Pattern Block Puzzles: Equal Parts of a Shape

Cover shapes with same-size parts and name each part as a unit fraction.

Hexagon puzzles

Name the fraction of the shape that each block covers.

In the math center, students cover a yellow hexagon with smaller blocks. In each puzzle, all the blocks are the same size, and they cover the shape with no gaps and no overlaps.

Jada covers the hexagon with 2 red trapezoids.

Each trapezoid covers of the hexagon.

Omar covers the hexagon with 3 blue rhombuses.

Each rhombus covers of the hexagon.

Priya covers the hexagon with green triangles. Each triangle covers 1/6 of the hexagon. How many triangles does Priya use?

A. 5 trianglesB. 3 trianglesC. 6 trianglesD. 12 triangles

Kevin finds that 2 green triangles cover 1 blue rhombus exactly.

Each triangle covers of the rhombus.

Rosa finds that 3 green triangles cover 1 red trapezoid exactly. What fraction of the trapezoid does one triangle cover?

A. 1/3B. 1/6C. 3/1D. 1/2

Jada's hexagon and Priya's hexagon are the same size. Jada used 2 trapezoids. Priya used 6 triangles. Which sentence is true?

A. Each triangle is bigger than each trapezoid, because Priya used more blocks.B. Each trapezoid is bigger than each triangle, because Jada's hexagon was split into fewer equal parts.C. Each trapezoid is the same size as each triangle, because both puzzles cover the same size hexagon.

Grid paper shapes

Each small square on the grid paper is 1 square unit. Find the area of each part. Then name the part as a fraction of the whole shape.

Marcus draws a square that is 3 units long and 3 units wide. He splits it into 3 strips with equal areas.

The whole square covers square units.
Each strip covers square units.
Each strip is of the square.

Elena draws a big square that is 4 units long and 4 units wide. She splits it into 4 parts: 2 strips that are each 4 units long and 1 unit wide, and 2 small squares that are each 2 units long and 2 units wide.

Each strip covers square units.
Each small square covers square units.
Each of the 4 parts is of the big square.

Nico builds a long rectangle out of 16 square tiles, so it covers 16 square units. He splits it into parts with equal areas and shades one part.

The shaded part covers square units.
The shaded part is of the rectangle.

10.

Mia splits a rectangle that covers 18 square units into 6 parts with equal areas. Circle every shape that has the same area as one of Mia's parts.

Check the puzzles

Sort the shapes, check a claim, and explain your thinking.

11.

Each shape is split into parts with equal areas. Sort each shape by the name of its parts.

12.

Zara covers a hexagon with 1 trapezoid, 1 rhombus, and 1 triangle, with no gaps and no overlaps. She says each block is 1/3 of the hexagon because she used 3 blocks. Is Zara right?

A. Yes, because 3 blocks cover the whole hexagon.B. Yes, because there are no gaps and no overlaps.C. No, because each block is 1/6 of the hexagon.D. No, because the 3 blocks do not have the same area.

13.

Tell one way to split a rectangle that covers 8 square units into 4 parts with equal areas. Give the area of each part and the fraction of the rectangle that each part is.