Montessori Linear Counting with the Hundred Chain and Thousand Chain

Table of Contents

What is the Linear Counting?
Introduction to the Hundred Chain
Introduction to the Thousand Chain
More About the Arrow Labels

What is the Linear Counting?

In Montessori, linear counting refers to the sequential counting of numbers from one to a thousand and beyond. This linear progression lays the foundation for understanding numerical patterns and relationships, preparing children for more advanced mathematical concepts.

Introduction to the Hundred Chain

The Hundred Chain is a key Montessori material used to introduce linear counting. It consists of a chain of beads, each representing a number from 1 to 100. The Hundred Chain enables children to see and feel the numerical progression in a concrete and visual way. Children count the beads, laying the foundation for numeral recognition and understanding of quantity.

Material

– Small mat for the arrows and a long mat for the bead chain
– Hundred chain of 10 ten-bars and 1 hundred-square
– Arrows with the number labels (1s, 10s, and 100 in varying color & width per category) in a container

Check out our printable DIY of the arrows HERE.

Prerequisite

– Teens and Tens

Control of Error

– In the counting and in the arrows

Direct Aims

This gives the child the opportunity to apply his knowledge of the traditional names for the combinations of hundreds, tens, and units from 1-100.

Indirect Aims

This prepares the child for the multiplication tables and for squaring.

Presentation (Hundred Chain)

1. Invite the child and show the materials and the two mats needed for this work.
2. Bring the materials to a work space that allows spreading the mat so the child will be able to read the arrows correctly.
3. Unroll the mats and invite the child to come to the bead cabinet, showing how to carry the bead chain, draped over both palms, then laying it horizontally on the mat.
4. Place the hundred square on the top left of the long mat.
5. Fold the chain where the ten-bars become side-by-side, turning into a square.
6. Place the hundred-square next to it and then on top of it, showing they are the same.
7. Remove the hundred-square then open the hundred chain slowly, pulling it into a straight line. The child sees it is made up of 10 ten-bars.
8. Introduce the arrow labels. Lay them out on the smaller mat, keeping the categories separate.
9. Say, “We’ll count each bead in this chain. When we count, we must touch each bead.”
10. Count and place the appropriate arrow labels under the first 9 beads.
11. When you get to 10, place the blue arrow label with the number 10.
12. When you count 11, ask, “Do we have an arrow for 11?” (No). Say, “Let’s keep counting anyway,”
13. Count up to 20. “Do we have a 20 arrow?” (Yes). Then place it under the 20th bead.
14. Count up to 100, placing the blue arrows under the 30, 40, 50 beads and so on. On the 100th, place the red arrow label with 100.
15. Place the hundred square at the end of the chain, next to the red arrow label.
16. Read the numbers on the arrows forward and backward with the child, counting by 10s.
17. Invite the child to do the activity on her own and then show how to put them back.

Introduction to the Thousand Chain

Building on the concepts learned with the Hundred Chain, the Thousand Chain is introduced. This chain represents numbers from 101 to 1,000, allowing children to explore linear counting on a larger scale. The Thousand Chain extends the child’s understanding of numerical patterns and introduces the concept of the thousands place.

Material

– Small mat for the arrows, a medium mat for the hundred chain, and a long mat for the thousand chain
– Thousand chain of 100 ten-bars, 10 hundred-squares, hundred chain, 1 thousand cube
– Arrows with the number labels (1s, 10s, multiples of 10s that are not hundreds, 100s, and 1000 in varying color & width per category) in a container

Check out our printable DIY of the arrows HERE.

Prerequisite

– Teens and Tens
– Hundred chain

Control of Error

– In the counting and in the arrows

Direct Aims

This shows the child the striking difference between the hundred chain and thousand chain, and promotes his knowledge of the traditional names for the combinations of hundreds, tens, and units from 1-1000.

Indirect Aims

This prepares the child for the multiplication tables and for squaring.

Presentation (Thousand Chain)

1. Invite the child and show the materials and the three mats needed for this work.
2. Bring the materials to a work space that allows spreading the mat (approximately 12 meters long) so the child will not need to walk over the material but work on it from left to right.
3. Unroll the mat and place the materials on their respective mats.
4. Show the thousand chain from the bead cabinet, pointing out how every large ring on the chain is on a hook. Show how to lift the chain one section at a time, hanging it vertically from your hand.
5. Lay the thousand chain from the left side of the long mat, straightening it so that each row looks like a 100- chain. Make sure to remove the kinks and overlaps.
6. Fold the thousand chain into 10 hundred-squares, leaving a small space in between.
7. Place each hundred square next to each folded square and then on top of them, showing they are the same.
8. Remove the hundred-squares, stacking them to form a cube, then compare it to the 1000 cube side-by-side. Then slowly stretch the thousand chain again, into one long line.
9. Introduce the arrow labels. Lay them out on the smaller mat, keeping the categories separate.
10. Count and place the appropriate arrow labels up to the first 100, similar with the hundred chain.
11. Place the hundred square at the end of the chain, next to the red arrow label of 100.
12. Continue up to 1000, placing the square next to the 100s arrows, and the thousand cube at the end.
13. Read the numbers on the arrows forward and backward with the child, counting by 10s.
14. Invite the child to do the activity on her own and then show how to put the arrows and the chain.
15. Pick up the first large ring placing it over your hand; skip the second and pick up the third.
16. Continue to pick up every other ring. Then, place the large rings on your hand on the hooks.

More About the Arrow Labels

Each arrow label corresponds to a specific number in the chain, and the numerals are written on the labels in sequence. For example, as you count along the Hundred Chain, you will encounter an arrow label with the number “10,” indicating that you have reached the 10th bead. This labeling continues throughout the chain, guiding children as they count from 1 to 100.

Similar to the Hundred Chain, the Thousand Chain features arrow labels, but these labels extend from 1 to 1,000, representing the numbers in the chain from 1 to 1,000. These arrow labels provide children with a visual and numerical reference point as they work with the material

You can make your own with our printable below:

GET the PRINTABLE ARROWS here

Montessori Linear Counting with the Hundred Chain and Thousand Chain

What is the Linear Counting?

Introduction to the Hundred Chain

Material

Prerequisite

Control of Error

Direct Aims

Indirect Aims

Presentation (Hundred Chain)

Introduction to the Thousand Chain

Material

Prerequisite

Control of Error

Direct Aims

Indirect Aims

Presentation (Thousand Chain)

More About the Arrow Labels

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