Mathematics · Year 6 · The Power of Place Value and Calculation · Autumn Term

Numbers to Ten Million: Reading & Writing

Students will read, write, and identify the value of digits in numbers up to 10,000,000.

• National Curriculum Attainment Targets
• KS2: Mathematics - Number and Place Value

About This Topic

Year 6 marks a significant jump in place value as students move from working with thousands to numbers up to ten million. This topic is the bedrock of the entire mathematics curriculum, ensuring students can read, write, and order increasingly large integers while understanding the relative value of each digit. It aligns with the National Curriculum requirement for students to determine the value of each digit and use rounding to check the reasonableness of their answers in complex problems.

Beyond simple identification, students must grasp how place value shifts during multiplication and division by powers of ten. This conceptual understanding is vital for later work with decimals and scientific notation. When students can explain why a digit's value changes as it moves across the columns, they develop a flexible number sense that prevents common calculation errors. This topic particularly benefits from hands-on, student-centered approaches where learners can physically manipulate digit cards or use place value counters to model the scale of these large numbers.

Key Questions

1. Analyze how the value of a digit changes when it moves three places to the left.
2. Differentiate between the value of a digit and its place in a number.
3. Predict the largest possible number that can be made using seven distinct digits.

Learning Objectives

• Identify the place value of each digit in numbers up to 10,000,000.
• Write numbers up to 10,000,000 in numerals and in words.
• Explain how the value of a digit changes when it is multiplied or divided by 10.
• Compare and order numbers up to 10,000,000.
• Create the largest possible number using a given set of distinct digits.

Before You Start

Numbers to One Million: Reading & Writing

Why: Students must be comfortable reading, writing, and understanding place value up to 1,000,000 before extending to ten million.

Place Value to Thousands

Why: A solid grasp of place value for thousands, hundreds, tens, and ones is fundamental for understanding larger numbers.

Key Vocabulary

Place Value	The value of a digit based on its position within a number. For example, in 5,234, the digit '2' is in the hundreds place and has a value of 200.
Digit	A single symbol used to write numbers. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Millions	The place value representing one thousand thousands. Numbers in this range go from 1,000,000 to 9,999,999.
Ten Millions	The place value representing ten million. Numbers up to 10,000,000 include this highest place value.

Watch Out for These Misconceptions

Common Misconception

Students believe that adding a zero to the end of a number always multiplies it by ten.

What to Teach Instead

This rule fails when students encounter decimals later on. Use place value sliders to show that the digits themselves are moving one column to the left, and the zero is simply a placeholder to maintain the structure of the number.

Common Misconception

Thinking that 'rounding to the nearest million' always means the number must get smaller.

What to Teach Instead

Students often struggle with the 'round up' rule for digits 5 and above. Peer discussion using number lines helps students see that rounding is about finding the closest multiple, whether it is higher or lower than the original value.

Active Learning Ideas

Stations Rotation: The Rounding Challenge

Set up four stations with real world data, such as UK city populations or distances to planets. At each station, small groups must round the figures to the nearest 10,000, 100,000, and 1,000,000, then discuss which rounded figure is most useful for a news headline.

40 min·Small Groups

Think-Pair-Share: The Digit Shift

Give students a seven digit number and ask what happens to the total value if the digit in the millions place is swapped with the digit in the hundreds place. Students work individually to calculate the difference, compare their methods with a partner, and then share the most efficient mental strategy with the class.

15 min·Pairs

Inquiry Circle: Number Detectives

Provide groups with a set of clues about a mystery eight digit number, such as 'the digit in the ten thousands place is double the digit in the units place.' Groups must use a large place value grid to test their theories and prove their final answer to the rest of the class.

30 min·Small Groups

Real-World Connections

• Demographers use numbers up to ten million to report population figures for large cities and countries, such as the population of London or the United Kingdom itself.
• Financial analysts and accountants work with large sums of money, reading and writing figures in the millions when discussing company profits, national budgets, or stock market values.
• Scientists track data in the millions, for example, the number of stars in a galaxy or the estimated number of bacteria in a sample.

Assessment Ideas

Quick Check

Write the number 7,452,913 on the board. Ask students to write down the value of the digit '5' and the place value of the digit '7' on a mini-whiteboard. Review responses to gauge understanding of digit value versus place.

Exit Ticket

Give each student a card with a number like 3,000,000 or 800,000. Ask them to write the number in words and then identify the largest possible number they could create using three distinct digits from their number. Collect these to check individual comprehension.

Discussion Prompt

Pose the question: 'If you move the digit '6' from the thousands place to the millions place, how many times larger does its value become?' Facilitate a class discussion where students explain their reasoning using place value concepts.

Frequently Asked Questions

How can active learning help students understand place value?

Active learning moves place value from abstract columns on a page to a physical concept. By using strategies like station rotations or collaborative investigations, students must explain their reasoning aloud. This verbalisation helps solidify their understanding of the scale of numbers up to ten million, as they have to justify why a digit in one column is ten times greater than the one to its right.

What is the best way to teach rounding of large numbers?

Use vertical number lines rather than just horizontal ones. This visual aid helps students see which 'million' a number is physically closer to. Combining this with real world contexts, like rounding the capacity of Wembley Stadium, makes the purpose of rounding clearer to Year 6 learners.

Why do students struggle with zeros in large numbers?

Zeros act as placeholders, and students often 'skip' them when reading or writing numbers like 7,040,201. Using place value counters in a collaborative setting allows students to see the 'empty' columns, reinforcing that every place must be accounted for to maintain the number's value.

How does Year 6 place value connect to secondary school maths?

A firm grasp of place value up to ten million is essential for understanding standard form and significant figures in Key Stage 3. If students understand the multiplicative relationship between columns now, they will find it much easier to work with very large and very small numbers in science and geography later.