## The three pigs

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.

## About this resource

Specific learning outcomes:

- Continue a sequential pattern.
- Systematically count to establish rules for sequential patterns.
- Skip count in 2s, 5s and 3s.

# The three pigs

## Achievement objectives

NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.

NA1-6: Create and continue sequential patterns.

## Description of mathematics

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 pattern is the same. The learning in this unit helps to reinforce the various concepts relating to pattern. In particular, it helps us understand the idea of a recurrence relationship 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.

### Numeracy links

This unit provides an opportunity to develop number knowledge in the area of Number Sequence and Order, in particular the 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, they focus their attention on the patterns that emerge and pose questions about the continuation of the patterns. The use of a hundreds chart will help students visualise the number patterns more easily and help them predict which numbers will be part of the patterns. Patterns of 2, 5, and 10 are a good place to start, but for students who 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:

- Which number comes next in this pattern? How do you know?
- Which number will be before 20 in this pattern? (or another number as appropriate) How do you know?
- What is the largest number you can think of in this pattern? How did you work it out?
- How many windows will there be in 5 houses? 10 houses? How did you work it out?
- If there were 22 chimneys in a street, how many houses would there be? How did you work it out?
- If a house had 6 chimneys how many doors would it have? How do you know?

## Opportunities for adaptation and differentiation

The learning opportunities in this unit can be differentiated by providing or removing support for students and by varying the task requirements. Ways to differentiate include:

- When choosing the numbers that you work with, some students may need more practice with multiples of 1, 2, and 3, while others may move on to larger numbers.
- allowing the use of equipment to explore the patterns.
- Using whiteboards as an easy method for drawing and revising the design of houses
- Strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension.
- Working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities

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.

## Required materials

- chart paper
*The Three Pigs*story (video or written versions available online)

## Activity

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.

**1.**

Set the context for the week’s activity by reading the story of *The Three Pigs*.

**2.**

Tell the students that they are going to design the three pigs’ homes. Each house will be the same.

**3.**

Discuss and make decisions on the following:

- How many windows will we put in each house?
- How many doors?
- How many chimneys?
- How many curtains?

**4.**

Record the decisions on a chart, for example,

Windows | 4 |

Doors | 2 |

Chimneys | 1 |

Curtains | 8 |

**5.**

Get each student to draw a picture of the house. Tell the students that they will need to show all of the windows, doors, and chimneys on the picture.

**6.**

Ask a volunteer to bring their house to the front of the class.

**7.**

Count and record on a chart the number of windows.

1 house | 4 windows |

**9.**

Discuss. Sharing the different strategies that students use to determine the number of windows is an important part of this activity. You might have students share their answers with a partner before giving feedback to the class.

- If we built the second pig’s house exactly the same as the first, how many windows would we need altogether?
- How did you work that out?
- Did anyone work it out a different way? How?

**10.**

Record the number of windows on the chart.

1 house | 4 windows |

2 houses | 8 windows |

3 houses | 12 windows |

**11.**

Repeat with the third house.

**12.**

Suppose that the three pigs have a friend, perhaps a duck, who wants a house exactly the same as theirs. Now ask the students to predict the number of windows that there will be in the four houses.

- How many windows would we need if we built 4 houses?
- How did you work that out?
- Did anyone work it out a different way?
- How could we check that we were correct?

**13.**

If no one has used the chart to solve the problem, then you will need to direct their attention to the patterns on the chart, in particular the ‘add 4’ pattern in the number of windows.

Over the next 2-3 days, we will use tables to record the number of doors, chimneys, and curtains that we need to construct houses for our village of pigs.

**1.**

Remind the students that yesterday we worked out how many windows we would need for the three pigs’ houses.

**2.**

Look at and discuss the chart, re-emphasising the pattern and the ‘add 4’ rule.

**3.**

Tell the students that they are going to find out how many doors, chimneys, and curtains will be needed for the houses they drew yesterday.

**4.**

Work with a partner to find out the number of doors, chimneys, and windows you would need for 1, 2, 3… of your houses.

**5.**

Encourage the students to share their ideas for doing this.

**6.**

As the pairs work, ask questions that focus on any patterns they are noticing in the charts they are creating.

- What numbers do you have on your chart?
- How are you working out the number of windows (doors, etc.) needed?
- How many houses have you worked it out for?
- How many houses do you think you could work it out for?

windows | doors | chimneys | ||

1 house | 5 | 3 | 2 | |

2 houses | 10 | 6 | 4 | |

3 houses | 15 | 9 | 6 | |

4 houses | 20 | 12 | 8 | |

**7.**

Allow time at the end of each session for the pairs to report back. Discuss the strategy they used and the method they used for keeping track of and recording their work.

**8.**

Repeat the above steps on the following days using different homes with different details, for example,

- trees
- flower pots
- paths (made with a set number of paving stones).

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 (for example, houses with 3 windows and houses with 3 doors).

## Home link

Dear parents and whānau,

This week in math, 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 there would be on that street. Once you have listened to your child's ideas, if they haven't already suggested them, 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 encouragement and help.

1 house | ? doors ? windows |

2 houses | doors windows |

3 houses | doors windows |

4 houses | doors windows |

**The quality of the images on this page may vary depending on the device you are using.**