Teaching Path

The number sequence, one-to-one correspondence, and cardinality.

Exit ticket: Count a set of 9 and answer "how many" without recounting.

Composing and decomposing numbers to 10.

Exit ticket: Give three different splits of 8.

Naming and describing 2D and 3D shapes.

Exit ticket: Name shapes in unusual orientations.

Sorting by attribute and counting categories.

Exit ticket: Sort one set by two different rules.

Ten-and-some-more, counting to 20 and past.

Exit ticket: Show 14 as ten and four.

Making sense of a question and explaining thinking.

Exit ticket: Restate a problem in own words.

Joining, separating, comparing, and missing parts.

Exit ticket: Match four story types to equations.

Place value to 120 and comparing two-digit numbers.

Exit ticket: Say what each digit in 74 is worth.

Equality as a relationship and missing numbers in any position.

Exit ticket: Solve 8 + ▢ = 15 and 12 = ▢ + 5.

Repeated units, rulers, clocks, and money.

Exit ticket: Measure to the nearest centimetre from zero.

Shape attributes, composing shapes, and equal shares.

Exit ticket: Split a rectangle into fourths two ways.

Counting by twos, fives, and tens; even and odd.

Exit ticket: Count by 5s and say what the numbers share.

Picture graphs, bar charts, and explaining thinking.

Exit ticket: Answer a "how many more" question from a chart.

Bridging ten, compensating, and splitting by place.

Exit ticket: Compute 68 + 25 mentally two ways.

The written algorithms as trades.

Exit ticket: Compute 503 − 247 and explain the trade.

The meaning of multiplication and division.

Exit ticket: Draw 4 x 6 three different ways.

Counting mixed coins, making change, telling time.

Exit ticket: Make change from $1 by counting up.

Commutative and associative reasoning.

Exit ticket: Rearrange a sum to make it easier.

Dot plots, bar charts, and mathematical practices.

Exit ticket: Build a dot plot and describe it.

Equal groups, arrays, and the two division questions.

Exit ticket: Model 24 ÷ 4 as sharing and as grouping.

Fractions as numbers, on a number line.

Exit ticket: Place 5/4 on a number line and explain it.

Equivalent fractions and comparing with benchmarks.

Exit ticket: Show 6/8 = 3/4 with a picture.

Unit squares, rectangle area, and distance around.

Exit ticket: Find area and perimeter of an L-shape.

Rounding to tens and hundreds; checking answers.

Exit ticket: Round 4,738 and check a product.

Undoing, checking, and number patterns.

Exit ticket: Solve ▢ x 7 = 91 by inverse reasoning.

Bar charts, shape hierarchy, and likelihood.

Exit ticket: Place five events on a likelihood line.

Multi-digit place value, comparison, and rounding.

Exit ticket: Say how many hundreds are in 30,507.

Partial products, the area model, and the algorithm.

Exit ticket: Match an area model to the algorithm for 34 x 27.

Long division and interpreting the remainder.

Exit ticket: Answer a van-loading problem correctly.

Factor pairs, divisibility, primes.

Exit ticket: List all factor pairs of 72 in order.

Mixed numbers, adding and subtracting, times a whole.

Exit ticket: Compute 3 1/4 − 1 5/6 with an estimate first.

Decimal place value and comparison.

Exit ticket: Order 0.7, 0.68, 0.702 by place value.

Measuring angles, classifying triangles, symmetry.

Exit ticket: Measure four angles and classify each.

Number patterns, rules, and multiplicative comparison.

Exit ticket: Find the 20th term of a pattern.

All four operations with decimals, with magnitude checking.

Exit ticket: Compute 7.2 ÷ 0.09 after estimating.

Area model, scaling, and prediction of size.

Exit ticket: Explain why 3/4 x 2/5 is less than both.

Measurement division and the reciprocal rule.

Exit ticket: Model 3 ÷ 1/4 and justify the rule.

Factor trees, GCF and LCM.

Exit ticket: Factorise 360 and use it to list factors.

Grouping, exponents, and precedence.

Exit ticket: Evaluate 12 + 3(8 − 2)² ÷ 9.

Volume of prisms and unit conversion.

Exit ticket: Find the volume of a triangular prism.

Plotting points and reading coordinates.

Exit ticket: Plot and name points in four quadrants.

Choosing units and judging reasonableness.

Exit ticket: Use units to check a multi-step answer.

Ratio language, equivalent ratios, and unit rate.

Exit ticket: Compare two buys by unit price.

Percent as rate per hundred and conversions.

Exit ticket: Find 15% of 240 two ways.

Integers, opposites, absolute value, and ordering.

Exit ticket: Order five integers and justify with the line.

Variables, writing and evaluating, properties, like terms.

Exit ticket: Simplify 4x + 3y − 2x + 7 − 5y.

Balance reasoning and solution sets.

Exit ticket: Solve (2/3)x = 10 and graph x >= −2.

Polygons, composite figures, nets.

Exit ticket: Find the surface area of an open box.

Statistical questions, displays, centre, and spread.

Exit ticket: Explain why the median beats the mean here.

Rates in context, algorithms, and data decisions.

Exit ticket: Write a procedure someone else can follow.

Adding, subtracting, multiplying, dividing signed numbers.

Exit ticket: Compute (−3/4) ÷ (−2/5) and justify the sign.

Constant of proportionality across representations.

Exit ticket: Find k from a table and interpret it.

Percent change, markup, discount, tax, tip, interest.

Exit ticket: Find the original price after 15% off.

Solving and reversing the inequality symbol.

Exit ticket: Solve −3x + 5 > 20 and justify the flip.

Angle pairs, circle measure, cross-sections, scale.

Exit ticket: Find the area of a quarter circle.

Sample spaces, theoretical vs experimental, compound events.

Exit ticket: Find P(sum is 7) from the full sample space.

Populations, samples, randomness, bias.

Exit ticket: Critique a survey design for bias.

Motion, mixture, assumptions, and estimation.

Exit ticket: Solve a two-train meeting problem.

Exponent laws, zero and negative powers, magnitude.

Exit ticket: Explain why 2^0 = 1 from the pattern.

Relations, functions, and the four representations.

Exit ticket: Classify four relations and justify each.

Slope, intercepts, equation forms, graphing.

Exit ticket: Interpret the slope of a cost graph.

Multi-step, both sides, and solution counts.

Exit ticket: Solve 4x + 7 = 4x − 2 and describe the set.

Graphing and substitution, and interpreting solutions.

Exit ticket: Classify three systems by solution count.

Rigid motions, dilations, similarity.

Exit ticket: Rotate then reflect a triangle on coordinates.

The theorem, its converse, and distance.

Exit ticket: Find distance between two points via a triangle.

Scatter plots, association, fit, and two-way tables.

Exit ticket: Fit a line and predict inside the data range.

Algebraic language, properties, multi-step and literal equations.

Exit ticket: Solve A = P(1 + rt) for r.

Solving, compound, and absolute value.

Exit ticket: Solve |2x − 5| < 9 and graph it.

Notation, domain and range, key features, rate of change.

Exit ticket: Find f(a + 1) and solve f(x) = 3.

Forms, graphing, parallel and perpendicular, systems, direct variation.

Exit ticket: Solve a system by elimination and verify.

Sequences, growth and decay, linear vs exponential.

Exit ticket: Classify three tables by differences and ratios.

Polynomial arithmetic, special products, factoring.

Exit ticket: Factor 6x² + 11x − 10 and check.

Zeros, the four solving methods, parabola features.

Exit ticket: Solve 2x² − 5x − 4 = 0 exactly.

Linear fit, residuals, and applied modelling.

Exit ticket: Fit a line and interpret its residual plot.

Definitions, notation, and compass-and-straightedge work.

Exit ticket: Construct a perpendicular bisector and justify it.

Angle pairs, parallels, and the first proofs.

Exit ticket: Prove the vertical angle theorem.

Rigid motions, congruence criteria, and CPCTC.

Exit ticket: Name the criterion proving two triangles congruent.

Dilations, similar triangles, and proportionality theorems.

Exit ticket: Find a tree height by similar triangles.

Pythagoras, special triangles, trig ratios, laws.

Exit ticket: Find an angle of elevation with inverse trig.

Parts, arcs, sectors, theorems, and the equation.

Exit ticket: Find the centre and radius by completing the square.

Distance, midpoint, slope arguments, analytic proof.

Exit ticket: Prove four points form a rectangle.

Surface area, volume, cross-sections, design problems.

Exit ticket: Compare two container designs on cost.

Transformations, inverses, composition, piecewise.

Exit ticket: Verify an inverse by composing to get x.

Completing the square, discriminant, complex arithmetic.

Exit ticket: Classify roots by discriminant and find complex ones.

Division, remainder and factor theorems, roots, graphs.

Exit ticket: Factor a cubic fully using the factor theorem.

Expressions, equations, asymptotes, extraneous roots, inverse variation.

Exit ticket: Solve √(x + 6) = x and reject the extraneous root.

Growth, e, logs, laws, graphs, and solving.

Exit ticket: Solve log(x) + log(x − 3) = 1 with a domain check.

Arithmetic and geometric sequences and sums.

Exit ticket: Sum the first 30 terms of an arithmetic sequence.

Unit circle, radians, graphs, identities.

Exit ticket: Graph y = 3sin(2x − π) + 1 with all features.

Counting, conditional probability, expected value, the normal model, and inference.

Exit ticket: Compute an expected value and advise on whether to play.

Optimisation under constraints, sensitivity, finance, units, and algorithmic description.

Exit ticket: Optimise an objective over a feasible region and state the assumptions it rests on.