Acc7.6 Functions and Volume

Lesson 1

  • I can write rules when I know input-output pairs.
  • I know how an input-output diagram represents a rule.

Lesson 2

  • I know that a function is a rule with exactly one output for each allowable input.
  • I know that if a rule has exactly one output for each allowable input, then the output depends on the input.

Lesson 3

  • I can find the output of a function when I know the input.
  • I can name the independent and dependent variables for a given function and represent the function with an equation.

Lesson 4

  • I can identify graphs that do, and do not, represent functions.
  • I can use a graph of a function to find the output for a given input and to find the input(s) for a given output.

Lesson 5

  • I can explain the story told by the graph of a function.

Lesson 6

  • I can draw the graph of a function that represents a real-world situation.

Lesson 7

  • I can compare inputs and outputs of functions that are represented in different ways.

Lesson 8

  • I can determine whether a function is increasing or decreasing based on whether its rate of change is positive or negative.
  • I can explain in my own words how the graph of a linear function relates to its rate of change and initial value.

Lesson 9

  • I can decide when a linear function is a good model for data and when it is not.
  • I can use data points to model a linear function.

Lesson 10

  • I can create graphs of non-linear functions with pieces of linear functions.

Lesson 11

  • I can explain that when a three dimensional figure is sliced it creates a face that is two dimensional.
  • I can picture different cross sections of prisms and pyramids.

Lesson 12

  • I can collect data about a function and represent it as a graph.
  • I can describe the graph of a function in words.

Lesson 13

  • I know that volume is the amount of space contained inside a three-dimensional figure.
  • I recognize the 3D shapes cylinder, cone, rectangular prism, and sphere.

Lesson 14

  • I can explain why the volume of a prism can be found by multiplying the area of the base and the height of the prism.

Lesson 15

  • I can calculate the the volume of a prism with a complicated base by decomposing the base into quadrilaterals or triangles.

Lesson 16

  • I can find and use shortcuts when calculating the surface area of a prism.
  • I can picture the net of a prism to help me calculate its surface area.

Lesson 17

  • I can solve problems involving the volume and surface area of children’s play structures.

Lesson 18

  • I can find missing information about a cylinder if I know its volume and some other information.
  • I know the formula for volume of a cylinder.

Lesson 19

  • I can find the volume of a cone in mathematical and real-world situations.
  • I know the formula for the volume of a cone.

Lesson 20

  • I can find missing information of about a cone if I know its volume and some other information.

Lesson 21

  • I can create a graph the relationship between volume and height for all cylinders (or cones) with a fixed radius.
  • I can explain in my own words why changing the height by a scale factor changes the volume by the same scale factor.

Lesson 22

  • I can create a graph representing the relationship between volume and radius for all cylinders (or cones) with a fixed height.
  • I can explain in my own words why changing the radius by a scale factor changes the volume by the scale factor squared.

Lesson 23

  • I can estimate the volume of a hemisphere by calculating the volume of shape I know is larger and the volume of a shape I know is smaller.

Lesson 24

  • I can find the volume of a sphere when I know the radius.

Lesson 25

  • I can find the radius of a sphere if I know its volume.
  • I can solve mathematical and real-world problems about the volume of cylinders, cones, and spheres.

Lesson 26

  • I can build a triangular prism from scratch.

Lesson 27

  • I can compare functions about volume represented in different ways.