Imaginesis: printable 3rd Grade Geometry worksheets for the United States (Common Core) — Halves and Quarters of Shapes and Sets, Identifying 2D Shapes and Quadrilaterals, Understanding Fractions as Numbers: word problems with hints, answer keys and step-by-step solutions as PDF, also as an A/B test.
A round tart tin on the table is divided into 4 equal parts. Fruit filling is poured into 2 parts. How many parts have no fruit filling?
Hint: Start with all 4 parts of the tart tin and take away the 2 with fruit. How many empty parts are left?
Answer: 2
A wooden garden marker has four straight edges and four right angles. The marker has a width of 7 centimetres. Look at the drawing. What is the name of this shape?
Hint: Check if the second edge of the marker has the same length as the width of 7 centimetres. If all four edges are equal, think of the special name for that four-sided shape.
Answer: square
A baking tray holds 15 cookies. Exactly 2/3 of them have chocolate chips. How many cookies have chocolate chips?
Hint: Read the fraction carefully: what does each of its two numbers tell you?
Answer: 10
Children learn to divide shapes and sets into two or four equal parts, identifying each share as the fraction 1/2 or 1/4 and finding the total amount from one part.
1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.3.G.A.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.3.NF.A.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.
In third grade, children connect visual sharing to formal fraction notation with denominators of 2 and 4. They partition shapes into two or four equal-area parts, naming each share as the unit fraction 1/2 or 1/4. They also extend this understanding beyond single shapes to collections of objects, splitting a set into two or four equal groups and determining the total size of a whole when given the quantity of just one part.
A common stumbling block is focusing on the number of pieces rather than equal size. Children often label any shape cut into four pieces as "quarters," even if the pieces have completely unequal areas. When working with sets of items, children frequently confuse the fraction asked for with what remains, such as mistakenly counting the unshaded items instead of the shaded fraction.
Worksheet tasks reinforce these concepts through varied representations. A child might check whether a divided circle or rectangle correctly shows a part of a whole, calculate a fraction of a set to find how many items make up one part, or solve reverse problems to figure out how many altogether if one part is known. Other tasks challenge them to spot and fix mistakes in uneven groups or evaluate true-or-false statements about unshaded parts.
Task types: Part of a whole (halves and quarters) · A fraction of a set: fix the mistake · Choose how many the fraction of the set is · Fraction of a set: how many is one part · How many altogether if one part is… · How many parts left unshaded: true or false · Invent sets that split into equal parts
Children learn to identify and name flat two-dimensional shapes, recognizing shared attributes like four sides in quadrilaterals even when figures are rotated or sized differently.
1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.K.G.A.2 Correctly name shapes regardless of their orientations or overall size.K.G.A.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).K.G.B.4 Analyze and compare two-and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).
In grade 3, children identify two-dimensional flat figures based on their defining attributes, such as their number of sides and angles. They recognize shapes such as triangles, pentagons, and hexagons, while paying special attention to quadrilaterals—four-sided figures that include squares, rectangles, and rhombuses.
A frequent stumbling block occurs when a shape is tilted or turned. Children often mistake orientation for a defining feature, incorrectly thinking a square turned on its corner is no longer a square, or failing to recognize a rotated rectangle because it does not sit horizontally.
Practice tasks reinforce these concepts by asking children to determine what a turned figure is called, answer true-or-false questions about shape names, count the number of triangles within a larger image, or spot and correct a mistakenly labeled drawing.
Children learn to understand fractions with denominators 2, 3, 4, 6, and 8 as numbers built from equal parts, locating them on number lines and identifying them in sets.
3.G.A.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.3.NF.A.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.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
In third grade, children learn that a fraction is an exact number representing equal parts of a whole. Working with denominators limited to 2, 3, 4, 6, and 8, they learn that a unit fraction such as 1/4 is one equal piece of a whole, while a fraction such as 3/4 represents three of those 1/4 pieces. They apply this on a number line from 0 to 1, dividing the space into equal intervals to locate fractions as precise points.
A frequent error occurs when children treat the numerator and denominator as separate, unrelated whole numbers rather than a single value. This often leads them to think that 1/8 must be larger than 1/4 simply because 8 is greater than 4, missing the concept that dividing a whole into more parts makes each individual part smaller. Children may also count divided sections without checking whether the parts are equal in size.
Practice tasks reinforce these ideas using visual models. In a fraction of a set: a/b of the whole task, a child sees a group of items—such as 8 stars divided evenly into parts—and identifies what fraction is shaded or circled, writing a/b (such as 3/8 or 5/8) to name that portion of the whole group.
