Twenty optional transfer problemsYear 11 Methods · T1 W1–2 · Practice Swaps

Each prompt uses invented numbers/context. Use one after a lesson or for a home extension; students can always do it on paper. They should show an exact expression and a short check or reason. Worked staff answers are separate and public. No personal data, real workplace measurements or purchase is needed.

Day 1 · Classification

• Book-display squares: areas 25 and 7 square units. Evaluate sqrt(25) and classify sqrt(7); bound the latter between whole numbers.
• Poster panels: areas 49 and 15 square units. Which side is an exact whole number? Between which integers is the other?

Day 2 · Factor transfer

• Mosaic draft: simplify sqrt(108) units using its largest square factor; square your result.
• Fictional screen tile: simplify sqrt(200) units and check the result by squaring.

Day 3 · Comparison

• Paper-track marks: compare sqrt(18) and sqrt(72) cm; give the exact difference.
• Gallery-cord samples: compare sqrt(27) and sqrt(75) cm; give the exact difference.

Day 4 · Addition

• Kite-frame segments: add sqrt(20)+sqrt(45) cm exactly; reject a radicand-addition shortcut.
• Fictional map strips: add sqrt(28)+sqrt(63) units exactly, showing common root parts.

Day 5 · Subtraction

• Prop-ribbon samples: compute sqrt(75)-sqrt(27) cm exactly; check the sign.
• Paper-lantern strips: compute sqrt(125)-sqrt(20) cm exactly; explain the shared root.

Day 6 · Products

• Rectangle sketch: sides sqrt(8) cm and sqrt(18) cm; find exact area with units.
• Symbolic animation scale: simplify (3sqrt(2))(2sqrt(10)); keep the whole-number coefficients visible.

Day 7 · Rationalising

• Pure design ratio: rationalise 5/sqrt(3) without changing its value.
• Another pure ratio: rationalise 6/sqrt(7) and give a quick decimal equivalence check.

Day 8 · Multi-step audit

• Cue index: simplify (sqrt(50)+sqrt(8))/sqrt(2) by two routes.
• Route index: simplify (sqrt(75)-sqrt(12))/sqrt(3) and locate the like terms.

Day 9 · Vertex form

• Abstract plotting card: for y=(x+1)^2+2, find turning point, axis, y-intercept and number of real x-intercepts.
• Digital-art plotting card: for y=2(x-1)^2+3, find the same four features and show one mirrored x pair.

Day 10 · Factor form

• Fictional graph A: y=(x-2)(x-6). Find both zeros, axis, turning point and y-intercept.
• Fictional graph B: y=-(x+2)(x-4). Find the same features and opening direction. Give one sign check between the zeros.