The focus of all of the resources on this website is to promote conceptual understanding by starting with context first. This makes them ideal low threshold, high ceiling lessons. Please read the notes below on how to use them. These resources and this idea is new and untested so feedback is welcomed! Please visit the website for more info on how to use these resources. (Some resources are borrowed or adapted from other places - Credit where it's due)
The focus of all of the resources on this website is to promote conceptual understanding by starting with context first. This makes them ideal low threshold, high ceiling lessons. Please read the notes below on how to use them. These resources and this idea is new and untested so feedback is welcomed! Please visit the website for more info on how to use these resources. (Some resources are borrowed or adapted from other places - Credit where it's due)
Much of this lesson references the idea of thinking about division in terms of multiplication. As such, the lesson starts with an exercise designed to provide students with a complete set of multiplication grids. You will need to print slide 1 for students and hand them to them on the way in to lessons. The answers are on slide 2.
Then follows a true or false exercise designed to refresher students understanding of division. Do this using thumbs up or thumbs down across the room (They can always do in the middle if they aren’t sure). The next activity gets students to think of division in terms of worded sentences e.g. How many 5’s are there in 15? followed by a look at fact families. This is to get students to remember and understand the inverse relationship between multiplication and division.
Similar to the other arithmetic lessons, there are then mental and written methods of division. The mental methods of division are a series of divisibility tests and what to look for to see if a number will divide to give an integer answer. Provide students with a copy of the green grid on slide 7 and fill in the rules as they go along. It’s fun to do the number sort activities at the board with some board pens. When they have all the rules, they should attempt to complete the orange grid on slide 13. Bonus points for any students who can recognize that all the divisions can be completed but some will give a decimal answer.
To lead in to the written division techniques, first is a reminder of some of the literacy such as dividend, quotient and divisor and a visual demonstration of how division works as a method of grouping. There is then an “I do, you do” section to teach bus stop method. Most students should have seen this before. There is then a differentiated challenge. Students should challenge themselves to get as far as they can.
The next section is about dividing decimals including giving decimal answers, dividing a decimal by an integer and giving recurring decimal answers and some practice on these skills. A trickier extension is to ask students to explain how to divide by a decimal. This slide includes a visual explanation of why it works and some practice.
Lastly, there is some problem solving questions and a division dot to dot. Students will need a copy of slide 28 and 29. Students should start at an underlined question. They then need to join the question number to it’s answer. The answer then becomes the next question number until they reach a dead end. They should then start at the next underlined number.
Activities included:
Timetable grid starter
Division True or False
Division as a sentence
Mental Divisibility tests
Division Literacy
Written division explanation & practice
Mixed decimal division
Dividing by a decimal
Problem Solving
Division Dot to Dot
The ‘Why’: Why does multiplication work the way it does?
This lesson starts with an exercise designed to get students to recognize that multiplication is a way of simplifying repeated addition. It is then followed by a refresher of the commutative and associative laws and why they work.
Similar to the addition and subtraction lessons, this is then split into mental and written techniques. Mental techniques covered include; doubles, using 10’s, hand tricks and partitioning. Students should be reminded that, whilst they may be able to answer quickly and another way, these are good techniques for them to have in their back pockets. The aim is to give a technique for as many time tables as possible. Each slide features an “I do, you do” example, followed by a time trail to see how many students can complete in one minute.
Following this is the written techniques that includes: bar models, grid method, lattice method and lines. Some of these descriptions are slight rewording of popular techniques. Grid method is the method by which the place value of each number is split and put in a table. The lattice method, is similar but features diagonal lines to give two digit answers followed by diagonal addition to give each place value. Lastly, line is the Japanese method of drawing a single line to represent each place value, followed by another line across is and then counting the points at which they cross.
The deliberate decision was made to not include column method as it will likely have been covered in primary and often leads students to an incorrect answer.
Towards the end of the lesson, there are some techniques for decimal multiplication including using similar sums and estimating followed by practice using any method. At the end is a mix of problem solving tasks including worded and spot the mistake problems.
Activities included:
Repeated addition starter
Commutative and associative law refresher
Mental multiplication methods
Written multiplication methods
Decimal Multiplication
Estimating and Using Similar Sums
Mixed Problem solving
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus it’s place in their learning journey and other skills that they will be building on
The ‘Why’: Why do we use the current number system?
Because Place value is taught to Primary students, many come in to lessons with a working understanding of ‘what’ place value is and ‘how’ it works.
What is often not made clear, is the motivations behind it.
The early part of this lesson gets students to understand that numbers (as we think of them today) are in fact symbols that represent a value and that many other systems existed before this.
It then gets students to understand why it would be inconvenient to have a new symbol for every single number and how handy the positional notation system is.
Some students will go on to ask “Why do we count in tens?”
This leads nicely into talking about different bases and binary as extension.
Activities included:
Number Symbols from the past
Counting systems throughout history
Representing Number activity
Design your own Number system
Where our symbols came from
The History of 10
Positional Notation activity
Problem Solving Questions
Different Bases
Counting in Binary
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
Topic Intro designed to introduce Year 8 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.
