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Build and Use a Complete 2D Shape Hierarchy

Students synthesize their understanding of shape properties to construct and use a complete hierarchy of two-dimensional figures, from polygons down to specific types of triangles and quadrilaterals. They use the hierarchy to make and justify claims about shape relationships.

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Build and Use a Complete 2D Shape Hierarchy

Grade 5 · Classifying 2D Figures · question 1 of 3

0 of 20

20 rungs. A star at the top.

LMNP

Choose the most precise name for quadrilateral LMNP.

Choose its name.

How it is taught

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A hierarchy stacks shapes from general to specific.

A subcategory keeps the family's properties and adds one.

A square sits at the specific end of that family.

1234

Read it: Every parallelogram is a trapezoid

5 figures. A trapezoid has at least 1 pair of parallel sides. How many are here?

  1. A trapezoid has at least 1 pair of parallel sides.
  2. Find every figure with a pair of arrow marks.
  3. 4 figures have one, so 4 trapezoids.

The names nest: every square is a rectangle, and every rectangle is a parallelogram.

A parallelogram has 2 pairs of parallel sides, so it is a trapezoid too.

A figure with no parallel sides is a quadrilateral, but it is not a trapezoid.

A figure keeps every name its marks earn. The most exact name says the most.

Saying 1 trapezoid, because only 1 figure looks like a trapezoid.

At least 1 pair of parallel sides is enough. The parallelograms have 2 pairs.

A rectangle, a rhombus, a parallelogram and a triangle. How many have 2 pairs of parallel sides? — 3. The rectangle, the rhombus and the parallelogram each have 2 pairs of parallel sides. The triangle has none.

Is every square a rhombus?

Shapes belong to families, just like people. Let's see where a square fits in the family tree.

At the very top: polygons. Any closed shape made of straight sides is a polygon.

Quadrilaterals are polygons with exactly four sides.

Parallelograms are quadrilaterals where both pairs of opposite sides are parallel.

Two special parallelograms branch off: rectangles have four right angles, and rhombuses have four equal sides.

A square sits at the bottom — it has BOTH four right angles AND four equal sides.

Here's the big question: is every square also a rhombus?

Let's trace the path. A square is a kind of rhombus if we can climb from squares up to rhombuses.

A square has four equal sides — and that is exactly what makes a shape a rhombus!

Where does a square fit?A journey up the shape family treeThe 2D Shape HierarchyPolygonsclosed, straight sidesQuadrilaterals4 sidesParallelogramsopposite sides parallelRectangles4 right anglesRhombuses4 equal sidesSquares4 right angles AND 4 equal sidesIs every square a rhombus?Square = 4 equal sides → matches rhombusANSWERYESevery square is a rhombus
Grade 5 · Climbing the shape family tree

Yes! Every square is a rhombus. Shapes lower in the tree inherit every property from the shapes above them.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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