Static & Dynamic Subtraction
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 of 31pcs (or 47pcs if continuing with Dynamic Subtraction)
- Free, printable Flockmen Maths sticker set
- Free, printable Flockmen Maths worksheets
- Attach stickers to your Flockmen
- 10pcs Stickered Green 1s (or 18 for Dynamic Subtraction)
- 10pcs Stickered Blue 10s (or 18 for Dynamic Subtraction)
- 10pcs Stickered Red 100s
- 1pcs Stickered Green, but with number 1000
Step 1: Introduce the concept
This is common for both, the Addition and Subtraction. Feel free to skip if you have a grasp on how to lead your child into it.
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 blue, 3 red, and 1 green. 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 Subtraction
Static Subtraction, much like Static Addition, refers to sums that require no trading (carrying) between units. Static Subtraction is able to occur when each unit of the initial number is a larger numeral than the corresponding unit in the second number.
On the grid paper write a large number, such as 865, and ask the student to layout the correct Flockmen to represent this number.
Write a smaller number underneath the initial number on the grid paper, such as 642, and introduce the subtraction sign. This time we will be taking away/subtracting the second number from the initial number.
Again we start with the ones unit. Take away 2 ones from the 5 Flockmen, place them to one side of your workspace still in a column (to encourage checking). Write the answer, 3, in the correct column on the grid paper. Continue with the 10s and 100s. Read your final answer aloud. Invite the student to check your answer by counting the Flockmen.
Step 3: Practice Static Subtraction Sums
Do as many sums together, as is appropriate to your student, until they are ready to practice the sums independently. You may like to allow the student to come up with the sums on their own, or use the worksheet provided to ensure they stay with Static Subtraction to begin with
Step 4: Dynamic Subtraction
Dynamic Subtraction refers to sums that require trading between units. If your student has been coming up with sums on their own they will likely come across the need for it very quickly. Using the concrete Flockmen is a great tool here, if you skip this concrete step some children will simply try to swap the numerals and end up either in a muddle, or with a hard to break habit that results in an incorrect answer.
Layout the sum 861 – 647 on your grid paper.
Invite the student to layout the correct amount of Flockmen for the initial number. Ask the student how many units are we going to take away? But there are not enough! We will have to trade one of our blue 10s Flockmen for 10 red 1s Flockmen. Put one of the red Flockmen away and place 10 new green Flockmen in the correct column. You can choose to notate the “trade” in units by crossing out the 6 from the tens column and writing a 5 (as we now have 5 blue Flockmen), or simply leave the written sum as it is.
Now take the 7 green Flockmen away from the 11, placing them in a column on the other side of your workspace.
Count the remaining (4) green 1s unit Flockmen, writing the answer in the correct column on your grid paper.
Continue with the rest of the sum. Read the final answer and encourage the student to check the sum.
Step 5: Practice Dynamic Subtraction
Do as many sums together, as is appropriate to your student, until they are ready to practice the sums independently. Allow them to come up with their own sums or use the worksheet provided.
Encourage the student to use the concrete materials for as long as possible. Some students will want to jump into completing the answers “in their heads” as soon as they have grasped the concept, but I stress again that it can be so easy for them to get into the habit of simply swapping the larger and smaller numeral around in their heads. Practicing with the concrete tools helps to firmly establish the correct order of taking away the bottom number from the top number, resulting in a correct answer.
Where to next?
By leading your student through these activities the Flockmen materials you have provided a bridging step between concrete and abstract mathematics. It is such an important step, and worth doing well. Once they have grasped the concepts you can ask if they would like to try without the Flockmen. Once completely proficient you can guide them to larger numbers.