Maths Optional Tasks

Below are further, more structured, optional tasks. These tasks focus on what we have worked on in class during the previous week. For example, Week 1 will begin on Monday 10th November and will reflect the learning taught during the week beginning 3rd November.

Each week is divided into three short sections: Fluency, Problem Solving, and Reasoning, followed by a Challenge task to stretch your thinking. Try to complete each section carefully and show your working where possible.

Still struggling?
There is a link at the bottom of this page to White Rose Maths videos, which are short ‘mini lessons’ explaining the key concepts and methods behind the maths we are studying.

You will be taken to a page with different sections (e.g. Multiplication and Division, Fractions A, Decimals and Percentages).
Click on the appropriate block, then find the video related to the topic you are currently finding tricky.

For example:
If you find Week 3 difficult, follow the link, choose the block Fractions A, and find the video titled “Convert improper fractions to mixed numbers.” This will help explain the method step by step.

Week 1 – W/B 10 November

Focus: Multiply and Divide by 10, 100 and 1000

Fluency

1. 3.5 × 10 = ___   0.6 × 100 = ___   4.2 × 1000 = ___

2. 6 300 ÷ 100 = ___   0.84 × 100 = ___

Problem Solving
3. A rope is 4.2 m long. It is 100 times longer than a string. How long is the string?
4. A bottle holds 0.75 L. What is the total volume of 10 bottles?

Reasoning
5. Explain why multiplying by 10 does not always mean “add a zero”. Give an example.

⭐ CHALLENGE 
When you multiply 3.4 by 100 and divide 34 by 10, the answers look similar.
Explain what is the same and what is different about them.

Week 2 – W/B 17 November

Focus: Equivalent Fractions (to Year 5 level)

Fluency

1. ½ = ___/4  2/3 = ___/9  3/5 = ___/10

2. Simplify 6/12 = ___  Simplify 8/20 = ___

Problem Solving
3. Shade an equivalent fraction of ½ on a shape divided into 8 equal parts.
4. Write two fractions equivalent to ¾ using different denominators.

Reasoning
5. Explain how you know that 2/4 and 6/12 are equivalent without using a fraction wall.

⭐ CHALLENGE 
Create two different fractions that are equivalent to 3/5 and explain the pattern between the numerators and denominators.

Week 3 – W/B 24 November

Focus: Convert Improper ↔ Mixed Fractions & Compare and Order Fractions

Fluency

1. Write 7/4 as a mixed number: ___ ___/4

2. Write 2 ⅗ as an improper fraction: ___/5

3. Order these fractions from smallest to largest: ⅖, ⅗, ½

Problem Solving
4. Sam has 2 ¾ m of ribbon and adds another 1 ¼ m. What is the total length?
5. Which is greater: 2 ⅓ or 2 ⅔? How do you know?

Reasoning
6. Explain why 9/4 and 2 ¼ represent the same amount even though they look different.

⭐ CHALLENGE 
Order these numbers: 1 ½, 11/8, ⅝, 2 1/8. Explain how you decided the order without using a calculator.

Week 4 – W/B 1 December

Focus: Add Fractions (including Mixed Numbers)

Fluency

1. ⅖ + ⅕ = ___  ¾ + ¼ = ___  ⅞ + ⅛ = ___

2. 2 ⅔ + ⅓ = ___

Problem Solving
3. A recipe uses ⅔ cup of sugar and ¼ cup of honey. How much sweetener is used in total?
4. Ben runs 2 ⅗ km on Monday and 3 ⅖ km on Tuesday. How far in total?

Reasoning
5. Why must the denominators be the same before you add fractions? Give an example.

⭐ CHALLENGE 
The answer to Ava’s question is 3 ½. What could her question have been if it involved adding two mixed numbers?

Week 5 – W/B 8 December

Focus: Subtract Fractions (including Mixed Numbers)

Fluency

1. ⅘ – ⅗ = ___  ¾ – ¼ = ___  7/8 – 3/8 = ___

2. 4 ⅖ – 1 ⅗ = ___

Problem Solving
3. A ribbon is 2 ⅞ m long. If you cut off ⅜ m, how much remains?
4. A cake weighs 3 ¾ kg. After a party, ¼ is left. How much was eaten?

Reasoning
5. Explain why you might need to “exchange 1 whole” when subtracting mixed numbers.

⭐ CHALLENGE 
Find two different ways to show 3 – 1 ⅔ using improper fractions and mixed numbers. Explain your method.

Week 6 – W/B 15 December

Focus: Mixed Review – All Skills**

Fluency

1. 0.35 × 1000 = ___  6 400 ÷ 100 = ___

2. ½ = ___/8    Change 2 ¾ to an improper fraction = ___/4

Problem Solving
3. Order these fractions: ⅖, ⅗, ¾, ⅚.
4. A recipe needs 1 ½ cups of milk and ¾ cup of water. How much liquid altogether?
5. A baker has 4 ⅗ kg of flour. He uses 2 ⅖ kg. How much is left?

Reasoning
6. When is it better to convert mixed numbers into improper fractions before calculating? Give an example.

⭐ CHALLENGE 
At a Christmas bake sale, Ruby uses ⅓ of a bag of flour on Monday, ⅖ on Tuesday and the rest on Wednesday. What fraction is used on Wednesday? Explain each step clearly.