Addition

This activity is a variation of the Montessori “Stamp Game”. A Montessori education progresses gradually from the concrete to the abstract, this activity being a particularly clever example of that transition.  Maria Montessori placed high value on beauty of the environment and learning tools, with a preference for natural materials. Sounds like Flockmen to a tee!

Using Flockmen for this game eliminates the need for specialised equipment. Simply stick on the coloured unit stickers and voila! A concrete tool to introduce the abstract idea that just a few objects can be used to represent and manipulate large numbers up to 1000.

What you will need:

• Flockmen Total 31 (or 47 if continuing with Dynamic Subtraction)
  • 10pcs Stickered Green 1s (or 18 for D.Sub)
  • 10pcs Stickered Red 10s (or 18 for D.Sub)
  • 10pcs Stickered Blue 100s
  • 1pcs Stickered Yellow 1000
• Grid Paper
• Pencil
• Optional: Flockmen Worksheets

Note Well: Whilst the Montessori method uses the same green for the 1000s unit we chose to use yellow to eliminate confusion between the pieces. 

Step 1: Introduce the concept*

IMPORTANT: This activity is dealing in the abstract. We are using a manipulative of a single size to represent many different values (1s, 10s, 100s, 1000s). This is no longer one-to-one correlation, or even matching sizes i.e. this large block is 1000 compared to this small 1s block. It may be your student’s first foray into the abstract of mathematics. Take the concept at your student’s own speed. The student should already have an understanding of unit value before tackling this activity.

Show the student the stickered Flockmen and ask them what they notice about them. Discuss what the stickers might mean and explain how we are going to use them to make big numbers.  (You may like to use the idea of pretending there are, for example, 10 Flockmen lined up behind one red 10 Flockman etc.)

 Demonstrate how to make a large number by selecting several Flockmen. For example 1345, select the 5 green, 4 red, 3 blue, and 1 yellow. Always begin with the ones value on the right and line the Flockmen into columns corresponding to the unit value. Demonstrate how to write the number, preferably using grid paper.

Invite the student to create their own numbers, writing them down on the grid paper and selecting the correct number of each unit Flockmen.

When your student has a solid grasp of using the Flockmen materials to represent large numbers you can introduce addition.

Step 2: Static Addition

Static Addition refers to simple concrete addition, in which there is no need for trading (carrying) units between tens and ones etc. Static Addition is able to occur when the sum of two corresponding place values is less than 10. (See Dynamic Addition for a comparison.)

Start with one number, such as 1345 as above (we will call this the initial number). Write the number on the grid paper and lay out the correct Flockmen formation.

Choose another number that will allow static addition, such as 652 (we will call this the second number).

Write this second number underneath the initial number on the grid paper, demonstrating correct layout and use of mathematical signs. Leaving a line between the numbers and the answer allows for a smoother transition to Dynamic Addition.

Ask the student to pass you the correct amount of Flockmen for the second number. As they pass them to you, count them out, arranging them in columns under the initial set of Flockmen, leaving a gap or placing a ruler, between the two layouts (this provides a visual reminder to check the sum.)

Add each column by counting the amount of Flockmen and recording the result of each on the grid paper. Read your final answer aloud. Invite the student to check your work, by counting the Flockmen[1].

Step 3: Practice Static Addition Sums

Do as many sums together, as is appropriate to your student. When they are ready allow them to practice sums independently. You may choose to encourage the student to come up with the sums on their own, or use the worksheet provided to ensure they stay with Static Addition to begin with.

Step 4: Dynamic Addition

The need for Dynamic Addition may arise quickly if you allow your child to come up with some addition sums for themselves.

Dynamic Addition is used to describe sums that require trading (carrying) of units between place values.  For example to add 637 and 124, we begin by adding the units 7 + 4 = 11. Eleven contains 1 ten and 1 unit, so instead of simply writing “11” in our unit value place, we will need to “carry” or trade to the tens. Work with the Montessori golden beads will have taught the child this concept. Now we are applying it to addition. We will continue with the above example.

Write the initial number (637) on your grid paper and ask your student to layout the correct amount of Flockmen.

Write the second number (124) and symbols to complete the sum on your grid paper. Ask your student to layout the Flockmen for the second number.

Count your unit Flockmen (11). You may like to ask the student what we should do with this number and help them to problem solve. Or simply point out that 11 is more than 10, so we can swap/trade 10 of our green unit Flockmen for 1 red 10s Flockmen.

Put the new red Flockman in the correct column in your layout, and write the “1” on the grid paper again in the correct column. You can point out we write it the same as we layout the Flockmen!

Ask the student to count the units again and continue with the sum as per Static Addition. Make sure you read your final answer aloud, and encourage checking the answer.

Step 5: Practice Dynamic Addition Sums

Do as many sums together, as is appropriate to your student, until they are ready to practice the sums independently. Now they can do Dynamic Addition it is simple for them to make up their own sums to practice too. An additional worksheet is provided for guidance. 

Once your student has a firm grasp of completing additions in this manner you can move on to Subtraction (to be described in the Part 2)

 

 

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References

[1] Early modeling and encouraging checking of an answer will produce a habit for success in future mathematics.

* We have streamlined the usual 3 period lesson style used by Montessori educators to guide a child. You may like to research this method more here (http://montessoritraining.blogspot.com.au/2007/09/montessori-method-three-period-lesson.html) and apply it if it suits your situation.