The bridge course

Year 7

The year before Year 7. The arithmetic a Year 7 book assumes you already have, taught properly — in order, and with the bar model running through all of it.

What's inside

1. Number bonds

   Seven is four and three — one fact that answers four questions. Everything after this is that idea getting bigger.

2. Making ten

   Ten is the number the whole system is built on, and getting to it is what makes adding in your head possible.

3. Place value

   Why 40 is four tens and not a four with a nought. The idea every written method quietly depends on.

4. Times tables

   Multiplication as equal groups, then as a rectangle you can see. The facts matter because thinking needs the room they free up.

5. Multiplying without tables

   Seven fourteens is seven tens and seven fours. The distributive law, two years before anyone writes a(b + c).

6. Two kinds of division

   Sharing between and grouping into are the same division seen from two sides. Separating them now is what makes dividing by a fraction a return rather than a shock.

7. Remainders

   What is left over, and what to do with it — which depends entirely on what was being shared.

8. Written methods

   Columns for adding, subtracting and multiplying, and why the carrying works rather than where to put it.

9. Fractions as parts

   A fraction is a count of slices, and the bottom number says how big a slice is. Nearly every later mistake starts here.

10. Comparing fractions

    Why a bigger bottom number means smaller pieces — the most reliable wrong answer in primary maths.

11. Adding fractions

    You can only count slices that are the same size, which is the whole reason for a common denominator.

12. Drawing the problem

    The bar you have been using all along, named at last: two bars, a total and a difference, and a box standing for what you do not know yet. That box is algebra, arriving without announcement.