Weights

Purpose

This problem solving activity has a measurement focus.

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
Balance scales and weights.


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. It also builds their experience making measurement calculations. 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

The 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 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?
    What else could we use to measure these things?
  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. Encourage them to write their measurements with the correct unit (g - 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 are you recording your measurements?
    How do you know that you are on the right track?
  6. Share solutions

Extension 

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.

Solution to the Extension

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

Attachments
Weights.pdf156.11 KB

Printed from https://nzmaths.co.nz/resource/weights at 10:23am on the 29th March 2024