Place Value

Digits and Words

Comparing Numbers

Number Scales

Multiplying by 10, 100 and 1000

Dividing by 10, 100 and 1000

Alternative Number Systems

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

Number

• 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.