Most maths lessons come down to practice and feedback, and that is where technology does its most reliable work. More of these lessons sit in Interactive Amplify than anywhere else, by some distance.
The pattern is the same from Year 1 to Year 13: students answer, the teacher sees every answer at once, and the lesson changes because of it. A Year 8 linear equations Kahoot has wrong answers built from common errors. A Year 5 Desmos card sort feeds a live teacher dashboard. Year 13 vote on what 60 heads in 100 tosses shows.
Technology can also check the mathematics itself. Year 10 solve quadratics by factorising, then test the answers against a Desmos graph. Year 9 test dice and coin predictions against 1,000 simulated trials.
Making is less common in maths, and worth a look when it appears: times-table circle patterns coded in p5.js, or a Google Sheets dashboard of the Mauna Loa carbon dioxide record. For one topic taught in every cell, see equivalent fractions, taught nine ways.
Creative Amplify
Each child makes a page for a class Book Creator book, drawing one fraction family and recording a spoken explanation, which families and Grade 2 then hear.
Pairs write three rectangle riddles that each have exactly one answer, post them on a private Padlet wall, and read the answers that pairs in the other Grade 4 class add underneath.
Students write a one-page revision guide for Grade 9 on finding the nth term of a quadratic sequence, with their own worked example and practice questions, and Gemini on hand to explain a step.
Creative Replace
Each child designs a sixteen-square quilt patch in Paint that is half, a quarter and two eighths in different colours, labels each colour with two equivalent fractions, and adds it to a class quilt.
Each child designs a zoo plan in Seesaw with five rectangular enclosures of 12, 16, 24, 30 and 36 m², chooses the length and width of each, and works out how much fencing the whole zoo needs.
Creative Transform
Each child programs a Scratch project that asks for two fractions, draws them as equal-length bars one under the other, and lets a partner test whether any pair is equivalent.
Pairs build a Desmos rectangle whose sliders set its sides and whose rules report area and perimeter, write three challenges for Grade 3, watch them try it, and rebuild whatever tripped them up.
Starting from a p5.js starter sketch, students code the times-table circle, where point n joins point k × n mod N, and investigate which multipliers make which curves.
Students build a Desmos graph with sliders that lets a classmate discover the rules for y = f(x) + a and y = f(x + a) without being told them.
Students turn NOAA's full monthly carbon dioxide record from Mauna Loa into a Google Sheets dashboard, with a filter by decade, a trendline and a seasonal-cycle chart.
Interactive Amplify
Teams of three answer ten picture questions on one more and one less in a teacher-run Kahoot, and the teacher stops the game to re-teach counting back when the class splits on 'one less than 20'.
Pairs play the first level of PhET's Fraction Matcher, saying why two cards match before they press Check, and use the smiley face or the number line to decide their next move.
Children drag six two-digit numbers onto a 0 to 100 line in a Seesaw activity and record why 47 goes where it does, while the teacher watches responses arrive and pulls a group for a Dienes re-teach.
Grade 3 play a live Kahoot whose wrong answers come from common fraction errors, and the teacher stops the game to reteach with a fraction wall when the answer spread shows the add-one mistake.
Pupils sort fraction cards, shown as digits and as fraction bars, into three equivalence groups in a Desmos card sort while the teacher watches every sort on the dashboard.
Pupils answer three self-paced rounds of ten mixed times-tables questions on Wayground, and the teacher reteaches the facts the class report shows are weakest before each new round.
Pupils choose the equation that matches each of ten word problems from four look-alike options, and the teacher uses the live response summary to discuss the most popular wrong choice.
Every student drags ten mixed values onto their own Desmos number line, and the teacher uses the live view of all thirty lines to pair up disagreements and choose what the class discusses.
Students plot a shape's vertices in all four quadrants in a Desmos activity, and the teacher uses the dashboard overlay to spot and fix quadrant errors as they happen.
Students answer a live Kahoot of linear equations whose wrong options come from common mistakes, and the teacher stops on any question where the answer chart splits.
Three days before an algebra assessment, students work through a Seneca assignment that keeps returning them to the skills they get wrong, and the class results decide Friday's warm-up.
Students predict three probability outcomes on Mentimeter, run 1,000 trials of each in a Google Sheets simulator, and pool the class's results to see which predictions held up.
Students solve quadratics by factorising, check each pair of roots against the graph in Desmos, and fix their own errors before moving on.
Students test the angle in a semicircle theorem by dragging a GeoGebra construction, write a proof, and post it to a Padlet column for their method so the class can compare approaches.
Students each draw a random sample from 200 anonymised CensusAtSchool records in Google Sheets, and a class chart of everyone's sample means shows sampling variation.
Students decide whether pairs of 3D lines intersect, are parallel or are skew, check in GeoGebra 3D, and the teacher uses the live Classroom view to pick errors to discuss.
Students vote for the best conclusion to a binomial hypothesis test, defend their choice in pairs on a Padlet, and re-vote after the teacher tackles the misconceptions.
Students differentiate the same function by the route of their choice, check it in GeoGebra, and post their working so the teacher can compare routes.
An adult names a start number and a target such as 'one more than 4', children predict and program the Bee-Bot along a 0 to 10 number track, and its landing shows at once whether they counted right.
Interactive Replace
Grade 3 drag fraction labels onto shaded shapes across six Seesaw pages and circle the two shapes on each page that show the same amount, including a 2/3 and 3/4 trap.
Grade 4 work out ten perimeter and area questions in their books and type each answer into a Microsoft Form, which the teacher reads after school and goes through with the class the next morning.
Students drag twelve graph cards onto twelve equation cards in a Desmos Classroom card sort, with three deliberate near-misses such as y = 2x + 1 against y = 2x - 1.
Grade 7 answer 30 mixed times-tables questions on a Microsoft Form at the start of the lesson, with results hidden, and the teacher reads the totals afterwards as they once marked the printed grid.
Pairs drag sixteen sequence cards into arithmetic, geometric and other columns on a Microsoft Whiteboard board, then find the nth term of every arithmetic one.
Interactive Transform
Pairs work through a week of micro:bit light readings from three places the class chose, find what fraction of each day each place was lit, and group the hours to build fraction families.
Pairs trace the boating lake in the local park with Google Earth's measure tool, first with 6 clicks, then 15, then 40, and track how the perimeter keeps growing while the area settles.
Passive Amplify
The teacher drags a GeoGebra slider that re-cuts a shaded bar into more and more equal parts while the shaded amount stays fixed, and Grade 3 watch 3/4 become 6/8, 9/12 and 12/16.
Grade 4 watch the teacher drag a GeoGebra rectangle whose perimeter stays at 20 cm, predicting on mini whiteboards what happens to its area as it changes from 1 cm by 9 cm to a 5 cm square.
Passive Replace
Grade 3 watch a short animation of a chocolate bar split into halves, quarters and eighths, drawing each stage in their books, and write their first fraction family.
Area and perimeter: follow the teacher's worked example of an L-shaped garden with two missing sides
Grade 4 follow the teacher's worked example of an L-shaped garden, 12 m by 9 m with a corner cut out, drawn in Microsoft Whiteboard on the board, copy it into their books, then answer six textbook questions.
The teacher narrates five worked examples of multiplying fractions on a PowerPoint that students follow on their iPads, trying a matching question in their books after each one.
Before their first circumference lesson, students read a teacher-built Sutori story on how mathematicians closed in on pi, then answer five questions in their books.
The teacher plays a 12-minute worked-solutions video on Pythagoras' theorem on the board, pausing between problems while Grade 8 copy the working, before they practise in their books.
Children watch the official Numberblocks episode about Five on the class screen, then make five on their fingers and with cubes on the carpet.
Passive Transform
The teacher runs a whole lunar month over the school's town in Stellarium in two minutes, stopping at every eighth of the cycle, and Grade 3 name the fractions and find that the 'first quarter' Moon is 2/8 of the way round.
Grade 4 watch slow-motion footage of a litre of water spreading over their chalked metre square, paused by the teacher at each half second so they can count squares and estimate the area as it grows.
Lessons that look like one cell but sit in another
Useful counter-examples when you are checking your own lesson placement on the PICRAT grid.
This page is one of a growing set of PICRAT examples by cell, subject and grade. Page maintained by Andy Perryer.