Year 8 Rates – Distance, time and speed

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Learning Intention: “Solve a range of problems involving rates and ratios, with and without digital technologies.”

It is very useful when travelling to be able to solve problems that involve time, distance and speed. For example, how long will it take for me to drive from Hawkesdale to Melbourne or if it takes me 2 hours to ride to Port Fairy, how fast was I riding? The equation we use is: velocity (speed) = distance divided by time. You need two of these variables to calculate the third.

BBC Bitesize has a good explanation and some problems to try.

In the example above, Google Maps shows that it takes 23 hours and 31 minutes to drive to Uluru, 2,157km away. So we have the time and the distance – what is the assumed speed we are travelling?

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Your tasks are:

(1)  Choose two locations and use Google maps to find out the distance between them. Then choose a speed to travel to calculate how long it will take to get there.

(2) Choose two different locations and calculate how fast you would need to travel to get there in one hour.

(3) Send me a copy of your questions and working out.

(4) Do the Bitesize Quiz and send me a copy of your score.

Great Victorian Coding Challenge

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Over the next few weeks we are working with Scratch to create projects that demonstrate maths concepts using simple drag-and-drop programming. Please make sure you have completed the following steps:

1. Join Scratch with your school Username (eg gow0054) and Password. Being a registered member allows you to save and share your work. Make sure Mrs Gow has recorded your Scratch username.

2. Join the Hawkesdale P12 College Studio and the Victorian Coding Challenge (1, 2 and 3) Studios on Scratch, so you can share your work and see what other students have created.

3. Challenge #1: Create a character that draws a shape and upload to the Hawkesdale P12 College page.

4. Draw your initials, like these students in 5/6 Clark/Smith. Can you translate and reflect your initials so they appear in all four quadrats?

5. Challenge #2: Create a project that explains a maths concept. For example:

  • Draw  your initials in block letters and calculate their perimeter and the area they cover. Use the Cartesian Co-ordinate grid as a background.
  • Explain how to calculate the perimeter of a polygon or circle.
  • Name the parts of a circle (radius, diameter, circumference, sector, arc)
  • Describe different triangles (equilateral, isoceles, scalene, right-angled, acute-angled or obtuse-angled)
  • Explain how the sum of angles in a triangle always equals 180 degrees.
  • Explain how the sum of angles in a quadrilateral always equals 360 degrees
  • Explain how to calculate the area of a polygon (triangle, rectangle, parallelogram, trapezium, kite) or circle
  • Describe right angles, straight angles and complementary (adds to 90 degrees), supplementary (adds to 180 degrees) and equal angles.
  • Describe ‘pi’ and how it can be used to calculate the circumference and area of circles.
  • Describe Euler’s Rule about the faces, vertices and edges of a polyhedron (Faces + Vertices – Edges = 2)

Make sure you add your project to the Hawkesdale P12 College Studio page.

6. Challenge #3: Create a simple game that uses maths concepts. It could be something like this Hungry Fish game. Someone even created a Scratch project for Co-ordinate Grid Battleships.

My favourite Middle Years Maths sites and resources

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This year I will be teaching both Year 7 and Year 8 students Maths in our small, rural school in SW Victoria. With relatively small class sizes and 1:1 BYOD we have great opportunities to engage students with high quality digital resources that help to foster a love of Maths learning.

Or, in the case of some teenagers, make them hate it a little less? Let’s face it, I work with adolescents every school day, and many of them haven’t yet found their passion. They have strong opinions about what they like (“Call of Duty” and One Direction, for example) and what they hate (mostly homework, uniforms and algebra). CoD and ID are much more relevant and useful than…..whatever.

So, to get on with this post, my intention is to share the middle years Maths resources that I find most useful, hopefully because students find them authentic, relevant or just plain fun, while addressing curriculum statements.

My Most Useful Sites and Resources:

  • ABC Splash – high quality resources, aligned to the national curriculum.
    • ConCensus – This game uses data from the Australian Bureau of Statistics to allow users to make graphs and diagrams using selected postcodes and categories.
    • Choose Your Own Statistics – This interactive activity has ten different categories (including demographics, weekly wages and homelessness) with infographics and a tool that allows users to visualise the data.
    • Area of a Triangle – a cartoon interactive that assists students to learn and practice the formula for calculating the area of a triangle.
    • Algebra – it’s a piece of cake – a series of eight videos that explain some simple algebraic concepts using a “number crunching machine”, recipes and simple patterns.
  • National Library of Virtual Manipulatives – Huge range of applets across all areas and age groups. (If you have difficulty accessing these interactive animations, try a different browser, update or enable your Java).
  • NRICH – enriching mathematics – Great problem solving activities for a variety of ages.

Hour of Code!

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This week is the beginning of the International Week of Computer Science, when tens of millions of students from over 180 countries participate in “Hour of Code”. This is a great activity to introduce students to computer science in a fun, easy and accessible way. Here are some resources to introduce coding in your classroom:

Hour of Code website

Khan Academy Introduction to Hour of Code – video and resources

Make a Flappy Game – a ‘drag and drop’ method to create your own version of the popular flappy bird game.

Code with Anna and Elsa from Frozen

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This week we have about 30 students from Year 7 to 9 attending school, while the rest participate in the end of year “Great Hawkesdale Bike Ride”. They enjoyed creating their own Flappy Bird and Angry Bird Games and then constructing Christmas scenes in Minecraft. Which games did you create, which was your favourite and why?

Windows Apps for Maths

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Our Year 7 and 8 classes received Microsoft Windows tablets at the beginning of last term, as part of a DEECD trial, “Inking your Thinking”. The students have enjoyed using these devices to access Mathletics, as well as playing the “2048” game in free time at the end of a lesson. However, there are some more good Windows apps that I would like each student to download onto their devices.

Number and Algebra

  • 100 chart (for prime numbers, multiples and factors)
  • Prime factors
  • Maths Wizard
  • Easy Fractions
  • Motion Maths – Fractions
  • Motion Maths – Hungry Fish
  • Fluid Math Online
  • Dragon Box ($5.99)

Measurement and Geometry

  • Geoboard
  • Math Geometry
  • Geometry 101
  • Solve Geometry Ver 2.0

Statistics and Probability

  • Charts
  • Bar Chart creator
  • Linear graph
  • GraphPad
  • Dice Roll simulator
  • Simple coin flipper

Graphs and Data

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Image created in Create-A_Graph

Last week you were working on a poster showing the results of a class survey in table and graphical form. This data is just a small sample of the school and state data. When governments and businesses want to plan for the future they need to know information about the whole population – for example, where roads, schools and hospitals need to be built. This information is obtained using a census. The national census is conducted every four years, when the Australian Bureau of Statistics asks every household to complete a survey.

Some of the data obtained in the 2011 census is recorded here. Choose one of the categories that you are interested in and create a graph of the data using “Create-A-Graph”. Email your graph to me and a copy to yourself.

Equivalent fractions with a Fraction Wall

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This week we will continue making our fraction wall and learning how to calculate equivalent fractions. Using your fraction wall, find equivalent fractions for the following: 1/2 (one half); 1/3 (one third); 1/4 (one quarter) 2/3 (two thirds) and 3/4 (three quarters). What are some other equivalent fractions that are “off the scale” – using fifteenths, sixteenths, twentieths or hundredths?

To add or subtract fractions we need to make sure they have the same denominator (bottom number). We can convert fractions so that they have the same denominator by multiplying both the numerator and the denominator by the same number. This interactive from NLVM helps to compare fractions and create fractions with the same denominator.

Here are some links to sites for learning more about fractions:

Area of a triangle

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Learning Intention: To understand how to calculate the area of a triangle and why the formula (A = 1/2 x base x height) works for all triangles.

Success Criteria: Students will complete the interactive “Area of Triangles” activity with at least 80% of answers correct.

Angles

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Learning Intention: “Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral.”

Success Criteria: Students will draw 2 copies of each of the triangles (acute, right-angled, obtuse, equilateral, isoceles and scalene) and show how, when the corners are removed, they can be placed on a straight line to form 180 degrees. This demonstrates that the sum of angles in a triangle is always 180 degrees.

This term we have started a new unit of work, learning how to estimate and measure angles. We have also identified and named triangles according to their side length and angles. Make sure you can identify and draw each of the following:

  • equilateral triangle (three equal angles)
  • isoceles triangle (two equal side and two equal angles)
  • scalene triangle (three different angles and three different side lengths)
  • acute angled triangle (all angles less than 90 degrees)
  • right angled triangle (one angle of 90 degrees exactly)
  • obtuse angled triangle (one angle greater than 90 degrees)

Remember that all the angles in a triangle always add to 180 degrees. The following links are to some interactive activities to investigate angles:

What’s my angle? from Ambleside Primary School.

Angle Activities from Ambleside Primary School.

Guess the angle from Crickweb.

Fractions interactives from NLVM

Fractions as we know them today weren’t used in Europe until the 17th century. However, Egyptians have been using fractions since at least 1800BC, although they never wrote fractions with a numerator greater than one. These are called unit fractions. Fractions with a numerator greater than one were expressed as the sum of unit fractions. Find out more at the History of fractions and Egyptian fractions.

The National Library of Virtual Manipulatives has a range of interactive applets that you can access to learn about fractions:

Try at least three of these interactives and write a comment below about what you have learned.