Math Connection

Real-World Math Applications in Science Pickle

Science involves data, and math extends how we understand the data, which expands our understanding of science. Bring some real-world connections into your explorations in math using the following activities found on Science Pickle.

Data

Graphs

Reading data from graphs using the Solar Declination web app. There are three types of activities within the app: 1) Explore, 2) Practice, & 3) Quiz in which all practice & quiz questions are randomly generated.

Contouring Spatially Organized Data

There are quite a few fields of US weather data to practice on. Compare results to the contoured fields as well as compare the change in variables across the US every 12 hours or compare spatial connections between weather variables.

Measurement

Accuracy and Precision

Use the Accuracy and Precision web app to explore accuracy and precision in one and two dimensions.

Algebra

Sequences and Linear and Absolute Value Equations

Find the sequence in the opening game levels of Suzie the Artist web app. Determine linear and absolute value equations for more advanced levels (there are 6 game levels). Games are randomly generated – so unlimited play and practice! There are two versions of the web app—one for smartphones and the other for larger screens (desktops, laptops, and tablets).

Geometry

Circles, Angles, Sectors, and Chords

There are so many in the Sun-Earth Connection section since you are analyzing circles, angles, sectors, and chords on many of the diagrams, but here are a few suggestions:

Show that the lowest latitude of 24-hours of darkness/sunlight = 90°- solar declination and the latitude with the sun directly overhead that day = solar declination using the Earth Illumination web app.

Right Triangles

Design Awnings for a given latitude that lets sunlight into a window during the winter yet is blocked from entering during the summer.

Trigonometry

Right Triangles

Calculate the concentration of sunlight on the ground based on the sun angle above the horizon using the Beam Concentration web app. Extension: Show that the shape of the beam does not matter when analyzing the concentration of sunlight on the ground.

Trig Functions

Calculate the time of the Sun’s position in the sky using the Time Declination Circle web app.

Identify the Sine Curve from a Graph

Use the Solar Declination app to calculate the sine curve of the daily solar declination. Extension: Plot your equation using Google Sheets or Desmos to compare to the one on the web page. Tip: Use the Julian date calendar for non-leap years.

Vectors

Introduction

There is quite a bit on vectors, starting with the introduction.

Magnitude & Direction and Vector Components

Vectors web app – Conceptually and mathematically go between magnitude and direction and vector components in two dimensions. There are two types of activities within the app: 1) Explore, 2) Practice in which all practice questions are randomly generated. There two conventions of direction to explore: 1) Trigonometry and 2) Navigation.

Vectors in Three Dimensions

Color Vectors web app – Explore working with vectors in three dimensions while learning about the additive and subtractive color space, RGB and CMY, respectively. Identify color based on the three color components or identify the color components for a given color. There are three types of activities within the app: 1) Explore, 2) Practice, & 3) Quiz in which all practice & quiz questions are randomly generated.

Adding Vectors

Visually Adding Vectors web app – Add two or three vectors graphically with an emphasis on visually seeing how it is done. There are unlimited randomly generated scenarios.

Adding Vectors web app – Mathematically and graphically add two or three vectors. Uses the trigonometry direction convention. There are unlimited randomly generated practice problems.

Balanced Forces web app – Add three or four vectors (graphically or mathematically) to decide if they add to zero or not. There are unlimited randomly generated practice problems.

Using Vectors

The Earth, Wind, and Forces section applies vectors to understand how the wind is created on Earth.

Algebra 2 and Precalculus

Function Transformations:

There two free activities available on the Function Transformations web page.

The first is an app created in Desmos. You may transform any parent function (for example, x is the parent function of linear equations, x² is the parent function of quadratic equations, and sin x is the parent function of all sine functions). The app is found in the section labeled “Features of a Graph of a Function.”

The next is an app, called the Transformations app (I know, original… but at least it is highlighted by a blue/green button!) that allows you to

explore function transformations of a simple two-linear segment function,
practice identifying what variables are being used to the transformation (which 1, 2, or 3 of the four coefficients are involved),
quiz yourself, but now you must identify the value of each coefficient involved (similar options to the practice options plus a fourth, in which any combination of the four coefficients may be involved).

All of the practice and quiz activities use randomly generated scenarios, so you cannot run out of problems to try! Plus, each answer you submit has visual and written feedback on how you did and what the correct answer is symbolically and looks like graphically.

The app starts by developing your conceptual understanding and works toward building your mathematical understanding of function transformations.

Calculus

Derivatives

Once the sine curve has been identified (see the Trigonometry activity above), calculate the slope of a sine curve using the Solar Declination web app at Extension: Create a Google Sheet and compare your calculations to slopes based on +/- 1 day using the sine curve.

Integration

Using the Earth Illumination web app, calculate the percent of the illuminated or shadowed northern/southern hemisphere for a given day of the year. Check values with those shown in the app.