Equal and Unequal Parts

3rd Grade MathFractions4 pages

About this worksheet

Twelve partitioned shapes, lettered A to L, open this 3rd grade sheet. Six have equal parts and six do not. Students write each letter in an equal or unequal column and give the unit fraction for each shape with equal parts. Some are tricky on purpose: a circle cut by evenly spaced lines has unequal strips, while a rectangle cut on its diagonal has two equal halves. Two short questions follow. Then students split a square, a rectangle, a circle and a hexagon into 2, 3, 4 and 6 equal parts. It covers Common Core 3.G.2, and the key shows sample partitions.

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$Equal and Unequal Parts: Fractions - page 1$

$Equal and Unequal Parts: Fractions - page 2$

$Equal and Unequal Parts: Fractions - page 3$

$Equal and Unequal Parts: Fractions - page 4$

Curriculum objectives covered

3.G.2

“Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.”

Question 4 asks students to partition four shapes into equal parts and name one part, and the sort asks them to judge equal area in shapes B, H and J.

3.NF.1

“Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.”

Each equal shape in the sort needs its unit fraction, such as 1/6 for hexagon F and 1/2 for rectangle H.

What's inside this worksheet

The Fraction Factory Mix-Up

Twelve shapes, including a square cut on both diagonals, a hexagon in six triangles and a triangle with a small top part.

Sort table and Think About Your Sort

A two-column table for equal and unequal parts. Below it, students name the hardest shape to place and describe one new shape for each column.

Partition the Shapes

Students draw lines to make 2 equal parts in a square, 3 in a rectangle, 4 in a circle and 6 in a hexagon, then write the unit fraction for one part.

Answers

The completed sort with a fraction for each equal shape, notes on why B, J and H trip students up, and drawn partitions for all four shapes.

How teachers use it

Print single-sided

The shapes are on page 1 and the sort table is on page 2. Print them on separate sheets so students can lay them side by side while they sort.

Argue about shape H

Ask whether H has equal parts before anyone writes it down. Cut a paper rectangle on the diagonal and stack the two halves to settle it.

Pattern blocks for the hexagon

For the hexagon on page 3, let students cover the yellow pattern block hexagon with green triangles first. Six triangles fit exactly, which gives them the 1/6.

More 3rd Grade Math worksheets

Multiplication and Division Place Value Measurement and Data Geometry

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