Just when they thought things couldn’t get any worse, the organisers of the Qatar Olympic Games are now tasked with trying to organise the chaos at the archery and gymnastic events! Use your knowledge of common factors to help them resolve their logistical nightmare!
More resources for Autumn Block 3 Step 3.
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Discussion points for teachers
1. Spectators must be seated in equal rows on both sides of the field. How many spectators could be sat on each row?
Discuss the numbers that have been given to you. What does a common factor mean? How could the seats be organised so that both sides of the field have rows made out of the same number of seats?
The common factors are : 1, 2, 3, 4, 6 and 12 so the most likely answer for rows of seats would be 12.
2. Is he correct? Explain why.
Discuss how many seats are shown in the array. Will this number allow for the seats on either side to be placed in equal rows? How can you prove this using arrays?
He is incorrect. There would be 1 too many seats in each row. 13 is not a factor of 48 or 60.
3. How many seats could there be on either side of the hall?
Discuss the information that has been given to you – which common factor would we need to use in order to generate two possible numbers? Would the numbers chosen fit the criteria set? This question is open-ended for the children to explore.
Various answers, for example: 42 seats on the left side of the hall and 84 seats on the right side of the hall. Both numbers would share a common factor of 7.
4. How many rows of arrows could each archer have been given?
Discuss the clues given. What common factor would be needed for both numbers of arrows? Which numbers would share a common factor? Do your chosen numbers match the criteria's shown?
Various answers, for example: Archer 1 could have 4 rows of 8 arrows (32 arrows), Archer 2 could have 7 rows of 8 arrows (56 arrows).
5. Using this information, how many arrows could each archer have been given?
Discuss which numbers would share a common factor of 16. Which two numbers would match the given criteria? Would the two numbers in your last answer work with this new fact?
Various answers, for example: Archer 1 could have 32 arrows (2 rows of 16 arrows), Archer 2 could have 48 arrows (3 rows of 16 arrows).
National Curriculum Objectives
Mathematics Year 5: (5C5a) Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
Mathematics Year 5: (5C8a) Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
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