This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating. This task addresses a very important issue about precision in reporting and understanding statements in a realistic scientific context.

This task is a refinement of ``Carbon 14 dating'' which focuses on accuracy. Because radioactive decay is an atomic process modeled by the laws of quantum mechanics, it is not possible to know with certainty when half of a given quantity of Carbon 14 atoms will decay. This type of question is very important in science and it also provides an opportunity to study the very subtle question of how errors behave when applying a function: in some cases the errors can be magnified while in others they are lessened.

This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

This task is a somewhat more complicated version of "Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly. Instead, students have to combine the algebraic techniques with some additional problem-solving (numerical reasoning, informed guess-and-check, etc.)

The solutions unit consists of the following: General points for discussion relating to the teaching of the mathematical content in the activities. Step-by-step mathematical solutions to the activities. Annotations to the solutions to assist teachers in their understanding the maths as well as teaching issues relating to the mathematical content represented in the activities. Suggestions of links to alternative activities for the teaching of the mathematical content represented in the activities.

In this activity, students explore the effect of chemical erosion on statues and monuments. They use chalk to see what happens when limestone is placed in liquids with different pH values. They also learn several things that engineers are doing to reduce the effects of acid rain.

Students conduct a simple experiment to model and explore the harmful effects of acid rain (vinegar) on living (green leaf and eggshell) and non-living (paper clip) objects.

Students are introduced to the differences between acids and bases and how to use indicators, such as pH paper and red cabbage juice, to distinguish between them.

Students play and record the “Mary Had a Little Lamb” song using musical instruments and analyze the intensity of the sound using free audio editing and recording software. Then they use hollow Styrofoam half-spheres as acoustic mirrors (devices that reflect and focus sound), determine the radius of curvature of the mirror and calculate its focal length. Students place a microphone at the acoustic mirror focal point, re-record their songs, and compare the sound intensity on plot spectrums generated from their recordings both with and without the acoustic mirrors. A worksheet and KWL chart are provided.

Students construct rockets from balloons propelled along a guide string. They use this model to learn about Newton's three laws of motion, examining the effect of different forces on the motion of the rocket.

An interactive applet and associated web page that demonstrate acute angles (those less than 90 deg). The applet presents an angle (initially acute) that the user can adjust by dragging the end points of the line segments forming the angle. As it changes it shows the angle measure and a message that indicate which type of angle it is. There a software 'detents' that make it easy capture exact angles such as 90 degrees and 180 degrees The message and angle measures can be turned off to facilitate classroom discussion. The text on the page has links to other pages defining each angle type in depth. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the three types of triangle: acute, obtuse and right. The applet shows a triangle that is initially acute (all angles less then 90 degrees) which the user can reshape by dragging any vertex. There is a message changes in real time while the triangle is being dragged that tells if the triangle is an acute, right or obtuse triangle and gives the reason why. By experimenting with the triangle student can develop an intuitive sense of the difference between these three classes of triangle. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

In this lesson, students will develop their fluency with addition and subtraction through a "real-world" application of collecting data about insects in the garden.

Adult Learners will review the previous lesson, measuring with a thermometer, to continue their application in horizontal number lines. Learners will use the number line to increase their understanding of integer values as well as apply their understanding to solving real world problems.

It is important to understand polynomials and to be able to classify them based on the number of terms, as well as recognize the coefficients, and degrees. You must also understand how to perform mathematical operations on them. This seminar will focus on combining polynomials using addition and subtraction. It will be important to understand the rules to make sure you are combining only like terms. You will apply techniques you have learned involving exponents and general addition and subtraction rules. You will use the techniques learned in this seminar to verify solutions to various other types of polynomial problems as you move forward. When adding and subtracting polynomials, you will first identify the like terms to combine polynomials to their simplest form.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.

This resource includes three tasks surrounding the Common Core Standard 5.NF.2 - Adding and Subtracting Mixed Numbers with Unlike Denominators Using an Open Number Line and Fraction Equivalence. The tasks involves looking at real Maryland snowstorm data and each task builds off the previous task.