compared with the reference values provided (2 and 2.9). 

*Additional information about dinosaur tracks in: Wright, J.L., & Breithaupt, B. H. (2002). Walking in their footsteps and what they left us: dinosaur tracks and traces. In J. Scotchmoor, D.A. Springer, B.H. Breithaupt & A.R. Fiorillo (Rds.), Dinosaurs—The Science behind the Stories (pp. 117–126). American Geological Institute

Guided discussion:                                                                                                        

1. What is the relation between the dinosaur footprint and the size of the legs of the dinosaur?

2. What is the relation between the stride or pace length and the movement of the dinosaur?

3. What can we learn from the extinction of dinosaurs to help protect endangered species today?

Appendix 1