Area and perimeter, taught nine ways.

Year 5 apply area and perimeter to a design brief. In a Seesaw activity, each child opens a 20 by 15 squared grid in which every square stands for 1 m², and designs a small zoo with five rectangular enclosures: 12 m² for meerkats, 16 m² for tortoises, 24 m² for otters, 30 m² for goats and 36 m² for wallabies. They choose the length and width of each in whole metres, draw it along the grid lines with the pen tool, and add text labels for its area and its perimeter, which is the fencing it needs. Then they total the fencing for the whole zoo. A child who draws 3 by 4, 4 by 4, 4 by 6, 5 by 6 and 6 by 6 needs 96 m of fence, and one who draws 1 by 12, 2 by 8, 2 by 12, 3 by 10 and 3 by 12 needs 130 m for the same five areas. Children submit the plan to their journal with nothing recorded and nothing shared, and the teacher checks every area and perimeter after the lesson, as with the plans last year's class drew in their maths books.

Tools: Seesaw Nine ideas for your own version in Generate

Year 5 pairs write 'Which rectangle am I?' riddles whose clues must leave exactly one answer. The teacher models the problem first: 'My sides are whole centimetres and my area is 36 cm²' fits five rectangles, from 1 by 36 to 6 by 6, and adding 'my perimeter is 30 cm' leaves only 3 cm by 12 cm. Each pair writes three riddles of their own, such as 'My perimeter is 26 cm and my area is 40 cm²' for 5 cm by 8 cm, and tests each in their books by listing every rectangle that fits the clues. They type the riddles as posts on a class Padlet wall, set to school login with author names hidden, with posts approved by the teacher and signed with a table number. The other Year 5 class does the same on a wall of its own, and for the last twenty minutes the classes swap walls, solve each other's riddles and add their answers as comments. Authors then read every comment under their riddles, reply to say which are right and, where a solver has found a second rectangle that fits, write in their books the clue that would have ruled it out.

Tools: Padlet Nine ideas for your own version in Generate

In a double lesson, Year 5 pairs build a rectangle explorer in the Desmos graphing calculator for Year 4, who are starting perimeter. The teacher's starter graph, opened from a link without signing in, holds one rectangle whose corners depend on two sliders, w and h. Each pair sets the sliders to whole numbers from 1 to 12, types a rule for the area, A = w × h, and one for the perimeter, and checks them against rectangles worked out in their books: 7 by 3 should show 21 and 20. A common first rule, P = w + h, shows 10, and pairs fix it. They add a fixed-fence version in which h is a rule, h = 12 − w, so the perimeter stays at 24, and type three challenges in a note, such as finding the fenced rectangle with the largest area. Year 4 visit with their teacher for twenty minutes and try the explorers while the authors watch without helping and note every wrong turn. Pairs then rebuild: a slider that reached 12 and flattened the fenced rectangle now stops at 11, and unclear challenges are reworded.

Tools: Desmos Nine ideas for your own version in Generate

Year 5 are consolidating a week on area and perimeter. Each child opens a Microsoft Form on a school tablet with ten questions, each showing a diagram: the perimeter and area of a 14 cm by 6 cm rectangle (40 cm and 84 cm²), the perimeter of an L-shape with two missing sides, the area of a classroom floor 9 m by 7 m (63 m²) and, near the end, the area of a square whose perimeter is 36 m (81 m²). Children do their working in their maths books and type each answer into the Form as a number. The teacher has built the Form without an answer key, so it tells children nothing about how they did when they press submit. The teacher circulates and helps at the tables as in any practice lesson, opens the responses as a spreadsheet after school and checks them against the answers, and goes through the three most missed questions on the board the next morning.

Tools: Microsoft Forms Nine ideas for your own version in Generate

Year 5 take metre sticks and tape measures to ten rectangles around the classroom and corridor, such as a table top, the door, the whiteboard, a display board, a floor tile and a PE bench top. Each pair measures four of them to the nearest centimetre, works out the perimeter and area in their books, and types the numbers into the pair's rows of a shared Google Sheet on school accounts. On the board the teacher filters the sheet to one object at a time: where three pairs give the door as 198 cm by 76 cm and one gives 189 cm, that pair goes back to measure again. Then the teacher sorts the whole table by area and again by perimeter, and the order changes. Pairs search the pooled rows for surprises and find that the whiteboard, 180 cm by 120 cm, and the display board, 240 cm by 90 cm, share an area of 21,600 cm² with perimeters of 600 cm and 660 cm, while the bench top, 300 cm by 25 cm, has a longer perimeter than the whiteboard and about a third of its area.

Tools: Google Sheets Nine ideas for your own version in Generate

Year 5 know that two rectangles can share an area and have different perimeters, and this lesson tests that idea on a real shape. On one laptop per pair, children open Google Earth in the browser, which the school's administrator has switched on for pupil devices beforehand, and find the boating lake in the town park. Using the measure tool, they click round the shore until the outline closes, and the tool reports its perimeter in metres and its area in square metres. Their first outline uses 6 clicks from high up, the second 15, and for the third they zoom in on each inlet and use about 40. One pair's table reads 380 m and 7,400 m², then 440 m and 8,100 m², then 520 m and 8,300 m². Pairs compare tables, and the teacher asks why the perimeter grew by 140 m while the area hardly moved after the second outline. Children then predict what will happen on the football pitch beside the lake, test it with 4 clicks and then 12, and write an explanation of why a wiggly edge adds perimeter without adding much area.

Tools: Google Earth Nine ideas for your own version in Generate

Year 5 can find the perimeter and area of a rectangle and now meet a rectilinear shape with sides that are not labelled. On the interactive board, the teacher draws an L-shaped garden with the pen in Microsoft Whiteboard: 12 m along the bottom and 9 m up the left side, with a corner 5 m wide and 3 m deep cut out of the top right. With all six sides labelled, the class adds them: 12 + 9 + 7 + 3 + 5 + 6 = 42 m. The teacher then rubs out the 7 m and 6 m labels and shows how to find them from the sides opposite: 12 − 5 = 7 and 9 − 3 = 6. Next the teacher finds the area by splitting the garden into a 7 m by 9 m rectangle and a 5 m by 6 m rectangle, 63 + 30 = 93 m², and checks it by taking the 15 m² corner away from the whole 12 m by 9 m rectangle. Children copy each worked example into their books as the teacher talks it through, then answer six questions on L-shapes from the textbook, which the teacher marks after the lesson.

Tools: Microsoft Whiteboard Nine ideas for your own version in Generate

Many of Year 5 think that shapes with the same perimeter must have the same area. On the board, the teacher opens a GeoGebra file made before the lesson: a rectangle on a centimetre grid whose perimeter is fixed at 20 cm, with a slider for its width and its area shown beside it. The rectangle starts at 1 cm by 9 cm, and children write on mini whiteboards whether the area will change as it gets wider. The teacher drags the slider slowly, stopping at 2 by 8, 3 by 7, 4 by 6 and 5 by 5, and the area climbs from 9 cm² through 16, 21 and 24 to 25 cm² while the perimeter stays at 20 cm. The teacher also stops between whole numbers, at 4.5 cm by 5.5 cm, where the area reads 24.75 cm², then sets the perimeter to 36 cm and asks which rectangle will have the largest area before dragging to the 9 cm square. Children record both tables in their books and write a sentence on which rectangle encloses the most space.

Tools: GeoGebra Nine ideas for your own version in Generate

At the start of the lesson, with the playground empty, Year 5 chalk a 1 m square in one corner and rule it into one hundred 10 cm squares. The class stands behind a school tablet on a tripod, framed on the grid alone with a running stopwatch laid beside it, and the teacher tips a litre of water onto the middle while the tablet films in slow motion. The water reaches its full spread in about three seconds, far too quickly to count anything. Back inside, the teacher plays the clip on the board and pauses each time the stopwatch in the picture shows another half second. At each pause children count the squares that are half or more wet, the method they use for irregular shapes in the textbook, and record an estimate: 5 squares at half a second, then 14, 26, 35, 40 and 42 at three seconds, which is 4,200 cm² because each square is 10 cm by 10 cm. They plot the six estimates as a line graph in their books and describe how the area grows quickly and then levels off.

Tools: Built-in camera (slow motion and time-lapse) Nine ideas for your own version in Generate