Mathematical discoveries happen every day. PEMDAS wasn’t even a thing until the 1900s! In this K12 Teaching Moment, our host, David, will walk you through the order of operations and how it became standardized across the world.

Scroll down to see the answer and how it is solved...


How to Solve: 20 − 5 ÷ (2+3)
Step 1: Solve what is in the parentheses (PEMDAS) first, so 2+3 = 5
Now the equation is 20 – 5 ÷ 5
Step 2: Do the division (PEMDAS), so 5 ÷ 5 = 1
Now the equation is 20 – 1
Step 3: Subtract the final numbers (PEMDAS), so 20 – 1 =19
And the answer is 19!

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Student teams act as engineers and learn about systems thinking and scale by reassembling the separated pages of the engaging picture book, “Zoom,” by Istvan Banyai. The book is a series of 31 wordless pictures that start very close-up and then zoom out—from a rooster’s comb to outer space. Like a movie camera, each subsequent page pulls back to reveal the context of the previous scene as something different than what you originally thought. When the 31 un-numbered pages are jumbled, it is a surprising challenge for teams to figure out how the pictures connect. The task prompts students to pause and look closer so as to adjust to new points of view and problem solve to find a logical sequence. It requires them to step back and take a broader view. Students learn that engineers work together as teams and look at things very closely so that they see different things and come up with more than one solution when problem solving. To conclude, students go outside and practice their skills by imagining and then drawing their own Zoom-like small booklet stories inspired by items found in nature. The classic duck/rabbit ambiguous drawing is provided as a kickoff visual aid.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music: Aimless Amos

Students learn a simple technique for quantifying the amount of photosynthesis that occurs in a given period of time, using a common water plant (Elodea). They use this technique to compare the amounts of photosynthesis that occur under conditions of low and high light levels. Before they begin the experiment, however, students must come up with a well-worded hypothesis to be tested. After running the experiment, students pool their data to get a large sample size, determine the measures of central tendency of the class data, and then graph and interpret the results.

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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more!

Music: Jessica- Joey Pecoraro

What do plants need? Students examine the effects of light and air on green plants, learning the processes of photosynthesis and transpiration. Student teams plant seeds, placing some in sunlight and others in darkness. They make predictions about the outcomes and record ongoing observations of the condition of the stems, leaves and roots. Then, several healthy plants are placed in glass jars with lids overnight. Condensation forms, illustrating the process of transpiration, or the release of moisture to the atmosphere by plants.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

View the full activity on TeachEngineering:
https://www.teachengineering.o....rg/activities/view/c

TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music: Believer

Students create models of objects of their choice, giving them skills and practice in techniques used by professionals. They make sketches as they build their objects. This activity facilitates a discussion on models and their usefulness.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music - Tyler Kimbell

Reduce, reuse, recycle—engineer! In this activity that focuses on environmental awareness, students research and read books about various items and buildings made from recycled or reused materials. They then plan, design, and construct a storage space for an individual snack using the engineering design process. They consider key elements such as temperature control, budget, materials, and size.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

View the full activity on TeachEngineering:
https://www.teachengineering.o....rg/activities/view/u

TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music: Epidermis the Sun Really Shines

Can you communicate without electricity? In this activity, students explore a problem in which a school’s power has gone out and they need to deliver an important message to a neighboring first grade classroom. However, they must stay within the following constraints: they cannot use cell phones and they have to stay in their classroom while doing so. Students research and use a variety of tools and materials to build, test, and retest a device that communicates sound the most clearly while learning about and demonstrating how sound causes vibrations.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

View the full activity on TeachEngineering:
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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music:

Students control small electric motors with Arduino microcontrollers to make simple sticky-note spinning fans and then explore other variations of basic motor systems. Through this exercise, students create circuits that include transistors acting as switches. They alter and experiment with given basic motor code, learning about the Arduino analogWrite command and pulse width modulation (PWM). Students learn the motor system nuances that enable them to create their own motor-controlled projects. They are challenged to make their motor systems respond to temperature or light, to control speed with knob or soft potentiometers, and/or make their motors go in reverse (using a motor driver shield or an H-bridge). Electric motors are used extensively in industrial and consumer products and the fundamental principles that students learn can be applied to motors of all shapes and sizes.

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TeachEngineering has over 1,500 FREE lessons and activities. Visit http://www.TeachEngineering.org for more!


Music: Fuggetaboutit

Student groups construct simple conductivity probes and then integrate them into two different circuits to test the probe behavior in solutions of varying conductivity (salt water, sugar water, distilled water, tap water). The activity culminates with student-designed experiments that utilize the constructed probes. The focus is to introduce students to the fabrication of the probe and expose them to two different ways to integrate the probe to obtain qualitative and quantitative measurements, while considering the application and utility of a conductivity probe within an engineering context. A provided handout guides teams through the process: background reading and questions; probe fabrication including soldering; probe testing and data gathering (including circuit creation on breadboard); probe connection to Arduino (including circuit creation and code entry) and a second round of testing and data gathering; design and conduct their own lab experiments that use the probes; online electrolyte/non-electrolyte reading, short video, comprehension check and analysis questions.

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https://www.teachengineering.o....rg/activities/view/n

TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more!

Music: Go To Town - Silent Partner

Students investigate how sound travels through string and air. First, they analyze the sound waves with a paper cup attached to a string. Then, they combine the string and cup with a partner to model a string telephone. Finally, they are given a design challenge to redesign the string telephone for distance. They think about their model as it compares a modern telephone and the impact the invention of the telephone has had on society.

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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

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Students learn how paper is made. Working together, student teams make their own paper. This activity introduces students to recycling; what it is, its value and benefits, and how it affects their lives.

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https://www.teachengineering.o....rg/activities/view/m
TeachEngineering has over 1,500 FREE lessons and activities. Visit http://www.TeachEngineering.org for more!

Music: Coffee Stains - Riot

Students learn how the force of water helps determine the size and shape of dams. They use clay to build models of four types of dams, and observe the force of the water against each type. They conclude by deciding which type of dam they, as Splash Engineering engineers, will design for Thirsty County.

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TeachEngineering has over 1,500 FREE lessons and activities. Visit http://www.TeachEngineering.org for more!

Music: Splashing Around - The Green Orbs

We design and create objects to make our lives easier and more comfortable. The houses in which we live are excellent examples of this. Depending on your local climate, the features of your house have been designed to satisfy your particular environmental needs: protection from hot, cold, windy and/or rainy weather. In this activity, students design and build model houses, then test them against various climate elements, and then re-design and improve them. Using books, websites and photos, students learn about the different types of roofs found on various houses in different environments throughout the world.

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TeachEngineering has over 1,500 FREE lessons and activities.
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Music: Why did you do it- Everet Almond

Students practice the initial steps involved in an engineering design challenge. They begin by reviewing the steps of the engineering design loop and discussing the client need for the project. Next, they identify a relevant context, define the problem within their design teams, and examine the project's requirements and constraints. (Note: Conduct this activity in the context of a design project that students are working on, which could be a challenge determined by the teacher, brainstormed with the class, or the example project challenge provided [to design a prosthetic arm that can perform a mechanical function].)

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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

music - Dream of A Day

Students are introduced to renewable energy, including its relevance and importance to our current and future world. They learn the mechanics of how wind turbines convert wind energy into electrical energy and the concepts of lift and drag. Then they apply real-world technical tools and techniques to design their own aerodynamic wind turbines that efficiently harvest the most wind energy. Specifically, teams each design a wind turbine propeller attachment. They sketch rotor blade ideas, create CAD drawings (using Google SketchUp) of the best designs and make them come to life by fabricating them on a 3D printer. They attach, test and analyze different versions and/or configurations using a LEGO wind turbine, fan and an energy meter. At activity end, students discuss their results and the most successful designs, the aerodynamics characteristics affecting a wind turbine's ability to efficiently harvest wind energy, and ideas for improvement. The activity is suitable for a class/team competition. Example 3D rotor blade designs are provided.

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Music: Straighty Baby - Audionautix

Straighty Baby by Audionautix is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Artist: http://audionautix.com/

Posed with a paradigmatic engineering problem, students consider and explore mathematical algorithms and/or geometric concepts to devise possible solutions. The problem: How should a robotic vacuum move in order to best clean a floor of unknown shape and dimensions? They grapple with what could be a complex problem by brainstorming ideas, presenting the best idea for a solution and analyzing all presented solutions, and then are introduced to an elegant solution. Rather than elaborately calculating the most efficient route and keeping track of which tiles the robot has visited, a random number generator determines which direction the robot will take when it hits a barrier. Students are able to visually confirm how an unfamiliar programming concept (a random number generator) can make for a simple and efficient program that causes an EV3 robot (that is suitably equipped) to clean a bare floor. Then students think of other uses for random numbers.

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TeachEngineering has over 1,500 FREE lessons and activities. Visit http://www.TeachEngineering.org for more!

Music: London Bayou - ALBIS

Students learn about various natural hazards and specific methods engineers use to prevent these hazards from becoming natural disasters. They study a hypothetical map of an area covered with natural hazards and decide where to place natural disaster prevention devices by applying their critical thinking skills and an understanding of the causes of natural disasters.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

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TeachEngineering has over 1,500 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music: EDM Detection Mode

Continuing the Asteroid Impact challenge, student teams test rocks to identify their physical properties such as luster, hardness, color, etc., and classify them as igneous, metamorphic or sedimentary. They complete a data table to record all of the rock properties, and then answer worksheet questions to deepen their understanding of rock properties and relate them to the cavern design problem.

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TeachEngineering has over 1,900 FREE lessons and activities. Visit https://www.teachengineering.org/ for more

Music: Elite_Syncopations
By: E's Jammy Jams