Problem
Dr Martin the chemist is weighing out some pills. He has some 5gm weights and some 7gm weights. Can he weigh exactly 38gm of pills?

What is this problem about?
This problem gives children the chance to do some numerical experiemtns using combinations of 5 and 7.  This helps extend their experience and knowledge of number,  It can also extend their experience of weights and the use of balance scales.

Achievement Objectives
Measurement (Level 2)
- carry out practical measuring tasks, using appropriate metric units for mass

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (be systematic, use equipment)

Resources
balance scales and weights (5g and 7g)
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- measure using grams
- apply addition to a measurement problem

Teaching sequence

1. Ask the children to find an object that they estimate weighs 20g. Check estimates on the balance scales.
2. Discuss children's ideas about how they made their estimates of 20g (eg, weight of small chip packet = 18g, flake bar = 30g). What object in your desk would weigh close to 38g? How did you decide that?
   How do you use weights on a balance scale?
3. Pose the problem.
4. As the children work on the problem in pairs ask questions that focus their understanding of the size of grams.
5. Focus their thinking on working systematically by asking questions about the way that they are keeping track of their work.
   What are you doing?
   How will you share what you have done with others in the class.
   How do you know that you are on the right track?
6. Share solutions

Extension to the problem
Can the chemist weigh out 52g ? Can this be done in more than one way?

Solution
Now 38 is not exactly divisible by 5 or 7. Hence both 5gm and 7gm weights are needed. Now 38 – 7 = 31, 38 – 2 x 7 = 24, and 38 – 3 x 7 = 17 are not divisible by 5. However, 38 – 4 x 7 = 10 = 2 x 5. So Dr Martin can use four 7gm weights and two 5gm weights.