Grade 7: Number

Warm up with a few quick number warm-ups on the board while the class settles, so every child starts thinking about the skill.

A square number comes from multiplying a whole number by itself (3 x 3 = 9). A square root undoes this: the square root of 9 is 3. This unit covers finding squares and roots of perfect squares, and estimating roots of numbers that are not perfect squares. Model the method clearly, thinking aloud:

• Build square numbers concretely first: an n by n grid of squares has n^2 squares in total.
• Teach square roots as the inverse operation: 'what number, multiplied by itself, gives this?'
• Memorise the perfect squares from 1 to 20 (1, 4, 9, 16, 25... 400) as a foundation for quick root-finding.
• For a non-perfect square, find the two consecutive perfect squares it falls between to estimate its root.
• Connect squares to area (a square with side length n has area n^2) to keep the concept concrete.

Work this through step by step on the board, then have the class talk you through a second one.

• Find sqrt(64)
• 8 x 8 = 64, so sqrt(64) = 8

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 practice worksheet independently while you circulate and support.

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

• Confusing squaring (multiply a number by itself) with doubling (multiply by 2).
• Assuming every square root is a whole number, when only perfect squares have whole-number roots.
• Estimating a root by rounding the number itself rather than comparing it to nearby perfect squares.
• Forgetting that a square root has both a positive and (mathematically) a negative root, even though this unit focuses on the positive root.

Pull the class back together. Ask one child to explain number 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.