Weights

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
NA2-1: Use simple additive strategies with whole numbers and fractions.
Student Activity Dr Martin the chemist is weighing out some pills.

He has some 5g weights and some 7g weights.

Can he weigh exactly 38g of pills?

Specific Learning Outcomes
Measure using grams
Apply addition to a measurement problem
Devise and use problem solving strategies to explore situations mathematically (be systematic, use equipment).
Description of Mathematics

This problem gives students the chance to do some number investigations using combinations of 5 and 7.  This helps extend their experience and knowledge of number,  and can also extend their experience of weights and the use of balance scales.

Required Resource Materials
Activity

Problem

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

Teaching sequence

1. Ask the students to find an object that they estimate weighs 20g. Check estimates on the (balance) scales.
2. Discuss students' 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? /How do you use these kitchen scales?
3. Pose the problem.
4. As the students 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

38 is not exactly divisible by 5 or 7. Hence both 5g and 7g weights are needed. 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 7g weights and two 5g weights.

Extension:

( 9 x 5, 1 x 7 ) or (6 x 7, 2 x 5)

Attachments
Weights.pdf146.77 KB