Develop a solid understanding of the manipulation of expressions to produce equivalent expressions. Given an expression, pupils rearrange it to create a new one. Their new functions must match the structure of the model expressions.

Examine and compare a linear and step function. The task provides two scenarios, one modeled by a linear function and the other a step function. Pupils create a graph for each and explain how each compares to the other.

Demonstrate linear and quadratic functions through contextual modeling. Young mathematicians explore both types of functions by analyzing their key features. They then relate these key features to the contextual relationship the function...

Model an oil spill cleanup. An engaging engineering lesson has groups using aerogels to simulate an oil spill cleanup (vegetable oil in water). Along the way, they learn about nanotechnology and hydrophilia/hydrophobia.

Develop a model of a wastewater treatment center. The last activity of the unit has pupils mix a lake water sample into a tank of water containing fertilizers. Over time, the algae from the lake water grows and removes the nutrient-rich...

Determine how cup stacking relates to linear equations. Pupils stack cups and record the heights. Using the data collected, learners develop a linear equation that models the height. The scholars then interpret the slope and the...

Explore the behavior of light waves with a lab activity. Scholars build new vocabulary through experimentation and observation. Using different mediums, they model reflection, refraction, transmission, diffusion, and scattering of light.

Rumor has it that an exponential can be undone. After playing a rumor game to model exponential growth, pupils learn about undoing exponential functions. They use the definition of the logarithm to convert exponential equations to...

Two vehicles move at a constant rate of speed toward each other, but when exactly will they pass? Pupils use still images from a video to determine the rate of speed and when the two cars meet. Then, they watch the complete video to...

Test mathematicians' knowledge of adding fractions with a brief assessment that challenges them to play teacher while correcting a peer's work. Scholars examine Carl's mathematical response, identify where he went wrong,...

No vacuum cleaner? No problem, just build your own. Scholars apply knowledge of currents to build a model of either a vacuum clear, a hair dryer, or a toy car. While the class completes the activity, instructors consider gender...

Hard boiled or raw? Which egg will you get? A hands-on activity has scholars explore the impact of conditional probability. Based on a skit from the Tonight Show, pupils model the selection of the two types of eggs using beads. They...

Going on up—and up and up! An open-ended task asks learners to model the movement of an amusement ride with parametric equations. They then analyze their equations to determine how the shadow of the ride's car moves as it rises at a...

Writing a general rule to model a specific pattern is a high-level skill. Your classes practice the important skill as they write rules describing the solutions to a system of equations with variable coefficients. As an added challenge,...

Take a dive into a three-dimensional task. Given a specific surface area, individuals must maximize the volume of a cylindrical swimming pool. They combine their understanding of surface area and volume to create a cubic function that...

How do you know if your pupils have a deep understanding of proportional relationships? Assessment is key! A helpful series starts with questions on proportional relationships modeled after the Smarter Balanced Assessment items....

Scholars become detectives and use science to solve a crime! A complete unit introduces DNA and includes hands-on activities that have learners model DNA and extract it from different food types. A culminating activity challenges...

Young scholars create a scale model to a castle using the dimensions they were given. They calculate the surface areas and volumes of each section of their castle.

Students explore the concept of graph theory. In this graph theory activity, students participate in hands-on activities that enforce graph theory. Students manipulate graph applets on the internet. Students create a graphical model...

students emulate a real world problem and model it with mathematics working in a small group. Observe and facilitate discussion as the groups use various strategies, such as (graphs, brainstorming, tables, and dialogue.

In this mathematics worksheet, students apply dimensional analysis to solving each problem. They identify the conversion factor and describe a unique characteristic of a conversion factor. Students also identify the unit in the final...

Second graders use physical models to represent and demonstrate place value concepts by using base-ten blocks and hundreds charts. They compare numbers to see which number is smaller or larger and put numbers in order from smallest to...

Students explore physics. They investigate the strategies used by an engineer to solve a problem. Students construct various models to solve the problem. They display their solutions and explain how they solved the problem.

Students practice representing problems found in the real world in terms that can be translated into mathematical expressions. The situations are represented in tables and graphs by students.