Course Discussion: Module 5, I Feel the Need … The Need for Speed

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

I Feel the Need … The Need for Speed

  1. Create an addition and subtraction problem for the purpose of teaching carrying complements across columns. Be sure to not make it too complex and include at least 4 addends/subtrahends.

  2. Which fluency strategy works for building your abacus skills?

  3. Construct a timeline for a student on your caseload learning the abacus based on what they currently know.

2
  1. 31+37+34
  2. One strategy that works for building abacus fluency is repeatative number addition and subtraction.
  3. For my student, I see some splinter skills. She is currently able to add and subtract two digit numbers that don’t require any regrouping. She needs to go back and learn the 5 and 10 compliments with objects, before or in unison with the abacus. Her movements and computation processes are slow, so she would also benefit from consistant daily practice.
    Review foundations (1 month)
    Compliments of 10 (2 months)
    Compliments of 5 (3 months)
    100’s (3 months)
    Multiplication (5 months) Hopefully she will be able to move here at this point. She is currently working on memorizing her multiplication facts.
    The biggest hurdle I see to this time line, is buy in from the district/classroom teacher. As an itinerant, I can’t be there all the time and I frequently find that staff does not follow through on practice, even when instruction and materials are provided.
3

Hi Lynda!
You have a great example of a problem with carrying across columns.
Your timeline sounds great. Might I suggest getting your student the Practice2Master Abacus app and loading banks of problems to practice around those special complements? Also, a chart for her to track that she practiced for 10 minutes helps as well.

4
  1. 84+29-55+38
  2. Adding the same digit repetedly, or adding sequential numbers up to 55 or subtracting down from 55. Or set 200 hundred, have repeated subtraction of a specific number for 1 minute, and see how far you can get. Do the opposite for addition. You can add 49+9, 49+8, 49+7 etc down to one. OR 50-1, 50-2, 50-3, etc up to 9.
  3. My student is proficient at adding directly in the ones, tens, and hundreds columns. She has not yet learned all of the complementary numbers, but is interested in this.
    I would provide two 20min lessons weekly, and indpendent practice (problems and fluency activities) that integrate Understanding bead movement and complementary numbers.
    Next we would we would work for 2 months on Complementary #s of 10 (addition and subtraction), then complementary #s of 5’s (addition and subtraction).
    Then we would spend 2-3 months on addition and subtraction of into the 100’s, then 3-5 months on multiplication (2, 5, 9, 3; then 4, 6, 7, 8; up to 4-digit by 1-digit). Then 2-3 months on division (2, 5, 9, 3; then 4, 6, 7, 8; up to 3-digit by 1-digit).
    Next, multiplication for 2-3 months working on mental multiplication and & 3-digit by 1 digit.
    And finally, division for 2-3 months working on mental multiplication and & 3-digit by 1 digit.
5
  1. 4 + 6 - 8 + 5 + 3 = 10
  2. I do really well with practice followed by a break. I found, during these modules, that my brain would have a harder time processing numbers movements if I didn’t take a break and do something unrelated to math. When instructing a student, it should be expected that breaks will need to take place so that the student has time to process the information. If there’s a particular sticking point and the frustration level is increasing, stop and take a break. Additionally, turning these skills into games (for example, rolling a die or dice) would increase interest and, as a result of the game activity, fluency.
  3. The student currently knows basic addition and subtraction facts and will be learning multiplication and division within the upcoming year. The student should be exposed to the Cranmer abacus, learn its function and how it’s set up, what the features are, etc. This student already has basic understanding of 10 and 5 pairs, so a review for fluency would first rule out/in any need for review of this skill. We would work on setting up numbers correctly on the abacus, first in the one’s place, then two digits, and (given exposure to larger numbers) into the thousands place up to 1,000,000. Calculations, though, will not go that high yet. The student would also be taught the correct finger movements for setting and removing beads. We would move on to addition within the one’s with 10 pairs, subtraction with 10 pairs, use of one and two digits, working with longer strings of single/double digit numbers, then move on to 5 pairs (addition, subtraction, one and single digit, then strings of single/double digits numbers). Once fluency in these areas is achieved, we could move on to working in the hundred’s place, setting numbers and working on correct movements for simple problems before working on 10 pairs, 5 pairs, and more complex calculations that require double bead and double rod movements.
6
  1. 34 + 68 -19 + 17=100
  2. Practice daily starting from easy (+2, -2) to hard (+9, -9) helped me.
  3. I have a student in 2nd grade. He has progressive vision loss and is struggling with counting manipulatives in the classroom. He was introduced to braille at the end of first grade. He is currently using the abacus to figure out basic facts he has not yet memorized.
    He currently nows +2, +5 and +3 (up through 9)
    My timeline for this student: Introduce numbers 10-100 on abacus-1 week
    Introduce complements of 5- 2 weeks
    Use complement of 5 to find +2 and +3 facts (ex: 2 +4)
    When he has mastered using the abacus for the facts he knows, use the abacus to find the novel +4 facts- 1 week
    Introduce the complement of 10 (Which was already taught in the Common Core in first grade, but not applied to the abacus at the time)- 2 weeks
    Use the knowledge of compliments of 5 and 10 to master the new+5 facts.-1 week
    The class is currently giving individual students facts to work on for the week depending on whether they passed the facts the week before. My student is currently on +4. I am hoping at the end of this month, to have my student using the abacus to find the remaining basic facts for 6,7,8, and 9.
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28 + 37 – 19 + 6

daily short bursts of structured repetition using targeted complementary number drills. I also benefit from verbalizing each movement (“plus ten, minus one”) to reinforce the logic behind each bead shift.

  • Grade: 4th
  • Current skills: Can set and clear numbers up to three digits with consistent accuracy. Can perform simple addition without complementary numbers. Hesitant with subtraction and not yet using 5- or 10-pair complements.

Timeline for Next 8 Weeks:

Weeks 1–2:

  • Strengthen number setting/review place value
  • Introduce subtraction without complements
  • Begin finger fluency drills (5 minutes per session)

Weeks 3–4:

  • Teach 5-pair complements in addition and subtraction (e.g., 3 = 5 – 2)
  • Guided practice with problems like 4 + 3, 6 – 2, 2 + 4

Weeks 5–6:

  • Introduce 10-pair complements (e.g., 9 = 10 – 1, 8 = 10 – 2)
  • Add 2-digit addition and subtraction with regrouping
  • Introduce verbal rehearsal: “plus 10, minus 2”

Weeks 7–8:

  • Practice carrying and borrowing across rods
  • Mixed addition and subtraction with complements
  • Fluency-building: 10-minute warm-ups, followed by problem solving tasks
  • Begin applying to simple word problems with abacus support
8
  1. 67 + 39 – 43 + 50 = 113
  2. The Fluency strategy I find most helpful is to practice cross bar exchanges such as adding 9 to 45, 46, 47, 48, and so on and then to subtract from 50 subtrahends 1, 2, 3, and so on.
  3. A time line for one of my students would be:
    • Exploring the abacus, learning its vocabulary, and counting with beads – 1 to 2 months
    • Setting single digit numbers, adding single digit numbers with sums 9 or less, and subtracting from 9 – 1 to 2 months
    • Learning 10 pair compliments – 2 to 3 months
    • Adding with 10 pair compliments sums less than 20 – 2 to 3 months
    • Subtracting 10 pair compliments from minuends less than 20 – 2 to 3 months
9
  1. 26+39-16+8 = 57
  2. Repeated addition or subtraction (+1 for a minute straight)
  3. My student is proficient on ones, tens, and hundreds as well as complementary numbers of 10s. We would start with fluency practice at this level as well as reviewing compliments of 10. We would then move on to compliments of 5 and to build complexity in numbers moving up. At 2-3 month intervals the student would work on adding to the complexity of adding and subtracting one, two, and three digit numbers. As addition and subtraction becomes more fluid, we will advance to multiplication and division.
10

Hi @appleton.thea
Your problem is complex but does not include a step where you need to carry a complement across columns.
I love your plan for your student. Hope to hear about their success!

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Hi @thejessica.solomon
Your problem has complements but not ones that require carrying complements across columns.
I look forward to seeing your student at the Abacus Bee someday - you have a great plan.

12

Hi @tpeterson
You have a great problem which practices carrying complements across columns.
I find it interesting you are choosing to start with instruction with the complements of 5 and then moving to the complements of 10. There is no right or wrong process - I just found it interesting. Did you have a reason for this?

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Hi @Mary_Tubilleja
While you have a complex abacus problem, it does not have carrying the complements across columns.
I find it interesting you are choosing to start with instruction with the complements of 5 and then moving to the complements of 10. There is no right or wrong process - I just found it interesting. Did you have a reason for this?

14

Hi @Kim_Shoffner
You have provided a great abacus problem for practicing carrying complements across columns.
I also found that practicing cross bar exchanges helpful when I wanted to speed up my abacus skills.

15

Hi @jfbamber
Your problem has some complexity but does not have an opportunity to carry a complement across columns.
Good luck with your student - learning new complements with less complexity is a great way to go.

16
  1. 8+39-16=31
  2. Adding sequential numbers up to a set number (like 100) or adding the same digit repeatedly.
  3. I don’t have a student on my case load yet, but all of the ideas that I’ve read in this forum seem like great places to start!
18

  1. 54-9+7-52-23

  2. I like the practicing of adding one repeatedly and subtracting one repeatedly, just to get the practice of moving the beads. Also, adding 1+2+3+4 etc to get to 55 and then subtracting from 55-10-9-8 etc until get back to zero.

  3. If I had a student on my caseload learning the abacus, I would start with familiarization with the abacus - terminology, finger movements, correct bead movements, understanding of complementary numbers and complementary understanding with objects outside of the abacus (2 months). I would then move on to the complements of 10 and reinforcing understanding of addition and subtraction with no more than 2 digits (1-2 months). Then move on to the complements of 5 and reinforcing understanding of addition and subtraction with no more than 2 digits.

19

27 + 36 + 48 – 29

Repetition and motor planning are the things that make the most difference for this particular student.

He is currently just starting to learn to make numbers to 20 on the abacus, and is not yet truly adding and subtracting yet. We are working on adding in the addition piece slowly and by the end of the school year hope to have him doing addition and subtraction up to 2 digits.