Exploring Partitioning Shapes in 3rd Grade Math

Henrietta Hedgehog demonstrates how to cut congruent rectangles into equal parts in different ways, ensuring the parts cover the same area. She shows examples with rectangles divided into four, six, and three parts, highlighting the importance of congruence and equal division. The video concludes with a question for viewers to apply their understanding.

What is required for pieces to cover the same amount of area when cutting congruent figures?

• The color of the figures must be the same.

• The figures must start as congruent and be cut into equal parts.

• The figures must be of different shapes.

• The figures must be cut into a different number of parts.

If two congruent rectangles are divided into four parts, what fraction does one part represent?

• One fourth

• One third

• One half

• One sixth

What is essential for two parts to cover the same amount of area in congruent figures?

• Unequal divisions

• Different sizes

• Equal divisions

• Different shapes

What conclusion can be drawn when congruent rectangles are cut into equal parts?

• The shape of the parts affects their area.

• Each part represents a different fraction of the whole.

• Each part represents the same fraction of the whole.

• All parts are of different areas.

Why can't each piece of the blue rectangle be considered one-sixth of the original?

• Because it was not cut into equal parts.

• Because it is not congruent.

• Because it has a different color.

• Because it was cut into more than six parts.

What do the pink and yellow rectangles demonstrate when cut into six equal parts?

• That color affects the area of the parts.

• That each part is one-fifth of the original.

• That unequal parts can cover the same area.

• That each part is one-sixth of the original.

What fraction represents the area of one part when a rectangle is cut into six equal parts?

• One sixth

• One eighth

• One third

• One fourth

Why is it incorrect to say each piece of an unequally divided rectangle represents a fixed fraction of the whole?

• Because the rectangle is not a square.

• Because the pieces are of different sizes.

• Because the pieces are of the same color.

• Because the rectangle is not congruent.

When congruent rectangles are divided into thirds and one third is shaded, what does the shaded area represent?

• One half of the original rectangle.

• One fourth of the original rectangle.

• One sixth of the original rectangle.

• One third of the original rectangle.

Is the area covered by shaded part L equal, greater, or less than the area covered by shaded part M?

• Less

• Greater

• Cannot be determined

• Equal