This learning video is designed to develop critical thinking in students by …
This learning video is designed to develop critical thinking in students by encouraging them to work from basic principles to solve a puzzling mathematics problem that contains uncertainty. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities.
A new instructional model, called Argument-Driven Inquiry (ADI), is introduced to elementary …
A new instructional model, called Argument-Driven Inquiry (ADI), is introduced to elementary teachers in this article. The author shows how school librarians and classroom teachers can collaborate to help students construct and communicate evidence, or arguments. Evidence buckets, a collaborative activity, and related online resources are presented. The article appears in the free online magazine Beyond Weather and the Water Cycle, which is structured around the seven essential principles of climate literacy.
This task applies reflections to a regular hexagon to construct a pattern …
This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.
This task applies reflections to a regular octagon to construct a pattern …
This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.
Student pairs are given 10 minutes to create the biggest box possible …
Student pairs are given 10 minutes to create the biggest box possible using one piece of construction paper. Teams use only scissors and tape to each construct a box and determine how much puffed rice it can hold. Then, to meet the challenge, they improve their designs to create bigger boxes. They plot the class data, comparing measured to calculated volumes for each box, seeing the mathematical relationship. They discuss how the concepts of volume and design iteration are important for engineers. Making 3-D shapes also supports the development of spatial visualization skills. This activity and its associated lesson and activity all employ volume and geometry to cultivate seeing patterns and understanding scale models, practices used in engineering design to analyze the effectiveness of proposed design solutions.
In this task students determine the number of hundreds, tens and ones …
In this task students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Students must, in some cases, decompose hundreds to tens and tens to ones.
This lesson integrates language arts, music, and math. The children will listen …
This lesson integrates language arts, music, and math. The children will listen to the story "Count on Bunnies". They will be given the opportunity to act out the story and solve bunny equations. After listening to the song "Five Young Rabbits," the children will take turns being rabbits and pantomiming the actions as the class sings. The children will combine the rabbits at the end of each verse to see how many rabbits have been added. Then they will work in pairs to create their own rabbit equations.
Unit 3: Unit Rates and Percentages Lesson 1: The Burj Khalifa In …
Unit 3: Unit Rates and Percentages Lesson 1: The Burj Khalifa
In the previous unit, students began to develop an understanding of ratios and familiarity with ratio and rate language. They represented equivalent ratios using discrete diagrams, double number lines, and tables. They learned that a:b is equivalent to every other ratio sa:sb, where s is a positive number. They learned that “at this rate” or “at the same rate” signals a situation that is characterized by equivalent ratios.
In this unit, students find the two values a/b and b/a that are associated with the ratio a:b, and interpret these values as rates per 1. For example, if a person walks 13 meters in 10 seconds, that means they walked 13/10 meters per 1 second and 10/13 seconds per 1 meter.
To kick off this work, in this lesson, students tackle a meaty problem that rewards finding and making sense of a rate per 1 (MP1). Note there is no need to use or define the term “rate per 1” with students in this lesson. All of the work and discussion takes place within a context, so students will be expected to understand and talk about, for example, the minutes per window or the meters climbed per minute, but they will not be expected to use or understand the more general term “rate per 1.”
This task operates at two levels. In part it is a simple …
This task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip. At a higher level, the task addresses N-Q.3, since realistically neither the car nor the bus is going to travel at exactly the same speed from beginning to end of each segment; there is time traveling through traffic in cities, and even on the autobahn the speed is not constant. Thus students must make judgements about the level of accuracy with which to report the result.
This course provides an introduction to applied concepts in Calculus that are …
This course provides an introduction to applied concepts in Calculus that are relevant to the managerial, life, and social sciences. Students should have a firm grasp of the concept of functions to succeed in this course. Topics covered include derivatives of basic functions and how they can be used to optimize quantities such as profit and revenues, as well as integrals of basic functions and how they can be used to describe the total change in a quantity over time.
This task provides a good entry point for students into representing quantities …
This task provides a good entry point for students into representing quantities in contexts with variables and expressions and building equations that reflect the relationships presented in the context.
Statistics is the study of variability. Students who understand statistics need to …
Statistics is the study of variability. Students who understand statistics need to be able to identify and pose questions that can be answered by data that vary. The purpose of this task is to provide questions related to a particular context (a jar of buttons) so that students can identify which are statistical questions. The task also provides students with an opportunity to write a statistical question that pertains to the context.
This is a task where it would be appropriate for students to …
This is a task where it would be appropriate for students to use technology such as a graphing calculator or GeoGebra, making it a good candidate for students to engage in Standard for Mathematical Practice 5 Use appropriate tools strategically.
There are two aspects to fluency with division of multi-digit numbers: knowing …
There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly.
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