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.

Expanded notation writes a number as the sum of each digit multiplied by its place value, expressed as a power of 10 (e.g. 4 x 10^3). It makes the value of each digit explicit and connects place value to exponent notation. Model the method clearly, thinking aloud:

• Review place value first: in 4,502, the 4 is worth 4,000, the 5 is worth 500, and so on.
• Introduce powers of 10 as a shorthand for place value: 1,000 = 10^3, 100 = 10^2, 10 = 10^1, 1 = 10^0.
• Write a number in expanded form by pairing each nonzero digit with its power of 10, then adding the terms.
• Practise the reverse: given an expanded form, add the terms to find the original number.
• Extend to larger numbers (millions, billions) to reinforce that the pattern of powers keeps working at any scale.

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

• Write 30,406 in expanded form
• 3 x 10^4 + 0 x 10^3 + 4 x 10^2 + 0 x 10^1 + 6 x 10^0
• Skip the zero terms: 3 x 10^4 + 4 x 10^2 + 6

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:

• Using the wrong power of 10 for a digit's position, especially miscounting for larger numbers.
• Including a term for a zero digit instead of leaving it out.
• Forgetting that the ones digit pairs with 10^0 (which equals 1), not 10^1.
• Adding the digits themselves instead of each digit's full place value when reversing the process.

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.