Counting Back and Counting On(1)

  • Counting Back and Counting On

    Links Away
    Grades: PreK to 2nd
    Periods: 1
    Author: Grace M. Burton


    Instructional Plan

    To set the stage for learning, choose a counting back book to read from the Counting Books Resource Sheet, such as Ten Sly Piranhas, Ten Little Ladybugs, or Five Little Monkeys Sitting in a Tree.

    pdficonCounting Books

    If no books are available, tell a story about counting back such as the following:

    There were eight candies on a plate. Zack took one of them; then Yula took one; then Xavier took one, and Wilma took one, and so forth.
    As the students listen to the story, have them model each number from the story with counters, links, or candies, then write the numeral and number word for each. Watching their responses will help you assess the students’ current level of understanding.
    524 chain links

    Next give each child 10‑12 links. Hold up a number and ask the children to make a chain with that many links, lay it flat on the desk and then record the number of links on their slates. Then ask them to add one link and record the addition they have just modeled using the equation (horizontal) format. Now show the same starting number and ask the children to make a chain with that many links. Have students record that number as before but this time to count away one link and then record the subtraction they have just modeled using the horizontal format.

    524 held links

    Now ask the students to build a chain of six links and hold the chain vertically so that it hangs down. Lead them in singing Six Little Ducks, from the Song Lyrics Resource Sheet, as they remove the links one at a time. Ask them to record each subtraction in vertical format.

    pdficonSong Lyrics

    When the children are ready, ask them to share one of their differences and the counting process that was used to get it. Summarize how students can count back to subtract one.

    Assessments and Extensions

    Assessment Options

    1. Document your observations during class discussions and student practice. Use the Class Notes recording sheet.
    2. Ask students to choose one subtraction example and write it in both vertical and horizontal format for an entry in their portfolio. Have them draw a picture that illustrates the subtraction fact.


    1. Put several counting back books in a math center along with paper, crayons and links. This availability will encourage children to continue to read books with a subtraction theme and to practice recording subtraction examples.
    2. Move on to the next lesson, Taking Away Sets.

    Questions and Reflections

    Questions for Students

    1. How many links are in this chain (show a chain with ten links)? On this chain (show a chain with nine links)? Which chain has more? How many more?

    [The chain with none links has more. It has one more link than the chain with ten links.]

    2. What number sentence would show that you started with 10 links and took one away?

    [10 – 1 = 9.]

    3. What was alike between the two ways we recorded subtraction? What was different?

    [The numbers we used were the same. We got the same answer. They look different because one is going across and one is going up and down.]

    4. How could you help a younger child model this subtraction sentence (write 10 – 1)?

    [Tell her to start with ten things and take one away.]

    5. What does the minus sign mean?

    [It means "take away."]

    6. What two symbols did you use to mean equals?

    [Two short lines and one long line. Students may point to the two symbols.]

    7. When you count backwards, what comes after seven?

    [Six comes after seven.]

    Teacher Reflection

    • Which books were best received? What others might you use?
    • Were the materials used for counting back appropriate?
    • Which students met all the objectives of this lesson? What extension activities would be appropriate for those children?
    • Which students did not meet the objectives of this lesson? What instructional experiences do they need next?
    • Do students understand the symbols for subtract and equals?
    • What mathematical ideas need clarification?

    Objectives and Standards

    Students will be able to:

    • Count to 10.
    • Model numbers to 10.
    • Count differences from numbers to 10.
    • Write and recognize numerals to 10.
    • Record differences in vertical and in horizontal format.

    Related Resources


    Taking Away Sets


    Grade: PreK to 2nd

    Subtract sets of concrete objects and record differences.

    Hopping Backward on the Number Line


    Grade: PreK to 2nd

    Count backwards on a number line to subtract.

    Finding the Balance


    Grade: PreK to 2nd, 6th to 8th

    Model subtraction equations using pan balances.

    Finding Fact Families


    Grade: PreK to 2nd

    Generate addition and subtraction fact families.

    Practice Makes Perfect


    Grade: PreK to 2nd

    Match addition and subtraction facts in the same fact family.

    Looking Back and Moving Forward

    Number and Operations

    Grade: PreK to 2nd

    Review subtraction with concrete and symbolic representations.