Demos and activities in this lesson are intended to illustrate the basic concepts of energy science -- work, force, energy, power etc. and the relationships among them. The "lecture" portion of the lesson includes many demonstrations to keep students engaged, yet has high expectations for the students to perform energy related calculations and convert units as required. A homework assignment and quiz are used to reinforce and assess these basic engineering science concepts.

Students familiarize themselves — through trial and error — with the basics of GPS receiver operation. They view a receiver's satellite visibility screen as they walk in various directions and monitor their progress on the receiver's map. Students may enter waypoints and use the GPS information to guide them back to specific locations.

The purpose of this lesson is to teach the students about how a spacecraft gets from the surface of the Earth to Mars. The lesson first investigates rockets and how they are able to get us into space. Finally, the nature of an orbit is discussed as well as how orbits enable us to get from planet to planet specifically from Earth to Mars.

Students construct a model roadway with congestion and apply their knowledge of level of service (LOS) to assign a grade to the road conditions. The roadway is simply a track outlined with cones or ropes with a few students walking around it to mimic congestion. The remaining students employ both techniques of density and flow to classify the LOS of the track.

Students use water balloons and a length of string to understand how the force of gravity between two objects and the velocity of a spacecraft can balance to form an orbit. They see that when the velocity becomes too great for gravity to hold the spacecraft in orbit, the object escapes the orbit and travels further away from the planet.

Student teams locate a contaminant spill in a hypothetical site by measuring the pH of soil samples. Then they predict the direction of groundwater flow using mathematical modeling. They also use the engineering design process to come up with alternative treatments for the contaminated water.

The purpose of this activity is to demonstrate some of the different parts of an airplane through the construction of a paper airplane. Students will build several different kinds of paper airplanes in order to figure out what makes an airplane fly and what can be changed to influence the flying characteristics of an airplane.

Students review the electrical appliances used at home and estimate the energy used for each. The results can help to show the energy hogs that could benefit from conservation or improved efficiency.

Students learn about porosity and permeability and relate these concepts to groundwater flow. They use simple materials to conduct a porosity experiment and use the data to understand how environmental engineers decide on the placement and treatment of a drinking water well.

Students keep track of their own water usage for one week, gaining an understanding of how much water is used for various everyday activities. They relate their own water usages to the average residents of imaginary Thirsty County, and calculate the necessary water capacity of a dam that would provide residential water to the community.

Students do work by lifting a known mass over a period of time. The mass and measured distance and time is used to calculate force, work, energy and power in metric units. The students' power is then compared to horse power and the power required to light 60-watt light bulbs.

Students use scaling from real-world data to obtain an idea of the immense size of Mars in relation to the Earth and the Moon, as well as the distances between them. Students calculate dimensions of the scaled versions of the planets, and then use balloons to represent their relative sizes and locations.

This division task asks studnets to consider the conceptual understanding of something usually taught as a rote procedure. To be successful with this task, students must make sense of the procedure and how place value is represented and abbreviated within it.

In past times, ocean navigators tossed a piece of wood over the side of their ships and noted how long until the ship passed the wood. They used this time measurement and the length of the ship to calculate their speed and estimate how far they had traveled. In this activity, students act the part of a GPS signal traveling to the receiver to learn how travel time is converted to distance.

The purpose of this activity is to demonstrate how aircrafts have decreased the amount of time it takes to transport people and cargo. Students will compute the time it takes to travel between two cities for several modes of transportation including trucks, trains and airplanes. Students will also do some critical thinking to determine why airplanes are not always used.

Students are introduced to the correct technical vocabulary for lighting, which is different than layperson's terms. They learn about lamp (light bulb) technology and how to identify the various types of lighting in their spaces. They are also introduced to lighting controls as a means for saving energy- reducing costs, human energy consumption, and greenhouse gas emissions on the environment. Using an accompanying worksheet, students embark on a guided audit in which they survey the lighting in their classroom and identify the potential savings from using controls.

Students take a hands-on look at the design of bridge piers (columns). First they brainstorm types of loads that might affect a Colorado bridge. Then they determine the maximum possible load for that scenario, and calculate the cross-sectional area of a column designed to support that load. Choosing from clay, foam or marshmallows, they create model columns and test their calculations.

Fractions and Decimals

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Multiply and divide whole numbers and decimals.
Multiply a fraction by a whole number.
Multiply a fraction by another fraction.
Write fractions in equivalent forms, including converting between improper fractions and mixed numbers.
Understand the meaning and structure of decimal numbers.

Lesson Flow

This unit extends students’ learning from Grade 5 about operations with fractions and decimals.

The first lesson informally introduces the idea of dividing a fraction by a fraction. Students are challenged to figure out how many times a 14-cup measuring cup must be filled to measure the ingredients in a recipe. Students use a variety of methods, including adding 14 repeatedly until the sum is the desired amount, and drawing a model. In Lesson 2, students focus on dividing a fraction by a whole number. They make a model of the fraction—an area model, bar model, number line, or some other model—and then divide the model into whole numbers of groups. Students also work without a model by looking at the inverse relationship between division and multiplication. Students explore methods for dividing a whole number by a fraction in Lesson 3, for dividing a fraction by a unit fraction in Lesson 4, and for dividing a fraction by another fraction in Lesson 6. Students examine several methods and models for solving such problems, and use models to solve similar problems.

Students apply their learning to real-world contexts in Lesson 6 as they solve word problems that require dividing and multiplying mixed numbers. Lesson 7 is a Gallery lesson in which students choose from a number of problems that reinforce their learning from the previous lessons.

Students review the standard long-division algorithm for dividing whole numbers in Lesson 8. They discuss the different ways that an answer to a whole number division problem can be expressed (as a whole number plus a remainder, as a mixed number, or as a decimal). Students then solve a series of real-world problems that require the same whole number division operation, but have different answers because of how the remainder is interpreted.

Students focus on decimal operations in Lessons 9 and 10. In Lesson 9, they review addition, subtraction, multiplication, and division with decimals. They solve decimal problems using mental math, and then work on a card sort activity in which they must match problems with diagram and solution cards. In Lesson 10, students review the algorithms for the four basic decimal operations, and use estimation or other methods to place the decimal points in products and quotients. They solve multistep word problems involving decimal operations.

In Lesson 11, students explore whether multiplication always results in a greater number and whether division always results in a smaller number. They work on a Self Check problem in which they apply what they have learned to a real-world problem. Students consolidate their learning in Lesson 12 by critiquing and improving their work on the Self Check problem from the previous lesson. The unit ends with a second set of Gallery problems that students complete over two lessons.

Students review the standard long-division algorithm and discuss the different ways the answer to a whole-number division problem can be expressed (as a whole number plus a remainder, as a mixed number, or as a decimal).Students solve a series of real-world problems that require the same whole number division operation, but have different answers because of how the remainder is interpreted.Key ConceptsStudents have been dividing multidigit whole numbers since Grade 4. By the end of Grade 6, they are expected to be fluent with the standard long-division algorithm. In this lesson, this algorithm is reviewed along with the various ways of expressing the answer to a long division problem. Students will have more opportunities to practice the algorithm in the Exercises.Goals and Learning ObjectivesReview and practice the standard long-division algorithm.Answer a real-world word problem that involves division in a way that makes sense in the context of the problem.