The kids start to recognize and appreciate geometric shapes around them during their early years. By the time kids enter school, they are able to recognize shapes by their non-defining attributes like color and size. With formal education in geometry, the children are able to identify and classify shapes according to their defining geometric properties. For example, the kids have in-depth knowledge about 2D and 3D geometric shapes by the end of grade 2. They are able to relate 2D and 3D geometric figures on the basis of their attributes.
Grade 3 Geometry has a strong connection with other fields of mathematics like number base ten and measurement. For instance, in grade 3, the children get an introduction to the concept of fractions. This enables them to identify the fraction names of the partitioned shapes. Also, partitioning circles in half, quarters and into twelve parts, lays the foundation for understanding an analog time clock. The children find it easier to understand the concept of telling time to half hour or quarter after they have develop understanding of partitioning shapes.
Overview of Grade 3 Math
In Grade 3, the focus is on four critical areas:
- Developing understanding and skills for multiplication and division within 100:The children understand the meaning of multiplication and division of whole numbers through problems involving arrays, equal-sized groups, and area models. They use properties of operations to solve multiplication and division problems involving single-digit factors. The children also learn the relationship between multiplication and division by comparing various solution strategies.
- Developing an understanding of fractions:The children are introduced to the concept of fractions in this grade. They understand that the fractional part is relative to the size of the whole. They understand that fractions can be used to represent numbers less than, equal to, and greater than one. They also learn to compare fractions by using visual models and strategies like comparing equal numerator and equal denominator.
- Developing an understanding of the arrangement of rectangular arrays and of the area: The children understand the concept of area as an attribute of two-dimensional regions. They learn this concept through a square that has sides of unit length; this square is considered as a standard unit for determining area. They find the area of any shape by determining the number of such same-sized squares needed to cover the shape without overlaps or gaps.
- Describing, analyzing and comparing two-dimensional shapes: The children classify and compare shapes by their angles and sides. They also develop skills to relate their understanding of fraction with geometry by partitioning shapes into parts with equal areas. And they then express each part as a unit fraction of a whole.
Progression of Geometry with Grades
Related-below grade common core geometry standard
Grade 2: The kids learn to identify and draw shapes according to the given attributes. They learn to draw shapes as per the specified number of faces or geometry angles. They are able to identify pentagons, hexagons, quadrilateral, and triangles. They also learn to partition a rectangle into same-size squares. They then count these squares to determine the size of the rectangle. The kids learn to partition rectangles and circles into two to four equal shares. They describe the partitioned shapes using the words like half of, third of, thirds, halves. They understand the wholes as four fourths, three-thirds, and two halves.
Grade 3:The kids understand the relationship between shapes according to their attributes. They learn about the larger category shapes with shared attributes. For example, the shapes with four sides are called quadrilaterals. They partition shapes into equal parts. They learn to express the area of each part as a unit fraction of the whole. For example, they partition a shape into three equal parts and describe the area of each part as 1/3 of the area of the whole.
Related-below grade common core geometry standard
Grade 4: The kids learn about points, line segments, lines, rays and types of angles. The kids identify these in two-dimensional figures. They also learn about parallel and perpendicular lines. They classify the figures on the basis of the parallel or perpendicular lines. They also classify the figures according to the angles of specified size. Also, they learn about the different triangles in geometry. The kids also learn about line of symmetry for a two-dimensional figure. They draw lines of symmetry and identify line-symmetric figures.
Overview of Grade 3 Geometry
Reason with Shapes:
In second grade, the kids learned geometric shapes names like triangles, quadrilaterals, pentagon, and hexagon. In grade 3, they study different types of quadrilaterals in details. They understand that the quadrilaterals are closed figures with four straight sides. They start recognizing the corners of polygons as angles. For example, they recognize the square corners as right angles. They understand the relationship between the opposite sides of a figure.
They use different attributes like parallel lines, right angles, side length to recognize different quadrilaterals. In grade 2, they learned about rhombuses and trapezoids. In grade 3, they learn about parallelograms.
Classifying Quadrilaterals:
They identify the differences and the similarities between the various categories of quadrilaterals. They categorize quadrilaterals into quadrilaterals that have both pairs of opposite sides parallel (parallelogram) and quadrilaterals that have only one pair of opposite sides (trapezoid). The shapes like rectangle, square, rhombus fall under the category parallelogram. They further categorize parallelograms into parallelograms that have all its sides equal (square and rhombus) and parallelogram that only opposite pair of sides equal (rectangle). They also understand that rectangle has opposite sides equal and have right angles. They further investigate the relationship between squares and rectangles. They understand that all squares are rectangles. They also understand that square is a special type of rhombus. Also, they identify kite as a quadrilateral that has equal adjacent sides.
The kids should be able to answer geometry questions like:
- Draw a picture of a parallelogram and a trapezoid. How are they different?
- Is rhombus a parallelogram? Is parallelogram a rhombus? Justify your thinking.
Partitioning Shapes:
In grade 3, the kids learn about fractions formally. They build on the idea of partitioning whole shapes into equal parts. These shapes can be rectangles or circles. The kids are expected to partition shapes into halves, thirds, fourths, sixths, and eights. They learn the fractional names of these equal parts. They investigate that a shape can be divided into various ways. For example, a rectangle can be divided into two equal parts in the following ways:
The kids should be able to find geometry answers to questions like:
- In how many equal parts should a rectangle be divided so that each part represents one-third of the whole?
- A circle is divided into six equal parts. What is the fraction name for each part?
The researches have shown that children learn better through games. In recent times, math games have become popular. One of the most important reasons to introduce learning gamesin Mathematical teachings is the excitement and enthusiasm it brings in to the kids. Math games enable children to experience success and satisfaction and thereby, develop confidence in their newly acquired skills. Mathematical field of geometry requires visualization for better understanding. Geometry games help develops visualization skills in children. Some interesting third grade math games are given below:
Game 1: Classifying Quadrilaterals
Objective: Classifying quadrilaterals on the basis of parallel and non-parallel sides.
Previous understanding: The players should identify quadrilaterals like parallelogram, trapezoid, and kite. The players should be able to identify parallel and non-parallel sides.
Number of players: 2 or more
Game Plot: Each player, in turns, needs to push the wheel for rotation. When the wheel stops the arrow will point to one of the three sections on the wheel. There is a geometrical attribute mentioned on each section. The player will need to mention all the 2D geometry shapes names they can relate with that attribute. E.g. If the wheel stops at “Only one pair of parallel sides” he/she can list trapezoid as the correct shape. This game guides the children to relate the properties with each of the shapes and also help them visualize these properties. The game invokes healthy competition between them along with improving their learning’s for geometrical shapes.
Game 2: Classifying Parallelograms
Objective: Classifying parallelograms on the basis of sides and angles.
Previous understanding: The players should identify parallelograms like a square, rectangle, and rhombus. The player should have knowledge about square angles or right angles.
Number of players: 2 or more
Game Plot: Each player, in turns, needs to push the wheel for rotation. When the wheel stops the arrow will point to one of the three sections on the wheel. There is a geometrical attribute mentioned on each section.
The players have a list of the names of different types of quadrilaterals they have learned. The player needs to tick all the shapes that fit the geometrical attribute on which the arrow has stopped. The player who correctly selects all the shapes first wins the game. E.g. If the wheel stops at “all angles have right angles” he/she can tick the square and rectangle that appears on the list. This game guides the children to relate the properties with each of the shapes in a fun way.
Classification skills require deep understanding and practice. The geometry games have the ability to induce much more practice in children than the traditional methods of teachings. While playing such geometry games, the children don’t mind repeating some procedures or facts over and over. This helps them master the concepts relatively faster.
