Using Children’s Literature to Reinforce Geometry

posted by Dr. Jeanne White

As young children are formally introduced to the names of shapes, they begin to notice these shapes in their surroundings.  They see their plate as a circle and their napkin as a square when they eat dinner.  They look at the windows and doors in a room and recognize them as rectangles.  Tana Hoban’s book Shapes, Shapes, Shapes (1986) uses photographs of familiar objects such as pots and pans, and scenes such as construction sites, to present various shapes. Children will find more shapes on each page as they look at the photos again and again, and as they learn to name more shapes such as trapezoids and ovals.

An activity that can follow the introduction of this book can be allowing children along with family members to take photos of shapes in their home, their neighborhood or school.  They can display and compare the photos and name the shapes in each other’s photo.a door

a bureau

a lamp

In addition to two-dimensional, flat shapes, young children should be introduced to three-dimensional, fat shapes.  Reading the book, Changes, Changes (Hutchins, 1987), can open a child’s mind to the endless possibilities of how to arrange 3D blocks to build structures.  In this wordless picture book, a wooden couple builds a house but it catches on fire, so they must build a fire engine, then a boat to deal with all of the water, and so on.  Encourage children to find 3D objects in their environment such as food containers that represent cubes, cylinders, and rectangular prisms.  They can build their own structure with these containers and name them as they build.a pic of food boxes

Once children are familiar with the names of shapes, they can expand their vocabulary to include attributes of shapes.  The book, If You Were a Triangle (Aboff, 2010), includes illustrations of triangles that are slices of watermelon, Yield signs, faces of pyramids, designs on wallpaper, and more.  The text repeats the phrase, “If you were a triangle…” and lists attributes such as “three sides,” or “three corners” and introduces the terms polygon and angle.  At the end of the book, specific triangles are shown—equilateral, right and isosceles—along with examples of these triangles put together to form a new, composite, shape such as a rectangle or rhombus.  Children can look for triangles in their environment as well as practice putting the triangle Pattern Blocks together to form new shapes.a pic of 2 shapes red and greana pic of 2 shapes blue and green

Another concept children learn in early geometry is relative position.  Young children are gradually exposed to words used to describe the position of an object or person relative to other objects or people such as above, below, beside, in front of, behind, and next to.  Young children are also starting to distinguish between their right and left and are learning to move, and count, forward and backward.  A book that is fun for children to use to learn these concepts is Bug Dance (Murphy, 2002).  The bugs in this book go to school together and in gym class they learn a dance that teaches them to take steps to the right and to the left, then hop forward and backward.  Young children can perform the dance as the book is being read over and over.

After children have practiced their dance moves they can practice the terms in the book, as well as other position words, to describe the position of Pattern Blocks.  For example, children might say: the square is below the hexagon; the triangle is on the right of the square; the trapezoid is on the left of the square; the triangle is next to the square. a pic of 4 shapes

There are many children’s books that are written to introduce shapes, however many use the word “diamond” instead of rhombus.  I try to avoid these books or let children know a diamond shape is called a rhombus when we are learning math.

Geometry II

Simple maps be one of the best ways we can introduce children to and reinforce basic concepts of spatial thinking.

Imagine drawing a simple map of your sand table.  On it, you indicate where certain small toys can be found (you have buried them there, previously).  Children (I would suggest one at a time) can go over to the table and using the map unearth the hidden objects.  Of course, children can simply dig around and find the objects, but if you design this activity specifically for the purpose of map use, the children will know that this is a game with a specific set of rules to follow.

You may have to help children under 4 orient the map so they can mentally imagine how the map lines up to the actual sand table.  This mental rotation of objects in space is a fundamental geometric skill.

This activity can be repeated using simple maps of areas all over your center, classroom, and outdoor spaces.  It works just like hide and seek except there is map, clues, and investigation involved.  If you create some good ones, go ahead and get them laminated and then they can be used and reused over and over again, with dry erase markers.

 

Geometry

Geometry is so much more than learning the names of shapes for young children.  When we think of Geometry, we might harken back to that high school class where we had to memorize loads of formulas to determine circumference, area, diameters, and volume. This is NOT what we do with young children.

For young children, geometry is really housed in a larger concept that we call “spatial thinking.”  This includes mathematical skills such as categorizing shapes and objects, measurement, perspective, mental transformation of shapes (being able to turn a shape upside down), scaling, proportion,and location. This list is in no way complete, as there are many more ways that spatial thinking can be taught and learned in the early years.

An examination of the physical environment is one sure-fire way to get kids talking about geometry.  Using examples from the area around you and them, try to look for shapes, edges, lengths, and areas.

Copying shapes using manipulatives such as tangrams is another way to explore geometry.  We are going to look broadly at tangrams another day, but for now, take a look at these two sets of tangrams and consider how children can explore them.

 

Geometry and Topology

Before children begin studying geometry the way we understand it, they explore the world of “topology.”  Topology is the study of space and shapes; their properties and their relationships.  They consider their own place in space, where they are, and how far they are from their others.  They think about the relationships between objects and the properties within objects.

When I ask new teachers why it is important to provide clay, play-doh, or silly putty in their program, they will often say that children need plenty of tactile experiences throughout the day.  I don’t disagree.  However, the manipulation of these materials is another way that children study topography.  Exploring the physical properties of clay, allows the children to take a ball and squish it into a snake.  The amount doesn’t change but the shape does. Rubber bands and geoboards provide other types of opportunities for children to explore shape by stretching and manipulating the rubber bands to create all sorts of shapes. geoboard-

Encourage vocabulary associated with topology by posing questions about where things are located or questions about direction.  Play games that ask children to move further away and closer toward.  Use systems that provide boundaries for children, like tape on the floor, or the edge of the rug.

Allow large block play everyday.  No excuses.

Topology is a much more engaging and realistic way to engage young children in early geometry.  It is far more interesting than asking them to draw shapes.

 

The Common Core – Geometry Pt. II

Analyze, compare, create, and compose shapes.

  • CCSS.Math.Content.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).
  • CCSS.Math.Content.K.G.B.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
  • CCSS.Math.Content.K.G.B.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

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This half of the Geometry Standard is quite complex and subsumes many aspects of the previous standards.  Take for instance the phrase, “number of sides and vertices/corners”.  This requires that the child can count the sides or vertices, using one-to-one correspondence, understands the attributes and the vocabulary of “sides” and “vertices”, and then is able to compare all of those aspects of a shape to another.

Of course, if we are talking about triangles or squares, this isn’t very complex.  But when we are talking about solid shapes (3 dimensional) and then moving them in space to present different orientations, the ability to meet this standard is much more difficult.

Breaking this standard down into smaller parts will make the most sense for teaching.  First, children need to have exposure to 2 and 3 dimensional shapes and solids.  Next they need repeated opportunities to use the associated vocabulary to describe their attributes.  Then they need to see several examples of shapes and solids using manipulatives and real-world objects.

Another way to introduce these concepts is by using the second substandard above to support the first substandard above.   When children are afforded opportunities to build and create shapes and solids in many sizes, using a variety of materials, they will experience them on a sensory level as well.

The third substandard above may come easily to some children and may be much more difficult for others.  Children who are naturally drawn to puzzles and tangrams and who can easily manipulate shapes so that an “upside down triangle” is still a triangle will probably be able to put 2 triangles together to create a square.  Other children’s spatial skills may not be as developed, so working with these manipulatives will be important, but may be frustrating. Take a look at this post about Tangrams to see how this type of manipulative can provide a foundation for shape building.

The Common Core – Geometry Pt. I

I split the Geometry Standard into 2 parts for easier unpacking and even though I have written extensively about Geometry over the months, there are additional dimensions to this standard that are definitely worth exploring deeply.

Identify and describe shapes.

  • CCSS.Math.Content.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 abovebelowbesidein front ofbehind, and next to.
  • CCSS.Math.Content.K.G.A.2 Correctly name shapes regardless of their orientations or overall size.
  • CCSS.Math.Content.K.G.A.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

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The first substandard above is complicated.  Not only are children expected to label objects based on their geometrical attributes but they must also place those objects in relative positions, using adverbs to describe the positions.  As far as I can tell, there isn’t a list of shapes that children are expected to know, but I will venture to guess that the list only includes a very straightforward group, i.e., circle, square, rectangle, triangle.

The way I see this playing out in the classroom is like this.

Teacher: Who can find the clock?

Child 1: It’s over there (pointing to the clock).

Teacher: Can you describe where it is?

Child 1: It’s over there (pointing again, more adamantly at the clock).

Teacher: Is it above the door or next to the door?

Child 1: It is above the door.

Teacher: What shape is the clock?

Child 2: It is clock-shaped.

Teacher: Is clock-shaped a circle or a square?

Child 2: Circle.

In other words, prekindergarten children will need prompting in order to work on this skill because thinking this way might not be a natural response.  I just don’t see children naturally, without prompting saying things like, “The round plate is on top of the square table.”  However, prompting questions that stimulate thinking about shape and placement will support these emerging skills.

There are some interesting manipulatives that support the 3rd part of this standard.  Click here to see a nice set of “solids” and click here and here to see two sets of 2-dimensional shape manipulatives.  Frequency of exposure to these materials can only be a good thing.

 

Goal 9 – Explore Concepts of Geometry and Spatial RelationsRecong

I have almost completely unpacked the new Illinois Early Learning and Development Standards.  This week and next we will explore Goal 9 and in two weeks Goal 10!  Phew, that took a LOT longer than I expected and we only covered the Math section.  Aren’t you glad that this isn’t the “Everything At Home” blog?

Goal 9 begins looking at geometry and spatial relations and is first explored by Learning Standard A – Recognize, name and replicate common shapes.

The Benchmarks are:

9.A.ECa  Recognize and name common two- and three- dimensional shapes, and describe some of their attributes.

9.A.ECb  Sort collections of two- and three- dimensional shapes by type (e.g., triangles, rectangles, circles, cubes, spheres, pyramids).

9.A.ECc  Idfentify and name some of the faces of common three-dimensional shapes using two-dimensional shape names.

9.A.ECd  Combine two-dimensional shapes to create new shapes.

9.A.ECe  Think about/imagine how altering the spatial orientation of a shape will change how it looks.

Example Performance Indicators

Identify the shape of various items in the classroom (e.g., state that the clock is shaped like a circle or that the table top is a rectangle).

Describe the attributes of common two-dimensional shapes (e.g., state that a square has four sides and a triangle has three sides).

Match triangles to triangles, squares to squares, circles to circles, and rectangles to rectangles, even when size (or proportion, in the case of triangles and rectangles ) differs among examples.

Use common two-dimensional shapes to create representations of things in the real world (e.g., place triangles around a circle to make a “flower”).

Describe the faces of common three-dimensional shapes such as cubes and cylinders, using two-dimensional shape names, such as squares and circles.

Rotate and flip shapes, such as blocks and puzzle pieces to make them “fit”.

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This blog has looked at all sorts of ways to support this learning goal over the past 9 months.  Take a look here and here and here for some examples.

Geometry is one of those skills that can be supported naturally in the early childhood environment.  Puzzles provide opportunities for children to explore spatial relations as they turn the pieces over and around to see how the shape changes depending on the orientation of the piece.  Identifying and labeling two-dimensional shapes is a frequent question asked of children, but how frequently do you take it to the next level by exploring three-dimensional shapes?   Here and here are some ideas about how to do that.

Remember, the only way that children will meet this learning goal is if the adults in their lives provide ample opportunities for geometric exploration along with explanations of attribute qualities and mathematical vocabulary.

Pattern Blocks

Pattern blocks come in all sorts of sets.  There are beginner sets for younger children (I really like these), and there are larger sets for older children. They usually have small and large triangles, small and large squares, a rhombus or two, a few trapezoids, and some hexagons.  They most often come in a variety of colors.

Pattern blocks help children see shapes, manipulate shapes, create patterns, and explore geometry.

You can make your own pattern block cards so that children can match the shapes to the shape on the card.  There are also books of pattern block patterns that you can buy.  Some sets include them….Check out the one below.

Geoboards

Geoboards aren’t that different in look and size from Peg Boards, but their purpose and use is completely different.  At the last preschool where I worked, we had homemade geoboards, which were fantastic.  They were solidly made and kids could really work to cover them with loads and loads of rubber bands.

Usually, the boards are about 12″ X 12″, made of wood or plastic.  Some people use push pins to create the grid, but I prefer heavy nails, pounded deeply into the wood so that the rubber bands can’t pull the pins out.  This picture shows a really well-made geoboard.Once you have your piece of wood, you can lay out a grid with an even number of spaces on each side.  Place the nails about 1 to 1 1/2 inches apart evenly, and pound them in securely.  Here is another “recipe” for making a geoboard.

What is the purpose of the geoboard? Geoboards support early math concepts such as geometry and number concepts.  As children use the rubber bands, they create shapes on their boards.  They can make squares, rectangles, triangles and other “sided” shapes.  Be sure to talk to the children about rubber band safety as those colorful missiles are going to be pretty attractive.

Here is a picture of a very simple geoboard.

Children will also explore number concepts as they try and put the rubber bands around a certain “number” of pegs.  They may try and pull it around 3 or 4 pegs or “all” of the pegs.  Initially, expect them to simply play with the boards as they are pretty enticing (especially if you have provided plenty of colorful rubber bands) and later, you can give them directions by asking them to create  a “square” or a “triangle.”  Of course, as children approach school age, they can create shaped that have specific dimensions, i.e,  4 X 4 square or a 3 X 5 rectangle.  The possibilities are endless.