Using algebra to describe patterns mathematically. This activity employs various visual patterns, constructed with matchsticks. Drag the matches around to study each pattern and work out its underlying mathematical nature. See if you can describe each pattern using algebra.

On MathsLinks: https://mathslinks.net/links/matchstick-patterns

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It is easy to forget that "summary statistics" such as mean, range, deviation, correlation etc are only summaries. Anscombe's Quartet is an informative demonstration of the dangers of overlooking this fact. This activity uses 3 sets of values from the quartet, as well as supports student experimentation using their own data. Calculation of sum, mean, standard devation and plotting of points is included.

On MathsLinks: https://mathslinks.net/links/exploring-data-different-data-same-statistics

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This applet lets you explore the domain and range of various functions.

On MathsLinks: https://mathslinks.net/links/domain-and-range-interactive-applet

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Four clearly different and visually distinct datasets produce the same summary statistics.

Check out the Datasaurus Dozen. While different in appearance, each dataset has the same summary statistics (mean, standard deviation, and Pearson's correlation) to two decimal places.

via Flowing Data

On MathsLinks: https://mathslinks.net/links/same-stats-different-graphs

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Dr James Maynard explains the Twin Prime Conjecture, it's history and recent progress.

On MathsLinks: https://mathslinks.net/links/twin-prime-conjecture

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Using only a pair of compasses, ruler and pencil, here's how to construct an egg shape from arcs of circles.

On MathsLinks: https://mathslinks.net/links/how-to-draw-an-egg

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Fatih Erikli uses a simulation that works like a disaster spread model applied to social networks to give an idea of how disinformation spreads.

On MathsLinks: https://mathslinks.net/links/post-truth-how-disinformation-spreads-in-a-network

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In this series of videos, Grant Sanderson (3Blue1Brown) want you to feel that you could have invented calculus for yourself.

In this first video, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.

More:

Chapter 2 - The paradox of derivative

Chapter 3 - Derivative formulas through geometry

Chapter 4 - Visualizing the chain rule and product rule

Chapter 5 - Derivatives of exponentials

Chapter 6 - Implicit differentiation, what's going on here?

Chapter 7 - Limits

Chapter 8 - Integration and the fundamental theorem of calculus

Chapter 9 - What does area have to do with slope?

Footnote - Higher order derivatives

Chapter 10 - Taylor series

Alternative link takes you to the YouTube playlist for this series.

On MathsLinks: https://mathslinks.net/links/essence-of-calculus-chapter-1

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An example of a heat map representing real-world data. Each cell shows the percentage of crashes at that time involving the selected factor. This is for US data.

On MathsLinks: https://mathslinks.net/links/fatal-traffic-when-and-where

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This is not just a multiplication grid, but an actual representation of the products.

On MathsLinks: https://mathslinks.net/links/true-scale-multiplication-grid

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Ben sparks demonstrates how seemingly random numbers can create amazing patterns.

Click through to the video for GeoGebra files.

On MathsLinks: https://mathslinks.net/links/chaos-game

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A comprehensive reference on the Golden Ratio by Dr Ron Knott, University of Surrey.

On MathsLinks: https://mathslinks.net/links/the-golden-section-ratio-phi

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Use this app to develop an understanding of how and where fractions exist on a number line. Students will begin to learn the relationship between improper fractions and mixed numbers.

On MathsLinks: https://mathslinks.net/links/fractions-on-a-numberline

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The connection between the Golden Ratio and works of art and architecture has been questioned in the last few decades, but there is no question that the Golden Ratio has fascinating ties to the Fibonacci numbers, two- and three-dimensional geometry, and more.

On MathsLinks: https://mathslinks.net/links/what-is-the-golden-ratio

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Reflections in convex and concave mirrors.

On MathsLinks: https://mathslinks.net/links/reflected-cats

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This is a bank of multiple choice, short response and extended response questions from the National Assessment of Educational Progress (NAEP) in the United States. Includes questions from the main Mathematics NAEP (grades 4, 8 and 12) and long-term trend NAEP (LTT Mathematics, ages 9, 13, 17).

On MathsLinks: https://mathslinks.net/links/naep-questions-tool

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Deane investigates making boxes out of squares of paper and considers which will give the maximum volume.

On MathsLinks: https://mathslinks.net/links/paper-box-designs

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The Advanced Data Grapher can be used to analyze data with box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots. You can enter multiple rows and columns of data, select which set(s) to display in a graph, and choose the type of representation.

On MathsLinks: https://mathslinks.net/links/advanced-data-grapher

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A comprehensive catalogue of data representation tools. Each includes a description and example.

On MathsLinks: https://mathslinks.net/links/the-data-visualisation-catalogue

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Statistics is a useful tool for understanding the patterns in the world around us. But our intuition often lets us down when it comes to interpreting those patterns.

On MathsLinks: https://mathslinks.net/links/the-seven-deadly-sins-of-statistical-misinterpretation-and-how-to-avoid-them

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