Year level: 5–6

Strand: Number / Measurement

Lesson length: 80 mins

In this third lesson in the series, we explore farm and paddock design as we delve into the world of fractions, decimals and perimeter using Cuisenaire rods or Unifix cubes as fencing materials.

Note: Year 5 (fractions only); Year 6 (includes decimals and percentages).

This lesson was developed in collaboration with the Australian Association of Mathematics Teachers (AAMT).

### Achievement standard

Year 5: Students order and represent, add and subtract fractions with the same or related denominators. They represent common percentages and connect them to their fraction and decimal equivalents. Students solve problems involving perimeter and area.

Year 6: Students order, add and subtract fractions with related denominators. They use all four operations with decimals and connect decimal representations of measurements to the metric system. They solve problems involving finding a fraction, decimal or percentage of a quantity.

### Content descriptions

Students solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies. AC9M5N05

Students solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units. AC9M5M02

Students apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers. AC9M6N04

Students solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions. AC9M6N05

Students solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate. AC9M6N07

Students establish the formula for the area of a rectangle and use it to solve practical problems. AC9M6M02

### General capabilities

Numeracy

Personal and social capability

Critical and creative thinking

• Reserve time at the end of the lesson for students to reflect and demonstrate their learning.
• Use Farm fence fractions exit ticket on the Teacher’s slides (Slide 11).
• Which one of these designs uses the most fencing? Prove your answer.
• Expect responses such as: Treating each piece as one whole; difficulty adding fractions with different denominators.

Basic arithmetic skills (addition, subtraction and multiplication).

Some students may:

• apply whole number thinking and incorrectly add both the numerators and denominators of fractions. Having students model the addition using blocks allows them to count the blocks and recognise that they still have a particular number of tenths (not twentieths)
• have difficulty adding decimals, relating decimal addition to whole number addition (for instance, applying rules about carrying over). Have students carefully align the decimal points in the column and ensure that whole numbers are also reflected to one decimal place, as in 1.0
• use sloping/diagonal fences (for instance, with non right-angled corners). Paddock fences may not join up if sloping sides are used, as sloping sides will not be rational number lengths. Students should be encouraged to change their designs to ensure that there are no gaps in the fence for animals to escape. Right-angled corners will ensure that this is the case
• get confused between the concepts of perimeter and area. Clarify the two different meanings: perimeter (total length of the boundary of the shape) and area (amount of interior space bounded by the perimeter) – see glossary. Explain that we need to find the length of the fence needed, which should make explicit the need to find perimeter, which is facilitated using concrete materials.

## What you need:

• Lesson plan (Word)

• Teacher’s slides (PowerPoint)

• Farm animal cut-outs sheet (Word)

• Large sheets of paper

• Scissors

• Cuisenaire Rods or Unifix Cubes

• Optional: stopwatches for Timekeeper

Preparation tips

1. Each Farm animal cut-outs sheet is divided into three sets of animals. One sheet provides cards for three groups.