Students will: Predict the kinetic and potential energy of objects Design a skate park Examine how kinetic and potential energy interact with each other

As science extension activities, this book of problems introduces students to mapping the shape of the Milky Way galaxy, and how to identify the various kinds of galaxies in our universe. Students also learn about the shapes and sizes of other galaxies in our universe as they learn how to classify them. The math problems cover basic scientific notation skills and how they apply to working with astronomically large numbers. It also provides exercises in plotting points on a Cartesian plane to map the various features of our Milky Way.

Challenge first graders with math problems that will help them master first-grade math skills! In first grade, students learn about money, time, measurements, and patterns. Building a solid number sense is important for students in this age range. First graders learn to recognize patterns and sort objects by color, shape, and function. They will also learn to recognize and differentiate between two-dimensional and three-dimensional geometric shapes like squares, triangles, cones, and cylinders. By the end of first grade, students should be able to count to one hundred by ones, twos, fives, and tens. They will also be introduced to the concepts of more and less, and have an opportunity to work with simple graphs.

Now that your child has mastered numbers and counting, it's time to take things to the next level with our first-grade math worksheets! Keep students' math minds sharp with daily first-grade math and critical thinking practice worksheets as well as daily homework and practice pages. Weekly word problems, first-grade algebra and geometry, counting and comparing numbers, and introduction to addition are just some of the engaging, no-prep first-grade math worksheets available on this page.

Students learn how to use and graph real-world stream gage data to create event and annual hydrographs and calculate flood frequency statistics. Using an Excel spreadsheet of real-world event, annual and peak streamflow data, they manipulate the data (converting units, sorting, ranking, plotting), solve problems using equations, and calculate return periods and probabilities. Prompted by worksheet questions, they analyze the runoff data as engineers would. Students learn how hydrographs help engineers make decisions and recommendations to community stakeholders concerning water resources and flooding.

Students learn about four forms of equations: direct variation, slope-intercept form, standard form and point-slope form. They graph and complete problem sets for each, converting from one form of equation to another, and learning the benefits and uses of each.

Play with functions while you ponder Art History. Explore geometric transformations and transform your thinking about linear functions, then have fun figuring out the mystery functions!

In this open-ended, hands-on activity that provides practice in engineering data analysis, students are given gait signature metric (GSM) data for known people types (adults and children). Working in teams, they analyze the data and develop models that they believe represent the data. They test their models against similar, but unknown (to the students) data to see how accurate their models are in predicting adult vs. child human subjects given known GSM data. They manipulate and graph data in Excel® to conduct their analyses.

Student teams use sensors—motion detectors and accelerometers—to collect walking gait data from group members. They import their collected position and acceleration data into Excel® for graphing and analysis to discover the relationships between position, velocity and acceleration in the walking gaits. Then they apply their understanding of slopes of secant lines and Riemann sums to generate and graph additional data. These activities provide practice in the data collection and analysis of systems, similar to the work of real-world engineers.

Game Over Gopher is an exciting tower defense game that guides students in plotting coordinate pairs, differentiating negative coordinates from positive coordinates, and identifying the four quadrants. Hungry space gophers are marching towards a prize carrot, and to defend it players place tools around the coordinate grid to “feed” gophers and make them lose interest. Ruby mines (which must be placed at designated x, y coordinates) yield currency that players spend to strategically place carrot launchers, garlic rays, corn silos, and beet traps – gopher feeding tools. To introduce students to the coordinate grid, Game Over Gopher introduces new skills via interactive tutorials and uses consistent visual clues (e.g., x red, y blue) to guide players in plotting coordinates. This means it’s not necessary to teach students coordinate plotting ahead of time. As the levels progress, the number of tools available increases, the level of math vocabulary increases, the scale of the grid changes, and players are asked to expand their mastery of the grid by reflecting points across axes. The game lowers intimidation about the coordinate grid, helps students understand how positive and negative numbers reflect each other across the axes, and helps students get comfortable with the four quadrants.

These games support student development of spatial sense and foster familiarity with the mathematical vocabulary of geometry.

Gingerbread men and gingerbread houses enjoy special popularity around the holidays, but many of these gingerbread activities are timeless and complement literature titles that teachers use at the beginning of school or after the holidays. It's very easy to incorporate mathematics into a study of gingerbread men, and students will enjoy the data collection activities and games while learning math skills and deepening their understanding of important mathematical concepts. Look through these math activities and add some to your repertoire. Consider broadening the gingerbread math to include measurement, games and problem solving this year.

Students learn about an important characteristic of lines: their slopes. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero or undefined. Students get an explanation of when and how these different types of slope occur. Finally, they learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.

The students will be able to identify questions and concepts in the ability to construct accurate graphs, recognize and analyze alternative explanations and models by the end of this activity.

Give students the graphing template.
Play any of the videos.
Have students graph the story!

Types of graphing includes: constant, decreasing, increasing, linear, parabolic, periodic, piecewise, step.

Students are introduced to different ways of displaying visual spectra, including colored "barcode" spectra, like those produced by a diffraction grating, and line plots displaying intensity versus color, or wavelength. Students learn that a diffraction grating acts like a prism, bending light into its component colors.

In a multi-week experiment, student groups gather data from the photobioreactors that they build to investigate growth conditions that make algae thrive best. Using plastic soda bottles, pond water and fish tank aerators, they vary the amount of carbon dioxide (or nutrients or sunlight, as an extension) available to the microalgae. They compare growth in aerated vs. non-aerated conditions. They measure growth by comparing the color of their algae cultures in the bottles to a color indicator scale. Then they graph and analyze the collected data to see which had the fastest growth. Students learn how plants biorecycle carbon dioxide into organic carbon (part of the carbon cycle) and how engineers apply their understanding of this process to maximize biofuel production.

Kindergartners measure each other's height using large building blocks, then visit a 2nd and a 4th grade class to measure those students. They can also measure adults in the school community. Results are displayed in age-appropriate bar graphs (paper cut-outs of miniature building blocks glued on paper to form a bar graph) comparing the different age groups. The activities that comprise this lesson help students develop the concepts and vocabulary to describe, in a non-ambiguous way, how height changes as children get older. The introduction to graphing provides an important foundation for both creating and interpreting graphs in future years.

Gait analysis is the study of human motion that can be utilized as biometric information or identification, for medical diagnostics or for comparative biomechanics. In this activity, students observe walking human subjects and then discuss parameters that could be used to characterize walking gaits. They use accelerometers to collect and graph acceleration vs. time data that can help in gait analysis—all part of practicing the engineering data analysis process. Students complete this activity before learning the material presented in the associated lesson.