Ratio, Percentages and Proportion

#TheCompleteSeries5lessons

This Complete Series of five Maths lessons for Year 6 clearly explain how to use 4-cell models to help visualise and solve missing number problems involving fractions, ratios and percentages. There's loads of opportunities to practise and develop problem-solving skills: the slides included with each lesson show a variety of word problems, along with explanations of effective strategies for solving them.

There's even a whole lesson dedicated to using ratio to describe distances and read maps! It includes valuable, practical strategies for children to use outside the maths lesson, as well as preparing them for those tricky scale ratio problems that they'll encounter!

As with all PlanBee KS2 Maths lesson plans, there's also a choice of learning activities included: each lesson has a 3-way differentiated tasks and a fun, alternative activity which addresses the lesson's objectives in a slightly different way.

#Lesson1Fractionandpercentagewordproblems

Teach children effective methods for visualising and solving a variety of fraction and percentage word problems.

In this, the first of five lessons in 'Ratio, Percentages and Proportion' for Year 6, take a look at ways of tackling tricky missing number word problems – in particular, those where the answers are expressed as fractions or percentages. The included slides share a variety of word problems for children to attempt, and clearly explain methods for solving them. These include a 4-cell 'Fraction Factory' model for solving missing number problems requiring multiplying or dividing fractions and a 2-column method for simplifying fractions. The teaching input on the plan (and the accompanying slides) help you demonstrate how to find percentages or fractions of amounts – both essential steps for solving word problems like these.

After that, there are opportunities for pupils to work independently or in pairs/small groups to visualise and solve more fraction and percentage word problems during either of the included learning activities (plus supporting resources).

#Lesson2Mapsandscalesratios

Consolidate children's understanding of ratio by solving a variety of problems involving maps and scale drawings.

Take a look at physical maps, digital mapping and scale drawings, and consider why ratios with a '1' (e.g. 1:25,000) are helpful when reading maps. In this, the second of five lessons in 'Ratio, Percentages and Proportion' for Year 6, children will answer a variety of ratio questions by reading maps and scales given as ratios. The included slides show how to calculate distances and answer ratio questions using maps and plans at different scales—including Ordnance Survey maps and Google maps, where the gridlines do not necessarily correspond with the given scale. As well as clearly explaining methods children can use to calculate ratio, the slides also show a number of problems for them to attempt themselves.

After the teaching input, there's a choice of two independent activities involving working out ratios. Children may either practise their newly-learnt skills by reading, measuring and drawing maps, or by writing and solving ratio word problems.

#Lesson3Howtoworkoutratioproblems

Teach children how to work out ratio word problems using their prior skills and knowledge, and a 4-cell model for solving missing number ratio problems.

In this, the third of five lessons in 'Ratio, Percentages and Proportion' for Year 6, children will apply their emerging ratio problem-solving skills and knowledge as they attempt to solve a variety of challenging maths questions. The included slides share several interesting problems for children to tackle, as well as clearly explaining how to use a 4-cell model (which we've called a 'Ratio Robot') to find missing numbers and scale ratios up or down, too.

After the teaching input, there's a choice of differentiated learning activities (each with supporting resources included) where children may continue to practise their ratio calculating skills, working independently to complete the ratio word problems worksheets, or taking part in a fun group activity involving ratio and repeating patterns.

#Lesson4Howtofindpercentagesofamounts

Teach children how to find percentages of amounts using written methods and a 4-cell model for solving percentage problems.

Having looked at missing number percentage problems in lesson one of 'Ratio, Percentages and Proportion', children are challenged to use their knowledge of times tables and factors to help solve more complex, two-step percentage problems. This challenging lesson includes lots of word problems where children can practise and develop the mathematical reasoning required for trickier problems like these. The included slides clearly explain how to find percentages of amounts, and how to convert fractions to percentages using a 4-cell model to help visualise and solve problems.

If you're after a 'real-world' percentages activity, this lesson also includes an alternative activity where children may explore how different calculators and calculator apps display percentages differently, and how their calculations may be interpreted.

#Lesson5Solveratiopercentageandproportionquestions

Challenge children to put all their problem-solving skills into practice as they solve a variety of ratio, percentage and proportion questions and word problems.

In this, the last of five lessons in 'Ratio, Percentages and Proportion' for Year 6, children will apply all of the skills they've learnt to visualise and answer a whole range of challenging proportion questions. The included slides revisit all of the skills taught in the previous lessons and show how a '4-cell' model may be used in a similar way to solve a variety of missing number problems, regardless of whether they must find a fraction, a ratio or a percentage.

Depending on how much time you have, you might even be able to fit in both of the included 'end of week' activities, where children can practise what they've learned, and even earn a certificate for their achievements!

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Curriculum Objectives covered

• Year 6 - solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
• Year 6 - solve problems involving similar shapes where the scale factor is known or can be found
• Year 6 - solve problems involving unequal sharing and grouping using knowledge of fractions and multiples