# PAR Word Skills now joined by Reasoning

PAR Word Skills which consists of a series of Vocabulary drills over 5 levels has proved popular with centres in the UK. Some have enthusiastically reported that they are finding it useful when preparing for 11+ Exams in particular. Of course, it has a much broader application as well; being designed to cover multiple levels.

More recently PAR Word Skills has been joined by Reasoning, which comes in 2 parts:
– 10 lessons that consist of various forms of Reading tests
– 50 Logic questions in a variety of forms and spread over 7 lessons.

As for all PAR resources, these are available as PDFs to enable printing paper copies if tutors wish to physically prepare students by actually carrying out a written practice exam.

# Integers

Here’s something for those encountering integers.

In Mathematics you can’t get far without negatives. We all know that if you’re multiplying and you want the end result to be negative you are going to have to use a negative and a positive.
[Tip: Encourage students to regard x + 2x 5x as x positive 2x negative 5x.]
So we teach:

+ x + = +
x = +          2 of the same will give a positive

+ x =
x + = –          2 different will give a negative

Students generally catch on to multiplying easily but with dividing there is often an uncertainty about whether the outcome will be a negative or a positive.

It’s easy – if you show them one thing. Look above at where any negatives are used. What do you notice?

Wherever any negatives were used there was always one positive out of the 3 signs involved.
When we divide and negatives are present there will have to be a positive used also.
Consider the following:

+6 ÷ +2 = +3
-6 ÷ -2 = +3

+6 ÷ -2 = -3
-6 ÷ +2 = -3

So when a student has a negative divided by a positive and wonders what the outcome will be, they can confidently expect a second negative. In the same way, if they are dividing a negative by a negative they can be assured they should get a positive answer.

The application of this reaches beyond the integers work often seen in the middle years at school. An example of the above being helpful is when students are doing such things as solving.

In 3x = -12 you need to divide the -12 by a [positive] 3. Result: x = -4

If the equation was -3x = -12 you’d be dividing the -12 by a -3 [negative]. Result: x = 4 [positive]

You can be positive in the way you use negatives; and to good effect. Try it.

# PAR Tables plan

Students begin by working on Learn Them and progress to Tables Workout. Once a student can do the Tables Workout in less than say 2 minutes they are ready to start testing out how many they can manage in 1 minute. So they try a 1 minute Tables Challenge. Any student who can score about 15 is probably ready for doing Tables Challenge.

Learn Them is for help to learn them.
Workouts is a practice tool.
Tables Challenge is a testing, evaluative tool (not a teaching tool).