The activities in this 6-lesson unit use fish-shaped crackers to help students develop their understanding of comparative subtraction by exploring five meanings of subtraction (counting, sets, number line, balance, and inverse of addition). Students investigate properties of subtraction, represent subtraction with objects and pictures, record subtraction with vertical notation and equations, create and solve problems, and carry out missing addend activities. Lessons include questions for student discussion and teacher reflection, extensions, printable student sheets, assessment options, and links to online applets.

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

In this lesson activity students use nonstandard units (baby steps) to measure lengths of different types of "steps" (giant, regular, umbrella, scissor, wooden-soldier, and backwards steps). Once each student gathers this data they will display their own data on a bar graph. Then the class will discuss the data and compare graphs among students. A students worksheet for data collection is included in PDF format.

This activity has students explore the patterns that emerge when connecting midpoints of triangles. The activity includes a student worksheet, discussion questions, and an interactive fractal tool.

This interactive Flash applet helps students develop number sense and fluency with addition and subtraction facts within 10. Okta hides some bubbles under a shell, and then either adds more bubbles or takes some away. Students determine how many bubbles are left under the shell. Users can choose a specific one-digit starting number or let the applet choose randomly. Users can select addition, subtraction or both.

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.

This lesson focuses learners on the concept of 1,000,000. It allows learners to see firsthand the sheer size of 1 million, while at the same time providing learners with an introduction to sampling and its use in mathematics. Learners use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

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.

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.

Spreadsheets Across the Curriculum module. Students build a spreadshet to calculate grams solute to add to liters solvent to produce solution of desired concentration (mol/L).

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 is an activity where students learn about inquiry by designing an experiment on bean plants with the goal of growing the tallest plant. Students work in groups to plan the growing conditions of the control and three experimental plants. Students collect data for about three weeks and analyze their data to see if their hypothesis is correct or not. The end product can be a report presented in a number of ways.

This activity is a center investigation where students learn about wind force using a fan/wind tunnel and objects.

SSAC Physical Volcanology module. Students build a spreadsheet to calculate velocity of rising magma in steady-state Plinian eruptions using conservation of mass and momentum.

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.