Each category is then grouped together and counted. The large number cards are retrieved to show the new larger quantity. **"When we take the same number two or more times, we call that multiplication."**

Collective Exercise - Static Multiplication (completed)

Collective Exercise - Static Multiplication (laying out the quantities)

When presenting multiplication, each of the children are bringing the **same quantity** to the mat (i.e. 2134 x 2 Two children each bring 2134 worth of beads to the mat). Instead of dumping the beads into the basket to give the sensorial impression of combining the quantities (as was done in addition), the quantities are laid out to give the **sensorial impression of the same quantity taken 'x' number of times** (in this example, 2 times).

**Question**:

I am a young mother with three children under the age of four. My 3 year old is in preschool and is struggling, especially with mathematical concepts. Her preschool curriculum is heavily based on work sheets which I think is part of the problem. I suspect she may not be able to relate math to her day to day activities. How can I help her? I work full time so I am only home in the evening and we have virtually no extra resources to buy all the fancy child learning materials.**Answer**:

This is a common problem among children who attend programs that focus heavily on 'paperwork'. At a young age, **children best absorb concepts through the manipulation of objects, every day conversations, and through real life experiences**. The kinds of experiences required to truly internalize mathematical concepts are hard to capture on paper. Therefore, children who are taught math concepts via paperwork (which tend to be very abstract), have difficulty absorbing the concepts and being able to demonstrate their knowledge of them.

Most **mathematical concepts can be applied during everyday life using common household objects and simple conversation**. While cooking, grocery shopping, putting toys away, and doing laundry, you can apply the concepts of numbers (symbols and quantities, easy addition/multiplication/subtraction/division, currency, fractions, geometry, etc). You don't have to give an entire 'lesson' each time, but every day conversations can hold some mathematical information that will slowly build a very strong understanding and foundation in a child's mind.

Some examples:

1) **Geometry**: Geometric shapes and solids can be found everywhere: inside your home, out in the garden, the shopping mall, the library, all over the place! The ring on your finger is a circle, a slice of pizza can be triangle, a ball is a sphere, a square box is a cube, a church steeple is a square based pyramid, a stop sign is an octagon, etc. You can talk about how many sides a square has, count the sides of a triangle, walk in a circle to determine it doesn't have any sides!

2) **Counting quantities** while grocery shopping: can you count 8 apples as I put them in to the bag?, lets count how many eggs are in the carton, lets count how many groceries we're buying as we put them on the check-out counter.

3) **Addition**: We each need a banana for lunch tomorrow - if there are 4 people in our family, how many bananas do we need to buy? One for Mommy, one for Daddy, one for Ben, and one for you! Let's count how many bananas there are all together.

4) **Division**: This bag of dinner rolls has 6 rolls in it. How many can each of us have? Show how to give each person 1 roll at a time until all rolls are divided equally.

5) **Fractions**: cutting a pizza in half, or quarters, eating 1/2 a pizza, eating 3/4 of a pizza. Slicing a cake or pie - it's all early fraction work that can be conveyed through the actions of cutting, eating, and simple conversations.

6) **Currency**: It's never to early to start talking about money! Start off simple with learning the names of each coin. Build on that with how many of each coin it takes to make a dollar. Talk about money when purchasing items. Teach them how to say the amount of money correctly. Show your child how to watch the register for the correct prices. Allow them to give the money to the cashier, and count back the change with them when they receive it.

7) Food prep, cooking, baking, setting the table are all other ways to talk about math. From counting, to measuring, adding more ingredients to make recipes larger, counting plates and cutlery, **a kitchen holds numerous ways to incorporate math**.

There are countless ways in which math is woven in to our every day life activities. It's just a matter of allowing the children to participate in these experiences. **Mathematical concepts that are concrete and applied directly to the child and their own life experiences are the best lessons a child will ever learn.**

**Question:**Your Math Teaching Manual is directing me to teach multiplication before subtraction. Why? **Answer:** For those of you who are not familiar with Montessori, it seems logical to present the process of addition and then move on to subtraction .... it's the way children have been taught in traditional schools for decades.

In Montessori, the Collective Exercises (using the Golden Beads on the mat) give the child the **sensorial impression** of addition, multiplication, subtraction and division, and visually makes clear the **relationships between the operations**.

When presenting addition with a group of children, they are all asked to bring a different quantity of golden beads to the mat. The golden beads are counted, the small number cards are placed on the mat, then the golden beads from each child are 'dumped' in to a basket to show the **combining of the beads**. The total quantity is then counted out on the mat by the children and the large number cards are retrieved to show the new larger quantity. We explain that **"when we take two or more quantities and put them together to make one larger quantity, we call that addition"**.

As you can see, it's logical that multiplication would be the next operation given after addition as it involves the same process. The end result of both addition and multiplication is a larger quantity. After both of these concepts are firmly rooted in the child, subtraction can be introduced.

Collective Exercise - Static Addition (completed)