Grade 4: Square Numbers

Warm up with a quick recall on the board. Show a square number as the area of a square array (3 x 3 = 9), link squaring to its inverse (the square root), and learn the first perfect squares so roots of perfect squares are quick to recall.

A square number is the result of multiplying a whole number by itself, so 6 squared (6²) is 6 × 6 = 36. They are called square numbers because that many dots or tiles form a perfect square. Recognising them fluently helps with area, factors and later work with square roots. Model the method clearly, thinking aloud:

• Make it visual: build squares of tiles (2×2, 3×3, 4×4) and count the total, that total is the square number.
• Introduce the notation: 6² means 6 × 6, not 6 × 2.
• Learn the first perfect squares to 144 (1, 4, 9, 16, 25 …) by heart, like times-table facts.
• Practise both ways: work out a square (7² = ?) and find which number was squared (which number squared is 49?).
• Link it to area, the area of a square with side 6 is 6² = 36 square units.

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• Reading 6² as 6 × 2 = 12 instead of 6 × 6 = 36.
• Confusing a square number with doubling.
• Forgetting the units are 'square' units when linking to area.
• Confusing squaring with doubling (thinking 3 squared is 6), and assuming every number has a whole-number square root.

Pull the class back together. Ask one child to explain square numbers in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.