Grade 10: 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 ratio compares two or more quantities of the same kind, such as 3 red to 2 blue counters. Simplifying a ratio, sharing an amount in a given ratio, and using rates and map scales are the core skills built on this idea across secondary school. Model the method clearly, thinking aloud:

• Teach simplifying a ratio the same way as simplifying a fraction: divide both parts by their highest common factor.
• Model sharing an amount in a ratio step by step: total the parts, find the value of one part, then multiply out.
• Introduce rate as a ratio between two DIFFERENT kinds of quantity (distance and time, cost and quantity), always carrying units.
• Use map scales (e.g. 1 cm represents 5 km) as a real-world ratio application, converting map distance to real distance.
• Keep early examples to nice, whole-number-friendly ratios before introducing awkward numbers.

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

• Share $60 in the ratio 2 : 3
• Total parts = 2 + 3 = 5
• Value of 1 part = $60 / 5 = $12
• 2 parts = $24, 3 parts = $36

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:

• Dividing by a common factor that is not the HIGHEST common factor, leaving the ratio not fully simplified.
• Sharing the amount by the number of PARTS in only one share, instead of the total number of parts.
• Confusing a ratio (same kind of quantity) with a rate (different kinds, with units).
• Multiplying instead of dividing the map distance by the scale factor when converting to real distance.

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.