The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.
These problems give students the opportunity to construct and compare linear, quadratic, and exponential models.
Students learn about infrared energy and how it is used to sense the surrounding environment. They review where infrared falls on the electromagnetic spectrum and learn how infrared sensors work, as well as various ways engineers and scientists create and apply infrared technology to study science and collect information for security, communications, medical, research and other purposes. Pre/post-quizzes and a take-home assignment are provided. Learning the concepts prepares students to conduct the associated activity in which they design and program Arduino-controlled robots that use IR sensors to follow a line and make designated stops, much like the automated guided vehicles used in industry and commerce.
Students first explore different materials to see what types reduce the most amount of sound when placed in a box. Each group is assigned a different material and they fill their box with that specific material. Students measure the sound level of a tone playing from inside the box using a decibel reader from outside the box. Students share this data with the class and analyze which types of materials absorb the most sound and which reflect the most sound.
When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder or a mixed number.
In this activity, students discuss the notion of time and how time can be measured. They build an hourglass to measure time and test it. This activity will allow students to have a better understanding of time and the instruments that can be used to measure it.
Students investigate three-dimensional objects. They compare what constellations look like when seen from different angles. They make a model of a constellation and look at it from different sides to discover that the relative position of the stars changes depending on our perspective. They understand that stars are not located on the same plane and or the same distance.
Students are introduced to the nano-size length scale as they make measurements and calculate unit conversions. They measure common objects and convert their units to nanometers, giving them a simple reference frame for understanding the very small size of nanometers. Then, they compare provided length data from objects too small to measure, such as a human hair and a flea, giving them a comparative insight to the nanotechnology scale. Using familiar and common objects for comparison helps students understand more complex scientific concepts.
The words compose and decompose are used to describe actions that young students learn as they acquire knowledge of small numbers by putting them together and taking them apart. This understanding is a bridge between counting and knowing number combinations. It is how instant recognition of small numbers develops and leads naturally to later understanding of fact families. This task helps them develop an understanding of number combinations.
Students are asked to analyze the data in a graph and determine if there is an association between the two variables.
The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.
Students act as food science engineers as they explore and apply their understanding of cooling rate and specific heat capacity by completing two separate, but interconnected, tasks. In Part 1, student groups conduct an experiment to explore the cooling rate of a cup of hot chocolate. They collect and graph data to create a mathematical model that represents the cooling rate, and use an exponential decay regression to determine how long a person should wait to drink the cup of hot chocolate at an optimal temperature. In Part 2, students investigate the specific heat capacity of the hot chocolate. They determine how much energy is needed to heat the hot chocolate to an optimal temperature after it has cooled to room temperature. Two activity-guiding worksheets are included.
This short video and interactive assessment activity is designed to teach second graders about which amount is not equal to a given amount of money?.
This task addresses knowledge related to interpreting forms of functions derived by factoring or completing the square. It requires students to pay special attention to the information provided by the way the equation is represented as well as the sign of the leading coefficient, which is not written out explicitly, and then to connect this information to the important features of the graph.
The purpose of this task is for students to explain how they know one quantity is greater or less than another quantity. Students will easily be able to identify which number is greater or less. However, explaining their reasoning will help them solidify their number sense skills.
In this task students see different ways of partitioning a circle and a rectangle into two or more equal shares.
In this task students compare 4/5 to 5/4 on a number line.
In this activity students compare objects and practice determining which objects are heavier and lighter.
An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available.
This video lesson will introduce students to algorithmic thinking through the use of a popular field in graph theory—social networking. Specifically, by acting as nodes in a graph (i.e. people in a social network), the students will experientially gain an understanding of graph theory terminology and distance in a graph (i.e. number of introductions required to meet a target person). Once the idea of distance in a graph has been built, the students will discover Dijkstra's Algorithm. The lesson should take approximately 90 minutes and can be comfortably partitioned across two class sessions if necessary (see the note in the accompanying Teacher Guide). There are no special supplies needed for this class and all necessary hand-outs can be downloaded from this website.