Year 5 - Fractions Learning Path (Purple Profile)

Before starting this Learning Path

Before starting this Learning Path, the student should have a basic knowledge of Fractions and understand how to add and subtract equivalent fractions.

‍

Learning Outcomes

Compare and order fractions
Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
Multiply simple pairs of proper fractions, writing the answer in its simplest form
Divide proper fractions by whole numbers
Associate a fraction with division and be able to divide simple fractions

‍

General teaching tips:

Students with the Purple Profile start with quite low self confidence, but they work hard and are extremely obedient- These students tend to learn methodically and through rote memorisation of a method so it is easy to shape the way they think about and approach a topic- Ensure their understanding by challenging their ability to apply a concept from different perspectives. These students tend to say they understand a topic, even when they may not holistically understand it. - These students will tend to want to ask questions but feel shy/embarrassed in doing so, causing a lot of internal frustration so ensure their clarity on each step before moving on.

Step 1

Step 1:

‍

Name: Equivalent Fractions

‍

Learning outcomes:

Identify, name and write equivalent fractions of a given fractionincluding tenths and hundredths (ENCY5)
Compare and order fractions whose denominators are all multiples of the same number (ENCY5)

‍

Introduce concept

Start right from the beginning and explain each step slowly and methodically. Take great care in giving them a real-life example. For example, using a recipe and scaling it down from serving 4 to 2 people. Use this worksheet for half of the session, then, move away from the topic to something they are more comfortable and familiar with.

‍

Worksheet: Equivalent fractions D 2

Step 2

Step 2:

‍

Learning outcomes:

Identify, name and write equivalent fractions of a given fractionincluding tenths and hundredths (ENCY5)
Compare and order fractions whose denominators are all multiples of the same number (ENCY5)

‍

Extra practice

Use this sheet for extra practice. These students are extremely diligent and are driven to complete the worksheet for homework.

‍

Worksheet: Equivalent fractions D 4

Step 3

Step 3:

Name: Add/subtract unlike fractions

‍

Learning outcomes:

Add and subtract fractions with the same denominator and denominators that are multiples of the same number (ENCY5)
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions (ENCY6)

‍

Introduce concept

Ask the student to try the question and wait to see if they are able to complete it. If they need a hint, tell them to put the two fractions in the same denominator to prompt them and then do a couple of questions together.

‍

Worksheet: Add subtract unlike fractions V 1

Worksheet: Add subtract unlike fractions V 2

Worksheet: Add subtract unlike fractions V 3

Step 4

Step 4:

‍

Name: Equivalent Fractions

‍

Learning outcomes:

Identify, name and write equivalent fractions of a given fractionincluding tenths and hundredths (ENCY5)
Compare and order fractions whose denominators are all multiples of the same number (ENCY5)

‍

Timed exercise

Apply a strong, 10-minute time pressure and emphasise that you want accuracy as well as speed. When marking the questions, ensure that any questions they have gotten wrong are clearly explained as these students tend to be afraid of asking for help.

‍

Worksheet: Equivalent fractions D 5

Step 5

Step 5:

Name: Add/subtract unlike fractions

Learning Outcomes:

Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions (ENCY4)
Compare and order fractions whose denominators are all multiples of the same number (ENCY5)
Add and subtract fractions with different denominators and mixed numbers (ENCY6)

Extra practice

As these students learn through rote memorisation of a topic, these repetitive questions are great for them to practice and train on.

‍

Worksheet: Add subtract fractions W 1

Step 6

Step 6:

Name: Add/subtract mixed fractions

‍

Learning Outcomes

Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number (ENCY4)
Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 asa mixed number (ENCY5)
Add and subtract fractions with the same denominator and denominators that are multiples of the same number (ENCY5)

Word problems

Use these questions to introduce the concept of Mixed Fractions to the student.

‍

Worksheet: Add subtract mixed fractions W 1

Step 7

Step 7:

Name: Simplify & multiply fractions

‍

Learning Outcomes:

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination (ENCY6)
Multiply simple pairs of proper fractions, writing the answer in its simplest form (ENCY6)

Timed exercise

Apply a strong, 10-minute time pressure and emphasise that you want accuracy as well as speed. When marking, ensure that any questions they have gotten wrong are clearly explained as these students tend to be afraid of asking for help.

‍

Worksheet: Simplify and multiply fractions D 2

Step 8

Step 8:

Learning Outcomes:

‍

PROBLEM.

Challenge questions

Once the student feels confident with the concepts and questions, challenge them with harder questions

‍

‍

‍

Step 9

Step 9:

‍

Name: Multiply/divide mixed fractions

‍

Learning Outcomes:

Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number (ENCY4)
Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (ENCY5)
Divide proper fractions by whole numbers and proper fractions (ENCY6)
Multiply simple pairs of proper fractions, writing the answer in its simplest form (ENCY6)

Introduce concept

Use this worksheet to explain that to multiply by a fraction is the same as saying 'of' (e.g. 1/2 x 5 is a half of 5). This is also helpful in seeing if students can apply cross-canceling to real-life applications. Try this question with them on the board: how many seconds are in 1/8th or 1/6th of 1/4th of a day and how many weeks is in 10! seconds?

‍

Worksheet: Divide mixed fractions D 3

Worksheet: Multiply mixed fractions D 3

Step 10

Step 10:

‍

Name: Block method

‍

Learning Outcomes:

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions (ENCY6)
solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts (ENCY6)

‍

Introduce concept

Use this worksheet to explain how to use the Block Method to solve Fraction questions.

‍

Worksheet: Block method fractions W 1

‍

Step 11

Step 11:

‍

Extra practice

‍

Step 12

Step 12:

Name: Fractions recap

Recap

Use this worksheet as a sum-up of the topic. Start off the sheet in the session and set the rest of it for homework as students should be familiar with all the concepts in the pack.