Worksheet

Pattern Block Puzzles: Equal Parts of a Shape

Grade 3 geometry: cover a hexagon with pattern blocks and split grid shapes into equal areas, then name each part as a unit fraction.

Grade 3MathInteractive · Printable

Aligned to3.G.A.2

Play online Play as a game

PrintLetter-size worksheet Answer keyPrintable answers

Assign to classAssign to your classes, or get a join code

What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
13 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 3
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Sorting, Short answer

About this worksheet

What students practice

Students split shapes into parts with equal areas and name each part as a unit fraction of the whole.
Students find the area of each equal part of a grid shape in square units.
Students explain why parts must have equal areas to be named with the same unit fraction.

How to use

If you have pattern blocks, let students build the hexagon puzzles in the first section before they write answers. For the grid shapes, students can draw each shape on graph paper.

Curriculum

Common Core standard covered

3.G.A.2

Split shapes into parts with equal areas and write each part as a unit fraction.

Preview

OwlSheets.com

Name Date

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 triangles
B. 3 triangles
C. 6 triangles
D. 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. 1/3
B. 1/6
C. 3/1
D. 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.

a strip 3 units long and 1 unit widea square 2 units long and 2 units widean L shape made of 3 square unitsa strip 6 units long and 1 unit widea strip 2 units long and 1 unit wide

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.

A hexagon covered by 2 trapezoidsA rectangle that covers 12 square units, split into 4 parts of 3 square units eachA rectangle that covers 15 square units, split into 3 parts of 5 square units eachA rhombus covered by 2 trianglesA hexagon covered by 3 rhombusesA square that covers 16 square units, split into 4 parts of 4 square units each

Halves	Thirds	Fourths

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.