Cheese blocks

Purpose

The purpose of this activity is to engage students in solving a problem involving volumes of cuboids.

Achievement Objectives
GM3-2: Find areas of rectangles and volumes of cuboids by applying multiplication.
Description of Mathematics

This activity assumes the students have experience in the following areas:

  • Finding the areas of rectangles.
  • Finding the volumes of cuboids (rectangular prisms).
  • Working with metric units of measurement for length, area, and volume.

The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.

The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.

Activity

 

A cheesemaker exports 25 kg slabs of cheese with a base area of 1000 cm².

If a 1 kg block of cheese has dimensions 15 x 8 x 4 cm³, how high is each slab?

 

 


The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.

Make sense

Introduce the problem. Allow students time to read it and discuss in pairs or small groups.

  • Do I understand the situation and the words? (Students may need support to understand the meaning of words like “slab”, “base area” and “dimensions”.)
  • Am I familiar with the units used in the question? (The symbols kg, cm2, and cm3 may need clarifying for students.)
  • What will my solution look like? (The solution will give the height of a slab and be supported by correct calculations.)

Plan approach

Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.

  • What strategies will be useful to solve a problem like this? (A physical model or diagram might be a good first start.)
  • What maths am I going to need? How do I calculate areas and volumes?
  • Is it possible to solve the problem even when I don’t know the side lengths of the base? How? (Student may assign dimensions such as 25 cm x 40 cm to the base or leave the side lengths unclosed.)
  • Can I estimate the answer? How?
  • What tools (digital or physical) could help my investigation? (A calculator may support the work of students by easing calculation load.)

Take action

Allow students time to work through their strategy and find a solution to the problem.

  • What should be my first steps? Why?
  • How I record my findings, so I do not miss anything or overload my working memory?
  • Am I finding the areas and volumes in the most efficient way?
  • Do the units I am using make sense to me?
  • Do I have a sense of how big the lengths, areas, and volumes are?
  • Am I checking that the size of the measurements make sense?

Convince yourself and others

Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.

  • What is my solution?
  • How does the solution compare to my estimate?
  • Is my working clear for someone else to follow?
  • How would I convince someone else I am correct?
  • Is there some mathematics I need to learn to solve similar problems?
  • What have I noticed that seems to work all the time in these types of problem?
  • Do I have words and symbols to name the measurements I found?

Examples of work

Work sample 1

The student uses multiplication by the edge lengths of the 1 kg block to calculate its volume in metric units. They divide by the base area to find the height of the slab in centimetres.

Click on the image to enlarge it. Click again to close. 

Work sample 2

The student calculates the base area of the 1 kg block and finds out how many of the blocks fit into 1000 cm2. By calculating how many layers of blocks will include 25 kg of cheese they work out the height. They show good understanding of fractions.

Click on the image to enlarge it. Click again to close. 

Attachments

Printed from https://nzmaths.co.nz/resource/cheese-blocks at 8:17am on the 29th March 2024