This week, we would like to provide a rationale for introducing the Multi-Base Bead Frame Premium Quality Complete Set to your learners. In the present time, arithmetic calculations are based on what is called the base ten model. This means we can only use nine numerals before needing two digits to represent more numerals (1, 2, 3, 4, 5, 6, 7, 8, 9). This system will encourage school-aged learners when learning higher math in the future. However, in real life, other bases may be used; take for instance processing blocks and hardware circuits, which use binary representation, which is the base 2 system. So we know it is important for learners’ sake to preserve their mathematical mind flexibility by providing them experience working with different base systems and to be able to convert from one system to another.
Multi-Base Bead Frame is a 2-part wooden frame with a movable piece atop. Within the frame are metal wires with color-coded beads representing the place values. On the movable part of the frame is printed the “n” which represents a variable number (the base on which one is working) and small numbers, which represent powers (n0, n1, n2, n3…). A small hole on the right side of the movable part is used to isolate a number that represents the base on which you are working. For example, if you are going to work on the Base 6 system, then you will bring 6 beads down on each wire, and leave the rest of the beads above. The movable frame will cover these unused beads and fall right over the number 6 on the right side, which is shown in the small hole as a reminder.
The Multi-Base Bead Frame can be mastered by any of your learners, thanks to our complete set which includes a Premium Quality Wooden Frame, a Lesson Plan book, and incrementally designed Task Cards. The Lesson Plan book will take you through each step of the process confidently, providing you with the steps and terms to use. The Lesson Plan are user-friendly and full of anticipatory tips to support diverse learners. After you have presented the lessons, your learners can be invited to use the Task Cards to further develop their understanding. The Task Cards do not replace presentations, they are meant to provide different contexts in which knowledge can be applied. You will find below a brief overview of each section from the Multi-Base Bead Frame Task Cards:
Materials:
- Multi-Base Bead Frame (Premium Quality) (Complete Set)
- Multi-Base Bead Frame
- Multi-Base Bead Frame Task Cards
- Related material: Flat Bead Frame
Multi-Base Bead Frame Task Cards
Task Cards S1 – Introductory Exercises
In this set of activity cards, learners practice setting up the Multi-Base Bead Frame to work on specific bases and reading numbers. For instance, 1111₇ is not “one thousand, one hundred eleven base seven,” but “one, one, one, one base seven). Reading numbers correctly is crucial since terms such as tens, hundreds, and thousands are strictly used for the base ten system.
Task Cards S2 – The Powers
In this activity set, learners develop an awareness of the base system as being comparable to working with exponents. To encourage learners to use this prior knowledge, the Task Cards ask that a learner bring some of the Bead Cabinet material to the working space to compare to the Multi-Base Bead Frame. For instance, to represent the base ten setting on the frame, learners bring set the frame to work with the base 10 system, bring one bead down (1) in the first 4 categories, and place a green unit below the first category on the left, then a ten golden bar below the second category, then a one hundred square below the third category, and finally a one thousand cube below the fourth category. Following this primer exercise, they repeat the same process but use another base such as base seven, which will require for them to bring one green unit, one 7-bead bar, one 7-bead square, and one 7-bead cube from the Bead Cabinet.
Multi-Base Bead Frame Task Cards – Power of 7
Task Cards S3 – Addition in Multi bases
In this set of activity cards, learners will further practice arithmetic calculations using the Multi-Base Bead Frame. Learners add numbers in various base systems. This allows them to get the good habit of keeping in mind what base system they are currently using and carrying out numbers based on this information. For instance, when adding in the base 7 system, learners must replace 7 units for 1 bead from the next category on the left.
Adding Numbers Using Base 6
Task Cards S4 – Subtraction in Multi bases
This set of activity cards invites learners to subtract up to 10-digit numbers. To further provoke the mathematical mind flexibility, the problem contains numbers as well as letters for bases greater than ten, which is all explained in our Lesson Plan book.
Subtraction
Task Cards S5 – Multiplication in Multi bases
In this set of cards, learners use the same method that they used when working with the Flat Bead Frame. Learners will use small pieces of paper (or tiles) to set up the multiplication equation. They will work with mixed problems that vary with single and multi-digit multipliers, multi-digit multiplicands, and some of which include letters.
Task Cards S6 – Converting from One Base to Another Base
Just as its name says, this set will help your learners jump from one base to another by converting and contrasting the same number expressed in different base systems. Ideally, learners use base 10 as a starter since it is the base they are most familiar with.
Converting One Base to Another
This concludes our exploration of the Multi-Base Bead Frame Premium Quality Complete Set. This material, when provided with the appropriate support for both guides and learners, is highly effective. There isn’t a better way than using concrete materials, to express base systems. This skill can be transferred to real life. Simply imagine packing 6 items in one small, 6 small boxes, one large box, 6 large boxes on one wooden pallet, 6 pallets in one truck, etc. We are working on a base six system! We hope our post has been inspirational and brought you more information about the Multi-Base Bead Frame.
For more Montessori math materials with instructional guides and supplement materials, please visit our website at www.alisonsmontessori.com.
