Completing the square; centre, radius, key features
- Cutting a rectangle into a corner — 3 tasks
- Completing the square in one variable — 3 tasks
- Three moves back to the built form — 3 tasks
- Draw it, then read it off — 3 tasks
- One family, one letter — 3 tasks
- Practice — 24 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Which Circle, If Any? Completing the Square for the Center — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 pieces, each the equation of a circle in its own layout, or an equation that is not a circle at all. Students complete both squares, write r², and sort: a circle with center (2, −3), a circle with center (−2, 3), or not a circle. Flipping the signs, adding to one side only, or taking a negative r² as a circle each puts a piece in the wrong row.
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Center and Radius: Completing the Square — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each with the equation of a circle in a different layout. Students complete both squares and pick the center and radius they get. Each wrong answer is a real mistake: r² written as the radius, the new numbers added to one side only, the signs of the center flipped, squaring without halving, or an equation that is not a circle taken as one. The row of box numbers at the foot is the check.
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Is the Next Line Right? Completing the Square for a Circle — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each with the equation of a circle and a student’s next line: both squares completed, the new numbers on both sides. Students decide whether the line is right. Fill it or leave it white, and a picture appears. The wrong lines are the classic mistakes: adding to one side only, squaring without halving, a negative square, and a term moved across without changing its sign.
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Untidy Equations: Completing the Square for the Center and Radius — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each with the equation of a circle in an untidy layout: terms out of order, the number on the left, an x or y term on the right, a common factor. Students complete both squares, read the center and the exact radius, then walk to the card showing their answer. Adding to one side only, flipping the signs of the center, squaring without halving, or writing r² as the radius lands on a card that sends the group back, and a clean run is 8 lines.