Much is made in teacher education classes about the importance of counting real objects vs pictures, but there is little empirical evidence to support this concern. What is much more important is for the counting to be first demonstrated by the teacher. The second most important thing is to be able to ensure that students focus on the right number of objects. These are very hard to do with manipulatives.
How to use counting objects worksheets in the classroom
Worksheets can ensure that students are focused on the right number of objects while the teacher demonstrates the counting exercise. Manipulatives, not so much! I have seen counting exercises (of manipulatives) lead students seriously wrong. Some students have the wrong number of manipulatives in front of them as the counting ensues while others change the amount during the exercise.
Step 1–the “I do” step: Always begin with a teacher demonstration
Here is part of the Rocket Math–Beginning Numerals Learning Track: Worksheet A. This shows the top part of the worksheet which is the “I do” or teacher demonstration part of the worksheet. The teaching suggestion for the “I do” step for the teacher reads as follows:
Using the six boxes at the top of each worksheet, model how to touch
and count the items in each box–then show the students that the correct
answer is circled. Have them touch the circled number. Confirm the
name of the numeral. Check to see that all students are touching it.
At a small table for instruction, the teacher could hold the worksheet up on a clipboard, or for a larger group, a document camera would be needed. The teacher gets all eyes on the demonstration and then models touching and counting. Skilled kindergarten teachers know to be quick, perky, and interesting to keep their students attention. Here’s the recommended narration:
I can do this. Watch me count. One, two, three.
There are three frogs in this box. So they circled the three.
Touch here where the three is circled next to the three frogs. Good.
How many were in this box, everybody? Yes, three.
Now watch me do the next box.
Watch me count. One, two,.
There are two frogs in this box. So they circled the two.
Touch here where the two is circled next to the two frogs. Good.
How many were in this box, everybody? Yes, two.
Now watch me do the next box.
Step 2–the “We Do” step: Lead the students to make the correct responses
Once kindergarteners can say the numbers by rote, the hard part is to develop the one-to-one correspondence between the words and the touching. This is much more difficult to do correctly than you might think. For starters, counting to ten by rote may seem like to little ones like a couple of long words, “Onetwothreefourfive sixseveneightnineten.” To teach them to touch each object and say only one word for each, the task must be done together, slowly and correctly, many times.
We Do: Touch and count. Start at zero and count each star
We Do: Narration to Count Objects in an Image
Every worksheet in the Rocket Math Beginning Numerals Learning Track has a “We Do” activity of counting stars. Here’s the recommended narration for the counting star’s activity pictured above entitled “We Do:”
Our ‘We Do’ says to touch and count. Start at zero and count each star.
We are going to touch and count the stars. Put your counting finger on zero,
everybody. We are going to start at zero and count each star. Let’s count.
One, two, three. We counted three stars. That was great!
Let’s do it again! Fingers on zero, everybody. Let’s count. One…
It doesn’t take much imagination to see that students will get this counting exercise right with the teacher’s help. If not on the first pass, by the third time, students will be correctly counting the stars. This counting exercise occurs on every worksheet in this Learning Track and gradually builds to counting up to 12 stars.
Step 3–the “You Do” step: Students demonstrate their learning
In the “You Do” portion of Worksheet A of the Rocket Math Beginning Numerals Learning Track (see above) it asks students to count the objects and select, rather than produce or write, the correct number for the number of objects they see in the box. This is identical to the teacher demonstration exercise at the top of the worksheet. The teacher has demonstrated how to do this task already. Students just need to remember that from the demonstration a few minutes prior.
Students are asked to make that distinction, to choose between two and three, by circling the right one–as was done in the top six boxes in the teacher demonstration part of the worksheet. The demonstration answers at the top of the worksheet will be available for students to use as a model of the correct answer. Students learn from practicing the correct answer rather than from practicing errors, so error-free work is the goal.
Benefits of using counting objects worksheets for kindergarten
Counting objects worksheets can focus on one thing to learn at a time
In the “I do” worksheet demonstration, the teacher is helping students develop one discrimination and one only. The task is learning to discriminate between counting two objects vs. counting three objects. The three different pictures demonstrate this; frogs, dice, and fingers. It becomes clear that the job is to get it right, to be able to tell the difference between two and three–that’s all. Students can learn one distinction like this with a high level of success. The worksheet allows the teacher to move back and forth between two objects and three objects quickly. Imagine how chaotic that would be to accomplish with manipulatives!
Counting objects worksheets can transition students to fingers and lines
Many lists of objectives include counting objects to 20. While the ability to count things up to 20 is important, that’s a lot of pictures. It is very easy to make a mistake in counting. It is much preferable to transition students to counting fingers, up to 10, and then to lines for numbers up to 20. A good worksheet program should include from the beginning pictures of fingers and lines to count instead of just cute objects. By introducing fingers and lines from the beginning, students will find it easy to transition to using only fingers or lines later.
Worksheets can properly space out the objects to be counted
A common issue in counting objects is to have the objects spaced far enough apart so that students are reliably not touching the same object twice in a row. In the “We do” portion of the worksheet, pictured above, it is clear that students will succeed by beginning with three stars spaced far enough apart that students have to move their fingers to count the next star. They won’t be confused as they can be by counting objects that are too close together.
A worksheet can establish a starting point for fingers before counting begins
Another problem in teaching counting is that students often begin counting by touching one of the objects they are counting. Then to begin counting they move to the second object and count, “One.” The end result will be off by one. Students must be taught to start with their counting finger somewhere else, and then move to the first object to be counted while saying, “One.” The Rocket Math Beginning Numerals (counting objects) worksheets always have students start with their finger on “zero,” which is pretty useful as a starting place. That’s where you start before you begin counting. I expect the savvy teacher will be saying, as students are getting their fingers ready to count, “We are touching the zero. Have we counted any stars yet? No! So we have counted ZERO stars. That’s why we are touching the zero.”
A worksheet can allow students to choose the correct answer rather than produce it
Counting worksheets that begin by requiring students to produce, or write, the numeral of the answer are asking too much of beginning students. When the written answer is wrong the teacher has no way of diagnosing whether the student counted incorrectly or forgot how to write the numeral. Much better to begin by having students select the correct answer from a limited number of choices. Teaching students (1) how to write numerals and then (2) write them from dictation are two different skills that should be taught in different instruction.
Worksheets can limit displays to numbers the students have learned.
Another advantage of worksheets is the ability to limit the examples to numbers of objects that students have already learned. When a teacher allows students to use manipulatives the ability to control the number of objects to count is lost. Instead, as shown in the “You Do” portion of Worksheet A, shown above, students only need to be able to distinguish two objects from three objects.
By having the answers present to choose from, the worksheet limits the distinctions that the students need to make. Many beginning kindergarteners confuse 4 and 5 early on. Therefore that distinction, between 4 and 5, should not be required until 1, 2, 3, and 4 are well established and at mastery. You see here on Worksheet A students are only required to distinguish between 2 and 3 objects. They make the same distinction between several examples of different objects.
Rocket Math Beginning Numerals (counting objects) worksheets will start kindergarten students out successfully
The Beginning Numerals Worksheets is the first of over 25 math worksheet Learning Tracks available as part of the Rocket Math Worksheet Universal Level Subscription. See all the other Learning Tracks available in the Worksheet Program. Go here to get a 60-day trial subscription for $15 with a money-back satisfaction guaranteed offer direct from the author, Dr. Don