Year 5 - Fractions Learning Path (Red 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:
Generally students who require a smaller group and more attention- Get them involved and engaged in the questions through verbal participation in sessions and sharing their answers with the tutor or the rest of the group- Encourage them to write their workings down and avoid rushing by giving them a specific structure to follow- Repeat the concepts frequently as it limits them forgetting the steps to tackling the problem
Step 1:
Name: Equivalent Fractions
Learning outcomes:
- Identify, name and write equivalent fractions of a given fraction including tenths and hundredths (ENCY5)
- Compare and order fractions whose denominators are all multiples of the same number (ENCY5)
Introduce concept
Students with the Red profile tend to skip certain steps and want to jump from one non-simplified Fraction to another. Use this worksheet to guide the students by explaining that they always have to convert the Fraction to its simplest form before being able to equate them.
Worksheet: Equivalent fractions D 2
Step 2:
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
Now that the student has had some practice, challenge them by setting a 10-minute timer for them to complete the following questions. This will encourage them to focus on their work and test their arithmetic speed.
Worksheet: Equivalent fractions D 4
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)
- Use common factors to simplify fractions; use common multiples to express fractions in the same denomination (ENCY6)
Introduce concept
Emphasise that an extra step is required to convert a Fraction so both Fractions have the same denominator. Encourage students with the Red Profile to complete this question in two separate steps by writing their workings out, instead of doing it in their head.
Worksheet: Add subtract unlike fractions D 1
Step 4:
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)
- Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1as a mixed number (ENCY5)
Recap
The student should have come across this in the previous year but go through the sheet again to ensure they remember. Students with the Red Profile tend to forget the steps that they have learnt in the past. For questions like S and E, prompt them to see that they can multiply one of the fractions so they match the denominator of the other, instead of multiplying both fractions by the other denominator. Tell the student that they have to simplify their answers to get the correct answer.
Worksheet: Add subtract unlike fractions W 1
Step 5:
Name: Add/subtract mixed fractions
Learning Outcomes:
- Recognise mixed numbers and improper fractions and convert from one form to the othr and write mathematical statements > 1 as a mixed number (ENCY5)
- Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions (ENCY6)
Extra practice
Use this sheet to allow them to practice the skills that they have learnt. Once understanding how to convert a mixed Fraction into an improper Fraction, they should be able to complete this step with ease.
Worksheet: Add subtract mixed fractions D 2
Step 6:
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)
Word problems
Use this worksheet to check that these students can apply the concepts they have learnt to word problems.
Worksheet: Add subtract fractions W 1
Step 7:
Name: Multiplying fractions
Learning Outcomes:
- Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams (ENCY5)
- Multiply simple pairs of proper fractions, writing the answer in its simplest form (ENCY6)
Introduce concept
Introduce the concept by explaining that 1/2 of 2 is the same as multiplying 1/2 by 2. Once you are confident that they are clear on that concept, move onto the rest of the worksheet. On each of the sections, students should be able to get three consecutive questions correct before moving on to the next section to ensure their understanding.
Worksheet: Multiply fractions and whole numbers V 1
Worksheet: Multiply fractions and whole numbers W 2
Worksheet: Multiply fractions and whole numbers D 1
Worksheet: Multiply fractions V 1
Worksheet: Multiply fractions D 1
Worksheet: Simplify and multiply fractions D 1
Worksheet: Simplify and multiply fractions D 2
Worksheet: Multiply mixed fractions D 2
Step 8:
Introduce concept
Explain the use of cross-cancelling on the board with a few examples. Once they are comfortable with the concept, challenge them with some harder examples before giving them this worksheet to try out.
Step 9:
Word problems
Encourage the student to write each step of their workings clearly.
Step 10:
Name: Multiplying 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 > 1as a mixed number (ENCY5)
- Multiply proper fractions and mixed numbers by whole numbers (ENCY5)
- Multiply simple pairs of proper fractions, writing the answer in its simplest form (ENCY6)
Timed exercise
Give the students a strict 7-minute timer to complete this worksheet.
Worksheet: Multiply mixed fractions D 3
Step 11:
Name: Dividing fractions
Learning Outcomes:
- Recognise mixed numbers and improper fractions and convert from one form to the othr and write mathematical statements > 1 as a mixed number (ENCY5)
- Divide proper fractions by whole numbers (ENCY6)
Worksheet: Divide fractions V 1
Worksheet: Divide fractions V 2
Worksheet: Divide mixed fractions D
Step 12:
Name: Dividing 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 > 1as 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)
Extra practice
Encourage them to try the questions on their own. If they are struggling, give them a hint and remind them to convert the mixed fractions into improper fractions before cross-cancelling.
Worksheet: Divide mixed fractions D 2
Step 13:
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.
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