Lesson 2

Counting On

Est. Class Sessions: 1–2

Developing the Lesson

Part 1: Counting-On Strategy

Begin this lesson by asking students to help you solve some problems. Place 4 beans (or other counters) on a display.

Ask.

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  • How many beans are here? (4)
  • Let's count them together.

Point to each bean as the students count out loud. Now cover the beans with your hand so they cannot see them.

Ask.

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  • How many beans are still under my hand? (4)

Put two more beans on the display, but do not cover them with your hand.

Ask.

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  • Here are two more beans. Count on with me as I put these two with the other beans.
  • How many beans do I have altogether? (6 beans)
  • How did you come up with your answer? (Possible responses: I remembered there were 4 beans under your hand, then I counted on the others.)

Uncover all the beans and ask the students to count them together to check.

Repeat this activity with another number of beans until students begin to understand the concept of starting with one number and counting on from that point. See Content Notes.

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Counting–On Strategy. This is a natural strategy, particularly for adding 1, 2, or 3. Children at this age usually start at one and count all the objects. The shift from counting from one to counting-on from a larger number is an important and efficient math strategy for addition facts and problem solving. Some children need extended time and multiple opportunities before counting-on is comfortable for them. Counters or beans may be used. As an example, consider 8 + 3. The students get 8 beans and then 3 more. This strategy requires the students to hold 8 in their head as a set instead of counting the first 8 again, then count on 3 more: "9, 10, 11." If no manipulative is used, finger gestures can help keep track of how many more have been counted on

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"Children explore quantities before they can count. They can identify which cup is bigger or which plate of potato chips has more chips. Soon they need to attach an amount to the quantities to explore them in greater depth. When you look at an amount of objects, sometime you are able to just 'see' how many are there, particularly for a small group. For example, when you roll a die and know that it is five without counting the dots, that ability to 'just see it' is called subitizing. . . . Naming these amounts immediately without counting aids in 'counting on' or learning combinations of number" (Van de Walle, 2013, p.129).

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