Templates of rectangles with quartering dots. Draw two lines - what different fractions can you create?

Practises using the diagrammatic form of the mental operation as used in Singapore text books.

Practices the diagrammatic form of the mental operation used in Singapore text books.

This worksheet models the "Singapore" idea of partitioning to transfer the numbers to more manageable ones.

This worksheet is a progression from sheet 1.

Images show the relationship between one third and two thirds; and one fifth and 3 fifths.

Dots are grouped in 10s, Can they use sheet A to find a quick method of finding the total number of dots? Can they cut out the images from sheet B to make a given number e.g. 43? 122? and stick them down to make a picture of that number.

This one models the shapes that can be expressed using 2² etc. Firstly, they interpret the diagrams, then calculate from a range of expressions.

An investigative exercise to partition arrays of circles (9s and 10s) according to a rule for the day e,g, lets colour in 6 circles. Contains ideas for lessons.

The digits are grouped to total 10. Can they recognise the 10s to find ways of finding the totals in Sheet A? They can write underneath which numbers they added to get the total. Sheet B can be used, more creatively, to find different ways of making a picture of a given number, e.g. 58? 136? The images can be cut out and stuck down with an accompanying 'proof' of how those images add up to the total.

2 of the 4 numbers in each box sum to 20. Tell them to put a ring around those two numbers. Now they can tell you what the sum of all 4 numbers is. They can cut out each box and stick it in the correct place on the other sheet to make a block graph.

The fundamental mental (!) skills of Doubling, Halving, Adding/Subtracting/Multiplying/Dividing by 10. Provides practise in using those operations to discover different outcomes. Pupils can check their answers with a calculator. The fifth sheet can be used to run off helpful physical tokens to assist with considering the options. Just like Numbergym's 'Smart Operations'.

Use the numbers from the four at the top to make the equations. I like to use Digit counters with this activity but it is not essential. However it does benefit lower attainers to have something physical that can be placed on the blank spaces.

Designed to accompany the Numbergym activities, it allows pupils to investigate relationships between factors and fractions. e.g. that dividing by 6 is halving the result of dividing by 3. The template allows you to begin by suggesting a number to be placed at the top e.g. what happens when you divide up 24, or 84 or 1 etc. or placing a number randomly in any of the other boxes. It also allows them to model "three-eighths of 40" or "two-fifths of 30"....

Two of the four numbers in each box sum to 100. Tell them to draw a ring around those two numbers. Now they can add all four numbers. They can cut out the box and stick it in the correct place on the other sheet to make a block graph.

Practises the funda mental processes of adding/subtracting 10, Doubling/Halving and multiplying/dividing by 10. This time the outcome of using two of the three operations is given. But which ones??? Pupils can check their (or their partner's) answers on a calculator. This exercise replicates the Numbergym puzzle activity 'Smart Operator'.

This expanded worksheet amends the previous one. It spells out the stages involved when adding or subtracting amounts that can be easily rounded.

Each box has a trio of numbers, two of which sum to 10. Tell them to put a ring around those two numbers. The box can then be cut out and stuck down in the correct place on the 'block graph'.

Put two different jointed lines on the board and ask 'how can we find out which one is longer?' Model how to measure each segment and add them together. Then offer the worksheet!

Linking fractions with rectangles is a time proven strategy. But many pupils fail to make the link between the dimensions of the rectangle and the denominator. This exercise alerts them to discover whether it is the length or the width which is the key to identifying the partitioning solution. See Numbergym for an activity to model a way of adding fractions.

A Powerpoint slideshow to apply using knowledge of multiples of numbers 3,4,5,9,16,25. Also template sheets for investigative use.