Why Not Try Something New When Teaching Mental Strategies
Are you struggling with how to better develop and support your students’ mental strategies for addition and subtraction?
If so, you are not alone! Many teachers are looking for new instructional settings to successfully teach addition and subtraction.
Maybe you are wondering if the 100-Bead String setting would support students’ mental strategies for addition and subtraction? So did we, so we put it to the test.
Did you just say, What is a 100-Bead String?
The Bead String Setting is an instructional setting containing 100 beads organized into 5s and 10s in order to support students’ visualization of numbers; The bead string ofen supports the use of Jump Strategies.
Take a look and listen as Katie Leadbetter, Thuc-Khanh Park, and Susan Whited share the 3-phases of instruction of Addition and Subtraction, and model how to use the 100-bead String as an instructional setting.
“Arithmetic in the range of 0 to 100, and indeed to 1000, is best done with facile mental strategies”
(Wright, Ellemor-Collins, Tabor, 2012).
Phase 1 of Addition & Subtraction to 100
Phase 1 of Addition and Subtraction to 100 (A&S to 100) lays a foundation that requires facility with
• Structuring Numbers to 20,
• Conceptual Place Value (CPV), and
• Higher Decade Addition & Subtraction (HDAS).
Students will use what they know about these three domains in their work with two-digit and three-digit addition and subtraction, so it is important to develop all three.
Higher Decade Addition & Subtraction
Having facility with HDAS allows students to mentally solve 1-digit and 2-digit addition and subtraction tasks
(see Box 6.1).
Don’t Forget 10-Frames!
(Wright, Ellemor-Collins, Tabor, 2012, pg. 113)
This is a very important component of A & S to 100 as it supports students with a range of mental strategies.
For example: How would you solve 57 + 5 mentally?
You may be thinking, one possible strategy could be partitioning the 5 into 3 and 2, adding 57 + 3 → 60 + 2 = 62.
This approach includes using structuring knowledge to partition the 5 and HDAS knowledge to add up to 60 and then to add up from 60.
Looking at the chart above, try solving the same problem using other strategies.
Let’s take a look at HDAS in action with the support of the 100-Bead String.
How was the 100-Bead String used to support the student in making sense of the mathematics?
Phase 2 of Addition & Subtraction to 100
Phase 2 of A&S to 100 consolidates a child’s early mental strategies.
This is another perfect spot to employ the bead string setting!
After the child verbally explains his/her mental strategy, the teacher can notate the child’s thinking on an empty number line and together they can use the bead string to demonstrate the child’s thinking.
Using the bead string confirms or clarifies the understanding of a mental strategy based on place value and composite strategies.
Take a look at how this teacher and student employed the bead string to support more sophisticated strategies.
Did you also notice how they are notating and labeling?
The teacher used notation after the student explained his mental strategy as a way of making the student’s thinking visible.
Notating after promotes mental strategies and builds confidence and certitude.
Phase 3 of Addition & Subtraction to 100
Phase 3 of A&S to 100 refines and develops generalizations for mental strategies.
In phase 3, we want to be very deliberate about task selection. In the table below, you’ll see some specific tasks, which lend themselves to thinking about the number relationships and strategies based on those relationships.
This deliberate task selection brings out the conversation about efficiency, flexibility, and elegance. When students see the number relationships in a task, curtailing the number of steps becomes much easier.
Let’s take a look at generalizing in action.
Be sure to notice how the 100-Bead String is used in this video.
| Small differences: | 32 – 29 41 – 37 62 – 58 93 – 87 |
| Just below a decuple: | 36 + 29 45 + 39 64 – 18 49 + 27 |
| Just above a decuple: | 51 – 16 92 – 35 63 – 27 71 – 44 |
| Near double: | 50 – 25 60 – 31 80 – 38 71 – 35 |
| Transformations: | 40 + 23 39 + 24 37 + 26 38 + 25 |
Additionally, in Phase 3 we work on formalizing with students.
Formalizing includes using bare number tasks and more formal notation.
We also work to increase the complexity of tasks – this includes tasks with missing addend and missing subtrahend, partitions of 100 (90+_= 100), partitioning decuples (60 is 10 and what?), and two-digit doubles (15+15).
We also think about extending the range of numbers to three and four-digit numbers.
Additionally, we want students to work with more than just two numbers when adding and subtracting.
With these larger numbers and more numbers, jotting also becomes a particularly useful skill in Phase 3.
Since we are moving towards formal notation and complexifying students’ thinking in phase 3, the 100-Bead String is used less in this phase. However, it can be used for support when needed.
So as you are considering the right setting for the right student at the right time, give the bead string a whirl.
We think you will find it to be a particularly powerful setting for students working through developing, consolidating, refining, and generalizing mental strategies in the range to 100.
For more lessons on using the 100-Bead String check out
Addition and Subtraction to 100: 100-Bead String Activities from the Math Recovery Store.
Want to learn more? Check out Professional Development Courses from Math Recovery®
Reference:
Wright, R.J., Ellemor-Collins, D., and Tabor, P.D. (2012). Developing number knowledge: Assessment, teaching, and intervention with 7-11-year-olds. SAGE.
You will also want to watch Practical Ways to Teach Math Strategies
How to Teach Mental Math Strategies to 100