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What's going on in this graph? Factors in determining success

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What's going on in this graph? Factors in determining success

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What’s Going On in This Graph? | Global Success Factors (Published 2022)

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What factors do young people think are most important in determining success? How do their answers differ in various countries?

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What's going on in this graph? Global temperature change

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What's going on in this graph? Global temperature change

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What’s Going On in This Graph? | Global Temperature Change (Published 2020)

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How do global temperatures compare to mid-20th century average temperature?

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What is a Center Pivot? Pivot 101 - Valley Irrigation

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Leaves as Thermometers

Do you ever wonder what the climate was like in Los Angeles during the Ice Age when mammoths, saber toothed cats, and giant ground sloths lived in our neighborhoods? With this activity you will learn how paleontologists measure ancient temperature from leaves. Try this activity at home and share your results with our scientists!
There are two parts to this activity:
1. First, you will collect leaves in your neighborhood to determine the mean annual temperature (MAT - the average daily temperature for a whole year) for Los Angeles today.

2. Second, you will use the same method to reconstruct temperature from pictures of leaves from species recovered as fossils from La Brea Tar Pits.

Part 1: What is the Mean Annual Temperature of your neighborhood?
To practice using the Leaf Thermometer and to measure what the mean annual temperature of Los Angeles is today, follow these steps:
1. Go outside and collect one leaf from 15-20 different species of broad-leaved trees (like a maple, oak, avocado, etc.).

2. Sort the leaves according to leaf type: 1) Smooth Edges and 2) Toothy Edges.

3. Count the number of Smooth Edge leaves and Toothy Edge leaves.

4. Determine the percentage of Smooth Leaves in your collection.

5. Plug in your % of smooth leaves value into the Leaf Thermometer to determine MAT of L.A. today.

6. Convert Celsius to Fahrenheit values using online search or this formula: (°C x 1.8) + 32 = °F

Part 2: What is the Mean Annual Temperature of Ice Age La Brea Tar Pits?

Our final task now is to use the Leaf Thermometer to determine the mean annual temperature for Ice Age times in Los Angeles based on the plant species shown below.
In addition to thousands of vertebrate fossils, the La Brea Tar Pits also preserve a diversity of plant fossils including leaves, wood, fruits and seeds. Paleobotanists have identified which species of plants these fossils belong to, and they have been able to make a list of the plants that lived at the Tar Pits during the Ice Age. Almost all of them are still living today and here are some examples. To measure the mean annual temperature of Ice Age La Brea Tar Pits, follow these steps:
1. Count the number of Smooth Leaves and Toothy Leaves in the image.

2. Calculate the percentage of Smooth Leaves.

3. Plug the % of Smooth Leaves into the Leaf Calculator.

4. Convert Celsius to Fahrenheit values using online search or this formula: (°C x 1.8) + 32 = °F

See for any guidance.

Share Your Data with our Scientists!

Enter the results of your experiments by clicking the button below and calculate the difference between the temperature of modern day Los Angeles and Ice Age Los Angeles ~40,000 years ago in degrees Fahrenheit (°F).

Background Information

Early in the 20th century, scientists recognized that leaves of trees can be used to predict the mean annual temperature (MAT -the average daily temperature for a whole year) of a given location. Consider that there are two kinds of leaves, those that have smooth edges like this one on the left, and those that have toothy edges, like the one on the right. This difference in leaf form is in part a physiological adaptation to temperature. Leaves that have smooth edges tend to grow in warm climates, while those that are toothy tend to grow in cooler environments.

Paleobotanists recognized that this observation could be used to calculate temperature from fossil plants to understand how warm a given place was long in the past, before the time of thermometers.

To do this, they traveled to living forests all over the world and collected leaves from tree species growing in particular areas and they determined the percentage of leaves that had smooth edges in each collection. Next, they obtained climate data for each of these locations from nearby weather stations and plotted the two variables together. Here is a simplified version.

Using this graph and the mathematical formula that defines the relationship between the variables, we can predict the mean annual temperature for a location by determining the % of leaves with smooth edges in a collection of leaves. We call the mathematical formula the Leaf Thermometer.

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Do you ever wonder what the climate was like in Los Angeles during the Ice Age when mammoths, saber toothed cats, and giant ground sloths lived in our neighborhoods? With this activity you will learn how paleontologists measure ancient temperature from leaves. Try this activity at home and share your results with our scientists!

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MetLink - Royal Meteorological Society Leaves as Thermometers -

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See how we can use fossilised leaves to tell us about past climate

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In this article we shall discuss how the analysis of the shapes of leaves can be used to reconstruct past climates.

In the previous article, we saw that if we know the environment preferred by a species, we can use it as a climatic indicator. We also noted that this is difficult when the species is extinct, since then we can no longer find by direct observation what climate is congenial to it.

But what if the morphology of a species was an indicator of the climate it prefers? In that case, we would be able to tell what climate it inhabited just by looking at its remains in the fossil record. One morphological feature commonly used for this purpose is the leaf shapes of plants.

Plants in temperate climates tend to have leaves with serrated margins, i.e. they have jagged edges; plants in warmer and more humid climates tend to have what are known in botanical jargon as entire margins, that is, smooth and unserrated. The difference is illustrated in the photographs to the right.

Rather than there being a sharp cut-off between the temperate and tropical styles of leaves, there is a continuous relationship between the climate and the mix of leaf types found in it: that is, as the climate gets a little hotter and wetter, the proportion of entire margins increases a little. This means that looking at a single leaf doesn't tell us that we are looking at a temperate or tropical climate; but looking at a whole lot of species will allow us to do something a whole lot better than simply dividing climates into tropical or temperate: we can actually estimate the average annual temperature.

So once we have established the relationship between climate and the proportions of leaf shapes in the flora, we can use this relationship to find out about past climates where leaves have been preserved in the fossil record. Although leaves are not the most easily preserved material, there are some environments, such as lacustrine sediment, where they are preserved and can be used as a paleoclimatic indicator.

Using leaf shape as a climatic indicator began with counting the proportions of serrated to entire margins, but it didn't end there. Other characteristics such as leaf length, leaf width, leaf area, the presence or absence of a pointed tip also have a relationship to the climate.

The CLAMP (Climate Leaf Analysis Multivariate Program) group has measured many more characteristics of leaves and have used sophisticated methods to produce a formula relating these characteristics to climate; their website can be found here.

Relationship between climate and leaf shape.

We can establish by observation that the ratio of temperate to tropical leaf styles is a surprisingly good indicator of average annual temperature, as illustrated by the graph to the right, showing the relationship between floras and temperature in the forests of East Asia (figure from J. A. Wolfe, 1979, Temperature parameters of humid to mesic forests of eastern Asia and relation to forests of other regions of the Northern Hemisphere and Australasia, USGS Professional Paper, 1106).

This means that if we look at the ratio of leaf types in the fossil record, we can use it to produce an estimate of the temperature at the time when the plants grew.

Now, you might wonder if this relationship between leaf types and temperature really held in the past. Well, the adaptation of fauna and flora to their environment does seem to be one of the great constants of nature, so in principle we would expect the relationship to have held in the past much as it does in the present. It is after all extremely unlikely on the face of it that serrated margins would suit temperate climates in the present and yet have been more suitable to tropical climates in the past.

However, it should be noted that the exact relationship between leaf types and climate varies from continent to continent: although more serrated leaves always correspond to cooler climates on every continent, the exact numerical relationship is not the same. So a graph similar to the one above but based on Australian data rather than Asian data would still be a good approximation to a straight line sloping downwards to the right, but the exact angle of slope would be different. Now, what can vary from place to place could also in principle vary from time to time. This means that although leaf shape is a useful indicator of past climate, it would be naïve to treat it as though the relationship between climate and leaf shape was quite so exact as the relationship between temperature and a thermometer.

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Historical Geology/Leaf shape and temperature - Wikibooks, open books for an open world

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In this article we shall discuss how the analysis of the shapes of leaves can be used to reconstruct past climates. In the previous article, we saw that if we know the environment preferred by a species, we can use it as a climatic indicator.

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Agricultural algebra: circles in the field

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Agricultural algebra: circles in the field

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Desmos sprinkler task - needs adaptation

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Desmos sprinkler task - needs adaptation

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This activity was created for the MVP math program, Secondary 2, Module 8. It is a simplified version to the task in 8.2.

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Task

Selina has a 9 meter by 12 meter lawn that she wants to water. She has two sprinklers, each of which can water grass within an 8.4-meter radius. Selina wants to set up the two sprinklers so that they are on corners of the lawn. She would like for the sprinklers to water as much of the lawn as possible, because she will have to manually water the part of the lawn that is not covered by the sprinklers.

1. Selina considers two different strategies for placing the sprinklers. One strategy is to put the sprinklers at opposite ends of a 12-meter side of the lawn. The other is to put the sprinklers at opposite corners of the lawn. (See the figures below.) Which strategy appears to be best? Justify your answer.

2. If Selina chooses the better of these two strategies, what percentage of the lawn will she be able to water with the sprinklers?

3. If Selina is allowed to put sprinklers in the interior of her lawn, how many sprinklers does she need to water the entire lawn?

IM Commentary

This task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7). It also engages students in some of the steps of the modeling cycle, in particular:

(2) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables,

(3) analyzing and performing operations on these relationships to draw conclusions, and

(4) interpreting the results of the mathematics in terms of the original situation.

Teachers who wish to engage their students in some of the more creative aspects of modeling can just skip parts (a) and (b) of the task and have students jump into part (c).

Teachers who wish to use this problem as a classroom task may wish to have students work on the task in cooperative learning groups due to the high technical demand of the task. If time is an issue, teachers may wish to use the Jigsaw cooperative learning strategy to divide the computational demands of the task among students while requiring all students to process the mathematics in each part of the problem.

Solution

1. In both sprinkler placements, each sprinkler covers a 90-degree sector of a circle of radius 8.4 meters. However, in each placement, the areas covered by the two sprinklers overlap. The placement that produces the smallest area of overlap will cover more area overall, since the total area covered is equal to the sum of the areas of the two 90-degree sectors minus the overlap.

If we draw the areas covered by the sprinklers in each of the two placements, it appears as though the overlap is slightly smaller if we place the sprinklers at the two corners. We will compute the total area covered by each placement in order to confirm this.

2. We'll start by computing the area covered if Selina puts the two sprinklers at opposite ends of a 12-meter side of the lawn.

Let A and B be opposite ends of the 12-meter side of the lawn where the sprinklers are placed. Let X be the point where the two quarter-circles of radius 8.4 meters centered at A and B intersect, and let M be the foot of the perpendicular from X to side AB. (This is also the midpoint of AB.)

We'll decompose the area covered by the two sprinklers into the isosceles triangle ABX and two circular sectors (one in each circle). We know that AM = 6 meters and AX = 8.4 meters, so by the Pythagorean Theorem, XM $\approx$ 5.88 meters. So the area of triangle ABX is approximately $$ \mbox{Area} = \frac12 \cdot XM \cdot AB \approx \frac12 \cdot 5.88 \cdot 12 \approx 35.3 \mbox{ m}^2 . $$ The measure of angle XAM is $\arccos \frac{6}{8.4} \approx 44.4^\circ$. So the remainder of the covered area consists of two 45.6-degree sectors of circles of radius 8.4 meters. Each of these sectors has area $$ \mbox{Area} \approx \frac{90 - \arccos \frac{6}{8.4}}{360} \cdot \pi \cdot 8.4^2 \approx 28.1 \mbox{ m}^2. $$ So the total area covered is approximately 35.3 + 2(28.1) = 91.5 square meters, or about 84.7 percent of the lawn.

Now we compute the area covered if Selina places the sprinklers at opposite corners of the lawn:

Let A and B be two opposite corners of the lawn, let P and Q be the two points at which quarter-circles of radius 8.4 meters centered at A and B intersect, and let X be the point at which the segments AB and PQ intersect. (This is also the center of the lawn.)

This time, we decompose the area covered into the rhombus APBQ and four circular sectors. The length of the diagonal AB is 15 meters by the Pythagorean Theorem, so AX = 7.5 meters. Since AP = 8.4 meters, by the Pythagorean Theorem, PX $= \sqrt{8.4^2 - 7.5^2}$ meters, and thus PQ $= 2\sqrt{8.4^2 - 7.5^2} \approx$ 7.57 meters. So the area of rhombus APBQ is $$ \mbox{Area} = \frac12 \cdot AB \cdot PQ \approx \frac12 \cdot 15 \cdot 7.57 \approx 56.8 \mbox{ m}^2. $$ Since $m\angle PAX = \arccos \frac{7.5}{8.4}$, the measure of angle PAQ is approximately $2\arccos \frac{7.5}{8.4} \approx$ 53.5 degrees. So the two sectors of circle A not covered by the rhombus add up to a 36.5-degree sector of a circle of radius 8.4 meters. The same is true of the two sectors of circle B not covered by the rhombus, so the remaining area is equivalent to approximately a 73.0-degree sector of a circle of radius 8.4 meters: $$ \mbox{Area} \approx \frac{73.0}{360} \cdot \pi \cdot 8.4^2 \approx 44.9 \mbox{ m}^2. $$ So the total area covered by the sprinklers in this case is approximately 56.7 + 44.9 = 101.6 square meters, or about 94.1 percent of the lawn. This confirms that the strategy of placing the sprinklers at opposite corners of the lawn is significantly better.

3. It is in fact possible to water the entire lawn with one sprinkler if we are allowed to place sprinklers in the interior of the lawn. Suppose we place one sprinkler in the center of the lawn. Then the corners of the rectangle are $\sqrt{4.5^2 + 6^2} = 7.5$ meters away, which is smaller than the sprinkler's reach. Since the corners of a rectangle are the points farthest from the center, one sprinkler placed in the center can water the entire lawn.

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Selina has a 9 meter by 12 meter lawn that she wants to water. She has two sprinklers, each of which can water grass within an 8.4-meter radius. Selina wants to set up the two sprinklers so that they are on corners of the lawn.

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Bluebird CN7 - Donald Campbell's Turbine Record Car

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Bluebird CN7 - Donald Campbell's Turbine Record Car

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Bluebird CN7 - Donald Campbell's Turbine Record Car

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Sir Malcolm Campbell sets a speed record in his Bluebird car at Daytona Beach, Fl...HD Stock Footage

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FIA World Records are motorsport distilled to its two most basic elements - distance versus time - to create the fastest recognised official speeds achieved by any wheeled vehicle on land. The Outright Land Speed Record, which currently stands at 763.035 mph(1227.985 km/h), is the most prestigious,…

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integral mathematics resources: log in to the site

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Integral Mathematics Resources: Log in to the site

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Borrow the Moon - activity 17: Our Earth under threat

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Designed as a virtual mission, students play the part of Near Earth Asteroid (NEA) scientists in the scenario of a possible asteroid impact with Earth.

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DON'T LOOK UP | Leonardo DiCaprio, Jennifer Lawrence | Official Trailer | Netflix

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How Progress 8 and Attainment 8 are calculated

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How Progress 8 and Attainment 8 are calculated

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Hook activity: compare students in a similar way to this voting activity. Who did better?

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Hook activity: compare students in a similar way to this voting activity. Who did better?

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Numberphile - speed distance time graphs - car collision

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Asteroid 'half the size of a giraffe' strikes earth

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Asteroid 'half the size of a giraffe' strikes earth

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For Want of Half a Giraffe | National Review

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Since when, exactly, did we measure asteroids in giraffes?

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Submitted ideas and questions from OCR teachers

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Submitted ideas and questions from OCR teachers