Students scale a triangle by a scale factor, find missing sides of similar shapes, and compare rectangles that are similar, congruent or neither (AC9M8SP01, nodes 2 and 3).
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 10 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need congruent triangles (last lesson) and multiplying by decimals.
The one idea: similar means every length times the same scale factor, with the angles unchanged. The common mistake is adding a fixed amount to every side (Mia's mistake).
Similarity conditions for triangles: AA, SSS (all sides in one ratio) and SAS (two sides in one ratio, the included angle equal). Only AA is practised much here; SSS appears in Practise. The link to transformations: translations, reflections and rotations give congruent shapes; an enlargement gives a similar shape.
Wider: measure something tall outside with shadows and a metre ruler.
Matching the sides. Ask students to say which side matches which (shortest with shortest) before they divide.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student adds the same amount to every side. | Would the picture look the same shape? | Find k by dividing, then multiply every side by k. |
| A student divides the wrong way (original ÷ copy). | Is the copy bigger or smaller? Should k be more or less than 1? | k = copy ÷ original. |
| A student says all rectangles are similar because the angles match. | Is a 4 by 2 rectangle the same shape as a 4 by 3? | For shapes other than triangles, check the sides' ratios too. |
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.
Stretch: A similar triangle has scale factor 3. How many times bigger is its area? Test it with the 3, 4, 5 triangle.
Support: A table with original sides in one column and copy sides in the next, with a ÷ column for k.
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 8 student in Australia. Help me understand the ideas in ONE lesson only, from the lesson "Similar shapes". The ideas: - Similarity conditions for triangles: I can Students identify and apply the conditions for triangle similarity (AA, SAS, SSS) and understand similarity as a scaled version of congruence. - Congruence and similarity in other shapes and transformations: I can Students explain the conditions for congruence and similarity in other common shapes and connect congruence to transformations. What understanding looks like: - Identifies similar triangles and states the condition used. - Correctly calculates a missing side using the scale factor. - Maintains consistent matching of corresponding sides. - States conditions for congruence and similarity for a given shape type. - Connects congruence to rigid transformations and similarity to enlargement. - Correctly identifies whether two given shapes are congruent, similar, or neither. Mistakes students often make here: - A student adds the same amount to every side. - A student divides the wrong way (original ÷ copy). - A student says all rectangles are similar because the angles match. 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. - If I seem to be missing the idea that comes before this one (Congruence conditions for triangles), check it quickly, then come back. - 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 "Similar shapes".
A 2 m by 3 m garden bed is enlarged so the 2 m side becomes 5 m. How long is the 3 m side now?
k = 5 ÷ 2 = 2.5, so 3 × 2.5 = 7.5 m.
This covers AC9M8SP01 nodes 2 and 3.
Where it leads: proving quadrilateral properties with congruent triangles (next lesson), congruence algorithms, and trigonometry in Year 10 (which rests on similar right-angled triangles).