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.

Rational numbers, fractions, decimals and negative numbers among them, can all be located on the same number line. This unit covers converting between fractions and decimals, ordering rational numbers, and finding a point exactly between two others. Model the method clearly, thinking aloud:

• Convert fractions to decimals by dividing, and decimals to fractions by writing the decimal over its place-value denominator and simplifying.
• Plot a mix of fractions, decimals and negative numbers on the same number line to build a sense of their relative size.
• Order a set of rational numbers by converting them all to a common form (usually decimals) first.
• Find the midpoint between two rational numbers by averaging them, connecting this to the same skill used for coordinate midpoints later.
• Use negative rational numbers alongside positive ones so the number line is not treated as starting at zero.

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

• Find the rational number exactly halfway between -4 and 10
• (-4 + 10) / 2 = 6 / 2 = 3

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:

• Converting a fraction to a decimal by subtracting instead of dividing.
• Ordering rational numbers by comparing only the digits, ignoring the sign or the decimal point's position.
• Forgetting to simplify a fraction after converting it from a decimal.
• Assuming the midpoint of two negative numbers must also be negative, without actually calculating it.

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.