Ratio - Mud Pies and Milkshakes

**Key Elements and Scene Summary**

The importance of ratio and other multiplicative situations are the focus. The scene is designed to introduce this concept of two quantities having a ‘per’ or ‘for every’ relationship. This develops from scaling of similar shapes, numbers of workmen required on a site, and comparing numbers of different insect sweets. A honeycomb puzzle and milkshake factory target a more numerical approach. Ideas of resource allocation and recipe ratio dependence give students a flavour of real-world relevance.

# Learning Objectives

Establish and write simple ratio relationships.{.info}

Understand the idea of equivalence and scaling of ratios.{.info}

Use multiplicative reasoning to solve problems about strength of drinks.{.info}

# Ratio Management: Report to Dig Site!{.objective .objective1}

- Students consider the blueprint to determine which rectangles are similar, building ideas of scaling and enlargements. They can consider this relationship from spatial ideas (‘why is the 1 by 3 rectangle not an enlargement of the 1 by 2 rectangle?’) and numerical ideas (‘why is 1:2 the same as 2:4? What has been done to the measurements of both sides of the rectangle?’)

# The Equiva-Hive{.objective .objective2}

- Students complete a honeycomb puzzle based on equivalent ratios. They should focus on the cells containing bees with ratios written, and can approach the task by thinking about scaling both sides, or the ‘horizontal’ relationship across the centre of the ratio: ‘1:3 – how many times bigger is the right hand side? Where else in the honeycomb has one that’s three times bigger?’

# Milkshake Emporium{.objective .objective3}

- With a slightly more rigorous approach, this task requires students to determine which relationship would produce the stronger drink. The first problem provides an accessible route, since it should be apparent that 1:1 is less strong than 2:1. This can be developed further into the second and third problems, providing insight on learners’ thinking and a chance to address common misconceptions (for example, discouraging additive thinking).

# Teacher Resources

### Download Teacher Notes

[](https://avnfs.com/AUlealfJu3gEKinDouD9marcGdJEJ5c65kDTuFYcsgI?size=1243218&type=application%2Fpdf&name=Ratio+-+Mud+Pies+and+Milkshakes+Teachers+Notes+1.pdf)

### Student Worksheet Answers Document

[](https://avnfs.com/jQztNSaZ9QKUNvUwGNOmteZTliUEQiNdMPrmE5S-T10?size=1092235&type=application%2Fpdf&name=Ratio+-+Mud+Pies+and+Milkshakes+Teachers+Notes+2.pdf)

### Download Worksheet Document

[](https://avnfs.com/V5wqr8Xbwy8LM_uS60QqmEEspP2IPEUJKAQPsuH3yr8?size=478732&type=application%2Fpdf&name=Ratio+-+Mud+Pies+and+Milkshakes+Teachers+Notes+3.pdf)