In Lesson , you wrote rules for patterns found in x → y tables

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Presentation transcript:

In Lesson 3. 1. 1, you wrote rules for patterns found in x → y tables In Lesson 3.1.1, you wrote rules for patterns found in x → y tables. In this lesson, you will focus on using variables to write algebraic rules for patterns and contextual situations. You will use a graph to help predict the output for fractional x-values and will then use a rule to predict the output when the input is too large and does not appear on the graph.

While working today, focus on these questions: How can you write the rule without words? What does x represent? How can you make a prediction?

3-10. JOHN'S GIANT REDWOOD, Part One John found the data in the table below about his favorite redwood tree. He wondered if he could use it to predict the height of the tree at other points of time. Consider this as you analyze the data and answer the questions below. Be ready to share and justify your answers with the class.

How much did the tree grow each year? How tall was the tree 2 years after it was planted? What about 7 years after it was planted? How do you know? How tall was the tree the year it was planted? Estimate the height of the tree 50 years after it was planted. How did you make your prediction?

3-11. John decided to find out more about his favorite redwood tree by graphing the data. On the Lesson 3.1.2B Resource Page provided by your teacher or using the John's Giant Redwood Student eTool (Desmos), plot the points that represent the height of the tree over time. What does the graph look like? Does the graph represent a proportional relationship? Justify your answer.

Does it make sense to connect the points? Explain your thinking. According to the graph, what was the height of the tree 1.5 years after it was planted? Can you use your graph to predict the height of the redwood tree 20 years after it was planted? Why or why not?

Extra Practice