Lesson 10: Rocket Height
Overview
Using the Design Recipe, students will work through a series of word problems about calculating the height of a rocket after a given number of seconds from launch. The functions they write will be used to animate the rocket launch.
Agenda
Getting Started
Activity
Extension Activities
Anchor Standard
Common Core Math Standards
- F.LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
Objectives
Students will be able to:
- Design functions to solve word problems.
- Use the Design Recipe to write contracts, test cases, and function definitions.
Links
For the Students
- Rocket-Height Design Recipe - Worksheet
Support
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Teaching Guide
Getting Started
Introduction
Functions are a key part of animation in computer programs. A function that draws a static picture of a bat, for example, can place the bat at a different location based on the input. When that input changes slightly based on time or user-interaction, the bat will appear to move. This is similar to the way that flip-book animations work, in which each page draws a static image that has changed by a small amount. When the pages are displayed quickly, the images appear to change smoothly.
Putting these images together, we arrive at an animation of the bat turning around.
In the online puzzles, students will see a function box which has no parameter inputs, which represents the function as a Type of data. This allows you to pass your function into the start function, where it can be used to control the rocket animation. By passing the rocket-height function into the engine we can call it repeatedly with new numbers as each second ticks by instead of running it with a specific value. The periodic execution creates the flip-book effect. As each second passes, the rocket-height function is executed again, the new location is calculated, and the rocket is re-drawn in its new location. This drawing and re-drawing in different locations gives the appearance of motion.
Lesson Tip
After creating simple linear movement, students will be asked to write functions to animate simple acceleration. Students will be given an input/output table from which to write their new function. You may want to work through these problems as a whole class, so that students can see how you might analyze an input/output table in order understand the relationship between input and output values.
Activity
Online Puzzles
In this stage you'll write functions that manipulate images to create animations. Head to Course A stage 10 in Code Studio to get started programming.
Extension Activities
Non-linear Animation
The final puzzle of this stage is a Free Play puzzle that will allow you and your students to experiment with other variations on the rocket-height formula. One activity that students find particularly interesting (and often challenging) is to write functions that produce non-linear acceleration. If your students are familiar with quadratics then you can call this out as such, but even younger students who haven't yet seen quadratics can enjoy this extension challenge.
Place the following input/output tables on the board and see if students can come up with functions that will produce the appropriate animation.
Challenge 1
| Input | Output |
|---|---|
| 1 | 10 |
| 2 | 40 |
| 3 | 90 |
| 4 | 160 |
Challenge 2
| Input | Output |
|---|---|
| 1 | 15 |
| 2 | 45 |
| 3 | 95 |
| 4 | 165 |
Once students have figured out the provided Input Output tables, encourage them to come up with non-linear animation functions of their own.
Student Instructions
Student Instructions
Follow the Design Recipe to create a function rocket-height which produces the height of a rocket traveling at 15 meters per second.
Student Instructions
Awesome, now can you update that function so that our rocket moves more quickly? Make sure to update the purpose statement, examples, and function definition to launch a rocket at 40 meters per second.
Student Instructions
Which function describes a rocket that reaches:
24 meters at 2 seconds
60 meters at 5 seconds
108 meters at 9 seconds
Student Instructions
Which function describes a rocket that reaches:
4 meters at 2 seconds
16 meters at 4 seconds
256 meters at 16 seconds
Student Instructions
Which function describes a rocket that reaches:
47 meters at 5 seconds
97 meters at 10 seconds
147 meters at 15 seconds
Student Instructions
Free Play: Experiment with your rocket-height function to make the rocket fly in different ways. Click "Finish" when you are done.
Standards Alignment
View full course alignment
Common Core Math Standards
BF - Building Functions
- F.BF.1 - Write a function that describes a relationship between two quantities.
- F.BF.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★
CED - Creating Equations
- A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
- A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constr
- A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
EE - Expressions And Equations
- 6.EE.9 - Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent va
- 7.EE.4 - Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
IF - Interpreting Functions
- F.IF.1 - Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
- F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
- F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
- F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers w
- F.IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★
- F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
- F.IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which
LE - Linear, Quadratic, And Exponential Models★
- F.LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
- F.LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
MP - Math Practices
- MP.1 - Make sense of problems and persevere in solving them
- MP.2 - Reason abstractly and quantitatively
- MP.3 - Construct viable arguments and critique the reasoning of others
- MP.4 - Model with mathematics
- MP.5 - Use appropriate tools strategically
- MP.6 - Attend to precision
- MP.7 - Look for and make use of structure
- MP.8 - Look for and express regularity in repeated reasoning
NS - The Number System
- 6.NS.8 - Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
OA - Operations And Algebraic Thinking
- 5.OA.1 - Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
- 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three t
Q - Quantities
- N.Q.1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
- N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling.