One of the arguments against the Core is that it expects what have been here-to-for 1st and 2nd grade outcomes for kindergarteners.  This is a real worry, especially for those of us who serve children under age 5.  If educators are forced to water down a grade-school curriculum for kindergarten, you better believe the trickle-down effect will appear in Pre-k classrooms, and G-d forbid, Infant and Toddler programs.

The article recognizes the push back from ece professionals.  I also appreciate that we now better than they do how to serve young children without sacrificing their childhood.

Check it out. 

Read how Karen Nemeth Ed.M. believes the Common Core will be/could be/might be interpreted and implemented for Preschool.

Check it out here.

• 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?”

_____________________________________________________________________

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.

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 above, below, beside, in front of, behind, 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”).

_________________________________________________________________________

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.

Classify objects and count the number of objects in each category.

• CCSS.Math.Content.K.MD.B.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.¹

• CCSS.Math.Content.K.MD.B.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.¹

Describe and compare measurable attributes.

• CCSS.Math.Content.K.MD.A.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
• CCSS.Math.Content.K.MD.A.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

___________________________________________________

Children explore “attributes” throughout their young lives.  Attributes help children distinguish observable qualities of objects, people, ideas, etc. into smaller and more comprehensible groups.

Although this standard focuses solely on “measurable” attributes ( (i.e., length, height, and weight) I would broaden the exploration of attributes with younger children to include any observable qualities (i.e., color, shape). I believe that the value in providing opportunities for children to distinguish and define the attributes all around them will prepare them for the kindergarten skill of comparing measurable attributes.  Understanding that a stuffed duck is “yellow” and “soft” relies not only on appropriate vocabulary but the ability to apply attribute qualities to the item.  This is a beginning skill that will eventually lead to comparing attributes – the yellow, soft duck is bigger than the green, hard frog.

Work with numbers 11-19 to gain foundations for place value.

• CCSS.Math.Content.K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

________________________________________________________________________

If you are not a math person, haven’t studied math in many years, or have any amount of “math fear” the words BASE TEN may be one of those things that make you sweat and tremble.  In general, I would venture to guess that many of us have heard about Base Ten, but have little to no idea what it really means.

Base Ten is the number system that we commonly use that describes the place of each number (ones, tens, hundreds, thousands, etc.).

Take a look at a number like  4,352

The 2 is in the one’s place, the 5 is in the ten’s place, the 3 is in the hundred’s place and the 4 is in the thousand’s place.  Each of those number is 10 times the value to the right of it (thus the idea of Base Ten- each place increases by a multiple of 10).

One of the common ways that teachers are currently teaching Base Ten is by introducing Base Ten Blocks like those below.

For the most part, I think these manipulatives are too sophisticated for pre-k children but they will be introduced to these in kindergarten and will probably use them quite extensively.

If I remember correctly, ones are called “bits”, tens are called “rods”, hundreds are called “flats” and thousands are called “blocks”.  Children begin to create a “rod” by putting 10 bits together, a “flat” by putting 10 rods together and so on.  There are all sorts of interesting and innovative ways teachers are incorporating these into their math teaching.

How can we support the early concepts associated with Base Ten for younger children? The best way we prepare children to understand place value is to reinforce counting, cardinality, ordinality, and one-to-one correspondence.  There are better manipulatives for younger children (Unifix cubes, and Cuisenaire Rods, for instance) that can reinforce these concepts through exploration and play.

Understand addition, and understand subtraction.

• CCSS.Math.Content.K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings¹, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
• CCSS.Math.Content.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
• CCSS.Math.Content.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
• CCSS.Math.Content.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
• CCSS.Math.Content.K.OA.A.5 Fluently add and subtract within 5.

¹ Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)

__________________________________________________________

I appreciate the authors’ intent in this standard as they have clearly limited the learning outcomes for kindergarten-aged children by specifically restricting the range of numbers that children should be able to compute to and from.  Keeping it within a manageable range recognizes the complexity of the standard and manages expectations of children.

In the early childhood world, we explore this algebraic thinking (simple addition and subtraction) through songs and finger plays (5 Little Ducks Went Out One Day, 5 Green and Speckled Frogs, Way up High in the Apple Tree) using our fingers as visual cues to help children see one less duck or frog by folding our fingers down.  Usually, children still need to count the fingers that are still out as they are not quite able to “take away” yet. “Taking away” requires that children can go backward – but remember, many young children have simply memorized the numbers in order but reversing the order is very hard to do.

Simple addition using objects should be introduced during play.  If children are playing with blocks and they need “1 more”, be sure to verbalize that, reinforcing the vocabulary and the concept that “1 more” is “adding 1” to the set.  Keep it simple with numbers under 5.  If you find that you have children who are grasping this fairly well, broaden the number range to 10.