Module 2 Calculations
Module Content Lesson Resources Lesson Plans Exam Questions Probing Questions

Calculations - Teacher Notes

Solvemymaths has produced pages like this for lots of topics


NRICH: Consecutive Numbers
NRICH: First Connect Three
NRICH: Twenty Divided by Six

NRICH: Reach 100
NRICH: Magic Matrix

NRICH:  Multiplication Square Jigsaw
NRICH:  Shape Times Shape
NRICH: Times Tables Matching Cards 
NRICH: Forgot the Numbers
NRICH: How Many Miles to Go?
NRICH: Largest Product
NRICH: Multiplying with Lines
NRICH: Fractions Jigsaw
NRICH: Ben's Game
NRICH: Guesswork
NRICH: Number Pyramids
NRICH: More Number Pyramids
NRICH: Napier's Location Arithmetic
NRICH: Dating Made Easier
: One and Three
Multiply Large Numbers
Video: Multiplying Negatives
Multiply Fractions Visual
Video Worked Examples:
Index notation 1  Introduction
Index notation 2  Multiply/divide
Index notation 3  Multiply/divide


Associating number facts

This video is on using known number facts to help work out other ones - Click here

Once pupils start to familiarise themselves with how to associate number facts, I like use the following types of questions:

How does knowing 5 4 = 20 help you work out 6 4?

I know that 10 7 = 70, how can I use that to find 9 7?

If I know that 20 3 = 60, what else do I know?

1 16 = 16
2 16 = 32
3 16 = 48
4 16 = 64
5 16 = 80
6 16 = 96
7 16 = 112
8 16 = 128
9 16 = 144
10 16 = 160
What is 16 16?
What is 176 16?

Routine practice in a fun way

This video of Jill Mansergh at an ATM conference shows a wonderfully simple way of bring out the links within the (17) times table. Being able to navigate from one multiplication fact to another is a crucial element of mastering them - Click here



Make it easier.

Find the Factors - @findthefactors

The object of the FIND THE FACTORS 1 10 (or 1 12) puzzle is to write the numbers 1 to 10 (or 1 to 12) in the top row and again in the first column so that once the factors are found, the puzzle works as a multiplication table. All of the puzzles require a basic, but not necessarily quick or perfect, knowledge of all the multiplication facts from 1 to 10 or from 1 to 12 - Full Explanation

An archive of previous puzzles set by Iva can be found by Clicking here


You can mark a square on the grid as long as you can think of two factors that you can multiply to get the number in the square. Students have multiplication tables available to them and were free to refer to them to help identify correct multiplication problems - Click here


Fours Operations HexaTrex

The object of the puzzle is to find the equation pathway that leads through ALL the tiles. 

For example the solution for this Hexa-Trex tile arrangement:



Click here for the rules and link at top to Differentiated Problems

Working with Brackets


Multiplication & Division

This spreadsheet allows you to enter a multiplication into the green squares and it then generates  10 related calculations for the students to work out - Click here

An extension of this is then to write a calculation on the board and ask the pupils to come up with related calculations.



Line Multiplication

Why does it work?  Compare with Grid Multiplication


Parabolic Multiplication - Video

Let's say you want to multiply 5 by 8. Do the following:

1.     Plot the graph of y=x2.



2.  Draw a line that crosses the parabola where x = -5 and where x = 8 on the parabola. (Ignore the fact that x = -5 and not +5 at the left intersection point; this calculator does not do signed arithmetic!)

3.    Note the value of y where the line crosses the y-axis.

4.    The value of y is 40 and indeed 5 x 8 = 40.


Can you figure out why this works? [See below]

Never mind that it's much more work to plot the graphs and determine where the line


Negative Numbers

Yellow = +1 and Red = -1

So 4 + -3 is shown here

You can now subtract a negative by taking a red one away 


Working out percentages without a calculator.

                     Percentage of an amount - ever wondered why? - JustMaths

                     Percentage Change Chain - Michael Sharman on TES 

                     Percentages Inquiry - Inquiry Maths

                     Percentages Revision -

                     Percentage deals - Median Don Steward


Teaching Fractions is Hard - Teaching Sequence and Lesson Ideas


Adding Fractions

Magic Squares - Don Steward


Adding Fractions


Multiplying Fractions


Dividing Fractions - Teaching Sequence


Fractions Investigation

Can you find other examples? Great way of getting pupils to practice the addition of fractions    


Speed Calculations