Understand Category and Subcategory Relationships in Shapes

Students understand that attributes belonging to a category of 2D figures also belong to all shapes in that category's subcategories. For example, all rectangles have four right angles, so all squares (a subcategory of rectangles) also have four right angles.

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

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A category is a family that shares attributes.

A subcategory is a tighter family inside it.

A square is still a rectangle, because it keeps those attributes.

Read it: Every parallelogram is a trapezoid

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

A trapezoid has at least 1 pair of parallel sides.
Find every figure with a pair of arrow marks.
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 square, a trapezoid, a parallelogram and a shape with no parallel sides. How many are trapezoids? — 3. The square and the parallelogram have 2 pairs of parallel sides, so they are trapezoids too.

Every square is a rectangle

Today we'll learn how shape categories work — like family trees for shapes.

Here's a rectangle. It's a four-sided shape with a special rule.

Grade 5 · Why squares belong inside the rectangles family

Every rectangle has four right angles — corners that measure exactly ninety degrees.

Now look at this square. What's special about it?

All four of its sides are the same length.

And just like a rectangle, every corner is a right angle. Four ninety-degree corners.

So a square follows the rectangle rule! It has four right angles too.

We say squares are a subcategory of rectangles. Squares live inside the rectangles family.

Here's the big idea: every rule that's true for the bigger category is also true for everything inside it.

That's why every square is a rectangle. Properties flow down the family tree!

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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