Year level: 7

Strand: Number

Lesson length: 60 mins

In this lesson, students are transported to a bustling ancient bazaar before the introduction of standardised measuring systems. They encounter the challenge of a shopkeeper who must determine how to weigh different quantities of spices most efficiently. Working in a financial context, students model this scenario using fractions, percentages and ratios, and communicate their solution in the form of a sign for their stall. This lesson is in two parts and is followed by Practical numbers: Part 2

### Achievement standard

Students use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios, in financial and other applied contexts, justifying choices of representation. They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies. Students choose between equivalent representations of rational numbers and percentages to assist in calculations.

### Content description

Students use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation. AC9M7N09

Students recognise, represent and solve problems involving ratios. AC9M7N08

Students find equivalent representations of rational numbers and represent rational numbers on a number line. AC9M7N04

Students use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies. AC9M7N06

General capabilities

Numeracy

Critical and creative thinking:

• interpret concepts and problems (Level 5)
• draw conclusions and provide reasons (Level 5)

Digital literacy:

• select and operate tools (Level 5)

Civics and citizenship, Economics and business, Geography, Literacy

The following on-going assessment opportunity for part 1 of this lesson is described below.

Review the warm-up sheets handed in to you and make a judgement on each student’s needs and requirements. Take a few minutes to think about how the class is responding to the lesson so far and whether you need to make any adjustments to Practical numbers: Part 2 ahead of time.

Some students:

• do not possess strong multiplicative strategies, or quick recall of the times-tables and will find it difficult to compare solutions to this problem
• find understanding the scenario and restrictions of the problem very difficult without sufficient demonstration of the scenario
• find fractions notoriously tricky and require a diagnostic assessment to highlight their interpretation of various fractions. There is also likely to be a wide variety of skill in this area among classes and cohorts.

It is recommended to familiarise yourself with this lesson and feel confident to explain the scenario in intricate detail and to describe the links with fractions, percentages and factors to a variety of skill levels. Prepare extra scaffolding materials, such as multiplication tables, if needed to support students as they progress through the parts of this lesson.

Students are:

• developing competence with decimals, place value and equivalent fractions
• identifying common denominators
• understanding percentage is a proportional relationship and a complete whole
• using percentages to represent relative sizes in real world scenarios
• recognising and understanding complementary percentages add to 100%
• understanding basic levels of commerce
• calculating a given quantity with respect to unit fractions
• converting fractions to percentages using a calculator
• learning the meaning of factors and factor pairs
• developing core arithmetic skills.

## What you need:

• Lesson plan (Word)

• Teacher's slides (PowerPoint)

• Fractions warm up (Word)

• Clay/Play-Doh or similar (per student or group)

• Craft materials for creating posters