Count Up -- Count Down

CONTENT AREAS: 

Whole number subtraction

 

GRADE LEVEL:  

1st-2nd grade

 

MATERIALS   NEEDED:  

Count up-Count down cards: 

        Large plain index cards

        Markers

Additional Supplies needed for Teaching with cards:

        Counting squares or disks

        Overhead with counting disks or squares

 

KEY   CONCEPTS:

Subtraction and counting


EALR'S (Make the connections clear and specific): 

          1.1 Use pictures to demonstrate understanding of whole numbers.

        In making their count-up, countdown cards they will make visual images to represent the subtraction problem.

         1.1 Show an understanding of whole number subtraction using objects.

        When doing their counting up or down students will be using manipulatives.

1.1 Use estimation to determine reasonableness of answers.

é       Students will need to estimate the answer in order to determine if it would be more efficient to add-up or count-down.          

 

GOALS:

            Students will learn to use count-up and count-down stradegies for finding the difference between to numbers.

 

OBJECTIVES:   

After a short teacher lesson about counting up and down and estimating the difference students should be ale to estimate the difference between two numbers in a subtraction problem with a small difference using count-up and countdown cards.  Once students have practiced estimating the difference, students should also be able to use counting up and down strategies to assist them with future subtraction problems. 

PROCEDURES:   

            This is a lesson that should be done as students are beginning to study subtraction. Students should have understanding that subtracting from a number means taking something away. To asses the students prior knowledge the teacher could ask questions such as:

1.       Who can tell me what we studied in math yesterday?

2.      What does it mean to subtract?

3.      How do you determine the answer to a subtraction problem? (Some students may describe counting-up or down to as a means.  If they do expand on what that means and introduce the terms counting-up and down.)

When describing counting-up and down tell the students that there are many strategies for solving subtraction problems.  One way is to determine how many more are needed.  Today we are going learn how to use counting-up and down to determine how many more are needed.(This works best with numbers that have a small difference.)

 

 Activity:

  1. (As you start the lesson this should be a completely new concept for many students so they will be in a state of disequalibrium.) Show the students a count-up card on the overhead then work through the problem with them. 
  2. Explain that because the card has an arrow up, students should count-up from the number being subtracted. In this particular case 5 would be the starting point.  Since you are staring with five, put five chips on the overhead. 

 

 

 

 

 

 

 

 


  1. Ask the class what number they will be counting to.  Make sure to get a few suggestions and ask for the reason why. 
  2. Once you have determined what number to count-up to lead the students in counting up. As you lead the students in counting-up add another chip to the overhead, make sure they are a different color or in a different pile than the starting chips.
  3. As you have reached 8, the whole number, ask the student how many more they added.  In order to figure that out the students can count the added chips.
  4. Once the students have counted up ask them to say the math problem out loud with the solutions.
  5. Explain that the class will now do some problems together.
  6. Pass out disks and cards.
  7. Before you start working through new problems be sure to show the students what the card looks like and tell them out loud what the subtraction problem is. From there follow steps 1-6. 
  8. Do this for at least 5 cards or until students begin to answer question with ease and appear to understand.
  9. Once they understand counting-up introduce counting down.  Follow the same format that you used for counting down  (steps 1-6) except show that you are down. Show the students a count down card on the overhead then work through the problem with them. 
  10. Explain that because the card has an arrow down, students should countdown from the whole number. In this particular case 9 would be the starting point.  Since you are staring with 9, put 9 chips on the overhead. 

 

 

 

 

 

 

 

 

 

 


  1. Ask the class what number they will be counting down to.  Make sure to get a few suggestions and ask for the reason why. 
  2. Once you have determined what number to countdown to lead the students in counting down. As you lead the students in counting down remove a chip from the overhead for each number, make sure they are a different color or in a different pile than the starting chips.
  3. As you have reached 7, the number being subtracted, ask the student how many chips they took away.  In order to figure that out the students can count the  removed chips.
  4. Once the students have counted up ask them to say the math problem out loud with the solutions.
  5. Explain that you are finding the difference between the two numbers.
  6. Explain that the class will now do some problems together.
  7. Before you start working through new problems be sure to show the students what the card looks like and tell them out loud what the subtraction problem is. From there follow steps 11-16. 
  8. Do this for at least 5 cards or until students begin to answer question with ease and appear to understand. Throughout this process students should be in a state of disequalibrium. 
  9. Once you have worked through several counting up and down cards, explain that you are going to try doing some problems that are not on cards.
  10.  When doing this it is important to say and write the problem.
  11. Ask the student if they should count up or down to solve this problem. Which one will be quicker?  Always ask why they came to this conclusion and encourage students to estimate if the difference between the number is large or small.  Make sure to emphasis that if the difference is large you should countdown if it small count-up.
  12. Do about 5 problems, switching between counting-up and down.  Make sure that you are demonstrating your process with chips for each problem.

(Throughout the process it is good to ask students to come up and demonstrate how to solve the problem on the overhead.)

Closure

You should already have the class’s attention and hopefully students will have crystallized understanding by now, but don’t expect everyone to.   Ask the class what they learned today? What new strategies did you learn for solving subtraction?   If the students don’t explain the process of counting-up and down or the importance of estimation to that process, you should summarize them for the students.  Explain that these are strategies the students can use anytime they are doing subtraction in the future.

 

POST-ASSESSMENT:

As students work in their small groups they should be writing down each math problem and the solution.  Once they are finished practicing they can hand in their work so that you can determine if they understand how to write math problems as well as if they are finding the correct solutions.  In addition it is important to walk around while the class is working on the cards to determine what strategies students are using to solve the problems of the card.  In order to do this I suggest observing students as well as asking them to explain their reasoning.  This checklist is one suggestion for ways to keep track of the different skills and techniques the students are using.