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Lesson 2: �Ratios and fractions

Objectives

Write a fraction as a ratio and vice versa
Divide a given quantity into parts in a given part–part and part–whole ratio
Solve multi-step problems using ratios and fractions
Use representations to provide insight into solving problems

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Buying lunch

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Amy and Bikram are buying a baguette to share for lunch.

RP_PRJ1403_W2_ph_004N

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Buying lunch

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Amy pays more so she wants to split the baguette in the ratio 3 : 2

Bikram wants to split the baguette half and half.

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Working in pairs

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Take turns to place a card.
Explain your reasoning for the match to your partner.
Your partner must agree, disagree or ask for more explanation.
Complete any blank cards.

YOUR

TURN

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Matching ratios and fractions

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YOUR

TURN

Handout�available

Explain that the class is going to explore different ways that Amy and Bikram could share the baguette. Arrange students into pairs and give each pair a copy of the ‘Sharing baguettes’ grid and the ‘Fractions’ cards. (Students will need scissors to cut the cards up if they haven’t already been cut into cards prior to the lesson.)

Note that some rows in the grid have more than one fraction card and some rows don’t have any. Students are not expected to create cards for rows that have no fraction but do need to complete the blank card F10, which they should place in a row that does not have a fraction card or as an additional card in a row that already has a card matched.

Observe students as they complete this task but try not to correct students’ mistakes at this stage. Instead, encourage students to explain their reasoning to each other and listen in to their explanations as you circulate. A common misconception that you may observe is assuming that the ratio 1 : 2 is equivalent to the fraction 1/2.

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Diagrams

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Handout�available

YOUR

TURN

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Descriptions

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Handout�available

YOUR

TURN

Once students have completed the ratio–diagram–fraction matches they can be given the set of ‘Descriptions’ cards.

Students may find it helpful to glue the grid onto an A3 piece of paper so that there is more space to the right of the grid to place the ‘Descriptions’ cards alongside the appropriate row.

Some rows have more than one description card and some rows don’t have any. Students are not expected to create cards for rows that have no description but do need to complete the blank card W8. They may choose to complete this card for a row that has no description card or add a further description to a row that already has a description card matched.

Observe students as they complete this activity and identify which descriptions cards will be particularly important to highlight in the whole class discussion. Students often struggle with ‘one and a half times as much’ (Card W6) and it may be appropriate to withhold this card in some cases.

Deepening understanding Students who have completed their matches can use the ‘More sharing’ handout to explore additional ways in which Amy and Bikram could share the baguette. The blank cards on the handout can also be used to add some additional fractions and/or descriptions to the existing scenarios A to I.

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Sharing baguettes

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REVIEW

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Answers (A to E)

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Answers (F to I)

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Ratios and fractions

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Ratios and fractions provide different ways to describe how something is shared.

DISCUSS

A	A	A	B	B

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Comparing ratios

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Bikram and Amy share the baguette in the ratio 3 : 1

Amy and Bikram share the baguette in the ratio 1 : 3

LET’S

LOOK

A	B	B	B

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Describing ratios

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REVIEW

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Sharing a baguette

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Amy

How are the numbers in a fraction linked to the numbers in a ratio?

I will get ⅔ �of the baguette

Amy and Bikram share the baguette in the ratio 2 : 3.

Bikram

Amy is wrong

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Going deeper: Paying for the baguette

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£1.20

A	A	B

A	A	B	B	B

Amy gets ⅔ of the baguette

Amy and Bikram share the baguette in the ratio 2 : 3

LET’S

LOOK

£1.20

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Practice question

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Chocolates with nuts : chocolates without nuts

1 : 3

Handout�available

REVIEW

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Lesson review: �Ratios and fractions

Objectives

Write a fraction as a ratio and vice versa
Divide a given quantity into parts in a given part–part and part–whole ratio
Solve multi-step problems using ratios and fractions
Use representations to provide insight into solving problems

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Suggested further steps/areas to work on

Use ratio notation, including a reduction to simplest form

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Lesson 2: �Credits

Photo acknowledgements

Shutterstock.com: MaraZe, Vectorfair.com

Text acknowledgements

Pearson Education Ltd: Pearson Edexcel GCSE (9-1) �In Mathematics (1MA1) Foundation (Non-Calculator) Paper 1F, Summer 2018 Publications Code 1MA1_1F_1806_MS

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