In this unit the students design and construct homes for the three pigs from the story The Three Little Pigs. Each of the homes is constructed in relation to the number patterns explored in the unit.
In this unit we look at number patterns that are very much the same as skip-counting patterns. The patterns here are obtained by adding the same, constant number of windows or doors to make the next number of windows or doors. This means that the difference between any two terms in the patterns is the same. The learning in this unit helps to reinforce the various concepts relating to pattern. In particular, it helps us to understand the idea of a recurrence relation between consecutive terms.
Patterns that have this common difference are also called Arithmetic Progressions. In secondary school these are considered again and expressions are found for both the general term of the progression and the sum of all of the numbers in the progression.
This unit provides an opportunity to develop number knowledge in the area of Number Sequence and Order, in particular development of skip counting patterns. It can also be used to focus on the development of strategies to solve multiplication problems.
As students create tables with numbers, focus their attention on the patterns that emerge, and pose questions about the continuation of the patterns. Use of a hundreds chart will help students visualise the number patterns more easily and help them to predict which numbers will be part of the patterns. Patterns of 2, 5 and 10 are a good place to start but for students that are coping well you can make it more difficult by using larger numbers. For example, if there were 13 steps by the door of each house how many steps would there be in 2 houses? 3 houses? What about 10 houses?
Working with larger numbers of houses will help students develop strategies to solve multiplication and division problems. Encourage students to talk about the way they are solving these problems. Are they using repeated addition or can they derive some of the answers from known multiplication facts? Ask questions, such as the following, to develop knowledge and strategy use:
The learning opportunities in this unit can be differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:
The activities in this unit can be adapted to make them more interesting by adding contexts that are familiar to them. The context of the Three Pigs' houses could be changed to relate to a favourite story of your class, to a māori legend, or to another made up story. Rather than parts of houses it could be hands, eyes, fingers, limbs, etc of people or animals that you are finding the totals of.
Te reo Māori kupu such as tatau (count), tauira (pattern), and tatau māwhitiwhiti (skip count) could be introduced in this unit and used throughout other mathematical learning.
Today we introduce the three pigs and the homes that they need to build (or your chosen, other context). Together we design the home for the first pig focusing on the patterns that we can use.
Record the decisions on a chart, for example,
Windows | 4 |
Doors | 2 |
Chimneys | 1 |
Curtains | 8 |
1 house | 4 windows |
Record the number of windows on the chart.
1 house | 4 windows |
2 houses | 8 windows |
3 houses | 12 windows |
Over the next 2-3 days we use tables to record the number of doors, chimneys and curtains that we need to construct houses for our village of pigs.
windows | doors | chimneys | ||
1 house | 5 | 3 | 2 | |
2 houses | 10 | 6 | 4 | |
3 houses | 15 | 9 | 6 | |
4 houses | 20 | 12 | 8 | |
On the final day display your homes with accompanying charts of repeated number patterns on the wall for others to share. Have students look for houses that have similar number patterns (e.g. houses with 3 windows and houses with 3 doors).
Dear parents and whānau,
This week in maths we looked at number patterns that came from the houses of The Three Pigs. With your child make a list of the number of outside doors and windows that your house has. Suppose that there was a street with 4 houses exactly like yours. Ask if your child could work out with you how many outside doors and windows would there be in that street? Once you have listened to your child's ideas, if they haven't already suggested it, you could make a chart like the one below and complete it together. Talk about the number patterns that you see. Perhaps your child could say how many doors and windows there would be with 5 houses. Ask them to tell you how they know.
Patterning is an important part of mathematics. Thank you for your encouragment and help.
1 house | ? doors ? windows |
2 houses | doors windows |
3 houses | doors windows |
4 houses | doors windows |
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/three-pigs at 8:38pm on the 26th February 2024