Number Talk 25 x 9 25 x 9 “We are going to start with a number talk. Your job is to mentally solve the problem. You won’t be talking or writing yet. When you have an answer, show me a thumb in front of your chest. Once you have an answer, think of another way to find the answer, and show how many ways you have on your fingers.” “Whisper your answer to your neighbor. Say your answer out loud.” Record answers. “Tell you neighbor one way you got your answer. Use a sentence frame to unpack your thinking” Call on non-volunteers, then take volunteers to share their thinking. Record students’ thinking under the document camera.
Objective Create and compare functions Create and compare functions
A function is a relationship Define a function as a relationship between input and output values.
Example f(x) = x + 5 Share as an example, f(x) = x + 5. x is the input. f(x) is the output. The function f defines a relationship where the output is 5 more than the input. Ask students to define function in their own words on their whiteboards.
Piggies and Pools “Today we will be reading about a situation and creating a mathematical model to represent it. This work should be a challenge for you, and I am expecting to hear you talking about your ideas, and to see your writing about the math. As you are working on your models, you will notice similarities and differences between the functions. Your job is to prepare to present your ideas to your classmates.”
Des be models #models f(x) = 2x^4 - 5x^3 + 7 “Your writing, along with your thinking in sentences, should include tables, graphs, and equations.” “What should your writing include?” Direct students to read question 1 round robin, each student reading a sentence.
#models Piggies and Pools Select a group or groups to present a table, graph, and equation for #1. Look for both explicit and recursive rules. Points to bring out: What type of relationship does this model? Discuss connected or disconnected graphs, and introduce vocabulary: discrete and continuous. Read question 2 round robin. Have students notice and wonder. Students will work on #2 and #6, writing down similarities and differences they see. Remind students that their job is to prepare to present their ideas to their classmates. Select students to share their table, graph, and equation for #2. Look for both explicit and recursive rules. Points to bring out: How is the number 2 represented in the table, graph, equation? Discussion of discrete and continuous in the context of questions 1 and 2. Where do we see the difference in the graph? In the table? Introduce the idea of domain Similarities and differences of the graphs
For your model you must include: Recursive Equation Explicit Equation Table Graph
For your model you must include: Recursive Equation Explicit Equation Table Graph
For your model you must include: Recursive Equation Explicit Equation Table Graph
For your model you must include: Recursive Equation Explicit Equation Table Graph
Reflection What is continuous and what is discrete? Give an example of a situation where the function would be continuous and another where it would be discrete. “Think about the comparisons you made in today’s functions. Think about what the difference is between discrete and continuous functions. Write down your ideas, and give an example of a situation that would be modeled by each type.” 1 minute think, 2 minute write. Share your situations with a partner. Leave your paper with the teacher.