A fable (The pitcher and the crow) was inspiration to this activity after researching linear investigations and spending some time with the candle clock investigation. Students in Grade 9 and 10 at my school were working on Linear relationships while some are extending into simultaneous equations (Hence the extension section).
The activity asks students to connect their initial understanding of slope, y-intercepts and rate of change to a context.
A Thirsty crow wishes to drink out of a pitcher of water and cant reach so they add pebbles to the pitcher to change its depth. The relationship is a linear one and students are asked to tabulate and plot the information. They will then be asked questions in context to uncover what all the components of a linear rule mean.
EXTENSION - Students use the two models to make comparisons with the y-intercepts and slopes and then decide on which pitcher is best used for the crow. This topic is more linked with the grade 10 curriculum in Australia but some extended grade 9's could have a go.