Pigs and ducks

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Purpose

This problem solving activity has a number (all operations) focus.

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Student Activity

Jennie the old sheep dog is lazing around in the paddock near the house.

She counts the number of animals in the paddock. There are 11 of them, pigs and ducks.

Then she counts the legs. She sees 28 legs.

How many ducks are there?

Decorative image of 3 ducks and a pig.

Specific Learning Outcomes
  • Solve a story problem using multiplication facts of 2 and 4.
  • Devise and use problem solving strategies (guess and check, guess and improve, act it out, draw a picture).
Description of Mathematics

This problem uses the multiplication facts of 2 and 4. It also gives students the opportunity to combine the operations of addition and subtraction. As there are many ways to solve this problem it will be accessible to a range of students. You could adapt the context of this problem to focus around horses, and horse riders, or tricycles and bicycles. 

Required Resource Materials
Activity

The Problem

Jennie the old sheep dog is lazing around in the paddock near the house. She counts the number of animals in the paddock. There are 11 of them, pigs and ducks. Then she counts the legs. She sees 28 legs.
How many ducks are there?

Teaching Sequence

  1. Read the problem to the class. Revise the 2 and 4 times-tables.
  2. Ask the students to highlight the important information.
  3. For beginning problem-solvers you might like to ask them to act out the problem, (or use pig and duck pictures to do so).
  4. Start with 4 students at the front of the room. Ask 2 of them to be pigs (on all 4's) while the other 2 stand (ducks). Ask the students to count the legs using their own strategy. As a class, skip count the number of duck legs (in 2s) and the number of pig legs (in 4s).
  5. Ask the students to think about what would happen if you "turned" one of the pigs into a duck. How many animals?  How many legs?
  6. Brainstorm other ways to solve the problem – list possibilities on board (draw, equipment, guess). This problem is a good opportunity to introduce the use of a table and to use it for guess and improve. 
  7. Support students to solve the problem - either in groups or pairs, or independently.
  8. Share the solutions and strategies used.

Extension

Get the students to write and solve their own problems by changing the numbers of animals and legs.

Solution

3 pigs, 8 ducks

If the first guess was 5 pigs and 6 ducks there are 32 legs. At this point the students should realise that to reduce the number of legs we have to reduce the number of pigs. Some students may be able to reason that when you reduce the pigs by one and add a duck you have reduced the number of legs by 2.

Attachments
Add to plan

Log in or register to create plans from your planning space that include this resource.


Level Two