Year 7 and 8 Statistics

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YEAR 7 Standards:

  • Investigate, interpret and analyse graphs from authentic data
  • Identify and investigate issues involving numerical data collected from primary and secondary sources
  • Construct and compare a range of  data displays including stem-and-leaf plots and dot plots
  • Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data.
  • Describe and interpret data displays using median, mean and range.

Resources for Year 7:

 YEAR 8 Standards:

  • Data representation and interpretation – Investigate techniques for collecting data, including census, sampling and observation
  • Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
  • Explore the variation of means and proportions of random samples drawn from the same population
  • Investigate the effect of individual data values, including outliers, on the mean and median

Resources for Year 8:

Supporting Australian Mathematics Project –

Probability and Percentage increases and decreases

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Following our assessment task yesterday it is clear that some students need to revise certain areas of the work we have done in term 1 and 2:

Probability – Relative frequency with ten questions to complete.

Percentages – How to convert fractions and percentages to a pie chart (360 degrees) with ten questions to complete.

Percentage increases and decreases – Worked examples and five problems to solve. 

Stem and Leaf plotsWorked example and thirteen questions to solve. 

Problem #1: You have a list of 7 numbers. The average of the numbers is 9. If you take away one of the numbers, the average of the numbers is 8. What number did you take away?

Problem #2: Martin has completed five Maths tests and received an average score of 80%. What is the highest average he could have after the next test?

Problem #3: A Year 7 class was asked “How many goals did you shoot at lunchtime?”. The lowest answer was 5 and the highest answer was 20. The total of all the answers was 60. What is the smallest number of students who could have been asked?

Transformations and Tessellations (Year 7)

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This last week of Term 2 we will be doing some transformations and tessellations. Our learning intention is to understand and describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates and to identify line and rotational symmetries.

Your first task is to use the letters of your name, on a poster, to demonstrate your understanding of translation (slide), rotation (turn), reflection (flip) and dilation (increase in size).

Your second task is to use a shape that tessellates (fits together with no gaps or spaces) to create an artwork, similar to the ones in these YouTube videos:

These links will help you to plan, design and construct your own:

 

Percentages from first principles (Year 8)

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“We have surveyed one hundred people and asked them the question….” I’m guessing all of you have watched Family Feud at least once and heard Grant Denyer read out all sorts of questions and received some surprising answers from the players. This game is based on percentages, which is our topic of study for the next week. There are a series of concepts you need to understand, with increasing levels of difficulty, listed below:

  •  I understand that percentage means “out of one hundred”. 30% means 30 out of every 100 or 3 out of every 10 or 0.3 out of 1.0
  • I can (always, usually, sometimes, never) convert between percentages, fractions and decimals. For example, 25% = 25/100 = 1/4 = 0.25
  • I can (always, usually, sometimes, never) calculate the percentage of an amount (with/without) using a calculator. For example, 15% 0f 300 = 15 x 3 = 45
  • I can (always, usually, sometimes, never) calculate a percentage discount, profit or loss. For example, a pair of $80 jeans were on sale with a 10% discount, what is the sale price? $80 – (10% of 80) = $80 – $8 = $72.00
  • I can (always, usually, sometimes, never) work out the percentage increase or decrease of two amounts. For example, the median house price rose from $150,000 to $175,000, so the percentage increase was (175,000 – 150,000)/150,000 = (about) 17%

Some resources:

  1. Introduction to Percentages (Maths is Fun)
  2. ABC Splash video – converting fractions to percentages
  3. BBC Bitesize – Percentages and BBC Bitesize – Finding Percentages
  4. A BBC activity about Percentages
  5. Solving problems with percentages from Math Planet (with two videos)
  6. ABC Splash video – How Banks make Money
  7. Five quick questions to test your percentages from Maths is Fun
  8. ABC Splash – Design a Farm

Percentages, Profit and Loss (Year 8)

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Learning Intentions: Solve problems involving profit and loss, and the use of percentages, including percentage increases and decreases, with and without digital technologies.

Whenever you buy something, the shop owner has to put a price on that item, usually so that he can make a profit. Food such as fruit and vegetables will usually have a smaller margin (percentage profit) than more expensive items such as clothing and appliances. In Australia, the “Goods and Services Tax” (GST) of 10% is applied to almost all consumer items, except fresh produce. So, if you pay $55.00 for an item, $50.00 is for the shopkeeper and $5.00 is the GST, which goes to the federal government tax office.

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.

Euler’s Formula with jubes and toothpicks

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Learning Intention: To distinguish between prisms and other three-dimensional shapes and to work out the relationship between vertices, edges and faces (Euler’s Formula).

These two Year 7 students are making three-dimensional models with jubes and toothpicks (or satay sticks) to record vertices, edges and faces. Start with simple shapes, such as triangular pyramids, cubes and square pyramids, distinguishing between shapes that are prisms and those that are not. When students have made at least six or more shapes ask them to see if they can find a relationship between V (vertices); E (edges) and F (faces). I usually give a clue that they only need to use addition and subtraction (not multiplication or division).

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Year 8 – Increasing volume with three little pigs

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Let me tell you a story about three little pigs. The first pig built a house that was 2 metres high by 3 metres wide by 4 metres long. The second little pig wanted a bigger house, so he doubled the dimensions – his house was 4 metres high, by 6 metres wide by 8 metres long. The third little pig wanted to have the biggest house, so he doubled the dimensions again and built a house that was 8 metres high, 12 metres wide and 16 metres long.

Your task is to calculate the surface area and volume of each of the three houses and work out the ratio of SA:V for each house. Assuming that all the houses were made of the same materials and labour was not included, which house would be the cheapest to build per unit volume?

Year 7 – Area of Triangles

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To calculate the area of a triangle use the formula:

Area = One half multiplied by the base multiplied by the height  (A=1/2 x bh)

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