Summer Holiday 2019 Solutions

Summer Holiday 2019 Solutions Deputy First Minister’s Maths Challenge MATHS ROCKS! Puzzle 1 – Family Archery Challenge 10 10 30 20 18 16 15 14 12 10 10 On their Summer holiday, the Archer family go to an archery activity and compete against each other. Based on the target scoreboard above, can you work out the following puzzles: All of the arrows land on the board and each round has 4 arrows. Round 1 – Mum scores 54, Dad scores 55, Iona scores 70 and Harris scores 58. Suggest how each family member might have scored with their arrows to get their total. There are a few ways, here is an example: Mum 14 18 12 10 54 Dad 15 14 16 10 55 Iona 30 16 14 10 70 Harris 10 14 16 18 58 Puzzle 1 – Family Archery Challenge Round 2 – Each member of the family scores the same total with their 4 arrows. Can you find a total where they managed this with different combinations of arrows? Scores on the target board can be used more than once. There are a few ways, here is an example: Mum 20 10 15 15 60 Dad 20 20 10 10 60 Iona 18 12 16 14 60 Harris 10 14 16 20 60 There is a sign offering anyone that scores over 60 with 3 arrows another game free. How many possibilities can you come up with for this, and what are they? Here is an example answer: 18 + 20 + 30 = 68 Puzzle 2 – Summer Holiday Packing Iona has packed 3 different t-shirts, 3 different pairs of shoes and 3 different pairs of leggings in her rucksack. How many different outfits can she make? Can you explain how you worked it out? The table below contains all the possible combinations of leggings and shoes that Iona can choose to wear: green leggings pink leggings + trainers blue leggings + trainers + trainers green leggings pink leggings + boots blue leggings + boots + boots green leggings pink leggings + canvas blue leggings + canvas + canvas If we now include the orange t-shirt with each legging and shoe combination, we can work out that there are 9 different outfits. If we include the green t-shirt with all of the above options = 3 + 3 + 3 = 9 If we include the pink t-shirt with all of the above options = 3 + 3 + 3 = 9 So a combined total of 3 x 9 = 27 Puzzle 3 – Puzzle Book + + = 45 + + = 25 + + = 33 + x = ? Iona and Harris cannot agree on the correct answer to the puzzle. Iona thinks it is 68 but Harris does not. What do you think is the correct answer? Can you explain this for Iona and Harris? The correct answer is 68. The values of parts of the puzzle is below: 15 9 8 4 Puzzle 4 – Scotland Team Activity The family are talking about their favourite players from the Scottish Women’s Football Team World Cup 2019 squad. They have turned this into a guessing game and are giving each other clues to help them find the player. Can you find the name of each family member’s favourite player? Mum Harris • she plays for a Scottish team • her goals scored total is a prime number • her caps and age are both even numbers • she is a Forward • her goals scored is 32 • the total of her age, caps and goals scored is a multiple of 10 Who could it be? Who could it be? Hayley Lauder Lisa Evans Iona Dad 1 • her age is 4 of 100 • the total of all three statistics is even • she has not yet scored any goals • she is in her 20s • her number of caps can be • she has one clean sheet divided equally by 17 and 2 Who could it be? Who could it be? Kirsty Smith Lee Alexander Puzzle 5 – Shape Task How many triangles can you see? Harris thinks the answer to the question is 26 but Iona thinks Harris is wrong. Who is right and why? There are 36 small triangles and 28 larger triangles within the larger shape overall. When looking for triangles, Harris spotted lots of other shapes. How many different shapes can you find? Look carefully, not all shapes are obvious at first glance! There are a range of regular and irregular shapes that can be found within the larger shape overall for example: quadrilaterals – parallelogram, rhombus, trapezium (4 sided shapes) pentagons – 5 sided shapes hexagons – 6 sided shapes heptagons – 7 sided shapes octagons – 8 sided shapes nonagons – 9 sided shapes decagons – 10 sided shapes hendecagons – 11 sided shapes dodecagons – 12 sided shapes .

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