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Level Two > Geometry and Measurement

Weights

Keywords:
Achievement Objectives:

Achievement Objective: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Achievement Objective: Use simple additive strategies with whole numbers and fractions.

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 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.
 

Required Resource Materials: 
Balance scales and weights (5g and 7g)
Copymaster of the problem (English)
Copymaster of the problem (Māori)
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?
  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

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

Extension:

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

AttachmentSize
Weights.pdf37.32 KB
WeightsMaori.pdf43.28 KB

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