Scaling diagrams for multiplicative relationships
Lesson details
Learning outcome
I can use a scaling diagram to represent a multiplicative relationship and connect to other known representations.
Key learning points
- A double number line can be used to represent a multiplicative relations.
- Double number lines and graphs of multiplicative relationships can be compared.
- A ratio table can be used to represent multiplicative relationships.
- The representations can be compared to see what is the same and what is different.
Keywords
Proportionality - If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.
Common misconception
Incorrectly drawing a scaled axis is common.
Use the approach where pupils count the number of intervals of the scale and divide the difference bewteen the intervals. For example, if there are 5 intervals and the difference is between 20 and 30, they divide 10 by 2, so each interval is 2.
Teacher tip
Using a scaled diagram illustrates that multiplication is scaling. Using a scaled diagram where the scaling is > 1 shows how the number line is > the original and using a scaling <1 shows the number line is < the original. This can be emphsised by pupils drawing their own scaling diagrams on MWB.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Proportion is a part to whole comparison. If two things are proportional then the ratio of part to whole is maintained and the ___________ relationship between parts is also maintained.
Q2.Which of these diagram types give a good representation of a proportional relationship?
Q3.85% of 40 is .
Q4.Match each percentage of a number with its answer.
Q5.Using this ratio table, work out 99% of 860.
Q6.Match the start of each statement to its correct conclusion.
Assessment exit quiz
6 Questions
Q1.A scaling diagram allows you to see ___________ as a scaling as it shows how one number maps to another.
Q2.Using the scaling diagram, match each percentage to the corresponding amount.
Q3.Using the scaling diagram, match each percentage to the corresponding amount.
Q4.Using the scaling diagram, match each percentage to the corresponding amount.
Q5.Using the scaling diagram to find the multiplier, match each amount or percentage with the corresponding value.
Q6.Use the scaling diagram to work out 60%.
To help you plan your 8 maths lesson on: Scaling diagrams for multiplicative relationships, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 8 maths lesson on: Scaling diagrams for multiplicative relationships, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Understanding multiplicative relationships: percentages and proportionality unit, dive into the full secondary maths curriculum, or learn more about lesson planning.