Algebra: Pens and patterns

'Algebra: Pens and patterns ' is a reimagining of classic V8 sequence 'Chicken boxes'

On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
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Lessons in this sequence

Year 6

Task 1 • Sheep pens

Students investigate sheep pen layouts, exploring how shared sides reduce panels. They describe rows of connected pens, develop counting rules, and compare equivalent rules.

Year 6

Students investigate pig pen layouts in rows and arrays, comparing how shared sides affect panel numbers. They develop rules using rows and columns, then apply them to compare efficient designs for a fixed number of pens.

Year 6

Task 3 • Show design

Students use their rules to design cost-efficient sheep and pig pens for an agricultural show, comparing layouts within space and cost constraints.

Build

Sheep in the background of the first prize ribbon they've won

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Credits for work used in this sequence

Credits & acknowledgements

Curriculum and syllabus alignment

Year 6

Number

Algebra

Level 6

Algebra

Number

Last updated 19/02/2026

Year 6

Number and algebra

Last updated 19/02/2026

Stage 3

Multiplicative relations B

Last updated 19/02/2026

Each task in this sequence uses the Launch–Explore–Connect–Summarise structure to support students to build, test, record and generalise visually growing patterns. The sequence is designed so that mathematical rules are developed in response to a design need: students must work out how many panels are required for different animal pen arrangements and decide which designs are more efficient.

In the first task, students investigate sheep pens for an agricultural show. They begin by exploring different layouts of square pens and noticing that shared sides can reduce the number of fence panels needed. A new constraint is then introduced, requiring pens to be arranged in a single row. Students build and compare rows of connected pens, describe the pattern using a step-by-step rule, and then develop a more efficient relational rule. Different student-generated counting strategies are compared and verified to show that different-looking rules can represent the same structure.

In the second task, students extend the investigation to pig pens arranged in two rows and then in rectangular arrays. They explore how connecting rows changes the number of panels required and how the number of rows and columns can both affect the total. Students compare methods for counting panels, including counting shared sides, organising panels by rows and columns, and using rules with more than one input. They then apply an agreed rule in a design challenge, comparing rectangular and non-rectangular arrangements to minimise the number of panels required for a fixed number of pens.

In the final task, students use the rules and methods developed across the sequence to solve a design optimisation problem. They plan an agricultural show for a given number of animals, choosing a combination of sheep and pigs, each with different housing requirements, arrangement constraints and panel costs. Students calculate total panels and total cost for competing designs, compare efficiencies, and refine their plan to produce the cheapest overall show design. A supporting spreadsheet is provided to automate calculations, enabling students to test scenarios, compare designs and iteratively improve their solution.

Sequence framework

This sequence framework presents an overview of the key elements in this sequence.

Learning goals

Students’ mathematical activity

Representation

Context

Task 1

Growing patterns can be described in different ways with step-by-step or relational rules.

Different rules can represent the same structure when they use the same input and produce the same output.

Students investigate sheep pen layouts and notice that sharing sides can reduce the number of panels needed. They first explore different possible layouts, then focus on a single row of connected square pens.

Students build rows, record how the pattern grows, describe a step-by-step rule, and develop direct counting rules. They compare different counting strategies and verify that different-looking rules can produce the same number of panels.

A top-view model is used to represent the pens in two dimensions.

Students use toothpicks or similar materials to represent fence panels.

Students record their thinking using drawings, tables, diagrams, number sentences or written explanations.

An agricultural show provides the design context. Students consider how pens could be arranged when space, access and number of panels matter.

The single-row arrangement is introduced as a specific constraint, not as the only possible or most efficient layout.

Task 2

Growing patterns can be described with step-by-step and relational rules.

Rules can involve more than one input, such as the number of rows and the number of columns.

Rules can be used to compare and optimise different designs.

Students investigate pig pens arranged first in two connected rows, then in rectangular arrays. They test whether two-row arrangements use fewer panels than a single row and develop a rule for two complete rows.

Students then explore arrays with different numbers of rows and columns, compare counting methods, and agree on a rule that can be used for rectangular arrangements. They apply the rule in a design challenge to compare efficient arrangements for a fixed number of pens.

A top-view model is used to represent pig pens arranged in rows and columns.

Students construct arrays with toothpicks or use a digital geometry tool. They may represent their thinking with physical models, sketches, tables, diagrams, number sentences, and worded rules.

The student sheet supports the 24-pen design challenge.

The agricultural show context continues with a different section of the hall for pig pens. A single long row is not suitable, so students investigate two-row arrangements and then rectangular arrays.

The access condition is adjusted for larger pig-pen arrays: farmers and judges can move around the outside of the whole area, and individual pens may include gates so pigs can be safely reached.

Task 3

Rules can be applied and interpreted to solve problems involving multiple conditions and constraints.

Complex problems can be systematically broken down into smaller cases to test, refine and justify a solution.

Students plan the layout of an agricultural show by choosing how many sheep and pigs to include and how their enclosures will be arranged.

They use the rules developed in Tasks 1 and 2 to calculate the total number of panels and total cost for different designs. Students compare options, refine their choices and justify the most cost-efficient design they can find.

Students sketch proposed enclosures using a top-view representation where each panel is a countable side.

A spreadsheet supports calculation, testing and refinement. Students can use it to represent pig-pen arrangements, compare scenarios and automate repeated calculations.

Students solve a design optimisation problem for an agricultural show with resource constraints. They must consider animal numbers, pen requirements, arrangement constraints, panel use and total cost.