Grade 8: 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.

This unit extends the four operations to negative numbers, and to signed fractions and decimals: adding, subtracting and multiplying integers, fractions and decimals that may be negative, using consistent sign rules. Model the method clearly, thinking aloud:

• Review the integer addition/subtraction rules with a number line: adding a negative moves left, subtracting a negative moves right.
• Teach the multiplication sign rule explicitly: same signs give a positive result, different signs give a negative result.
• Extend the same sign rules to fractions and decimals once integer operations are secure, using a common denominator for fraction addition.
• Mix integer, fraction and decimal problems together so students practise identifying which sign rule applies each time.
• Have students predict the SIGN of an answer before calculating its value, as a quick self-check.

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

• Calculate: -7 + (4)
• -7 + 4 = -3
• Calculate: (-1.5) x (2)
• -1.5 x 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:

• Forgetting that subtracting a negative number is the same as adding its positive.
• Applying the multiplication sign rule incorrectly, e.g. assuming two negatives always give a negative.
• Losing track of a negative sign partway through a multi-step calculation.
• Adding signed fractions without a common denominator, or forgetting to carry the sign through the simplification.

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.