Place Value

Students learn how to use place value to write numbers in words and digits and how to compare the size of decimals using inequality symbols.  As learning progresses they use the this to multiply and divide by a given power of ten.

This unit takes place in Term 1 of Year 7 and follows on from the introduction to secondary maths topic.

Problem Solving Lessons
Prerequisite Knowledge
  • Find 1000 more or less than a given number
  • Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  • Order and compare numbers beyond 1000
  • Identify, represent and estimate numbers using different representations
  • Round any number to the nearest 10, 100 or 1000
  • Solve number and practical problems that involve all of the above and with increasingly large positive numbers
  • Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.
Key Concepts
  • The ability to arrange digits in a place value table is crucial to accessing future topics such as fractions, percentages and many more.
  • When multiplying and dividing by 10, 100 and 1000 students can benefit from visualising the digits shift between columns in the place value table.
  • To interpret a number scale students need to have a secure understanding of using the place value table.
  • Students often confuse the direction of the inequality symbols when comparing numbers.
Working mathematically

Develop fluency

  • Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals.

Reason mathematically

  • Extend their understanding of the number system; make connections between number relationships,

Solve problems

  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
Subject Content


  • understand and use place value for decimals, measures and integers of any size
  • order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
  • use the four operations, including formal written methods, applied to integers and decimals.

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