Place Value

October 7, 2016

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.

Place Value Lessons

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.

Mr Mathematics Blog

Practical Tips for Using Mini-Whiteboards in a Mathematics Lesson

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

Showing Progress during a Mathematics Lesson

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]

Plotting and Interpreting Conversion Graphs

March 26, 2019

Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]