Archery

Intention
This activity can be modelled as a whole class activity followed by children working in pairs or small groups during the main part of the lesson.

Outcomes
Children will use the relationship between multiplication and division to help them make sensible approximations. 
They will make use of their previous answers to refine the solution.
Some children will use the memory function of the calculator.

NNS references

Years 6 

Numbers and the number system

Fractions, decimals, percentages, ratio and proportion

• Order a mixed set of numbers with up to three decimal places

Calculations

Understanding multiplication and division

• Understand and use the relationship between the four operations

Pencil and paper procedures

• Approximate first. Use informal pencil and paper methods to support record and explain multiplications.

Using a calculator

• Develop calculator skills and use a calculator effectively

Solving problems 

Reasoning and generalising about numbers

• Explain methods and reasoning orally

• Solve mathematical problems or puzzles, recognise and explain patterns and relationships...

Resources

A random number generator.
An overhead projector and calculator.
Children's set of calculators, activity sheets and pencils.

Activity

Children work in pairs or in small groups. One team generates a three-digit number less that 200, this is the bull (the target number).
The other team generates a two-digit number, this is the arrow.
Teams take it in turns to enter a multiplication in the calculator, using the 'arrow' as one of the numbers. They must aim to get as close to the 'bull' as possible. 
Each team has three attempts; they should record each calculation and score their best attempt.
Teams record their scores for each round and the overall winner is the team with the highest total score. 

Scoring

A bull scores 9 points
A red – (coming within 1 of the bull) scores 7 points
A blue – (coming within 2 of the bull) scores 5 points
A black – (coming within 4 of the bull) scores 3 points
A white – (more than 4 from the bull) scores 1 point

Observation, intervention questions to ask

Is the calculator being used appropriately?
Children's calculations show that they are refining their ideas and taking note of opponents' calculations.
For example:
Target 133 Arrow 31

Team 1 1st shot 31 x 4.0 = 124
Team 2 1st shot 31 x 4.5 = 139.5
Team 1 2nd shot 31 x 5 = 155
Team 2 2nd shot 31 x 4.3 = 133.3
Team 1 3rd shot 31 x 4.7 = 145.7
Team 2 3rd shot 31 x 4.29 =132.99

Team 1 is showing some evidence of refining their calculations, but is not taking note of Team 2's results.
Team 2 has shown evidence of using Team 1's results as well as refining their own calculations.

"Is your answer too big or too small?"
"How do you have to adjust your calculation to get closer to the bull?"
"Which of these numbers is bigger/smaller? How do you know?"

What learning has taken place?

Children approximate their answers by using knowledge of multiplication and division facts.
Children can refine their calculations making use of their ability to order decimals.
Some children can use the memory function.

Extension activities

Make the 'bull' a larger number.
Children use numbers involving two or more decimal places.



Archery

Write down the calculations you do for each shot.
Your best shot scores.