Integer Tiles for School Maths Lab

Quick Answer: Integer Tiles are small flat tiles of two kinds, one standing for +1 and the other for −1, used to model positive and negative numbers. Maths classes use them to show zero pairs and to explain the rules for adding, subtracting and multiplying integers.

Zero Pairs: the Idea Behind the Tiles

Every lesson with these tiles rests on one fact: a positive tile and a negative tile together make zero. Such a zero pair can be added to or removed from any collection without changing its value. With that single idea students can model every integer operation using objects they move and count.

Addition is combining. For 5 + (−3), put out five positive and three negative tiles, remove the three zero pairs, and two positives remain. Subtraction is taking away, and this is where the tiles earn their place. To work out 2 − 5 there are not enough positives to remove five, so the student adds three zero pairs, takes five positives away and is left with three negatives: −3. The same method makes 3 − (−2) clear: add two zero pairs, remove the two negatives, and five positives remain.

Multiplication extends the idea to groups. Three groups of two negative tiles make −6. Multiplying by a negative number means removing groups, so −3 × −2 starts from a pile of zero pairs, removes three groups of two negatives and leaves six positives. The same zero-pair reasoning carries straight into algebra tiles, where a larger piece stands for x.

Applications

• Representing positive and negative integers as collections of unit tiles
• Adding integers by combining tiles and removing zero pairs
• Subtracting integers, including subtracting negatives, by inserting zero pairs
• Modelling multiplication of integers as adding or removing groups
• Preparing students for algebra tiles and equation solving

Care & Handling

• Sort the integer tiles by kind into separate trays after the lesson so the next class starts with balanced sets.
• Wipe grubby tiles with a damp cloth and let them dry before they go back in the box.
• Give each pair of students a mat or tray to work on so tiles do not scatter off the desk.

Specifications

Why Choose LabEquip

These tiles are normally ordered as one set per pair or small group, since every student needs to move pieces during the lesson. LabEquip lists them in its Mathematics School Lab Products range next to the Integer Number Line Bar for teachers who use both models; send group numbers through the LabEquip contact page.

Frequently Asked Questions

What is a zero pair?

A zero pair is one positive tile and one negative tile. Together they are worth zero, so any number of zero pairs can be added to or removed from a set of tiles without changing its value. This idea is used in every tile calculation with integers.

How do the tiles show 2 – 5?

Start with two positive tiles. Five positives cannot be removed, so add three zero pairs, giving five positives and three negatives. Remove the five positives and three negative tiles remain, so 2 – 5 equals -3.

Why does subtracting a negative give a positive result?

To take away negative tiles you may first need to add zero pairs. For 3 – (-2), add two zero pairs to the three positives, remove the two negatives, and five positives are left. Removing negatives leaves extra positives behind.

Can the tiles be used for multiplication?

Yes. 3 × (-2) is three groups of two negative tiles, giving -6. For -3 × (-2), start with zero pairs and remove three groups of two negatives, leaving six positives, which shows why the product of two negatives is positive.

How are these tiles different from algebra tiles?

They contain only unit pieces for +1 and -1. Algebra tiles add larger pieces for x and x², so they can model expressions, factorising and equations. Students who are confident with unit tiles find algebra tiles easier because the zero-pair idea carries over.

Are the tiles suitable for whole-class demonstration?

Desk sets suit hands-on work by pairs or small groups. For whole-class demonstration teachers draw the tiles on the board or use magnetic pieces, then let students copy each move with their own sets.

Last Updated: September 2026