This task requires students to think of dimes and pennies as fractions of dollars.
This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.
The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.
Spreadsheets Across the Curriculum module. Students use spreadsheets to help find the difference in percentages of salaries between dirty and clean jobs.
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi. Then students learn a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they find numbers close to phi. They solve a squares puzzle that creates an approximate Fibonacci spiral. Finally, the instructor demonstrates the rule of the Fibonacci sequence via a LEGO® MINDSTORMS® NXT robot equipped with a pen. The robot (already created as part of the companion activity, The Fibonacci Sequence & Robots) draws a Fibonacci spiral that is similar to the nautilus shape.
Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.
The lesson is 23 pages and about the Pythagorean Theorem. It starts off with the mathematical goals and standards for the lesson. The resource is laid out with easy to follow instructions. There are various bolded titles starting with an introduction, materials needed, it gives a suggested lesson outline, along with practice examples. The lesson is about discovering for understanding the Pythagorean Theorem. The resource uses black and red text to show the difference between what the teacher needs to do/say and wha the student needs to do.
Definitions and basic algorithms for Fourier analysis for discrete-time signals.
This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation.
The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.
This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.
Learners follow step-by-step instructions for dividing algebraic fractions. They begin by reducing the fractions to their simplest form. Immediate feedback is provided. This activity has audio content.
This task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.
Students will have opportunity for review of division. Both the place value and area models will be reviewed. Upon review, an opportunity for practice is available.
The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.
In this 6-lesson unit, students use dominoes to explore four models of addition: counting, number line, sets, and balanced equations. They learn about the commutative property, the relation between addition and subtraction, the result of adding 0, and the concept of doubles. Students write story problems which involve the operation of addition and begin to memorize the addition facts. They represent addition in pictures. The various models of addition help students develop a rich conceptual schema for addition. Included are a Bibliography of Counting Books, student materials, questions for student and teacher reflection, assessment and extension ideas. [Suggestion: Use the alternate applet, Pan Balance - Numbers, listed as a Related Resource, rather than Pan Balance - Shapes, in Lesson 4.]
Students learn about biomimicry and the engineering design process as they design and build model ptarmigan feet.
These word problems address common errors that students make when adding fractions.
This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).