Learn about conservation of energy with a skater dude! Build tracks, ramps ...

Learn about conservation of energy with a skater dude! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. You can also take the skater to different planets or even space!

During this two-day lesson, students work with a partner to create and ...

During this two-day lesson, students work with a partner to create and implement a problem-solving plan based on the mathematical concepts of rates, ratios, and proportionality. Students analyze the relationship between different-sized gummy bears to solve problems involving size and price.Key ConceptsThroughout this unit, students are encouraged to apply the mathematical concepts they have learned over the course of this year to new settings. Helping students develop and refine these problem solving skills:Creating a problem solving plan and implementing their plan systematicallyPersevering through challenging problems to find solutionsRecalling prior knowledge and applying that knowledge to new situationsMaking connections between previous learning and real-world problemsCommunicating their approaches with precision and articulating why their strategies and solutions are reasonableCreating efficacy and confidence in solving challenging problems in a real worldGoals and Learning ObjectivesCreate and implement a problem-solving plan.Organize and interpret data presented in a problem situation.Analyze the relationship between two variables.Use ratios.Write and solve proportions.Create rate tables to organize data and make predictionsUse multiple representations—including tables, graphs, and equations—to organize and communicate data.Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

This lesson unit is intended to help you assess how well students ...

This lesson unit is intended to help you assess how well students are able to: Perform arithmetic operations, including those involving whole-number exponents, recognizing and applying the conventional order of operations; Write and evaluate numerical expressions from diagrammatic representations and be able to identify equivalent expressions; apply the distributive and commutative properties appropriately; and use the method for finding areas of compound rectangles.

Students conduct experiments to determine what environmental factors favor decomposition by soil ...

Students conduct experiments to determine what environmental factors favor decomposition by soil microbes. They use chunks of carrots for the materials to be decomposed, and their experiments are carried out in plastic bags filled with dirt. Every few days students remove the carrots from the dirt and weigh them. Depending on the experimental conditions, after a few weeks most of the carrots have decomposed completely.

This activity simulates the extraction of limited, nonrenewable resources from a "mine," ...

This activity simulates the extraction of limited, nonrenewable resources from a "mine," so students can experience first-hand how resource extraction becomes more difficult over time. Students gather data and graph their results to determine the peak in resource extraction. They learn about the limitations of nonrenewable resources, and how these resources are currently used.

Using plastic straws, wire, batteries and iron nails, student teams build and ...

Using plastic straws, wire, batteries and iron nails, student teams build and test two versions of electromagnets one with and one without an iron nail at its core. They test each magnet's ability pick up loose staples, which reveals the importance of an iron core to the magnet's strength. Students also learn about the prevalence and importance of electromagnets in their everyday lives.

In this math activity, students conduct a strength test using modeling clay, ...

In this math activity, students conduct a strength test using modeling clay, creating their own stress vs. strain graphs, which they compare to typical steel and concrete graphs. They learn the difference between brittle and ductile materials and how understanding the strength of materials, especially steel and concrete, is important for engineers who design bridges and structures.

With the help of simple, teacher-led demonstration activities, students learn the basic ...

With the help of simple, teacher-led demonstration activities, students learn the basic concepts of heat transfer by means of conduction, convection, and radiation. Students then apply these concepts as they work in teams to solve two problems. One problem requires that they maintain the warm temperature of one soda can filled with water at approximately body temperature, and the other problem is to cause an identical soda can of warm water to cool as much as possible during the same thirty-minute time interval. Students design their solutions using only common, everyday materials. They record the water temperatures in their two soda cans every five minutes, and prepare line graphs in order to visually compare their results to the temperature of an unaltered control can of water.

Rate Type of Unit: Concept Prior Knowledge Students should be able to: ...

Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers. Understand quantity as a number used with a unit of measurement. Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities. Understand that a ratio is a comparison of two quantities. Write ratios for problem situations. Make and interpret tables, graphs, and diagrams. Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

During this two-day lesson, students work with a partner to create and ...

During this two-day lesson, students work with a partner to create and implement a problem-solving plan based on the mathematical concepts of rates, ratios, and proportionality. Students analyze the relationship between different-sized gummy bears to solve problems involving size and price.Key ConceptsThroughout this unit, students are encouraged to apply the mathematical concepts they have learned over the course of this year to new settings. Help students develop and refine these problem-solving skills:Creating a problem solving plan and implementing their plan systematicallyPersevering through challenging problems to find solutionsRecalling prior knowledge and applying that knowledge to new situationsMaking connections between previous learning and real-world problemsCommunicating their approaches with precision and articulating why their strategies and solutions are reasonableCreating efficacy and confidence in solving challenging problems in a real worldGoals and Learning ObjectivesCreate and implement a problem-solving plan.Organize and interpret data presented in a problem situation.Analyze the relationship between two variables.Use ratios.Write and solve proportions.Create rate tables to organize data and make predictions.Use multiple representations—including tables, graphs, and equations—to organize and communicate data.Articulate strategies, thought processes, and approaches to solving a problem, and defend why the solution is reasonable.

Most of the flavoring in gum is due to the sugar or ...

Most of the flavoring in gum is due to the sugar or other sweetener it contains. As gum is chewed, the sugar dissolves and is swallowed. After a piece of gum loses its flavor, it can be left to dry at room temperature and then the difference between its initial (unchewed) mass and its chewed mass can be used to calculate the percentage of sugar in the gum. This demonstration experiment is used to generate new questions about gums and their ingredients, and students can then design and execute new experiments based on their own questions.

The earliest explorers did not have computers or satellites to help them ...

The earliest explorers did not have computers or satellites to help them know their exact location. The most accurate tool developed was the sextant to determine latitude and longitude. In this activity, the sextant is introduced and discussed with the class. Students will learn how a sextant can be a reliable tool that is still being used by today's navigators and how computers can help assure accuracy when measuring angles. Also, this activity will show how computers can be used to understand equations even when knowing how to do the math is unknown.

Students conduct an experiment to determine how varying the composition of a ...

Students conduct an experiment to determine how varying the composition of a construction material affects its strength. They make several adobe bricks with differing percentages of sand, soil, fibrous material and water. They test the bricks for strength by dropping them onto a concrete surface from progressively greater heights. Students graph the experiment results and use what they learn to design their own special mix that maximizes the bricks' strength. During the course of the experiment, students learn about variables (independent, dependent, control) and the steps of the engineering design process.

Learn to connect position-time and velocity-time graphs. Explore velocity using an animated ...

Learn to connect position-time and velocity-time graphs. Explore velocity using an animated car icon connected to either a position-time or a velocity-time graph, or both. Then investigate other motion graphs.

Earthquakes happen when forces in the Earth cause violent shaking of the ...

Earthquakes happen when forces in the Earth cause violent shaking of the ground. Earthquakes can be very destructive to buildings and other man-made structures. Design and build various types of buildings, then test your buildings for earthquake resistance using a shake table and a force sensor that measures how hard a force pushes or pulls your building.

In this lesson, students represent quantitative relationships involving rates using tables, graphs, ...

In this lesson, students represent quantitative relationships involving rates using tables, graphs, double number lines, and formulas. Students will understand how to create one such representation when given another representation.Key ConceptsQuantitative relationships involving rates can be represented using tables, graphs, double number lines, and formulas. One such representation can be used to create another representation. Two rates can describe each situation: the rate and its inverse. For the water pump situation, there are two related formulas: a formula for finding the quantity of water pumped for any amount of time, and a formula for finding the amount of time for any quantity of water.Goals and Learning ObjectivesUnderstand that tables, graphs, double number lines, and formulas can be used to represent the same situation.Compare the different representations within a situation and the same representation across similar situations.Understand each representation and how to find the rate in each one.

In this lesson, students use their knowledge of rates, graphs of rates, ...

In this lesson, students use their knowledge of rates, graphs of rates, and formulas to solve problems.Key ConceptsThe formula for a rate is a mathematical way of writing a rule for computing a value. Rate formulas describe a constant relationship between two quantities. Each point on the graph of a rate shows a pair of related values. A graph of a constant rate is a straight line.Goals for Learning ObjectivesUncover any partial understandings and misconceptions students have about rate, graphs of rates, and formulas.Develop a more robust understanding of rate.Help identify which Gallery problems students should work on.

Students create and implement a problem-solving plan to solve another problem involving ...

Students create and implement a problem-solving plan to solve another problem involving the relationship between the sound of thunder and the distance of the lightning.Key ConceptsThroughout this unit, students are encouraged to apply the mathematical concepts they have learned over the course of this year to new settings. Help students develop and refine these problem-solving skills:Creating a problem-solving plan and implementing their plan systematicallyPersevering through challenging problems to find solutionsRecalling prior knowledge and applying that knowledge to new situationsMaking connections between previous learning and real-world problemsCommunicating their approaches with precision and articulating why their strategies and solutions are reasonableCreating efficacy and confidence in solving challenging problems in a real worldGoals and Learning ObjectivesCreate and implement a problem-solving plan.Organize and interpret data presented in a problem situation.Analyze the relationship between two variables.Create a rate table to organize data and make predictions.Apply the relationship between the variables to write a mathematical formula and use the formula to solve problems.Create a graph to display proportional relationships and use this graph to make predictions.Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

Using the same method for measuring friction that was used in the ...

Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct an experiment to determine if weight added incrementally to an object affects the amount of friction encountered when it slides across a flat surface. After graphing the data from their experiments, students can calculate the coefficients of friction between the object and the surface it moved upon, for both static and kinetic friction.

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