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.

In this video segment from Cyberchase, Inez estimates whether she has enough jelly beans in her large container to decorate all of the cookies in her batch.

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 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.

You are an employee of Green Valley Dairy and your job is to determine the mass of the company’s corn silage pile. Your boss knows that this pile is the limiting factor as to whether or not he can add animals to the herd. He is contemplating adding 500 head of cattle and needs to make sure there is enough feed in storage before they make the expansion...don’t mess up your measurements and calculations, as this is pivotal information.

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.

A lesson plan for 4th grade science. Kids create a version of the marble roll project to simulate a manufacturing process.

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.

As written, this problem gives students all of the information they need to estimate the thickness of a soda can.

his is a version of ''How thick is a soda can I'' which allows students to work independently and think about how they can determine how thick a soda can is. The teacher should explain clearly that the goal of this task is to come up with an ''indirect'' means of assessing how thick the can is, that is directly measuring its thickness is not allowed.

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match.

These problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.