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The Three Pigs

Purpose: 

In this unit the students design and construct homes for the three pigs. Each of the homes is made and filled with patterns that we explore.

Achievement Objectives:

Achievement Objective: NA1-6: Create and continue sequential patterns.
AO elaboration and other teaching resources
Achievement Objective: NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
  • continue a sequential pattern
  • systematically count to establish rules for sequential patterns
  • skip count in 2s, 5s and 3s
Description of mathematics: 

There are many similarities between this unit and Beetle Wheels, Level 1, so the maths here is very similar to the maths there. 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.

Patterns that have this common difference are also called Arithmetic Progressions. In secondary school these are considered again and expressions for both the general term of the progression and the sum of all of the numbers in the progression are found. These are both reasonably simple algebraic expressions.

This unit is a good exercise to help reinforce the various concepts relating to pattern. In particular, it helps us to understand the idea of a recurrence relation between consecutive terms.

Numeracy Links

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 the numbers involved focus their attention on the patterns that are emerging 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?

Questions to develop knowledge / strategy use
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?

Required Resource Materials: 
"The Three Pigs" story
Chart paper
Key Vocabulary: 

 patterns, how many?

 

tahi, rua, toru, wha, rima, ono, whitu, waru, iwa, tekau....tekau ma tahi, tekau ma rua.... rua tekau, toru tekau....

tasi, lua, tolu, fa, lima, ono, fitu, valu, iva, sefulu... sefulu-tasi, sefulu-lua, ..........lua- sefulu, tolu-sefulu

 

 

Activity: 

Getting Started

Today we introduce the three pigs and the homes that they need to build. 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 today we 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 we will 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

       
       
  8. 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?
  9. Record the number of windows on the chart.

    1 house

    4 windows

    2 houses

    8 windows

    3 houses

    12 windows

       
       
       

  10. Sharing the different strategies that students use to determine the number of windows is an important part of this activity.
  11. Repeat with the third house.
  12. Suppose that the three pigs have a friend, a duck perhaps, who wants a house exactly the same as theirs. Now ask the students to predict the number of windows that there would 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.

Exploring

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.

  1. Remind the students that yesterday we worked out how many windows we would need for the 3 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 in 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 and recording their work.
  8. Repeat the above steps on the following days using different homes with different details, e.g.
    • trees;
    • flower pots;
    • paths (made with a set number of paving stones).

Reflecting

On the final day we display our homes with accompanying charts of repeated number patterns on the wall for others to share. We look for houses that have similar number patterns (e.g. houses with 3 windows and houses with 3 doors)