Here is an aerial photo of our school grounds, with a little scale bar in the corner. Take a good look at the yard. Roughly how much space do you think it covers, in square metres? And here is the real question: how could we work out its area without laying metre sticks over every single square metre of it? Hands up with one idea for measuring something this big.

Let's find the area of the same yard three different ways, and watch how the answers land close together. Our yard measures 20 paces along the long side and 12 paces along the short side.

Way 1: Pace and scale

Way 2: Break into rectangles

I split the yard into two rectangles, find each area, then add them. A 10 m × 8.4 m piece is 84 m², and a 4 m × 8.4 m piece is 33.6 m², so the total is 84 m² + 33.6 m² ≈ 118 m². Predict again: will measuring on the photo land near these two answers, or far off?

Way 3: Measure on the photo, then scale up

The scale bar tells us that 1 cm on the photo stands for 3.5 m of real yard. I measure the long side on the photo with a ruler and get 4 cm, so the real long side is 4 × 3.5 = 14 m. The short side measures 2.4 cm, so the real short side is 2.4 × 3.5 = 8.4 m. Now the real area is 14 m × 8.4 m ≈ 118 m². Look at our three answers side by side: pacing gave 118 m², breaking into rectangles gave 118 m², and the photo gave 118 m². They all came out the same, and that closeness is exactly the point.

Today we work through this together: in small groups, estimate the area of one space in our school using two different methods — pacing-and-scale, and breaking-into-rectangles. Then compare your two estimates and decide which you would trust more, and why.

Today you combined pacing and area to model a space far too big to measure all at once, and you learned that two estimates agreeing closely is how we trust an answer. Next, we take on a second modelling project: planning an end-of-primary celebration that has to balance a real budget, using money, percentage and ratio together.