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.