In this activity using a balance scale students practice weighing items to see how heavy they are. Cubes are used in the balance as units of measure so students may easily count them.

Use an astrolabe to measure the height of objects, and see seasonal changes over time.

Spreadsheets Across the Curriculum module. Students build spreadsheets to calculate the edge length of cubes and diameter of spheres of various rocks starting with their mineralogic composition.

Spreadsheets Across the Curriculum module. Students calculate the volume of the Great Pyramid and, following Napoleon, estimate whether its volume is large enough to make a wall around France.

Students work in pairs to measure length by lining up cubes along the longest side of an item. They count and record length by counting the number of cubes.

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.

This is a lesson about representative sampling. When given parts of the Hubble Deep Field image, learners will count the number of galaxies in one sample section of the image. Then, they will calculate how many galaxies there are in each whole image and how many objects the Hubble Space Telescope could see in the entire Universe. This is Activity H-6 of Universe at Your Fingertips 2.0: A Collection of Activities and Resources for Teaching Astronomy DVD-ROM, which is available for purchase.

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 activity focuses on the role of photosynthesis in a sustainable future. Students explore the effect of photosynthesis and respiration in a 'closed systems' containing plankton, marine plants, and fish. By calculating carbon dioxide uptake and production in these systems, they predict a plant: animal ratio sufficient to maintain a system in carbon dioxide 'balance' for one hour.

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

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.

Spreadsheets Across the Curriculum module/Geology of National Parks course. Students calculate an answer from a bathymetric map by summing volumes of vertical prisms.

This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids and a simple question concerning the amount of work involved in pumping water out of two full containers having the same shape and size but different spatial orientations.

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.