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The World of Maths
Transcript of The World of Maths
By Karina Potter
Cartoon man holding maths symbols (n.d.)
The aim of this presentation is to provide the viewer with an understanding of the similarities and differences between mathematics and numeracy. This presentation will also share ways in which math is incorporated in the real world, with some exciting examples for teaching, all while helping to shed a positive light on mathematics.
Mathematics Vs Numeracy
“The terms ‘numeracy’ and ‘mathematics’ are sometimes used interchangeably but the relationship between the two is actually quite complex” (National Numeracy, 2013).
According to the Collins English Dictionary, mathematics is “a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation” (mathematics, n.d.). Mathematics is the actual process involved in working out calculus, equations and statistical information. “Mathematics is abstract and platonic, offering absolute truths about relations among ideal objects” (Steen, 2001), meaning a theoretical but approachable formula can be used to find an exact and truthful answer to a mathematical question.
According to national numeracy (2013), numeracy is being able to grasp numbers and data and the arithmetic and reasoning essential for everyday life. It is the ability to use math in the real world. Numeracy does however use mathematical techniques to make sense of the world; all numeracy is underpinned by some mathematics. While it does involve understanding some mathematical techniques, numeracy is based more on applying it in real world situations for example: being able to manage family budgets, bank accounts, shopping in supermarkets; and being able to read sports statistics like graphs and numbers in the daily newspaper.
Year Level: 1
Learning Area: Mathematics – Shapes and patterns
Time: 2x morning sessions
Lesson Format: Team teaching and single subject specific
By the end of the lesson, children will have an understanding of the different shapes and patterns used and found in everyday life. Children will also feel more comfortable identifying basic shapes and symmetry.
Children will recognize and classify familiar two-dimensional shapes objects using obvious features. – As per the Australian Curriculum (ACARA n.d.).
Children will need prior knowledge of basic shape identification and introduction to patterns.
The Learning Environment: Basic shapes will be drawn on the whiteboard for reference, each in a different colour with the colour written next to it.
- Square/rectangle - GREEN
- Circle - BLUE
- Triangle – RED
- Other strange shapes – ORANGE
- 1 camera with one supervisor/helper (maybe a parent or teachers aide)
- Clipboard and paper for note taking
- Coloured textas and/or highlighters
Body of the Lesson:
DAY 1 – Morning activity
Section 1 – (30mins)
An introduction about shapes, symmetry and patterns in the real world presented by the teacher whilst drawing examples on the whiteboard. Tell students what this lesson will be about and what will be happening.
Section 2 – (approximately 2 hours – 20-30mins per group)
Students to be split up into groups of 5-7 and one group at a time go on a walk around the school and select a building or house to take a photograph of, this is so children can look and understand shapes can be found in anything. The child can take the photo with the help of the adult supervisor. The adult/supervisor will note down on paper the child’s name and what number photo is theirs. On their journey children are to collect one piece of nature that resembles a shape and/or pattern and take it back to the classroom with them.
Whilst the groups are out on their walk the teacher can talk with all remaining students about shapes, ask the children to spot shapes in objects around the classroom starting with circle. Each student to go separately, stating a circle object or something with a circle shape in it, until all have had a turn. This will get the children into practice with the next leg of the activity spotting shapes in the real world.
Section 4 (approximately 1 hour)
Once all children are back, sit in a large circle on the floor, each child with their piece of nature. Each child is to take in turns explaining what shapes they can see in it and with the help of the teacher any patterns. Can include class discussion on what others think.
TO BE COMPLETED BY TEACHER
Teacher to print off each child’s photo (with the number printed on it) on A4 paper in light grey scale. The photo is to fit the page. Teacher to refer to the helpers notes to identify which photo belongs to each child.
DAY 2 – Morning activity
Section 1 – (1hour)
Mathematics - Shapes and patterns - wk 2 activity.pdf
Children will be given a copy of their photo printed in light gray scale blown up in full on A4 paper. Each child is to refer to the examples and the colours on the whiteboard to trace shapes that they can see in the photo, for example squares in green (the window outlined in green).
Each child’s photo with the outlines drawn on them gets displayed around the room as a reminder of the lesson and for parent display.
Concluding the Lesson:
In a group discussion ask the children the places they found square shapes, then circle shapes, then triangle shapes. Ask them if they found any different shapes. Discuss what these might be. Were there any shapes found in strange places? Was their building symmetrical?
Mathematics in Sport usually appears as player or team statistics, this helps also with chance and probability odds for sports betting. Whether you are watching a game of basketball, football, tennis or even a car race; different things like scores, hits, kicks, time outs, time and lap time gets calculated using equations for averages and data recorded using statistical analysis. Mathematics can also appear in athletics for example marking out distances and lines for running tracks using geometric equations and formula to work out the starting points and distances around an oval. Mathematics in sport is the actual calculation of statistics or geometry.
Numeracy in Sport is being able to read, understand and evaluate statistics or team ladders in the newspaper, talk about such chosen sport scores with friends, and during a game know who is winning, how many more goals or points are needed to win and how much time is remaining. Numeracy is needed by sports fans to assess the statistics and results after or even during a game.
Year level: 4
Learning area: Data representation and interpretation
Time: 2-3 hours
Lesson format: Integrated and single subject specific
A great activity to make this concept exciting to students could be to watch a basketball game; whether you visit a high school or watch a quarter or so on screen, each student is given a player to watch and count their goals. At the end of the game students will share with the class their results which can be written up on the whiteboard. Each student is to create a graph showing each player and the number of goals each scored. The Australian Curriculum recommends that children in year 4 should learn to “construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values” (ACARA, n.d.).
Maths and Numeracy in Sport
Helping hands home repair - Front of small house (n.d.)
Maths and Numeracy in Money
Maths and Numeracy in Cooking
The Fibonacci Sequence
Maths in architecture
The Fibonacci sequence is named after its founder Fibonacci; also known as Leonardo Pisano. The Fibonacci sequence is a pattern of numbers where a number is found by adding up the two numbers before it (Horn, 2013).
The sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89……
- The 2 is found by adding together the two numbers before it (1+1)
- Similarly, the 3 is found by adding together the two numbers before it (1+2)
- The 5 is (2+3), and so on.
Other than just being a sequence or a pattern written down on paper, the Fibonacci sequence can often be found in nature and in every day occurrences such as in flowers, leaves, fruit, pine cones, shells, brick walls, honeycombe and much more.
Fibonacci Flower (Britton, 2011)
Fibonacci Spiral (Maths is fun, 2013)
Spiral and shell. (Knott, 2013)
Red Flower. (Platt, 2011).
Fibonacci Flower, (Britton, 2011)
Leonardo Pisano, Fibonacci (Fibonacci Numbers and the Golden Section, n.d.)
Front of small house. (Helping Hands Home Repair, n.d.).
From pyramids in Egypt, to religious domes in Rome, to the lines and angles found in the modern buildings of today and in our homes, architecture is largely based on shapes. The mathematical qualities of shapes are essential to the design of any standing structure; you can't construct any building without an understanding of this (Rugland, 2013).
Children during their foundation year start by sorting, describing and name familiar two-dimensional shapes and three-dimensional objects in the environment (ARACA, n.d.).
Australian Note Money. (ewealth, 2013)
According to the Ministerial Council for Education, Empoyment, Training and Youth Affairs (MCEETYA), Numeracy is defined by the use of mathematics to meet the everyday demands of school, at home, at work and for participation in life (as cited in the National Numeracy Review Report, 2008).
Money is a great part of everyday life and numeracy is applying math to the everyday involvements in managing family budgets, managing bank accounts and credit cards, and grocery and accessory shopping., for example being able to calculate the right amount of change.
Mathematics is about knowing the formulas necessary to calculate these everyday situations with money. Addition, subtraction, division, multiplication, estimation, rounding, how many cents to $1.00, and the value of notes and coins are all necessary math skills.
Year Level: 3
Learning Area: Money and financial math
Time: 3 hours
Lesson format: Team Learning
A fun activity for a year 3 class would be to set up a mini shop in the classroom with various shops. The children have ‘fake’ Australian money and they will take in turns in being the customer; buying items and handing over the right money. Then being the shop keeper and calculating the right change. According to ACARA year 3 students will be able to learn to “represent money values in multiple ways and count the change required for simple transactions to the nearest five cents” (n.d.).
Numeracy in cooking is being able alter recipes according to the amount of people you are serving using the correct ratios and applying math to it.
Mathematics in cooking is using the formula and calculations for conversions in temperature and measurement. Math in cooking requires knowledge of addition, subtraction, multiplication, division, fractions, ratios, estimation, cost and time. It is most important to understand how to multiply fractions. If the recipe calls for ¾ cup of water and you want to make 3 times the amount that the original recipe creates, you need to know the correct formula to use for example:
Not knowing the correct way or just using estimation may result in a poor outcome for your cooking.
Sydney City Buildings. (The Planning Boardroom.net, 2011)
Throughout this presentation we have discussed that maths and numeracy are big parts of everyday lives. The Department of Employment, Education, Training and Youth Affairs states the "students without appropriate levels of numeracy are at risk in their learning and general progress at school" (1997, p 12).
A positive attitude is the first step to success in maths, but yet the last thing we get from students (Willis, 2010).
It is up to parents and teachers to shed a positive light on mathematics; by using some of the examples in this presentation or creating your own, we need to help make learning maths fun.
Thank you for watching my presentation
Mathematics and numeracy are similar in the aspect that they both involve the same content areas for example: numbers, patterns, measurement and geometry, statistics and probability.
Children can be taught this is the classroom by giving them a real recipe, and asking them to calculate enough to serve the whole class. Once it is done the children get to taste test the recipe that the teacher prepared earlier - this is an added incentive!