The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

In this lesson, the students will discover the relationship between an object's mass and the amount of space it takes up (its volume). The students will also learn about the concepts of displacement and density.

Students explore combinations in this open-ended Nrich task. Students are asked to discuss and document their work pictorially and numerically.

Students examine an image produced by a cabinet x-ray system to determine if it is a quality bone mineral density image. They write in their journals about what they need to know to be able to make this judgment. Students learn about what bone mineral density is, how a BMD image can be obtained, and how it is related to the x-ray field. Students examine the process used to obtain a BMD image and how this process is related to mathematics, primarily through logarithmic functions. They study the relationship between logarithms and exponents, the properties of logarithms, common and natural logarithms, solving exponential equations and Beer's law.

Experiment with rocket designs and a PVC launcher to discover how high—and how far—you can make your rockets go.

This Nrich activity challenges students to translate oral directions into actions to build a pattern with blocks.

This lesson will give students an idea of what to expect when they head to the computer lab. It begins with a brief discussion introducing them to computer lab manners, then they will progress into using a computer to complete online puzzles.

Students will begin using Evaluation Blocks to explore the concept of math as a language, and more specifically, a programming language. By composing arithmetic expressions with Evaluation Blocks, students will be able to visualize how expressions follow the order of operations.

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.

To compute more than just numbers, students will need to learn about two new data types, Strings (any string of alphanumeric characters) and Images. Using these new data types, we'll compose programs that produce and manipulate images.

Contracts provide a way for students to better understand and discuss functions. Through this lesson, students will look at known functions and come up with the contracts that describe those functions.

Students will work their way through a number of new functions, first using each to solve a problem, and then writing a contract which describes it.

In this activity, students will learn to define variables that can be used to reference values and expressions. Once defined, their variables can be used repeatedly throughout a program as substitutes for the original values or expressions.

In the past lessons students have defined Variables and written Fast Functions. In this stage, they will continue to explore function writing with ever increasing complexity.

In the last stage, students wrote some very simple functions - but more sophisticated functions demand a more thoughtful approach. The Design Recipe is a structured approach to writing functions that includes writing a purpose statement and test cases to ensure that the function works as expected. Once students have mastered the Design Recipe process, they can apply it to any word problem they encounter.

In this stage students practice using the Design Recipe to write functions which solve for word problems. Towards the end of the lesson students should be ready to begin using the Design Recipe on problems from your own math curriculum.

Determining when objects on the screen touch is an important aspect of most games. In this lesson we'll look at how the Pythagorean Theorem and the Distance Formula can be used to measure the distance between two points on the plane, and then decide whether those two points (or game characters) are touching.

Students discuss the components of their favorite video games and discover that they can be reduced to a series of coordinates. They then explore coordinates in Cartesian space, identifying the coordinates for the characters in a game at various points in time. Once they are comfortable with coordinates, they brainstorm their own games and create sample coordinate lists for different points in time in their own game.

To finish up their video games, students will apply what they have learned in the last few stages to write the final missing functions. We'll start by using booleans to check whether keys were pressed in order to move the player sprite, then move on to applying the Pythagorean Theorem to determine when sprites are touching.

Students get their first look at the inside of their own video games. They will start development by substituting in new Images, Strings, and Numbers for existing variables.