Addition of Integers

Teaching Ideas

Number bonds are extremely important for pupils to be quick and accurate with addition. Rather than just learning by wrote, get pupils to see relationships in number bonds…

Fingers are good for learning number bonds of 10. Put a divider between two fingers and count how many are on each side. Those two numbers are number bonds of 10.

Games like ‘Number Bond Snap’ are good. Each player gets a pile of cards with digits 1 to 9. They take it in turn to lay a card and if the card they lay summed with the last one makes 10 they shout ‘snap’ and the first person to do so wins that pile of cards. First person to get all the cards is the winner.

Number Bond Target Grid is good. Show a grid of numbers up on the board and ask questions like “give me two numbers that sum to make 10”, or “how many pairs of numbers can you find that make 100?”

Once number bonds of 10 are sorted you can use them to quickly work out other additions, for example “if 4 + 6 makes 10, what must 4 + 7 make?”

Another approach to develop pupils’ addition skills is to use Hundred Squares. If pupils get familiar with the layout and patterns of these they can learn that to add 10 you just move one square downwards. To subtract 10 you move one square upwards. To add 1 you move one square to the right, to subtract 1 move one square to the left. If you go off the left or right of the hundred square you just wrap round like you do on a snakes and ladders board. Adding 33 then becomes a movement of three squares down, three to the right. If pupils are familiar with the number squares they can often visualise this movement, or draw small diagrams to help. Here is a link to an interactive 100 square that you can use on the board.

When pupils are proficient with adding on 10s, you can teach them to use numberlines to help them with their calculations.

As they grow in confidence they can be encouraged to jump in other multiples of 10.

Being confident with this approach is useful when it comes to teaching directed (negative) numbers.

Traditional column addition is another approach. With this method pupils must line up the numbers correctly, units above units, tens above tens etc…




Resources and Activities

MEDIAN Criptarithms– each letter stands for a number in these column addition questions. Can your pupils work out which letter is which number?

MEDIAN Olympic Rings- lovely addition puzzle

MEDIAN Close to 1000- great investigation into reversible numbers that sum to 1000

MEDIAN Prime Sums– investigation into summing three consecutive primes

MEDIAN Eight Odds– add eight odd numbers to get twenty. How many solutions can you find?

MEDIAN Fiveways– like arithmagons, but making five lines that sum to the same total

MEDIAN Impossibilities- investigations into addition problems that are impossible

MEDIAN Two Digadds Making 200- investigation into number bonds of 200

MEDIAN Deletions- magical, engaging addition activity to hook pupils’ interest

MEDIAN 7 Regions- putting digits into a Venn Diagram to give each circle the same total

MEDIAN Sum 46– super number puzzle using odd numbers to sum to 46

MEDIAN Subsets– in any five integers you can always find three that sum to a multiple of three… investigate!

MEDIAN Addition– little column addition investigation looking for a unique solution

MEDIAN Forwards and Backwards– investigation into finding numbers that can be made by adding numbers with their reversals

NRich Tis Unique– column addition puzzle using all ten digits

NRich Eleven– column addition substitution puzzle

NRich Countdown- the classic arithmetic game in a nice interactive applet

NRich Read This Page– another lovely column addition substitution puzzle

NRich Addition Equation Sudoku– a challenging twist on the classic Sudoku

NRich Adding and Taking Away- lots of NRich activities for primary school pupils on addition and subtraction

NRich KS2 Addition and Subtraction- a selection of super NRich addition and subtraction resources for primary school teachers

NRich Playing with Numbers- a selection of NRich addition resources for primary school teachers

NRich Introduction to Magic Squares- a nice article introducing magic squares and their history. Includes links to activities

NRich Adding with the Abacus- a super article explaining how to add up on an abacus. Links to interactive versions

Math Salamanders Addition Worksheets– a super collection of addition worksheets at all levels

Math Salamanders Money Worksheets– adding and subtracting with money worksheets

MathsMaster.Org Column Addition of Whole Numbers Video– a YouTube video I made explaining column addition of whole numbers

MathsMaster.Org Column Addition of Decimal Numbers Video– a YouTube video I made explaining  column addition of decimal numbers

Arithmastars– a fun arithmetic activity based on moving around stars.

Making 100 Arithmetic Activity– a superb arithmetic activity where pupils have to use the digits 0 to 9 and the four operations to make 100.

Tutpup Games– online gaming to practice arithmetic. Very engaging