Elementary Montessori classrooms are unique in the way that they have some of the most remarkable mathematical materials. The Cubing Material is one of those materials that are intriguing and enticing for learners. It is used to represent algebraic equations that are converted into arithmetic equations. It consists of 1 cube for each number from 1-9 and 27 corresponding squares for each cube. The material is color-coded based on the Bead Stairs (1-red, 2-green, 3, pink, 4-yellow, 5-light blue, 6-purple, 7-white, 8-brown, 9-dark blue). This color coding ensures that learners intuitively know the size of the parts they are working on. For instance, the light blue square corresponds to the number 5; therefore, a square is 5 cm. x 5 cm. x 1 cm. These characteristics of the Cubing Material accelerate arithmetic computation.
When used in conjunction with our newly created Cubing Material Task Cards, children will have opportunities to utilize the material after they have received formal presentations. In this post, we would like to share the sequence of our Task Cards and demonstrate how you can increase your learners’ interactions with the Montessori Cubing Material – Complete Set.
Materials
- Cubing Material – Complete Set (Value Line)
- Cubing Material – Complete Set (Premium Quality)
- Cubing Material (Task Cards)
- Cubing Material
Cubing Material with Task Cards
The Task Cards are created for the sole purpose to offer extension work to Montessori learners. They are placed on the shelf near the Cubing Material and are recommended for use after learners have received formal presentations, which can take months. You may recommend your learners use specific sections only as you introduce specific concepts. Our Task Cards contain a control for errors on the back (pictorial or written) which makes your learners more autonomous.
Section 1 – Calculating the Powers
In this section, children reacquaint themselves with the material. They are required to calculate a specific power of a given number by gathering the physical material and writing their answer in their notebook.
Section 2 – Constructing Successive Cubes
In this section, children are given a specific cube to work with and are invited to construct a successive cube. For instance, if the cube is 5, a learner will attempt to build a 6 cube by using additional 5 squares and perhaps unit squares (1) if no colored sticks are available. A colorful visual control of errors can be found on the back of each card. Once the cube is constructed, children write the arithmetic equation in their notebooks and solve it to ensure that the equation is balanced.
Section 3 – Constructing Non-Successive Cubes
In this section, children will work with more complex cube structures that involve more parts; therefore, children are to solve more complex equations.
Section 4 – Using the Algebraic Binomial Cubing Material
In this section, children use the algebraic binomial cubing material to calculate a given cube. This method helps children work with the expanded notation of a cube. For instance, children are asked to calculate the square of 12. They will need to use an algebraic formula: (a + b)3 =a3 + 3a2b + 3b2a + b3. To get a value for a and b, learners use expanded notation so 12 is (10 + 2), giving a = 10 and b = 2. Now, learners can calculate the formula and find the numerical value of a cube. Learners use their prior knowledge from working with the Binomial Cube.
Section 5 – Using the Algebraic Trinomial Cubing Material
In this section, learners use the algebraic trinomial cubing material to calculate a given cube. Learners use larger number that they expand to calculate the volume of the cube. For instance 125 is expanded to (100 + 20 + 5) . Learners use the algebraic formula (a + b + c)3 = a3 + b3 + c3 + 3a2c + 3b2a + 3c2a + 3c2a + 6abc to calculate a cube of 125. This method had been learned using the Trinomial Cube.
Section 6 – Cubing Binomial and Trinomial Cubes
In this section, children are invited to use the cubing material to “cube” a binomial and a trinomial. Binomial cubes have 2 terms (a + b)3, while trinomial cubes have 3 terms (a + b + c)3.
Cubing Binomial and Trinomial Cubes
This summarizes how your learners’ experience with the Cubing Material can be optimized using our Task Cards. Children will have long-lasting visual impressions when abstractly working on algebra, thanks to the Cubing Material! We would like to invite you to explore more of our Montessori supplemental materials on our website at www.alisonsmontessori.com!
