3D REGROUPING FOR HANDS ON LEARNING

Abstract

The present invention relates to a mathematical learning module for educating students learning arithmetic through kinesthetic learning and relates particularly to a system that explains the concept of regrouping in carrying forward and borrowing by introducing the concept for two- or three-digit number regrouping. This type of learning can lead to increased retention of the material and is a way for students to practice developing their problem-solving skills.

Description

BACKGROUND

Field of the Invention

The invention described herein relates to teaching aids for mathematics.

Background of the Invention

There are traditional methods in teaching primary school mathematics in a base ten system, however these methods may not effectively provide a stimulating concrete experience that is also simple and engaging for students in learning mathematical concepts. In order to provide such experiences, firsthand interaction with manipulatives provide conceptual mathematical ideas that give students a tactile and visual model in developing their understanding.

SUMMARY OF THE INVENTION

A primary aim of the present invention is to provide a manipulative tool that will help teachers to teach students by engaging them physically and visually in understating a process of making groups of tens when carrying out operations forward (addition) and borrowing (subtraction) with two-digit numbers or larger. When utilizing typical manipulative techniques, the explaining process frequently is so complicated that students get lost and may not remember the process the next time they are asked to recall the information.

The 3D Regrouping Boxes of the present invention may be summarized as including three different sized receptacles that stack within one another to allow students to move cubes to indicate mathematical functions and their interrelations, allowing a student to actually handle and visualize each operation.

The current invention is comprised of a total of six different receptacles. The first, second, fourth, and fifth receptacles are quadrilateral shape being of a cubic form with four sides or edges and four vertices or corners with interior angles that add up to 360 degrees, where all sides and angles are equal. The third and sixth receptacles are of a parallelogram form being of rectangular form, where opposite sides or edges are parallel and of equal length and four vertices or corners with an interior angle of ninety degrees each.

The 3D Regrouping Boxes is a manipulative tool where counting cubes are utilized within the receptacles. The first, second, and third receptacles each hold respectively counting cubes from up to one thousand, one hundred, and ten. The first receptacle holds up to one thousand counting cubes in increments (or groups) of one hundred. The second receptacle holds up to one hundred counting cubes in increments of ten. The third receptacle holds up to ten counting cubes in increments of one.

The initial receptacles (first, second, and third receptacles) each have a corresponding receptacle which is a cap or cover. Once an initial receptacle is filled with counting cubes, then the initial receptacle is topped with a corresponding receptacle cap or cover (respectively fourth, fifth, and sixth receptacles) to show that the initial receptacle is filled with the maximum counting cubes for that initial receptacle. The receptacles may be made of a sturdy material such as various plastics, metal, cardboard, shaped foam sheets, wood, or any suitable material.

The 3D Regrouping Cube is arranged so that the breakdown of the counting cubes are easily discernable into group of ten. For example, the third receptacle can be filled with a maximum of ten counting cubes. Once the ten counting cubes fill the third receptacle, it is covered or topped with the corresponding receptacle cover to indicate a complete group of ten. Analogously, the second receptacle corresponds to one hundred counting cubes and is filled by ten groups of ten, i.e., ten filled third receptacles. Likewise, for the first receptacle corresponding to one thousand counting cubes filled by ten groups of one hundred. The counting cubes that are to be utilized are common products already available in the market; the 3D Regrouping boxes will be manufactured to accommodate the desired counting cubes.

The initial receptacles are nestled within one another. For example, the third receptacle is inserted at a position within the second receptacle; with the second receptacle positioned within the first receptacle. The initial receptacles can be either nestled with or without the corresponding cap or cover once that receptacle is filled.

In one example, when adding ninety to twelve, an initial set of counting cubes corresponding to ten would fill one of the third receptacles leaving two counting cubes out. Then the third receptacle would be inserted into the second receptacle to indicate a complete group of ten tens, a total of one hundred counting cubes.

In one example, when adding ninety to twelve, an initial set of counting cubes corresponding to ten would fill one of the third receptacles leaving two counting cubes out. Then the third receptacle would be inserted into the second receptacle to indicate a complete group of ten tens, a total of one hundred counting cubes.

For example:

• • 90+12
  • 90+10+2 [nine base ten added to one base ten and two counting cubes]
  • (90+10)=100 [the base ten are grouped together]
  • 100+2=102 [the grouped base ten are added to the two counting cubes]

The second receptacle is not limited to accommodating only one of the third receptacle but can hold multiple third receptacles. To further a student's understanding that a regrouping is complete the corresponding cover is capped over the filled receptacle. By capping, this indicates to the teacher and student that there is a completed base ten problem.

On the other hand, if we were to borrow eight from one hundred, then the third receptacle would be disengaged from the second receptacle.

For example:

• • 100−8 [the one hundred will be broken down to ten base ten]
  • 100=90+10 [ten base ten are broken down to nine base tens and one base ten, the nine base ten will be pushed aside to be incorporated at the end]
  • (10−8)=2 [one base ten is broken down to eliminate eight counting cubes, the corresponding cap to the third receptacle would be removed to indicate that the base ten is not complete]
  • 90+(10−8=2)=92 [there is nine base ten available with two counting cubes from the elimination of eight counting cubes from a base ten]

Furthermore, here is an example utilizing the first receptacle accommodating one thousand counting cubes corresponding with ten of the second receptacle or one hundred of the third receptacles.

Such as:

• • 1000−128 [1000 will be broken down to ten second receptacles]We will need to borrow (subtract) from the second receptacles 128, by breaking down two second receptacles.
  • 1000=800+200 [200 will be broken down to two second receptacles, leaving eight second receptacles to be pushed to the side to be incorporated at the end]]
  • 200−128 (the two second receptacles are broken down to eliminate 100 counting cubes and 28 counting cubes, taking away one second reciprocal entirely and eliminating 28 counting cubes from the one second reciprocal)
  • 100−28 [there is ten base ten, in which two base ten are taken away entirely with a third base ten broken down to eliminate eight counting cubes leaving two counting cubes]
  • Now the regrouping of 800+70+2=872

BRIEF DESCRIPTION OF FIGURES

Various other objects, features and advantages of the present invention will become fully appreciated as the same becomes better understood when considered in conjunction with the accompanying drawings. To summarize the drawings:

FIGS. 1a, 1b, 1c, 1d, 1e, and 1f illustrate various views of the first receptacle according to an embodiment of the present invention.

FIGS. 2a, 2b, 2c, 2d, 2e, 2f, and 2g illustrate various views of the second receptacle according to an embodiment of the present invention.

FIGS. 3a, 3b, 3c, 3d, and 3e illustrate various views of the third receptacle according to an embodiment of the present invention.

FIG. 4a illustrates a perspective view of a fourth receptacle with a first receptacle, according to an embodiment.

FIG. 4b illustrates a perspective view of a fifth receptacle with a second receptacle, according to an embodiment.

FIG. 4c illustrates a perspective view of a sixth receptacle with a third receptacle, according to an embodiment.

FIGS. 5a-5e, 6a-6g, 7a-7h respectively illustrate various methods sequentially to demonstrate the use of the regrouping boxes, according to an embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The illustrative embodiments of the present invention are described below. The following explanation provides specific details for a thorough understanding of and enabling description for these embodiments. One skilled in the art will understand that the invention may be practiced without such details. In other instances, well-known structures and functions have not been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise,” “comprising,” and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to.” Words using the singular or plural number also include the plural or singular number, respectively. More than one term may be interchangeable, particularly the terms “wall” and “facet”.

The 3D mathematical tool presented utilizes three different shaped receptacles to facilitate an understanding of arithmetic regrouping. Referring to the figures, the receptacles are comprised of a first receptacle 100, second receptacle 200, and third receptacle 300. In which the receptacles 100/200/300 utilize counting cubes (not shown). The third receptacle 300 can be engaged within either the second receptacle 200 or the first receptacle 100, whereas the second receptacle engages within the first receptacle 100.

FIG. 1a and FIG. 1b show a plan view of a first receptacle 100 being a three-dimensional cubic shape that is bounded by six square facets/walls, with three facets meeting at each vertex, twelve edges, and eight vertices. One square facet/wall is an open side that is unobstructed surrounded by a perimeter of four obstructed square planar facets/walls 110. A sixth side that is partially obstructed square facet/wall (referred also as a base end) 160 opposite the open side of the unobstructed square facet 115. The first receptacle 100 is able to hold exactly one thousand counting cubes (not shown). The unit size of each counting cube is 1×1×1, with the first receptacle 100 being a unit size of 10×10×10 in comparison to the counting cube. Additionally, the first receptacle 100 is able to hold ten second receptacles 200, one hundred third receptacles 300 and or a combination of counting cubes (not shown) and receptacles 200/300.

FIG. 1b shows a cutaway view for first receptacle 100, having an inner void surrounded by one or more side facets/walls 110 with one or more outer flat surface. The first receptacle 100 has one open side that is an unobstructed open facet 115 that is bordered by side walls 110. The first receptacle 100 has one partially closed facet 160 with an inner extending perimeter ledge that surrounds an inner void 165 of the partially obstructed (closed) side 160 that is opposite of the unobstructed (open) side 115 with the inner extending perimeter configured to be a ledge in which either counting cubes or alternate receptacles (second and or third receptacles) 200/300 are secured within the first receptacle 100.

FIGS. 1c, 1d, 1e, and 1f, show an alternate view of the first receptacle 100 having one to ten channels 135 formed in an inner surface 120 of one or more said side wall(s) 110 with a vertical length ten-unit size of counting cubes (not shown). The formed channel(s) 135 can be placed at various positions within the inner surface 120, either at an end point of a side wall or along any preferred position for placing counting cubes or an alternate receptacle (second or third receptacles) 200/300. FIG. 1e shows two parallel channels 135 at an inner perimeter 120 of the obstructed side walls 110, where indentations are formed along the upper portions of the inner perimeter of the first receptacle 100. The indentations 130 may take the form of a term, shape, or numeral, for example. FIG. 1d shows a cutaway view of the channels 135 formed from the top of the first receptacle at the unobstructed facet extending down to the partially obstructed base end 160. FIG. 1c shows on an outer periphery face 110 of the first receptacle 100 having an overlay 140 with either a desired, numeral, term, or design.

FIGS. 2a-2b show a plan view of a second receptacle 200 being of a three-dimensional quadrilateral bounded by six facets, three facets meeting at each vertex, eight edges, eight vertices, and all parallel sides or facets equal in size to one another. One square facet is an open unobstructed side 215 surrounded by a perimeter of four obstructed (closed) rectangular planar facets 210. Opposite of an unobstructed open side 215, a sixth partially closed/obstructed facet 225 has an inner extending perimeter ledge(s) that surrounds an inner void 240. The extending ledge(s) has a length ten-unit sizes of a counting cube and a height equal to one unit size of a counting cube. FIG. 2a further illustrates the second receptacle 200 having an area measuring one-hundred-unit sizes of a counting cube, i.e., 10×10.

FIGS. 2c-2d illustrate the second receptacle 200 having an outer perimeter edge 260 extending around the outer surface of the partially obstructed side 225/240, in which the outer perimeter edge 260 engages with the channels of 135 of the first receptacle 100. FIGS. 2d-2g show the second receptacle 200 with parallel channels 230 formed in an inner surface 220 of one or more side wall(s) 210 having a horizontal length of ten-unit size counting cubes. The figures further show opposite parallel facets/walls having corresponding parallel indentations 235 consisting of either a term, shape, or numeral, in which the indentations 235 are arranged along the inner surface perimeter 220 of the second receptacle 200. An overlay 250 is on an outer periphery face of the second receptacle 200 being either a desired numeral, term, or design.

FIGS. 3a-3b illustrate a third receptacle 300 that is parallelogram being a rectangular form, having a channel 315 with one unobstructed open facet 305 and an opposite obstructed facet 320 being a base, two or more raised side walls 310 being of a height equal to one unit size counting cube with a length equal to ten-unit size counting cubes forming a channel 315 with a void within the parallelogram. FIG. 3c further illustrates an outer perimeter edge 340 around the base 330, in which the outer perimeter edge 340 engages with the first or second receptacle 100/200 either by inserting, snapping, resting, or sliding into a corresponding channel 135/230. FIG. 3d illustrates in the third receptacle 300 indentations 325 formed on the inner surface of the base 330 a form of either a term, shape, or numeral. FIG. 3e shows on an outer periphery face of the first receptacle 300 having an overlay 350 with a desired numeral, term, or design.

FIG. 4a illustrates a fourth receptacle 400 that is a cover/cap that is placed over the first receptacle 100, to indicate that the first receptacle 100 is filled with the proper number of counting cubes or alternate receptacles 200/300 (not shown). The fourth receptacle 400 is a cubic form having one obstructed facet with a parallel unobstructed facet in which an inner void engages with the first receptacle 100. The cover/cap 400 has an optional outer overlay (not shown) with either a numeral, term, or design could be added. Once the first receptacle 100 is filled with the proper corresponding number of counting cubes, and the fourth receptacle 400 is placed upon the first receptacle 100 this will indicate as being tallied 450.

FIG. 4b illustrates a fifth receptacle 500 that is a cover/cap that is placed over the first receptacle 100, to indicate that the second receptacle 200 is filled with the proper number of counting cubes or third receptacles 300 (not shown). The fifth receptacle 500 is a cubic form having one obstructed facet (closed side) with a parallel unobstructed facet (open side) in which an inner void engages with the second receptacle 200. An outer overlay (not shown) with either a numeral, term, or design could be added. Once the second receptacle 200 is filled with the proper corresponding number of counting cubes, and the fifth receptacle 500 is placed upon the second receptacle 200 this will indicate as being tallied 550.

FIG. 4c illustrates a sixth receptacle 600 that is a cover/cap that is placed over the third receptacle 300, to indicate that the third receptacle 300 is filled with the proper number of counting cubes. The sixth receptacle 600 is rectangular form having one obstructed facet (closed side) with a parallel unobstructed facet (open side) in which an inner void accommodates the third receptacle 300. An outer overlay (not shown) with either a numeral, term, or design could be added. Once the third receptacle 300 is filled with the proper corresponding number of counting cubes, and the sixth receptacle 600 is placed upon the third receptacle 300 this will indicate as being tallied 650.

FIGS. 5a-5e, FIGS. 6a-6g, and FIGS. 7a-7h illustrate the utilization of the 3D Regrouping Boxes. FIGS. 5a-5e, demonstrates an example using the third receptacle to determine the sum of fifteen plus seventeen. FIGS. 5a-5c, illustrates base ten counting cubes, with two units of ten and twelve units of one. FIG. 5d goes on to illustrate utilizing the third receptacle, filling it with the single unit counting cubes. Once the third receptacle is filled it is grouped with the two ten units as in FIG. 5e to indicate the sum of fifteen plus seventeen is thirty-two.

FIGS. 6a-6g further illustrate the utilization of the 3D Regrouping Boxes to demonstrate an example using the second and third receptacle to determine the sum of fifty-five plus fifty-seven. FIG. 6a-6d, illustrates base ten counting cubes, with ten units of ten and twelve units of ones. FIGS. 6c-6e, goes on to illustrate utilizing the third receptacle, with step #1 &step #2 the third receptacle is filled with the single unit counting cubes. Once the third receptacle is filled it is capped and then moved to be grouped with the ten units to indicate a complete ten unit. In step #3, the ten units with the third receptacle are positioned in the second receptacle as further illustrated in FIG. 6f-6g. After filling a second receptacle indicating a sum of one hundred units it is added with the remaining ten unit and two single counting cubes giving a sum of one hundred and twelve.

FIGS. 7a-7h further illustrate the utilization of the 3D Regrouping Boxes to demonstrate an example using the first, second, and third receptacles to determine the sum of five hundred and fifty-five plus five hundred and fifty-seven. FIGS. 7a-7b, illustrates base ten counting cubes, with five units of hundreds, ten units of tens, and twelve units of ones. FIG. 7c-7e, goes on to illustrate step #1 utilizing the third receptacle with the single counting cube. Step #2 further illustrates that once the third receptacle is filled it is capped and then moved to be grouped with the ten units to indicate a complete ten unit. FIG. 7e, step #3, the ten units with the third receptacle are positioned in the second receptacle. FIG. 7f, step #4 once the second receptacle is filled this indicates a sum of one hundred units, the receptacle is capped off and added with the hundred units which in turn is placed within the first receptacle as indicated in FIGS. 7g-7h. Once the first receptacle is filled it is capped to indicate that there is one thousand counting cubes and the remaining one hundred unit, and one ten unit and two single counting cubes gives a sum of one thousand one hundred and twelve as illustrated in FIG. 7h.

Claims

1. An arithmetic tool comprising: a first receptacle;a second receptacle; anda third receptacle;wherein said first, second, and third receptacles are configured to hold counting cubes;said first receptacle is configured to hold exactly ten said second receptacles, said second receptacles is configured to hold exactly ten said third receptacles, said third receptacles is configured to hold exactly ten counting cubes.

2. The arithmetic tool as in claim 1, wherein said first receptacle is a hollow cube;said first receptacle having said one or more side walls with a surface area one hundred units of a counting cube;said first receptacle having one open side;said open side bordered by said side wall(s);a wall of said first receptacle opposite said open side having a partial opening; andsaid wall having the partial opening with an inner perimeter ledge that borders said partial opening;wherein said inner perimeter ledge is configured to receive one or more counting cubes, one or more second receptacles, one or more third receptacles or a combination of cubes and receptacles.

3. The arithmetic tool as in claim 2, wherein said first receptacle has two or more channel(s) having a height of ten counting cube units; and said channels are formed on an inner surface of two or more said side walls parallel to one another extending the along the height of said side walls.

4. The arithmetic tool as in claim 2, wherein indentations are present along upper portions of the inner perimeter of the first receptacle; and said indentations are spaced to indicate one counting cube unit.

5. The arithmetic tool as in claim 2, wherein an outer periphery face of said first receptacle has an overlay with one or more of a numeral, term, or design.

6. The arithmetic tool as in claim 1, wherein a fourth receptacle is a hollow cubic form; said fourth receptacle having one or more closed side wall(s);said fourth receptacle having one open side parallel to one closed side wall; andsaid open side for receiving said first receptacle within said fourth receptacle.

7. The arithmetic tool as in claim 1, wherein said second receptacle is a quadrilateral, with four vertices and four congruent sides; said second receptacle having a surface area accommodating one hundred counting cube units;said second receptacle having one open side parallel to one partial open side;said partially open side having an inner perimeter ledge that borders said partial opening; andsaid inner perimeter ledge configured to receive one or more counting cubes, one or more third receptacle, or a combination of cubes and receptacles;wherein said inner perimeter ledge is a length of ten counting cube units and a height and width of one counting cube unit.

8. The arithmetic tool as in claim 7, wherein said partially open side of said second receptacle having an outer perimeter edge encompassing said perimeter of said partially open side; and said outer perimeter edge is configured to engage with said channels in said first receptacle.

9. The arithmetic tool as in claim 7, wherein said second receptacle has a channel formed in an inner surface of three or more said side wall(s) with a vertical length of ten counting cube units.

10. The arithmetic tool as in claim 7, wherein the indentations border the inner perimeter of the second receptacle; and said indentations are spaced to indicate one counting cube unit.

11. The arithmetic tool as in claim 7, wherein a fifth receptacle is a hollow square form; said fifth receptacle having one or more closed side wall(s);said fifth receptacle having one open side parallel to one closed side; andsaid open side is configured to receive said second receptacle within said fifth receptacle.

12. The arithmetic tool as in claim 7, wherein an outer periphery face of said second receptacle has an overlay with one or more of a numeral, term, or design.

13. The arithmetic tool as in claim 1, wherein said third receptacle is a parallelogram form; said third receptacle having a channel with one closed, one open side, and two raised side walls being equal in height to one counting cube unit and a length of ten counting cube units.

14. The arithmetic tool as in claim 13, wherein said closed side has an encompassing outer perimeter edge; and such that said outer perimeter edge is configured to engage with said channels of said second receptacle for receiving one or more third receptacles.

15. The arithmetic tool as in claim 13, wherein a sixth receptacle is a hollow rectangular form; said sixth receptacle having an open side parallel to one closed side for receiving said third receptacle;said sixth receptacle having one or more closed side wall(s); andsaid open side is configured to receive said second receptacle within said sixth receptacle.

16. The arithmetic tool as in claim 13, wherein an outer periphery face of said third receptacle has an overlay with one or more of a numeral, term, or design.