MathematicsGeometryAges 9–11

Classifying shapes by line properties

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category

Lesson

Set out your lesson

Classify by side relationships and right-angle properties, allowing overlapping categories and rotated figures.

Before teaching

Use this short check, then start teaching.

Activity

Ask the learner to draw a pair of parallel lines and a pair of perpendicular lines. Have them indicate a right angle. If they use “looks straight” instead of side relationships, rehearse those ideas before sorting.

If Not Ready

Pause the fresh check. Revisit the named prerequisite or repeat the Show with smaller steps; record supported practice rather than an independent result. Authored predecessor existence never proves this learner is ready.

Printer, credit, and teaching notes

Allow 25 minutes. Cards are supplied as diagrams and coordinate descriptions; no scissors or printer are needed. Say labels aloud or write groups on spare paper. Grids are exact geometric givens, not a request for ruler measurement.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

Adult extras

Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

Coordinate-text access changes the task from purely visual recognition to grid/coordinate reasoning; record the mode used.
Finite task opportunities, not learner mastery or universal canonical coverage.
Use the supplied materials on screen or print one current sheet; physical printing can vary.
Record the actual response and assistance; completing a task does not establish mastery.

Use paper or the supplied screen materials in a comfortable place. No special equipment or purchase is needed. Stop or take a break when wanted.

Record the learner’s actual words or work, task ID and any help. Do not prefill success. Allow oral, pointing or written responses as appropriate; oral independent reasoning is not automatically supported. Copied/scribed text is not independent composition or handwriting. No name, account, upload or real family record is required.

Share teaching feedback

Entire curriculum

1858 concepts · 9 subjects

Continue learning

Share and support

Compare teaching approaches

Teaching approaches

Gakuva’s recommended starting approach is selected. You can still compare every option.

1 approach

Selected Default Gakuva

Classify by side relationships and right-angle properties, allowing overlapping categories and rotated figures.

Family records and proof options

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

View learner plans ($12/mo per learner) See sample family archive

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

Illustrative Mathematics · Practice link — not the full lesson

Defining Attributes of Rectangles and Parallelograms

Open practice(new tab)

Before you open · source notes

Rectangle and parallelogram attributes support classifying shapes by line properties. Not every circle theorem.

Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.

Before you open

Ask how a rectangle and a parallelogram are alike and different using sides or angles.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.

Illustrative Mathematics. “Defining Attributes of Rectangles and Parallelograms.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.

CC BY-NC-SA 4.0 — link only

Check understanding

Sort a set of quadrilaterals into those with parallel sides and those without
Identify which triangles in a set are right triangles
Classify shapes that have both perpendicular and parallel sides

“If you show your child a mixed set of triangles and quadrilaterals, can they sort them into groups — like "shapes with at least one right angle" or "shapes with parallel sides" — and explain their reasoning?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Geometry
Age range: Ages 9–11

Standards

ccss-math:4.G.2the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-E1.1