Students cut a parallelogram along its height and move the triangle to make a rectangle, see that sliding the top keeps the area, and use A = bh with the perpendicular height (AC9M7M01, node 1).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 8 min · Investigate 12 min · Modify 10 min · Practise and Make 10 min
Do the Run board yourself first. Students need area of rectangles by counting rows of squares (Year 6) and the meaning of cm².
The one idea: a parallelogram rearranges into a rectangle with the same base and height, so A = bh. The common mistake is using the slanted side (Ruby's mistake); the board's dashed height with its right-angle mark is the fix.
Choosing the perpendicular height when a slanted side is also labelled. Ask students to trace the right-angle mark with a finger before they multiply, rather than telling them which number to use.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies by the slanted side (Ruby's mistake). | Which length meets the base at a right angle? | Use the perpendicular height: the dashed line with the ∟. |
| A student adds base and height. | How many rows of squares, and how many in each row? | Area is rows × squares in a row: multiply. |
| A student writes cm for an area. | Are we counting lengths or squares? | Squares: cm². |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: Draw three different parallelograms on squared paper, each with area 24 cm², none of them a rectangle.
Support: Cut paper parallelograms and rearrange them; count squares on the board for small cases.
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 7 student in Australia. Help me understand ONE idea only, from the lesson "Area of parallelograms". The idea: Deriving the triangle area formula: I can Students understand why the area of a triangle is half the area of a related rectangle or parallelogram, and can state the formula A = ½bh. What understanding looks like: - States the area formula for a triangle and explains its derivation. - Correctly identifies the base and corresponding perpendicular height. - Does not confuse the slant side with the perpendicular height. Mistakes students often make here: - A student multiplies by the slanted side (Ruby's mistake). - A student adds base and height. - A student writes cm for an area. How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Area of parallelograms".
A parallelogram has base 9 cm, slanted side 5 cm and perpendicular height 4 cm. Find its area.
9 × 4 = 36 cm² (the 5 cm slanted side is not used).
Next: Area of triangles (node 1), half of a parallelogram.
Where it leads: area of trapeziums and composite shapes (Year 8), and volume of prisms (the base times the height again).