This task uses student generated data to assess standard 7.SP.7. This task could also be extended to address Standard 7.SP.1 by adding a small or whole class discussion of whether the class could be considered as a representative sample of all students at your school.

The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.

These two fraction division tasks use the same context and ask ŇHow much in one group?Ó but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.

This task gives children an opportunity to subtract a three-digit number including a zero that requires regrouping. The solutions show how students can solve this problem before they have learned the traditional algorithm.

In this lesson and its associated activity, students conduct a simple test to determine how many drops of each of three liquids can be placed on a penny before spilling over. The three liquids are water, rubbing alcohol, and vegetable oil; because of their different surface tensions, more water can be piled on top of a penny than either of the other two liquids. However, this is not the main point of the activity. Instead, students are asked to come up with an explanation for their observations about the different amounts of liquids a penny can hold. In other words, they are asked to make hypotheses that explain their observations, and because middle school students are not likely to have prior knowledge of the property of surface tension, their hypotheses are not likely to include this idea. Then they are asked to come up with ways to test their hypotheses, although they do not need to actually test their hypotheses. The important points for students to realize are that 1) the tests they devise must fit their hypotheses, and 2) the hypotheses they come up with must be testable in order to be useful.

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

In this problem, the variables a,b,c, and d are introduced to represent important quantities for this esimate: students should all understand where the formula in the solution for the number of leaves comes from. Estimating the values of these variables is much trickier and the teacher should expect and allow a wide range of variation here.

This task requires students to find linear equations with different numbers of solutions.

Students will study through investigation the effects of light pollution on night sky observation. They will share their results and suggest improvement within the community.

In this lesson, we learn how insects can fly in the rain. The objective is to calculate the impact forces of raindrops on flying mosquitoes. Students will gain experience with using Newton's laws, gathering data from videos and graphs, and most importantly, the utility of making approximations. No calculus will be used in this lesson, but familiarity with torque and force balances is suggested. No calculators will be needed, but students should have pencil and paper to make estimations and, if possible, copies of the graphs provided with the lesson. Between lessons, students are recommended to discuss the assignments with their neighbors.

Students investigate how mountains are formed. Concepts include the composition and structure of the Earth's tectonic plates and tectonic plate boundaries, with an emphasis on plate convergence as it relates to mountain formation. Students learn that geotechnical engineers design technologies to measure movement of tectonic plates and mountain formation, as well as design to alter the mountain environment to create safe and dependable roadways and tunnels.

Students relate thermal energy to heat capacity by comparing the heat capacities of different materials and graphing the change in temperature over time for a specific material. Students learn why heat capacity is an important property of thermal energy that engineers use in many applications.

The purpose of this task is to help students see the connection between aÖb and ab in a particular concrete example. The relationship between the division problem 3Ö8 and the fraction 3/8 is actually very subtle.

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.

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.

Pennies have a monetary face value of one cent, but they are made of material that has a market value that is usually different. It is the value of the materials that requires attention in this problem. While it is interesting to compare the face value with the value of the materials, this does not have any bearing on the calculations. Interference between these two notions of value is a possible area of difficulty for some students.

Students follow weather forecasts to gauge their accuracy and produce a weather report for the class. They develop skills of observation, recording and reporting.

Michael Pflug, the K-12 STEAM Curriculum Designer for Prosper ISD believes that learners must be put in situations that replicate what they will be doing in the real world. “The way our society is going we need to prepare students with technical skills and prepare them for all post-secondary options. Project Based Learning (PBL) does that.

In this lesson, students will learn about types of land use by humans and evaluate the ways land is used in their local community. They will also consider the environmental effects of the different types of land use. Students will assume the role of community planning engineers and will create a future plan for their community. (Note: Teachers will need to check out the following book from the local or school library: Durell, Ann, Craighead George, Jean, and Paterson, Katherine. The Big Book For Our Planet, New York: Dutton Children's Books, 1993).