Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Philosophy of mathematics wikipedia , lookup
Mathematics and architecture wikipedia , lookup
Mathematics and art wikipedia , lookup
Mathematics wikipedia , lookup
History of mathematics wikipedia , lookup
Critical mathematics pedagogy wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Ethnomathematics wikipedia , lookup
Secondary School Mathematics Curriculum Improvement Study wikipedia , lookup
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 240 ÷ 4 = 60 12 X 5 = 60 ÷ 4 12 x 5 Which number must go into the box on the right side of the scales to balance them with the left side? Answer 240 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Amy has 6 different coins in her purse. She has £2.68 altogether Which six coins does she have? Write your answer starting with the smallest coin. 1p, 2p, 5p, 10p, 50p, £2 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jack colours the empty triangles on this shape red How many sixteenths does he shade red? 10 16 5 8 X2 = 10 16 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 200C The arrow indicates the temperature in a town at 9:00 a.m. By mid-afternoon the temperature has risen by 70C. 120C The temperature then falls by 130C. What is the new temperature? 00C -10C - 10C -200C PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 In his cricket innings Tom scores 47 runs. His score is made up of: two sixes, three fours, one three and seven twos. The rest he scores in singles. How many singles does he score in his innings? 2 x 6 = 12 3 x 4 = 12 1 x 3 = 3 7 x 2 = 14 Total 41 47 - 41 = 6 6 singles PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 24cm Diameter is 9.5cm x 2 = 19cm 19cm 24cm The short side of the rectangle is the same length as the diameter of the circle. The radius of the circle is 9.5 cm. What is the perimeter of the rectangle? 19cm + 24cm = 43cm 43cm x 2 = 86cm 86cm PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The shape above is rotated one quarter turn to the right. Draw the shape in its new position below. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jason subtracts 0.25 from each of these decimals. Rewrite the new decimals in order starting with the smallest 0.55 0.5 1.8 0.35 1.5 0.3 0.25 1.55 0.1 1.25 0.1 0.25 0.3 1.25 1.55 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 At sports day Joe makes a standing jump of 1.8 m. Jade jumps 25 cm more than Holly. Tom jumps 10 cm more than Jade. Holly jumps 15 cm less than Joe. How far does Tom jump? 1.8m Joe 1.65m Holly 1.9m Jade 2.0m Tom 2m or 200cm PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 It takes Amy 25 minutes to walk to school. School starts at 8:55 a.m. She likes to arrive 10 minutes early. What time does Amy normally set off for school? 8:55 - 10 min. = 8:45 8:45 - 25 min. = 8:20 8:20 a.m., 08:20, twenty past eight PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Three different children do the calculations below. They then add up their answers. What is the total of their three answers? Ben calculates a quarter of 464 116 Amy calculates 20% of 900 180 Alex calculates the product of 7 and 45 315 611 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 How many different rectangles are there in this drawing? 10 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Each face of this cube has a surface area of 81cm2 Chelsey wants to build a tower of cubes 216cm tall. How many cubes does she need? 24 cubes The edge of one face is √81cm2 216cm ÷ 9 = 24 = 9cm PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The rule for the sequence below is find a quarter and add two. Which two numbers complete the sequence? 24 8 4 3 2¾ 4 ÷ 4 = 1 1 + 2 = 3 3 ÷ 4 = ¾ ¾ + 2 = 2¾ PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 1 QUESTION NUMBER 20 Calculate one eighth of a quarter of a third of one-half of 72 Your answer will be a fraction. 3/8 72 ÷ 2 = 36 36 ÷ 3 = 12 12 ÷ 4 = 3 3 ÷ 8 = 3/8 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The product of three numbers is 48. Two of the numbers are 2 and 3. What is the third number? 8 2 x 3 = 6 48 ÷ 6 = 8 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Joe has one of each coin up to and including £2. How much less than £10 does he have? £6.12 £2 + £1 + 50p + 20p + 10p + 5p + 2p + 1p = £3.88 £10 - £3.88 = £6.12 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 15 sheets of paper weigh 7.5 grams. How much does one sheet of paper weigh? 0.5g 7.5g ÷ 15 = 0.5 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 400 A 700 X 600 C B 700 In the sketch the isosceles triangles A, B and C are the same size. Calculate angle X 600 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 91 37 63 49 39 27 51 61 43 35 19 85 21 93 29 15 Identify the five prime numbers located in the grid. What is the total of the five numbers? 189 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 1 5 4 9 2 7 2 The top number in this puzzle is found by adding all the digits below together. The bottom number is the product of the three numbers above. Calculate the two answers needed to complete the puzzle and add together your two answers. 87 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 8 The area of this square is 64cm2. The drawing below is made up of squares the same as this one. What is the perimeter of the new shape? 80 cm 8cm 12 sides each 4cm 8cm 8cm 8cm 4cm x 12 = 48cm 8cm x 4 = 32cm 48cm + 32cm = 80cm PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 By Christmas a football team has scored 18 goals. This is 25% of their final total for the season. Jack scores 1/3 of the season’s total goals. Tom scores five less than Jack. 13 goals were scored in January. Irrelevant How many goals were scored by the rest of the team? 29 The team scores 18 x 4 goals a season. Total 72 Jack scores 72 ÷ 3 = 24 goals Tom scores 24 - 5 = 19 goals Jack and Tom score 24 + 19 = 43 goals The rest score 72 - 43 = 29 goals PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 28 46 85 57 18 63 102 45 The numbers in the squares are the sum of each number in the circles on each side. Which numbers are missing from the blank shapes? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 180km AYTOWN 360km BETOWN CETOWN Train X sets off from Aytown at 11:30 and travels at 90km per hour. Train Y sets off from Cetown at 12:15 and travels at 80km per hour. How much later does train Y arrive at Betown than train X? 3hrs 15min, 3 ¼ hours, 195 minutes PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A litre of water weighs 1kg. Jack fills a plastic bottle with 0.75L of water. Together the bottle and water weigh 835g. What is the weight of the bottle? 85 g The water weighs 750g Subtract the weight of water from the combined weight of the water and the bottle. The bottle weighs 835g - 750g = 85g PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A palindrome number is one that reads the same backwards as it does forwards, e.g. 8558. Which of the calculations below produce palindrome numbers? A 29 X 24 900 1233 696 B 30 X 30 C 11 X 11 X 11 1331 D 1437 + 2006 3443 E 232 + 1001 A, C, D PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 14cm 14cm The area of each circle is 38cm2 The diameter of each circle is 7cm. What is the area of the grey shaded background? Area of the grey square 14cm x 14cm = 196 cm2 Area of the four circles 152 cm2 44cm2 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Say whether these statements are true or false A All three digit numbers are divisible by 3 without a remainder B If you add the digits of a four digit number your answer will be an even number C All prime numbers are odd D A square number cannot also be a triangular number E Numbers ending in 0 are multiples of only 5 and 10. All are FALSE PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 What fraction of the large square is shaded grey? Answer in lowest terms 10/16 5/8 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of this square is 64cm2. The drawing below is made up of squares the same as this one. What is the area of the new shape? 208cm2 ¼ of a large square is 16cm2 There are two whole squares 64cm2 x 2 = 128cm2 There are 5 quarter squares. Area is 16cm2 x 5 = 80cm2 128cm2 + 80cm2 = 208cm2 Alternatively PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of this square is 64cm2. The drawing below is made up of squares similar to this one. What is the area of the new shape? 208cm2 Insert lines to make each large square into quarters ¼ of a large square is 16cm2 There are13 quarter squares. Area is 16cm2 x 13 = 208cm2 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 19 40% of a number is 120. What is one-third of the number? 100 10% of the number is 120 ÷ 4 = 30 100% - the whole number - is 30 x 10 = 300 One-third of 300 is 100 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 ÷ 4 12 x 5 Which number must go into the box on the right side of the scales to balance them with the left side? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Amy has 6 different coins in her purse. She has £2.68 altogether Which six coins does she have? Write your answer starting with the smallest coin. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jack colours the empty triangles on this shape red How many sixteenths does he shade red? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 200C The arrow indicates the temperature in a town at 9:00 a.m. By mid-afternoon the temperature has risen by 70C. The temperature then falls by 130C. What is the new temperature? 00C -200C PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 In his cricket innings Tom scores 47 runs. His score is made up of: two sixes, three fours, one three and seven twos. The rest he scores in singles. How many singles does he score in his innings? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 24cm The short side of the rectangle is the same length as the diameter of the circle. The radius of the circle is 9.5 cm. What is the perimeter of the rectangle? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The shape above is rotated one quarter turn to the right. On the shape below draw the missing pieces in their new position to complete the drawing. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Jason subtracts 0.25 from each of these decimals. Rewrite the new decimals in order starting with the smallest 0.55 0.5 1.8 0.35 1.5 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 At sports day Joe makes a standing jump of 1.8 m. Jade jumps 25 cm more than Holly. Tom jumps 10 cm more than Jade. Holly jumps 15 cm less than Joe. How far does Tom jump? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 It takes Amy 25 minutes to walk to school. School starts at 8:55 a.m. She likes to arrive 10 minutes early. What time does Amy normally set off for school? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Three different children do the calculations below. They then add up their answers. What is the total of their three answers? Ben calculates a quarter of 464 Amy calculates 20% of 900 Alex calculates the product of 7 and 45 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 How many different rectangles are there in this drawing? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Each face of this cube has a surface area of 81cm2 Chelsey wants to build a tower of cubes 216cm tall. How many cubes does she need? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The rule for the sequence below is find a quarter and add two. Which two numbers complete the sequence? 24 8 4 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 1 QUESTION NUMBER 20 Calculate one eighth of a quarter of a third of one-half of 72 Your answer will be a fraction. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The product of three numbers is 48. Two of the numbers are 2 and 3. What is the third number? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Joe has one of each coin up to and including £2. How much less than £10 does he have? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 15 sheets of paper weigh 7.5 grams. How much does one sheet of paper weigh? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A 700 X C B In the sketch the isosceles triangles A, B and C are the same size. Calculate angle X PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 91 37 63 49 39 27 51 61 43 35 19 85 21 93 29 15 Identify the five prime numbers located in the grid. What is the total of the five numbers? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 4 9 2 The top number in this puzzle is found by adding all the digits below together. The bottom number is the product of the three numbers above. Calculate the two answers needed to complete the puzzle and add together your two answers. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 8 The area of this square is 64cm2. The drawing below is made up of squares similar to this one. What is the perimeter of the new shape? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 By Christmas a football team has scored 18 goals. This is 25% of their final total for the season. Jack scores 1/3 of the season’s total goals. Tom scores five less than Jack. 13 goals were scored in January. How many goals were scored by the rest of the team? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 85 57 63 45 The numbers in the squares are the sum of each number in the circles on each side. Which numbers are missing from the blank shapes? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 180km AYTOWN 360km BETOWN CETOWN Train X sets off from Aytown at 11:30 and travels at 90km per hour. Train Y sets off from Cetown at 12:15 and travels at 80km per hour. How much later does train Y arrive at Betown than train X? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A litre of water weighs 1kg. Jack fills a plastic bottle with 0.75L of water. Together the bottle and water weigh 835g. What is the weight of the bottle? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 A palindrome number is one that reads the same backwards as it does forwards, e.g. 8558. Which of the calculations below produce palindrome numbers? A 29 X 24 B 30 X 30 C 11 X 11 X 11 D 1437 + 2006 E 232 + 1001 PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of each circle is 38cm2 The diameter of each circle is 7cm. What is the area of the grey shaded background? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 Say whether these statements are true or false A All three digit numbers are divisible by 3 without a remainder B If you add the digits of a four digit number your answer will be an even number C All prime numbers are odd D A square number cannot also be a triangular number E Numbers ending in 0 are multiples of only 5 and 10. PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 What fraction of the large square is shaded grey? Answer in lowest terms PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 The area of this square is 64cm2. The drawing below is made up of squares similar to this one. What is the area of the new shape? PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009 SEMI-FINAL ROUND 2 QUESTION NUMBER 19 40% of a number is 120. What is one-third of the number?