Solving Math Problems with Patterns and Quantities

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Explore mathematical problem-solving strategies with scenarios involving quantities and patterns. From determining the number of flowers based on vases to calculating slices of cheese and tomato needed for sandwiches, these interactive examples enhance your understanding of basic mathematics concepts.


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  1. www.ncetm.org.uk/masterypd

  2. www.ncetm.org.uk/masterypd

  3. For every 1 vase, there are 5 flowers. If there are 3 vases, how many flowers are there? 1 5 = 5 3 5 = 15 www.ncetm.org.uk/masterypd

  4. For every 1 vase, there are 5 flowers. If there are 15 flowers, how many vases are there? 1 5 = 5 3 5 = 15 5 5 = 1 15 5 = 3 1 1 5 = 1 5 15 = 3 5 www.ncetm.org.uk/masterypd

  5. For every 10 grapes that Ralph eats, Lily eats 1. www.ncetm.org.uk/masterypd

  6. For every 5 blue marbles, there are 3 red marbles. If there are 15 blue marbles, how many red marbles are there? www.ncetm.org.uk/masterypd

  7. For every 5 blue marbles, there are 3 red marbles. If there are 15 blue marbles, how many red marbles are there? www.ncetm.org.uk/masterypd

  8. Each team in a family quiz is made up of 2 adults and 3 children. There are 12 adults in the competition. www.ncetm.org.uk/masterypd

  9. To make a cheese and tomato sandwich we need 2 slices of bread, 3 slices of cheese and 4 slices of tomato. www.ncetm.org.uk/masterypd

  10. What do we need to make 12 sandwiches? www.ncetm.org.uk/masterypd

  11. If we use 21 slices of cheese, how many slices of tomato do we need? www.ncetm.org.uk/masterypd

  12. A loaf of bread contains 26 slices. How many sandwiches can we make? What else do we need? www.ncetm.org.uk/masterypd

  13. Yukti puts 1 apple and 3 oranges in each bag. If she uses 8 apples, how many oranges must she use? www.ncetm.org.uk/masterypd

  14. Yukti puts 1 apple and 3 oranges in each bag. If she uses 15 oranges, how many apples must she use? www.ncetm.org.uk/masterypd

  15. Yukti puts 1 apple and 3 oranges in each bag. How many apples if there are 20 pieces of fruit altogether? www.ncetm.org.uk/masterypd

  16. Ingredients for 2 smoothies. What do you need to make 4 smoothies? What do you need to make 20 smoothies? www.ncetm.org.uk/masterypd

  17. What do you need to make 1 smoothie? www.ncetm.org.uk/masterypd

  18. If you use 1 litre of yoghurt, how many strawberries will you need? www.ncetm.org.uk/masterypd

  19. www.ncetm.org.uk/masterypd

  20. How many different outfits? www.ncetm.org.uk/masterypd

  21. How many different outfits? www.ncetm.org.uk/masterypd

  22. www.ncetm.org.uk/masterypd

  23. www.ncetm.org.uk/masterypd

  24. Rocky Island is 40km away. What would this distance be on the map? www.ncetm.org.uk/masterypd

  25. What would 15cm on the map represent in real life? www.ncetm.org.uk/masterypd

  26. There is a pond 0.4km away from the camp. How far would this be on the map? www.ncetm.org.uk/masterypd

  27. 1 cm on this drawing represents 30 cm in real life. Fill in the real-life measurements. 12 cm 4.5 cm 2 cm 8 cm 2 cm www.ncetm.org.uk/masterypd

  28. ___ cm on this drawing represents ___ cm in real life. Fill in the real-life measurements. ___ cm ___ cm ___ cm ___ cm ___ cm www.ncetm.org.uk/masterypd

  29. 15cm on the drawing represents 5m in real life. www.ncetm.org.uk/masterypd

  30. www.ncetm.org.uk/masterypd

  31. side-length of C = side-length of A 3 1 3 side-length of A = side-length of C www.ncetm.org.uk/masterypd

  32. www.ncetm.org.uk/masterypd

  33. www.ncetm.org.uk/masterypd

  34. dimensions of A : dimensions of C = 1 : 3 dimensions of C : dimensions of A = 3 : 1 www.ncetm.org.uk/masterypd

  35. www.ncetm.org.uk/masterypd

  36. Scale the lengths of the sides by a scale factor of 2. www.ncetm.org.uk/masterypd

  37. www.ncetm.org.uk/masterypd

  38. www.ncetm.org.uk/masterypd

  39. www.ncetm.org.uk/masterypd

  40. www.ncetm.org.uk/masterypd

  41. Compare the short sides Compare the long sides 3 = 1 3 6 = 2 3 height of B = height of A 3 width of B = width of A 3 dimensions of A : dimensions of B = 1 : 3 dimensions of B : dimensions of A = 3 : 1 www.ncetm.org.uk/masterypd

  42. www.ncetm.org.uk/masterypd

  43. www.ncetm.org.uk/masterypd

  44. www.ncetm.org.uk/masterypd

  45. www.ncetm.org.uk/masterypd

  46. www.ncetm.org.uk/masterypd

  47. www.ncetm.org.uk/masterypd

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