# Middle Level Math

Making Math Stick at the Middle Level through Hands-On Learning

### Top Math Categories

#### Curriculum Titles

OVERVIEW
In Astronomy, students learn about the solar system and their relationship to it from a mathematical perspective. They investigate the Sun-Moon-Earth system and the characteristics, sizes, and distances of planets in the solar system. They construct a small refracting telescope and learn how it functions. They explore gravity and orbits, distinguish between weight and mass, and relate the kinetic energy equation to crater impacts.

STUDENT OBJECTIVES

• Use a planetarium model to investigate Sun-Moon-Earth movements.
• Relate gravity to orbits and distinguish between circular and elliptical orbits.
• Distinguish between weight and mass.
• Use the equation F = ma to calculate force, given mass.
• Learn the characteristics of the Sun and planets.
• Develop scale models comparing sizes and distances in the solar system.
• Explain the differences between reflecting and refracting optical telescopes and calculate magnification.
• Understand the kinetic energy equation KE = 1/2 mv² and relate it to crater impacts.
• Express solar system distances in scientific notation.

ACTIVITIES
Students complete three performance assessments: 1) Planetary Motions – use the planetarium model to explain Earth’s rotation and revolution, day-night cycles, seasons, and tides; 2) Planetary Distance – develop a scale model of solar system distances and calculate distances using both scientific notation and astronomical units; and 3) Telescopes – identify the parts of a refracting telescope, explain functions of its lenses, define focal length, and explain its relationship to magnification.

OVERVIEW

In this MATH Expedition, students analyze data concerning population growth and available resources for a fictional city. They create and graph linear and exponential functions from the data to determine trends.

ESSENTIAL QUESTION

How do population growth, employment growth, and resource availability affect people’s decisions in relocating to an urban setting?

OVERVIEW
In BioEngineering, students explore topics related to kinesiology and sports performance. They cover mathematical concepts including measuring and classifying angles, absolute values, positive and negative rational numbers, data collection, and simple algebra. Students perform flexibility tests, take digital images of the tests, and use the computer to analyze their flexibility.

STUDENT OBJECTIVES

• Practice absolute value, number lines, and positive and negative numbers.
• Measure, classify, and identify angles using a protractor, a goniometer, a digital camera, and imaging software.
• Gather, graph, and interpret data on projectiles, relating angle size to distance achieved.
• Relate angle measurement to physical therapy, physical fitness, and sports performance.

ACTIVITIES

Students complete three performance assessments: 1) Projectile Data – estimate and justify the best angle from which to release a projectile in order to achieve a maximum distance; 2) Measure Body Angles – demonstrate and explain how to measure a joint angle using both a goniometer and a protractor; and 3) Angle Analysis – explain how angles apply to the function of the flexibility tester and identify the angle of joint ROM required in order to achieve maximum reach.

OVERVIEW

In the Building with Patterns MATH Expedition, students examine patterns used to build and design tetrahedron and box kites. The patterns include both physical and economic models that are associated with building both styles of kites. Students build a base model and then expand the model to more complex arrangements.

ESSENTIAL QUESTION

How can functions help investors make wise decisions?

OVERVIEW

In the Built to Last MATH Expedition, students work as chief engineers of a high-rise construction project that is having to make adjustments to the project due to earthquake concerns.

ESSENTIAL QUESTION

What ways can math be used to predict how best to maintain safety while minimizing costs in building construction?

OVERVIEW

In this MATH Expedition, students compete as designers of bungee cords, using rubber band chains as their bungee cords. The students create three bungee cords: one that will allow for the fewest measurable bounces of a mass, one that will allow for the greatest number of measurable bounces of a mass, and one that will allow for a mass to come closest to the ground without any part of the mass touching the ground. To create the best design in each category, the students conduct a series of tests on several types of rubber bands. Then, they graph and analyze their data to determine any linear or exponential relationships.

ESSENTIAL QUESTION

What can make a regular bungee jump even more exciting?

OVERVIEW
Are you curious how chemists determine what to put together and just what quantity to use when making things such as perfume or medicine? In Chemical Math, students see the math that chemists use on a daily basis. Students balance equations, solve inequalities, use scientific notation, and learn basic chemistry concepts. Students use Avogadro’s number and create Lewis dot structures of atoms. In Chemical Math, the numbers behind chemistry are the focus.

STUDENT OBJECTIVES

• Locate melting points on a number line.
• Calculate and compare densities of different substances.
• Learn the structure of an atom and of the periodic table.
• Express sizes of atoms and atom components using scientific notation.
• Calculate atomic mass based on isotope percentages.
• Explore the mole concept and Avogadro’s number.
• Translate and solve algebraic expressions involving masses and moles of substances.
• Explore and solve examples of one- and two-step equations used in chemistry.
• Evaluate serial dilutions using inequalities.

ACTIVITIES
Students complete three performance assessments: 1) Scientific Notation – explain the structure of an atom, show a number in correct scientific notation, convert a given number to scientific notation, and explain the use of scientific notation in chemistry; 2) Balancing Equations – define equation and give an example, explain chemical equations, and balance a given equation; and 3) Solving Equations – solve given equations, solve given inequalities, and explain the process of serial dilution.

OVERVIEW

In this MATH Expedition, students design a competitive and fair dragster competition. Throughout the Expedition, students use measurement and units to guide them as they decide on rules for the competition, what kind of design specifications or constraints to place on the dragsters, how winners will be determined, and how race results will be communicated. Several experiments with the AP Mini Dragster and its launch system are conducted. Students use the data from these experiments to determine appropriate units for measurement and use dimensional analysis to convert units from one measurement system to another. Students also investigate the roles that accuracy and precision play in making the competition fair for all participants.

ESSENTIAL QUESTION

What factors contribute to the design of a competitive, yet fair, competition?