The purpose of this learning video is to show students how to ...

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

The purpose of this learning video is to show students how to ...

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

This trick from Exploratorium physicist Paul Doherty lets you add together the ...

This trick from Exploratorium physicist Paul Doherty lets you add together the bounces of two balls and send one ball flying. When we tried this trick on the Exploratorium's exhibit floor, we gathered a crowd of visitors who wanted to know what we were doing. We explained that we were engaged in serious scientific experimentation related to energy transfer. Some of them may have believed us. If you'd like to go into the physical calculations of this phenomenam, see the related resource "Bouncing Balls" - it's the same activity but with the math explained.

In this optics/mathematics activity, learners use two hinged mirrors to create a ...

In this optics/mathematics activity, learners use two hinged mirrors to create a kaleidoscope that shows multiple images of an object. Learners discover that the number of images reflected in the mirrors depends on the angle between the mirrors. Learners also observe that when they set the hinged mirrors on top of a third mirror, they create a reflector that always sends light back in the direction from which it came. Use this activity to introduce basic principles of light and optics including angle of reflection and angle of incidence.

This lesson unit is intended to help you assess whether students recognize ...

This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller.

In this activity, learners use pattern blocks and mirrors to explore symmetry. ...

In this activity, learners use pattern blocks and mirrors to explore symmetry. Learners work in pairs and build mirror images of each other's designs. In doing so, learners will examine principles of symmetry and reflection.

This learning video presents an introduction to the Flaws of Averages using ...

This learning video presents an introduction to the Flaws of Averages using three exciting examples: the ''crossing of the river'' example, the ''cookie'' example, and the ''dance class'' example. Averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, however, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages. The essential prerequisite knowledge for this video lesson is the ability to calculate an average from a set of numbers. During this video lesson, students will learn about three flaws of averages: (1) The average is not always a good description of the actual situation, (2) The function of the average is not always the same as the average of the function, and (3) The average depends on your perspective. To convey these concepts, the students are presented with the three real world examples mentioned above.

This problem asks the students to represent a sequence of operations using ...

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

This task can be used as a quick assessment to see if ...

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match.

A dynamically simplified solar system is constructed from online data to explore ...

A dynamically simplified solar system is constructed from online data to explore the real solar system on many different scales.

The realistically scaled solar system is surprising because nothing is visible due to the presence of many different scales. That is why it is usually rescaled in animations or illustrations. This is nice but gives us a wrong sense of distances and sizes. This Demonstration is intended to show the solar system's different scales in their full glory.

Since it is hardly possible to see anything when the real scales are used, controls have been added to modify the sizes of the celestial bodies.

This resource provides a variety of information and activities that teachers may ...

This resource provides a variety of information and activities that teachers may like to use with their students to explore the Islamic Middle East collections at the V&A. It can be used to support learning in Maths and Art. Included in this resource are sections on:

Principles of Islamic art and design Pre-visit activities Activities to do in the museum Activities to do back at school Islamic art explores the geometric systems that depend upon the regular division of the circle and the study of Islamic art increases appreciation and understanding of geometry. The use of these geometric systems creates a harmony among Islamic decorative arts and architecture, which is consistent with the Islamic belief that all creation is harmoniously interrelated.

Approaching an abstract subject in a concrete way provides a means of extending maths into other curriculum areas. The context of the Museum expands and enriches students' appreciation of the application of geometry in a cultural context and develops the sense of different cultural identities. Students have the opportunity to become familiar with the relationship between geometry and design and this can give confidence to students who have never seen themselves as 'good at art'.

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: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

This activity lets learners participate in the process of reconstructing a phylogenetic ...

This activity lets learners participate in the process of reconstructing a phylogenetic tree and introduces them to several core bioinformatics concepts, particularly in relation to evolution. Groups of learners (at least 10) repeat a secret message (five to seven similar-sounding words) like the game "Telephone". In this version of the game, however, learners write and then code what they hear, creating a model of a phylogenetic tree and using a species distance matrix. This resource includes background information about phylogenetic trees, maximum parsimony, and matrix theory (see page 6-7 of PDF).

The objective of this lesson is to illustrate how a common everyday ...

The objective of this lesson is to illustrate how a common everyday experience (such as playing pool) can often provide a learning moment. In the example chosen, we use the game of pool to help explain some key concepts of physics. One of these concepts is the conservation of linear momentum since conservation laws play an extremely important role in many aspects of physics. The idea that a certain property of a system is maintained before and after something happens is quite central to many principles in physics and in the pool example, we concentrate on the conservation of linear momentum. The latter half of the video looks at angular momentum and friction, examining why certain objects roll, as opposed to slide. We do this by looking at how striking a ball with a cue stick at different locations produces different effects.

In this math activity, learners observe and sketch cracking patterns in pavement. ...

In this math activity, learners observe and sketch cracking patterns in pavement. Learners use a protractor to measure and label the angles of their sketches and conclude if some angles are more common than others.

This task compares the usefulness of different forms of a quadratic expression. ...

This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.

This lesson focuses on students making decisions about what tools to apply ...

This lesson focuses on students making decisions about what tools to apply to solve different problems related to quadratic expressions and equations. It is also intended to build awareness of the form an answer will take in order to help students make sense of the kind of problem they are solving. (9th/10th/11th Grade Math)

This tasks is an example of a mathematical modeling problem (SMP 4) ...

This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.

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