Course Discussion: Module 2, The Complementary Abacus

Core Curriculum The Abacus: A Million Manipulatives in Your Pocket
1

The Complementary Abacus

  1. Previously, when did you typically introduce a calculator to your students? What might you do differently now?

  2. Create an addition and subtraction problem for the purpose of teaching the compliments of ten. Be sure to include at least five single digits.

  3. Write a script describing the steps of adding nine to six.

2

  1. I usually introduce the calculator in 5-6 grade in preparation for when they will be able to use it on state testing, unless student need dictates otherwise.

  2. 6+9+3-7-5

  3. Set 9
    Set 10
    Clear 6 complementary number; 4
    Answer: 15

1 Like
3

Hi Lynda!
You problem is spot on for practicing addition and subtraction using complements of 10. Your instructions are short and sweet but I bet students would like it that way.

4

  1. I typically introduce a calculator around fifth grade, sometimes before if their class is using them, then I would introduce before. It really is dependent on the student and what is happening in their classroom.

  2. 6+5+3-2

  3. Set 6
    add 5- the pair’s equivalent is 5;
    move over to tens place and set 10
    add 3 in the ones
    subtract 2
    answer 12

5

Hi Melissa!
Your problem does have an addition complement of 10. Nice work. I see you explained your own problem in #3 (sort of). In your instructions for your own problem you do not indicate removing the 5 bead from the ones column after you set the one bead in the ten’s column.

Do you want to try writing a script describing the steps of adding nine to six?

6

I am not a teacher yet but I feel like a calculator wasn’t introduced to me until middle school or late elementary.

7 + 3 - 5 + 6 - 2

Start with 7
Add 3: 7+3=10
7+3=10 (This demonstrates the complement of 7 and 3 making 10)
Subtract 5: 10−5=5
Add 6: 5+6=11
Subtract 2: 11−2=9
Final result: 9

7
  1. Previously, I introduced a talking calculator to my students at a young age, to check calculations done on their braille writer or abacus. However I didn’t provide them an abacus to use in class until the same time as their peers - about 6th grade. I don’t think I would change when I teach these skills.
  2. 8+7-5+4-2 = 12
  3. Write a script describing the steps of adding nine to six.
    We are going to add 9+6. We will start by first setting nine in the ones column of the abacus. Set nine by pushing a 5 bead down and 4 ones beads up. Now that we have our 9 set, we can add 6. To add 6, we look at the ones column, and notice that there are no beads for us to to set. This means that we will go to the tens column, and push up 1 ten bead. Now we have to ask ourselves, what is the complement of 10 and 6? It’s 4! We will clear (or push down) 4 ones beads from the ones column. This should leave us with 1 ten, and 5 ones, which is 15, so our sum is 15.
8

Hi nieberding.28, your problem is actually quite complex with multiple complementary number movements. At this time you and your student have only learned the complements of 10. I suggest 7 + 3 + 5 + 3 - 2 so your student has more success.

9

Hi appleton.thea, would you still wait until sixth grade to introduce the abacus?
Your problem is a great introduction to the complements of 10 for your student.

10

Ooops! That was a mis-type!
I start showing them a basic abacus in preschool for counting. We work on abacus a lot more in elementary, and some students choose to use it in class. Some students fight it. I introduced a talking calculator to my students at a young age, as a way to check calculations done on their braille writer or abacus. However, I didn’t provide them a TALKING CALCULATOR to use at-will in class until the same time as their peers - about 5th or 6th grade. I don’t think I would change when I teach these skills.

1 Like
11

  1. I’m not a teacher, but I believe I started using calculators the beginning of 6th grade.

  2. 6+1+1+9-1

  3. Write a script describing the steps of adding nine to six.

Set up the number 6 (5 bead & 1 bead)
Add 1 extra bead
Add another 1 bead
To add the 9, we will have to look at the tens column and push up 1 ten bead. We must remember the complement number of 10 and 9, which is 1. We will push down 1 bead from the ones column.
Lastly, we will remove 1 bead.
We are left with 10 and 6, and the total would be 16.

12

Hi mohamoud.25!
Your problem is a great starting problem to introduce the complementary addition of 9 and 1.
The first two steps in your directions for adding nine and six are unusual. I am not sure why you are doing these parts: ‘add 1 extra bead; add another 1 bead’
In addition, your last step, ‘lastly, we will remove 1 bead’ seems unnecessary. With all of these unneeded steps, you have come to the wrong answer of 16. The answer should be 15.

The only directions you need are:
Set up the number 6 (5 bead & 1 bead)
To add the 9, we will have to look at the tens column and push up 1 ten bead. We must remember the complement number of 10 and 9, which is 1. We will push down 1 bead from the ones column.

13

The Complementary Abacus

  1. Previously, when did you typically introduce a calculator to your students? What might you do differently now?

  2. Create an addition and subtraction problem for the purpose of teaching the compliments of ten. Be sure to include at least five single digits.

  3. Write a script describing the steps of adding nine to six.

  4. The only students who I have had on my caseload who needed VI-specific calculators were ones who were identified as needing IEP services later in their academic careers. By that point, they were in need of talking graphing calculators and talking large print calculators. I have been fortunate to witness and do some instruction with colleagues’ students with the Cranmer abacus, though. If I were to get a student who is young enough to begin working with either a beginner or Cranmer abacus and is emergent with math skills, then I would push for inclusion of this device as a tool to be used in the classroom, at home, and during testing. Depending on where the student is with math skills (PreK, kinder, elementary), I may pace the lesson differently, but I would still spend time orienting the student to the layout and function of the abacus. The student will need to build familiarity with the tool before being able to use it properly.

  5. 9 + 6 - 7 - 5 + 9 = 12

  6. First, set the abacus to six by pulling down a 5 bead with the index finger and pushing up a 1 bead with the thumb. Check to make sure the Reckoning Bar has the 5 and 1 bead. Then add 9 - but wait! We can’t add 9 in the one’s column, so we move left to the 10’s column and add a 1 bead with a thumb. We learned that 9’s partner, or complement, is 1, so when we add 10, we take away a 1 bead. We are left with 1 bead in the 10’s column and the 5 bead in the one’s column. Our answer is 15.

14
  1. I typically introduce talking calculator to my students at the same time as their peers are beginning to use the regular calculator. Introducing it as a way to check their work on the abacus in 2nd grade I think would be a better way. That way as the problems get more complex, they are improving on their calculator skills instead of learning to use one when their math skills are more efficient than their calculator skills
  2. 5 + 5 - 6 + 7 -3
  3. Today, you are going to add 9 + 6 on the abacus. What will you start with?
    Prompt student until they have all beads on the left moved to the center. Now you need to add 6. What is the ten compliment of 9? So if 1 +9=10, what will you do to add 6? Prompt student to move the beads to the edge and move one 10 bead. Then 6-1=? What bead shows that 5. What is your answer? 10 and 5 is what number?
    Some of these prompts may be skipped depending on the student’s mastery of the basics of abacus with this problem.
15
  1. I introduce the calculator around 5th grade. At this point, I do not have students who would require an abacus. Leaning to use the abacus is new to me and I am having so much fun with it! I feel I would introduce it as an awareness device in 3rd or 4th grade.
  2. 7+8+3-7-5
  3. Set 6, add 10, clear the compliment of 9 which is 1. Anwer: 15
16

Previously, I would introduce the calculator when academic content (especially in upper elementary or middle school) began to move faster than their manual calculation skills. The focus was often on keeping pace with grade-level content.

Now, I would take a more balanced approach. This module reinforced that the abacus builds strong mental math and place value understanding, and those are critical foundations for long-term numeracy and problem solving. Instead of introducing the calculator as soon as a student struggles, I might first strengthen abacus strategies, particularly using complements. I’d also consider using the abacus alongside the calculator for a time, letting the student build independence with both tools based on the task.

2 + 8 – 4 + 7 – 3

Set 9
Set 10
Clear 4 (6’s complementary for 10)
to get 15

17
  1. Typically, I introduced a calculator to my students when the classroom teacher needed them to use one. We have always started with manipulatives for math and number sense. I am seeing the value now with the abacus and will make it part of my math lessons with my early PK students.
  2. 3+6-2+1+2
  3. Set 6, to add 9 we must add a 10-bead and subtract 1 from the ones column. Set 10, clear 1. Your answer should be 15.