Cartesian Co-ordinate Practice

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“The coordinate system we commonly use is called the Cartesian system, after the French mathematician René Descartes (1596-1650), who developed it in the 17th century. Legend has it that Descartes, who liked to stay in bed until late, was watching a fly on the ceiling from his bed. He wondered how to best describe the fly’s location and decided that one of the corners of the ceiling could be used as a reference point.” ~ https://wild.maths.org/ren%C3%A9-descartes-and-fly-ceiling

Since 1650, the Cartesian plane has been the model for almost all mapping systems and enabled a connection between algebra and geometry. Using such a coordinate system it is possible to solve geometric problems using algebra, and vice versa.

To better understand the co-ordinate plane system we are going to practice plotting points in a few different ways. Cartesian Co-ordinate Battleships is a game you can play to ‘sink’ an opponents ships, by calling out a series of cartesian co-ordinate pairs, while  they try to ‘sink’ your ships.

Maths Nook has some online games to draw suprise shapes by plotting points on a cartesian plane:

https://www.mathnook.com/math2/graphing-puzzle.html

https://www.mathnook.com/math2/graphing-puzzle-2.html

https://www.mathnook.com/math2/graphing-puzzle-christmas.html

More cartesian coordinate games here: https://www.mathnook.com/math/skill/coordinategridgames.php

Linear and Non-Linear Graphs

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Geogebra Interactive

Victorian Curriculum Link: “Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs.” (VCMNA285)

Only one of the containers in this activity shows a constant increase in height of liquid over time. So, only one of the relationships between height of liquid and time is a linear relationship. Which container is it?

This is a useful worksheet to start recognising the relationship between everyday situations and graphs. Which graph is which?

Dan Meyers has some great resources for learning about non-linear graphs too: Graphing Stories is a series of short videos that can be used to demonstrate various non-linear relationships. Here is a student worksheet you can use with the GraphingStories.pdf

More Graphing Stories here.

Matemagi has some more great graphing story videos.

Scratch for Maths!

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Scratch, from MIT, is a website and a simple drag-and-drop programming language, that students can use to create animations. It is comprised of a range of backgrounds and sprites (characters) that can move according to user’s directions. Your task is to create an animation in Scratch that explains a maths concept. It could be about prime numbers, square numbers, geometry, measurement, probability or statistics. Here as an example: Four triangles

“Design and implement mathematical algorithms using a simple general purpose programming language (VCMNA254)”

Algebra Balance Scales

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When I returned to teaching a year 7 Maths class, after a break of two years, I went searching for a virtual manipulative that I had used to improve understanding of algebra concepts. The National Library of Virtual Manipulatives has a great range of visuals, but unfortunately, most rely on Java, which is not supported by any current browser. Luckily, someone over at Hood Math has converted or upgraded the applet, so Algebra Balance Scales can be used by students in class.

 

Week 1: 2016

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2016

Basic operations – Using the four digits 2, 0, 1 and 6 and the four operations (addition, subtraction, multiplication and division) can you make equations that equal all the numbers from zero to 20?

Multiplication –

  • Which multiplication tables do you know best?
  • What do all the multiples of 2 and 4 and 8 have in common?
  • How do you know if a number is divisible by 5 or 10?
  • Write down all the multiples of 3 in order and see if you can determine something that they all have in common (clue – add the digits together).

How much are your pancakes?

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pancakes

This recipe serves 4 people, 2 pancakes each

  • 2 cups self raising flour, sifted (250g at 0.32c per gram)
  • 2 large eggs, separated (40 cents each)
  • 2 cups milk (500ml at 0.25c per ml)
  • 2 tsp sugar (8 grams at 0.024c per gram)
  • 50g butter, melted plus extra butter or oil for cooking (at 0.88c per gram)

How much do you think it costs to make pancakes at home? How much do you pay at a cafe or McDonalds? When restaurant owners and chefs calculate the cost of their menu they need to take into account the cost of ingredients as well as staff costs, overheads (rent, power, telephone, gas etc) and also make a profit.