WO2023180678A1

WO2023180678A1 - Apparatus for teaching place value, counting and mathematical operations

Info

Publication number: WO2023180678A1
Application number: PCT/GB2023/000018
Authority: WO
Inventors: Stephen ASTWOOD
Original assignee: Astwood Stephen
Priority date: 2022-03-25
Filing date: 2023-03-16
Publication date: 2023-09-28
Also published as: GB2617819A; GB202204219D0

Abstract

The present invention is directed to apparatus for teaching place value, counting and mathematical operations wherein a plurality of interlocking components and holding carriers are used to present numbers very clearly as groupings of ones. These are grouped and stacked together to form tens and hundreds, using a unit of one cube, a ten carrier and a hundred carrier. The ten carrier apparatus represents the unit of ten when loaded with ten individual one units, the hundred carrier represents the unit of one hundred when loaded with ten fully loaded ten carriers. Therefore; said apparatus presents numbers very clearly as groupings of ones for the purpose of simplified earning within schools or other learning institutions.

Description

APPARATUS FOR TEACHING PLACE VALUE, COUNTING AND MATHEMATICAL OPERATIONS

Field of the Invention

The present invention relates to apparatus for teaching place value, counting and mathematical operations and the use of counting cubes as an apparatus to assist in this form of education.

Background

The use of base ten apparatus for teaching place value and mathematical operations is common and a resource can be found in every school in the country where it has been a useful tool to aid children in their understanding. In addition to helping a child identify the value of the digits in a given number, they are also used to demonstrate, as a visual representation, what is taking place when we add, subtract, multiply or divide numbers._Although they are produced in a variety of subtly different designs, what is common to all is that they employ three distinct components: the hundred square, the tens rod and the ones cube. As such they encourage children to think of numbers in terms of hundreds, tens and ones. For example, the number 254 is composed of two hundreds, five tens and four ones. A potential problem with this way of partitioning a number is that some children come to a limited understanding of how the number is made. It is possible that they become so focused on tens and hundreds that they lose sight of the fact that all numbers are made by grouping ones.

For example, when asked how many ones are in the number 254, a child will often answer that there are four ones in the number. It is believed this misunderstanding is a direct result of Base Ten equipment presenting the number as distinct units of ones, tens and hundreds, rather than 254 ones that have been arranged in units of ones, tens and hundreds. Another very common problem with base ten equipment in its traditional form is encountered when children use it for addition, subtraction, multiplication and division. In order to cross a tens boundary, a complicated process of removing ten ones to change into one ten (or vice versa for subtraction and division) is rendered necessary due to the fixed

SUBSTITUTE SHEET (RULE 26) units of ten and hundred. This totally unnecessary process confuses many children and is fraught with many opportunities for error caused by miscounting.

The use of apparatus for teaching counting and mathematics is known in the prior art as follows:

This is shown in patent EP0713203 (WALDENBERG, HOFFMAN) discloses an assembly for teaching mathematical concepts includes a plurality of interlocking components (10), each having at least one connecting end so that the components can be combined in any order or length. Each component (1 0) is assigned a mathematical value according to its length, and this value may be indicated by indicia on its face or by colour coding. A base (16) is also provided for retaining the columns of components (10) in vertical formations. Means are provided on the platform of the base for engaging the bottom component in each column.

Patent GB2575968 (HASLAM, HARDSTAFF) discloses a learning rod educational toy set comprising a plurality of extruded plastic rod elements of different lengths 1 ,4, 6. Each rod element having an indication on or in an external surface of its length. The rods are connectable with each other end-on-end, via a coupling element 17, to form one or more learning rods 22 of total length equal to the sum of the lengths of the rods that were connected to make it. The coupling element includes a visual indication of the end of a rod element and the junction with the next rod. Further disclosed is a method for manufacturing the learning rod educational toy. Optionally the coupling element can be formed of plastic.

Patent US2901839 (HUFF) discloses an educational device which may be utilized in the teaching of elementary mathematics, such as the multiplication tables to children or others requiring rudimentary mathematical education. A primary object of the invention is the provision of such a device wherein various symbols as for example, numbers and combinations of such numbers are associated with a particular colour, whereby recognition of the colour will assist in the recognition of the symbol or numbers combination, thereby facilitating the determination of the correct response to that particular problem situation.

Patent US7914287 (NGUYEN) wherein Numero Cubes and the Whole Number System are disclosed. In one embodiment, the system may comprise cubes, pegs, magnets, dividers, shafts, and a number placement panel. The shafts may comprise individual marks representing the base ten number system. The system may provide a method of learning mathematics through a cognitively authentic learning experience in constructing and building numbers.

Patent US6758675 (KARABAIC) discloses a kit containing an instructor unit sized for presentation to a group and multiple Child training units both set up to allow

SUBSTITUTE SHEET (RULE 26) students to visually model and relate addition, subtraction, multiplication, and division in primary mathematics. The manipulative units include a plurality of coloured cubes arranged in slots so that the movement of particular cubes from one side of the slots to the other side represents numbers in a mathematical operation. Tally trays of five slots may be removed from the device and hold up to 10 cubes to demonstrate regrouping operations on a mat.

Patent US5137452 (POLLOCK) discloses a Base-ten blocks apparatus for teaching arithmetic to children, in which each block (19) has a projecting boss (27) with curved (bowed-out) sides (29) and an aperture (33) with straight sides (35), so that blocks (19) can be securely joined together to form multiples of units. A row of integral blocks (37) has common wall thicknesses (42) between adjacent blocks equal to twice the thickness of the end wall (45) of the row so that the row can be correctly mated with a row of single blocks or end-to-end rows of shorter blocks. Integral rows (37) of ten blocks each have two end bosses (41 ) for joining to other rows (37) to make flats (47) of one hundred units. Each flat has four bosses (51 ) for joining to other flats (47) to make a cube of one thousand units. The blocks have one colour for units, a different colour for rows of tens, a different colour for flats of one hundred, and a still different colour for cubes of one thousand. The blocks can be used to teach addition, multiplication, subtraction, division, etc., to children.

The prior art therefore shows that there is a need for a more simplified apparatus for the teaching and therefore the learning of counting and mathematics by presenting each unit within a given number very clearly as groupings of ones. In this way ten is not only seen as a separate unit, rather it is also clearly displayed as ten ones. Also due to the use of the hundred square and ten square, one hundred, as well as being a complete unit is also presented as a grouping of 10 groups of ten ones. In this way it demonstrates with clarity that one hundred is the same as 100 ones.

A further major difference can be seen when using counting cubes for the four operations of addition, subtraction, multiplication and division. Because it abolishes the fixed units of ten and hundred by replacing them with removable ones cubes, the crossing of the tens boundary can now be completed without the need for the complicated and confusing exchange of one set of units for another, to be fully explained.

The present invention aims to provide an improved counting apparatus by which the above features can be used.

SUBSTITUTE SHEET (RULE 26) Summary of The Invention

According to the present invention there is provided apparatus called Counting Cubes which is presented as a system which offers a significant improvement to base ten resources currently available. It is likely that some form of base ten resource can be found in every school where it has been a useful tool to aid children in their understanding of place value within number. Although they are produced in a variety of subtly different designs, what is common to all is that they employ three distinct components: the hundred square, the tens rod and the ones cube. In addition to helping a child identify the value of the digits in a given number, they are also used to demonstrate, as a visual representation, what is taking place when we employ the four operations of addition, subtraction, multiplication and division.

Place value: Traditional base ten designs encourage children to think of numbers in terms of hundreds, tens and ones. For example, the number 254 is composed of two hundreds, five tens and four ones.

A potential problem with this way of presenting a number is that some children come to a limited understanding of how the number is made. It is possible that they become so focussed on tens and hundreds that they lose sight of the fact that the units of ten and hundred are made by grouping ones. They may correctly recognise that the digit 4 in the number 254 represents 4 units of one, but struggle to recognise that there are 254 ones in total within the number.

This apparatus and method has been developed as a plurality of interlocking and grouping components to overcome this issue. It does this by presenting numbers very clearly as groupings of ones. The unit one is still represented by a cube (Figure 1 ). The unit ten employs the ten carrier (Figure 2). This represents the unit ten when it is filled with ones cubes (Figure 3) and is a rectangular tray with four shallow sides and a bottom side. The unit one hundred employs the hundred carrier (Figure 4). This represents 100 when it is filled with 10 fully loaded ten carriers (Figure 5). In this way the unit ten is clearly displayed as being composed of ten ones. The hundred carrier is a square tray with four shallow sides and a bottom side. Similarly, the unit one hundred is presented as a grouping of 10 units of ten and 100 units of one. It demonstrates with clarity that one hundred is the same as 10 tens and 100 ones.

A child is able to see how many total units of one, ten or a hundred there are in any given number

Counting: A child can practice their one-to-one correlation, placing one cube (Figure 1 ) at a time into a ten carrier (Figure 2) and counting in ascending order as they do so.

SUBSTITUTE SHEET (RULE 26) The ten carrier keeps the process neat by not allowing the cubes to scatter and it also makes obvious when ten has been reached, as the tray will be full of cubes (Figure 3).

Where traditional base ten equipment would now require the removal of the ten ones cubes in order to replace them with a ten rod (a process that is as confusing as it is prone to error), this design offers the opportunity to simply place the full ten carrier into the tens column. This process, as well as simplifying the operation, further emphasises the fact that the number ten, as well as being a complete unit, is made by grouping ten ones. If counting is to continue beyond ten, a second ten carrier in the ones column can now be employed as the child continues counting through the teens and on to twenty.

This same process also applies when counting beyond 100. As fully loaded ten carriers (Figure 3) are deposited into a hundred carrier (Figure 4), we see the number increasing by ten with the addition of each carrier. Again; it is clear when 100 is reached as the hundred carrier is now full (Figure 5). Then, rather than exchanging 10 tens rods for a hundred square, as required with previous models, simply slide the full hundred carrier into the hundreds column.

This new design of apparatus allows a child to focus on the process of counting without the interruption caused by the need to exchange pieces of equipment and the associated risks of error involved.

Adding: Another very common problem with base ten equipment in its current form is encountered when children use it for addition. As is often seen, in order to cross a tens boundary, a complicated process of removing ten ones cubes to exchange for one tens rod or removing 10 tens rods and exchanging them for a one hundred square is rendered necessary due to the fixed units of ten and hundred. This totally unnecessary process confuses many children and is fraught with many opportunities for error caused by miscounting. The new design removes this risk of error due to the units of 10 and 100 no longer being fixed but rather being composed of ones. The crossing of the tens boundary can now be completed without the need to exchange of one set of units for another.

For example, when asking a child to solve the problem 27 + 18, the numbers can be displayed in columns, one above the other, using full ten carriers (Figure 3) to represent the units of ten in each number and partially filled ten carriers to represent the units of one in each number.

The top row will contain 2 full ten carriers in the tens column (2 units of ten) and 7 cubes in the ones column (7 units of one). The bottom row will contain 1 full ten carrier in the tens column (1 unit of ten) and 8 cubes in the ones column (8 units of one).

We teach children to start with the lowest value column, which in this instance is the Ones column. The child now combines (adds) the ones in the ones column by transferring cubes from one ten carrier to another until one carrier is full. This will

SUBSTITUTE SHEET (RULE 26) result in one full carrier plus 5 remaining in the second. The full Ten carrier is now placed in the Tens column leaving the five remaining cubes in place in the ones column. The child is now ready to combine the digits in the Tens column. They do this by collecting together the full ten carriers into one group. This will result in 3 full carriers plus the one they have brought across from the ones column.

The tens column now contains 4 ten carriers each containing ten cubes and the ones column contains 5 remaining cubes. They have 4 units of ten and 5 units of one. The child has demonstrated that the sum of 27+18 is 45.

Subtraction: Using current models of base ten equipment to illustrate subtraction has often been a complicated and frustrating process due to the need to exchange one representation of a value for another. Once again it is demonstrated how we are able to use this new design to execute this process relatively easily. For example, the cubes can be used to solve the calculation 32 - 17.

The number 32 can be displayed as 3 full ten carriers to represent the three units of 10. A ten carrier containing two cubes represents the two units of one. Once again, we start with the ones column as this represents the lowest value column. This requires the child to subtract seven ones. Traditional base ten equipment presents us with a problem, as there are not enough ones cubes to perform the operation. This requires the child to exchange a tens rod for ten extra ones cubes in order to complete the subtraction.

However, the new design clearly shows that there are plenty of ones available - they are simply in the tens column. The child is therefore able to slide a fully loaded ten carrier from the tens column into the ones column making 12 ones available. They are now able to subtract the 7 ones required by the calculation.

This now leaves 2 fully loaded Ten carriers in the tens column plus 5 ones in the ones column. They are now required to subtract from the tens column. The equation asks them to subtract one ten, which they are now able to do leaving one full Ten carrier in place. They now have one full ten carrier in the tens column and 5 ones in the ones column. They have 1 unit of ten and 5 units of one. With relative ease they have shown that 32 - 17 = 15

Multiplication: The apparatus can also be used to significantly improve the way base ten resources are used to demonstrate multiplication.

This is illustrated in terms of multiple addition. 24 multiplied by 5 can be seen as 24+24+24+24+24.

With the increase in the number of units being used comes an increase in the opportunity for miscounting when using current base ten designs due to the need to remove and exchange one group of units for another.

SUBSTITUTE SHEET (RULE 26) As has already been demonstrated, the redesign completely removes this risk as children use the ten carriers and hundred carriers to quickly and easily arrange the individual cubes into groups of ten, and tens into groups of one hundred.

Division: Using current base ten designs to illustrate division is a complicated process once again involving the removal of one unit in order to exchange it and represent it as a collection of alternative units. For example, to demonstrate the division of 104 by 4: Using current designs a child is unable to divide the one hundred due to it being a fixed square. This therefore requires the removal of the hundred square in exchange for 10 tens rods.

The child is now able to divide the ten rods into four groups of two. Having 2 rods remaining, which they are unable to divide into four, they need to remove them and exchange them for 20 cubes, giving them 24 cubes in total. These cubes can now be divided equally among the groups, giving 6 cubes in each group.

104 divided by 4 results in the quotient of 26. The new design renders obsolete the need to remove hundreds and tens in order to execute the division. Due to the hundred carrier containing ten fully loaded ten carriers, The hundred can be easily divided into four groups of two tens by simply removing each ten carrier in turn.

Similarly, a child no longer needs to remove two tens which remain and carefully count out 20 ones in exchange. They are now able to remove the ones cubes from the ten carriers and divide them equally between the groups. This new design offers a unique approach to how base ten equipment can be used to demonstrate the value of any given number and significantly improves a child’s understanding of the four operations of addition, subtraction, multiplication and division. Trials have shown that the number of mistakes caused by the previous need to exchange one fixed unit for another have been totally eradicated.

In this respect, before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of also being practiced and carried out in a number of various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting.

As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for the designing of other structures, methods and systems for carrying out the several purposes of the present invention. It is important, therefore, that the claims be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the present invention.

SUBSTITUTE SHEET (RULE 26) Further, the purpose of the foregoing abstract is to enable the Patent Office and the public generally, and especially the scientists, engineers and practitioners in the art who are not familiar with patent or legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The abstract is neither intended to define the invention of the application, which is measured by the claims, nor is it intended to be limiting as to the scope of the invention in any way.

It is therefore an object of the present invention to provide a new and improved apparatus for teaching place value, counting and mathematical operations which has all the advantages of the prior art apparatus and none of the disadvantages.

It is another object of the present invention to provide a new apparatus for teaching place value, counting and mathematical operations which may be easily and efficiently manufactured and marketed.

It is a further object of the present invention to provide a new and improved apparatus for teaching place value, counting and mathematical operations which is of durable and reliable construction.

An even further object of the present invention is to provide a new and improved apparatus for teaching place value, counting and mathematical operations which is susceptible of a low cost of manufacture with regard to both materials and labour, and which accordingly is then susceptible of low prices of sale to the consuming public, thereby making such a product available to the buying public.

Still yet another object of the present invention is to provide a new and improved apparatus for teaching place value, counting and mathematical operations which provides in the apparatuses and methods of the prior art some of the advantages thereof, while simultaneously overcoming some of the disadvantages normally associated therewith.

These together with other objects of the invention, along with the various features of novelty which characterize the invention, are pointed out with particularity in the claims annexed to and forming a part of this disclosure. For a better understanding of the invention, its operating advantages and the specific objects attained by its uses, reference should be had to the accompanying drawings and detailed descriptive matter in which there is illustrated preferred embodiments of the invention.

SUBSTITUTE SHEET (RULE 26) Brief Description of Figures

Figure 1 shows a dimensional view of the unit of one cube, cube representing the unit of one.

Figure 2 shows a dimensional view of the ten carrier.

Figure 3 shows a dimensional view of the hundred carrier.

Figure 4 shows a dimensional view of the ten carrier representing the unit of ten with a row ten ones cubes installed.

Figure 5 shows a dimensional view of the loaded hundred carrier representing the unit of one hundred, with multiple rows of filled ten carriers installed.

SUBSTITUTE SHEET (RULE 26) Detailed Description of Figures

A typical embodiment of the device or apparatus for teaching counting is shown in the accompanying Figures. With Figure 1 showing the apparatus of the unit of one cube 1 , with the one cube representing the unit of one.

Figure 2 shows the ten carrier apparatus, with the ten carrier 2 representing the unit of ten when loaded with ten ones units.

Figure 3 shows a dimensional view of the hundred carrier 3, the hundred carrier representing the unit of one hundred when loaded with ten fully loaded ten Carriers.

Figure 4 shows a dimensional view of the loaded ten carrier representing the unit of ten, unit of one cube 1 and the ten Carrier 2.

Figure 5 shows a dimensional view of the loaded hundred carrier 3 representing the unit of one hundred, made up with ten individual ten carriers 2 installed within it, each filled with ten rows of unit one cubes 1.

SUBSTITUTE SHEET (RULE 26)

Claims

1 ) An apparatus for teaching counting and mathematics comprising; a plurality of interlocking components including a unit of one cube, a ten carrier and a hundred carrier.

2) An apparatus for teaching counting and mathematics according to claim 1 wherein a ten carrier is a rectangular tray with four shallow sides and a bottom side.

3) An apparatus for teaching counting and mathematics according to claim 1 wherein a hundred carrier is a square tray with four shallow sides and a bottom side.

4) An apparatus for teaching counting and mathematics according to claim 1 wherein said apparatus presents numbers as groupings of ones.

5) An apparatus for teaching counting and mathematics according to claim 1 wherein ten carrier represents the unit of ten when loaded with ten individual one units.

6) An apparatus for teaching counting and mathematics according to claim 1 wherein the hundred carrier represents the unit of one hundred when loaded with ten fully loaded ten carriers.

SUBSTITUTE SHEET (RULE 26)