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Kindergarten Essentials: Combinations for Numbers Through 10

What does Kindergarten math look like? What are the essential skills that every Kindergarten student should master prior to Grade 1? Believe it or not, fact fluency starts in Kindergarten when students learn to compose and decompose numbers! Now, before you whip out those flashcards (the way many of us learned our “facts”) or start cursing me about how children are losing their childhood, read on to see exactly what I mean and for Kindergarten games and activities that are more fun than work.

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First, let’s take a look at the Kindergarten Common Core Math Standards (CCMS) related to developing fact fluency. Even if you are not in a state that follows the CCMS, your state probably has similar standards in Kindergarten. I am in Texas, for example, and you will find very similar standards in our TEKS.

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).

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.

Fluently add and subtract within 5.

Need that in plain English? First of all, understand that they are sequential. In other words, each standard builds on the previous one. Read below for a translation of each of the standards. Then scroll down for additional information and for free activities to practice the skills.

  • The first standard says that for every number up through ten, children should know all the different ways to make (compose) or break apart (decompose) that number. Let’s start with 5. Five can be made (composed) of 0 and 5, 1 and 4, or 2 and 3. It can also be broken apart (decomposed) into those same parts. Do not overlook the fact that students need to acquire this skill using objects and pictures before recording each decomposition as an equation or drawing. Students should work on one target number at a time and master all of the combinations for that number before moving on to the next number.
  • In our number system, ten is a special number and that’s why it gets a specific standard. The skill is really no different than the first standard.
  • This skill addresses automaticity. It means that while students may still need objects and/or pictures for the combinations for the numbers above five, they should know all the combinations for the numbers up to five automatically by the end of Kindergarten.

Decompose Numbers in More than One Way

Determining a Child’s Target Number

It’s important to understand that children should master the combinations for one number before moving on to the next. It does no good for a child to practice composing and decomposing 6 if he does not know the combinations for 5. That’s where differentiation comes in. A routine called the “hiding assessment” can be used to determine a child’s fluency with each number. To determine if a child knows all the combinations for 3, ask the child to count out 3 counters. Anything can be used as a counter–dried beans, pasta, pennies. Any small object, really. I like these small centimeter cubes because they fit easily under my hand and can be used for lots of different activities. I recommend using all of the same color, so the child focuses on the quantity, not the color. So, for example, if you are working with 5, use 5 green cubes.

Hide some counters and show some, asking your child to identify how many are hidden. For example, hide 1 counter and show 2. “If I have 3 counters and 2 are showing, how many are hidden?” Continue this routine for each combination for 3 (hide 3, show 0; hide 2, show 1; hide 0, show 3). If your child can name all the missing parts for 3, try the combinations for 4.  When your child can no longer easily name the missing parts, that becomes her number. Every few weeks, “test” your child to determine if she is ready to move on to a new number. Here’s a video of the hiding assessment in action.

You’ll notice how this child knew the combinations for 5 automatically, but slowed down on 6, specifically, 2 and 4 for making 6. While I went on to test the child for 7, the number he needs to practice–his target number–is 6. I imagine he would only need to work on 6 for a short while. Then I would retest him for 6 and try 7. Likely, his new target number would then be 7.

Practicing a Child’s Target Number

Now that you’ve determined your child’s target number, it’s time to play! Remember, you can use these activities over and over with different target numbers as your child advances.

The first game is called Shake and Spill. Basically, you use your child’s target number; let’s say 5, for example. Put 5 counters in a cup, shake it, and spill the counters onto the mat. The child then describes how many fell on the picture and how many fell off (e.g., 3 on the duck, 2 off the duck, 3 and 2 makes 5). Continue this process trying to find all the combinations for the target number. Here’s a tip. Put the Shake and Spill Mat inside something, like the box shown in the picture. It contains the “spillage.”

Kindergarten compose decompose

Next up is a game that can be either called In the Cave, if you happen to have teddy bear counters, or Under a Rock, if you don’t. It’s basically a game version of the hiding assessment. To play, you’ll need counters or bears and a plastic cup (can’t be transparent). Use a number of bears or other counters equal to the target number you are practicing. For example, if you are working on the number 5, use 5 bears. The child closes her eyes while you put some of the bears “in the cave” (under the cup). Then, she opens her eyes and tells how many bears are hidden. Be sure to have your child say the combination (eg., 2 and 3 makes 5) so she is practicing her combinations out loud. You can also have your child write the equation that matches each combination (eg., 2 + 3 = 5).

Here are links to posts with some other resources for practicing the combinations of each number:

  1. Mathemagician Make Ten, played with a deck of cards; can be adapted to practice any number
  2. Make 5 Go Fish, played with a deck of cards
  3. Seven on Top, played with a deck of cards
  4. This post has some cards you can download with a variety of ways to use them
  5. Here’s a printable booklet for practicing all the combinations for ten

Finally, here is an awesomely addictive game for practicing the combinations of any number from 5 through 12.

Kindergarten compose decompose

If you have additional suggestions for ways to practice this important skill, please add them in the comments!

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    1. I realize that’s a big need for everyone right now! I’m sorry but I don’t have any posts on that topic yet.

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