Maths Optional Tasks – Autumn Term

Below are optional tasks. These tasks focus on what we have worked on in class during the previous week.

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.

Week 1 – W/B Monday 21st September

Focus: Place Value – Numbers to 1,000,000

Fluency

1. What is the value of the 6 in each number?
   364,215 = ______
   621,450 = ______
   156,782 = ______
2. Write these numbers in words:
   425,310 = ______________________________
   703,056 = ______________________________
3. Write 582,407 in expanded form.

Problem Solving

1. A number has:

   • 4 hundred thousands
   • 7 ten thousands
   • 3 thousands
   • 8 hundreds
   • 2 tens
   • 5 ones

   What is the number?

2. Sophie says the digit 5 has the same value in 152,000 and 512,000.
   Is she correct? Explain.

Reasoning

Explain how you know the value of each digit in the number 346,725.

⭐ CHALLENGE

Using the digits 2, 3, 5, 6, 7 and 9 once each, make:

• the largest possible six-digit number
• the smallest possible six-digit number

What is the difference between your two numbers?

Week 2 – W/B Monday 28th September

Focus: Place Value – Powers of 10 and Number Lines

Fluency

1. Complete:

   4,500 × 10 = ______
   4,500 ÷ 10 = ______
   32,000 × 10 = ______
   320,000 ÷ 10 = ______

2. Complete the sequence:

   120,000, 130,000, ______, ______, 160,000

3. A number line runs from 200,000 to 300,000.
   What number would be halfway between them?

Problem Solving

1. A number is multiplied by 10. The answer is 450,000.
   What was the starting number?

2. Eva says:

   “When you multiply a whole number by 10, you just add a zero.”

   Is this always a good way to think about multiplying by 10? Explain using place value.

Reasoning

Explain what happens to the value of each digit when a whole number is multiplied by 10.

⭐ CHALLENGE

I am thinking of a number.

• It is between 300,000 and 400,000.
• It is greater than 350,000.
• When rounded to the nearest 100,000, it rounds to 400,000.
• The tens of thousands digit is 7.

Give three numbers that could be my number.

Week 3 – W/B Monday 5th October

Focus: Place Value – Compare and Order Numbers

Fluency

1. Add <, > or =:

   345,621 ___ 354,621
   708,009 ___ 708,090
   450,000 ___ 449,999

2. Put these numbers in ascending order:

   425,000
   452,000
   405,200
   425,500

3. Put these numbers in descending order:

   601,250
   610,025
   600,125
   612,500

Problem Solving

1. Four towns have these populations:

   Town A: 156,420
   Town B: 165,240
   Town C: 156,204
   Town D: 165,024

   Which town has the largest population?
   Which has the smallest?

2. Sam says 398,999 is greater than 400,001 because it has more 9s.
   Explain Sam's mistake.

Reasoning

When comparing two six-digit numbers, explain why you should start by comparing the digits with the greatest place value.

⭐ CHALLENGE

Use the digits 1, 3, 4, 6, 8 and 9 once each.

Create a number that is:

greater than 500,000 but less than 700,000.

How many different numbers can you make?

Week 4 – W/B Monday 12th October

Focus: Place Value – Rounding Numbers

Fluency

1. Round to the nearest 10:

   4,327 = ______
   8,995 = ______

2. Round to the nearest 100:

   6,749 = ______
   12,351 = ______

3. Round to the nearest 1,000:

   34,650 = ______
   78,499 = ______

4. Round 367,891 to the nearest 100,000.

Problem Solving

1. A football stadium has 48,762 supporters inside.

   Approximately how many supporters is this to the nearest:

   • 1,000?
   • 10,000?

2. A number rounds to 50,000 when rounded to the nearest 10,000.

   What could the number be?
   Give three possible answers.

Reasoning

A pupil says:

“46,501 rounds to 46,000 because the hundreds digit is 5.”

Explain the mistake.

⭐ CHALLENGE

Find a number that:

• rounds to 70,000 to the nearest 10,000
• rounds to 74,000 to the nearest 1,000
• is an odd number

How many different answers can you find?

Week 5 – W/B Monday 19th October

Focus: Place Value – Roman Numerals and Place Value Review

Fluency

1. Write these Roman numerals as numbers:

   XII = ______
   XXIV = ______
   XL = ______
   LXVII = ______

2. Write these numbers in Roman numerals:

   8 = ______
   19 = ______
   35 = ______
   49 = ______

3. Complete:

   L = ______
   C = ______
   D = ______
   M = ______

Problem Solving

1. A building was completed in MMXXVI.
   What year was it completed?
2. Freddie says IIII is the correct Roman numeral for 4.
   Do you agree? Explain.

Reasoning

Explain why IX represents 9 but XI represents 11.

⭐ CHALLENGE

Write the year 2026 in Roman numerals.

Now work out:

• the year you were born
• the current year
• the difference between the two years

Can you write all three answers using Roman numerals?