Week 1: 2016

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?

pancakes

This recipe serves 4 people, 2 pancakes each

  • 2 cups self raising floursifted (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.

Year 7 and 8 Algebra

Algebra_balance_scales

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There are many skills to learn to master Algebra, but we have already made a great start – You :

1. Can recognise and continue a pattern

2. Understand that a pro-numeral (a letter) represents a variable (changing number)

3. Understand that it is mathematical convention to leave out the multiplication sign in expressions and equations involving pro-numerals.

4. Can substitute positive and negative numbers into an equation

5. Can plot points on a cartesian plane

6. Can determine the equation from a table of values

7. Can solve an equation using backtracking

The next step is to be able to solve an equation by doing the same operation to both sides. Try these online activities:

Algebra Balance Scales (a virtual manipulative from Utah State University)

Algebra Balance Scales with negatives (same as above, but with negative numbers)

Equation Buster – from MathsNet

Year 7 and 8 Statistics

Candies

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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

stem_leaf1

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)

moth_tessellation

 

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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)

family_feud

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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