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 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.

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.

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.

In this kinesthetic activity, the concept of energy budget is strengthened as students conduct three simulations using play money as units of energy, and students serve as parts of a planetary radiation balance model. Students will determine the energy budget of a planet by manipulating gas concentrations, energy inputs and outputs in the system in this lesson that supports the study of climate on Mars, Mercury, Venus and Earth. The lesson supports understanding of the real-world problem of contemporary climate change. The resource includes a teacher's guide and several student worksheets. This is the second of four activities in the lesson, How do Atmospheres affect planetary temperatures?, within Earth Climate Course: What Determines a Planet's Climate? The resource aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level (e.g, 6.EE.5). By asking students to reason about solutions without explicily solving them, we get at the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.

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.

This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division.

Students set up and run the experiments they designed in the Population Growth in Yeasts associated lesson, using simple yeast-molasses cultures in test tubes. Population growth is indicated by the amount of respiration occurring in the cultures, which in turn is indicated by the growth of carbon dioxide bubbles trapped within the culture tubes. Using this method, students test for a variety of environmental influences, such as temperature, food supply and pH.

Students measure and analyze forces that act on vehicles pulling heavy objects while moving at a constant speed on a frictional surface. They study how the cars interact with their environments through forces, and discover which parameters in the design of the cars and environments could be altered to improve vehicles' pulling power. This LEGO® MINDSTORMS® based activity is geared towards, but not limited to, physics students.

Students play a game in pairs to read and recognize numbers using a 100 chart.