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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-5
Featured UK Key Stage 3-5; US Grades 6-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3-5
Featured UK Key Stages 3 & 4; US Grade 6-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Why do this problem?
encourages students to get into the real meaning of graphical representation without getting bogged down in algebraic calculations or falling back into blind computation. It will also encourage the students to think about the various differences and similarities between growth processes in the sciences.
This problem works well in group discussion. For each idea, try to encourage students to explain their reasoning as precisely and clearly as possible. You could split the class into different groups and see who can produce the most valid examples for each graph.
How many 'growth processes' in science can you think of. Would any of these graphs match those processes?
How might you label the scales for each example?
This type of problem is rich with extension possibilities. We suggest two:
Are there other shapes of graph which could be used to model other natural growth processes?
How might you describe these curves algebraically? Can you write down equations, the graphs of which match the shape of the curves in this question?
Look up the profile of a biphasic bacterial growth curve and understand the conditions that produced such a curve. Wikipedia is a useful place to start. Two clear phases of growth are seen due to:
1) The depletion of glucose from the nutrient medium
2) Transcription of $\beta$-galactosidase and associated enzymes to allow lactose metabolism
Is there any similarity to some of the curves given to you in the question?
You might naturally try
Let students leaf through a science textbook searching for graphs and charts. Do they notice that the same shapes of charts appear frequently? Can they match any to the graphs in this question?
STEM - living world
Processing and representing data
Families of Graphs
Transformation of functions
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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