Week 6 Probability and Assessment MATHS Week 6 Probability and Assessment

Multiplication Challenge Multiplication Challenge! You have 5 minutes to fill in as many as you can – good luck!

Answers

What are we going to do this week? Ratio recap! Probability Use probability vocabulary, write probabilities as fractions, decimals or percentages and use a probability scale Understand the difference between theoretical and experimental probability Fractions Use and understand proper and improper fractions Convert between proper and improper fractions Assessment

Find value of one share if you know the value of the whole amount…

£350 £??

£350 £?? How did you work it out?

£350 £70 350 ÷ 5 = 70

£350 £70 £70 £70

£350 £70 £70 £70 3  70 = 210

£350 £210

£350 £210 £??

Find value of one share if you know the value of the other share…

£20

£20 ??

£20 £30

£20 £30 How did you work it out?

Try these problems, some in pictures and some in words…

Jim’s Jemima’s Write down the ratio using the colon notation…

£800 Jim’s Jemima’s Find the value of Jim and Jemima’s shares…

£?? £280 £?? Find the value of the whole amount and the missing share…

Write down the ratio using the smallest whole numbers you can…

Best Buy

Tesco sell pineapples at £4.20 for 3. Where should the minions shop? The minions go shopping for pineapples! Asda sell pineapples for £3 for 2. Tesco sell pineapples at £4.20 for 3. Where should the minions shop? What is the cheapest the minions can pay for 12 pineapples? 3 ÷ 2 = 1.5 1.5 x 12 = 18 £18 at Asda 4.20 ÷ 3 = 1.4 1.4 x 12 = 16.8 £16.80 at Tesco

The minions go banana-shopping. Bob finds 4 bananas cost 88p. Pete finds 9 bananas cost £1.89 Which is the cheaper deal…? 0.88 ÷ 4 = 0.22 £0.22 for 1 banana for deal 1 1.89 ÷ 9 = 0.21 £0.21 for 1 banana for deal 1

One shop sells 100g of pineapple for £2.20. Another sells 250g of pineapple for £5.40. Which is cheaper? If the minions need 1kg of pineapple, what is their cheapest option? 2.2 ÷ 100 = 0.022 0.022 x 1000 = 22 £22 for 1kg OR 2.2 x 10 = £22 for 1kg 5.4 ÷ 250 = 0.0216 0.0216 x 1000 = 21.6 £21.60 for 1kg OR 5.4 x 4 = £21.60 for 1kg

Probability

Washing Line Activity Yes! ? No! Maybe

Probability Scale: ¼ ½ ¾ Probability is given as a value between 0 and 1, with 0 being impossible and 1 being certain 0.25 0.75 1 0.5 ¼ ½ ¾ 25% 50% 75% 100%

Probability The probability of an event happening is: The number of ways that event can happen The total number of possible outcomes

What is the chance of getting a 6 with one dice?

What is the chance of getting a 6 on this spinner? 2 4 6 6 2

What is the chance of getting an odd number on this spinner? 1 2 3 4 5

What are the chances of getting a 6 on this spinner? 5 4 3 3 6

True or false? 14 questions – true or false?

1. When you roll a fair six- sided dice, it is harder to roll a six than a four. False – a fair dice, so all numbers have equal chance

2. Scoring a total of three with two dice is twice as likely as scoring a total of two. True – look at the combinations: next slide

True – look at the combinations: A score of two can only be obtained in one way – a 1 on each dice. A score of three can be obtained in two ways – 1 and 2 or 2 and 1, so the three is twice as likely.

3. In a lottery, the six numbers 3, 12, 26, 37, 44, 45 are more likely to come up than the six numbers 1,2,3,4,5,6. False – each number has the same chance

The probability of two heads is therefore 4. When two coins are tossed there are three possible outcomes: two heads, one head, or no heads. The probability of two heads is therefore False – look at the combinations: next slide

False because there are four outcomes: HH, HT, TH, TT So the probability of HH is one out of four, or

5. In a ‘true or false’ quiz with ten questions, you are certain to get five right if you just guess.  False – you would expect five right, but because of chance it won’t happen every time.

6. After tossing a coin and getting a head five times in a row, the next toss is more likely to be a tail than a head. False – only gamblers believe their luck will change. The probability will be 1/2 each time, whatever happened before.

7. My friend has four daughters. If she has another baby, it is more likely to be a girl than a boy. False, same as with the coin, unless you look at scientific results, which might suggest various things.

There is an evens chance of it raining on any given day. 8. There is an evens chance of it raining on any given day. False – just look at any weather records. It really does not rain on half the days of a year.

The probability of there being an eclipse at noon tomorrow is zero. 9. The probability of there being an eclipse at noon tomorrow is zero. True – again, look at the records.

10. If I play the national lottery, I have just as much chance of winning as anyone else. False – some people may buy lots more tickets than you.

Probabilities add up to 1

Harder exam questions

Theoretical & Experimental Probability When asked about the probability of a coin landing on heads, you would probably answer that the chance is ½, 0.5 or 50% right?

The theoretical probability is what you expect to happen, but it isn't always what actually happens. The table below shows the results after Sunil tossed the coin 20 times.

The experimental probability of landing on heads is: 13/20 = 0 The experimental probability of landing on heads is: 13/20 = 0.65 It actually landed on heads more times than we expected.

Now, Sunil continues to toss the same coin for 50 total tosses Now, Sunil continues to toss the same coin for 50 total tosses. The results are shown below. Now the experimental probability of landing on heads is 26/50 = 0.52 The probability is still slightly higher than expected, but as more trials were conducted, the experimental probability became closer to the theoretical probability.

Improper FRactions

Mixed Number – Top Heavy Fraction 1 4 5 Step 1 – multiply the whole number by the denominator. Step 2 – then add the numerator. 9 5 1 x 5 = 5 REMEMBER that the denominator ALWAYS stays the SAME. 5 + 4 = 9 2 1 3 Step 1 – multiply the whole number by the denominator. Step 2 – then add the numerator. 7 3 2 x 3 = 6 REMEMBER that the denominator ALWAYS stays the SAME. 6 + 1 = 7

Mixed Number – Top Heavy Fraction 1. 1 3 10 2. 3 3 4 3. 1 2 7 4. 2 1 4 6. 2 4 5 7. 5 3 8 8. 8 7 9 5. 9 1 2

Top Heavy Fraction – Mixed Number 11 4 Work out how many 4’s go into 11. 2 remainder 3 2 3 4 This gives you: REMEMBER that the denominator ALWAYS stays the SAME.

Top Heavy Fraction – Mixed Number 14 5 13 3 19 2 23 7 1. 2. 3. 4. 14 10 55 6 35 8 12 11 7. 8. 5. 6.

Operations with mixed number fractions 2 2 5 ×1 1 2 12 5 × 3 2 = 36 10 =𝟑 𝟔 𝟏𝟎 1 1 5 ÷2 2 4 6 5 ÷ 10 4 = 24 50 = 𝟏𝟐 𝟐𝟓 2 3 4 + 5 1 2 11 4 + 11 2 = 22+44 8 = 66 8 =𝟖 𝟐 𝟖 2 1 5 −1 2 4 11 5 − 6 4 = 44−30 20 = 14 20 = 𝟕 𝟏𝟎

Half Term Mini Assessment You now have one and a half hours to complete the mini assessment. You are expected to stay for the full time. If you finish the assessment early, use the time wisely to check through your answers.