Linear Counting · Math · Montessori Materials

The Red and Blue Rods

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The Red and Blue Rods are a beautiful Montessori material and give such a wonderful concrete representation of the abstract numerals used in counting. Children using this material can physically see and feel the quantity of the numbers 1-10. Even if they can already count to 10 (or even 20) the hands on exploration and manipulation of this material leads them to the internalization of “What is a number?”.

The lessons are described below in the sequence they should be introduced. Introduce one lesson at a time, giving your child opportunities to work with the material on their own or with you until they have mastered that concept and/or you feel they are ready for the next lesson. Always “follow your child”  when deciding when to give a lesson, provide more practice, re-present a lesson, or move on to the next lesson. Working along side your child during the lesson and observing them as they work with the material on their own or with you will give you the cues you need to make those academic decisions.

The Material:

Ten rods measuring in increasing length from 10 cm to 100 cm. The colors alternate red and blue sections in 10 cm lengths to facilitate counting. Each rod is a fixed quantity allowing the child to focus on counting, naming and recognizing a quantity and not building the quantity (yet). It is the first lesson in the Montessori linear counting math sequence.

I purchased the Red and Blue Rods from Adena Montessori. You can also make your own, which I have done as well.

Purpose:

  • To give a concrete representation of the quantity one through ten (not the written numeral).
  • To teach a correlation between the spoken numeral and the quantity when counting.
  • To give a visual comparison between quantities.
  • To teach order, organization, and concentration.

Age:

3-6 years old

The Lessons

The Sensorial Lesson

When you are homeschooling it really isn’t feasible to outfit your home with every material a school would have, nor do you really need to do that. The precursor to the Red and Blue Rods are the Red Rods from the sensorial curriculum in the Montessori classroom. The Red Rods are exactly the same as the Red and Blue Rods sans the blue. The Red Rods are used purely as a sensorial experience: To grade the rods by length from shortest to longest. The control of error is visual, children learn the concept of length and benefit from the concentration and organization the work requires. Children also gain the vocabulary “longest” and “shortest” when doing this work. Rather than purchasing the Red Rods with a limited home budget, or adding another material to a limited  home school space it makes sense to allow children the purely sensorial experience of the Red Rods using the Red and Blue Rods before introducing them to the mathematical use for the material.

First Presentation

  • Get out a large rug or towel.
  • Show your child how to carry each rod with two hands to the rug beginning with the shortest and continuing to the longest. Ask them to bring the “next longest” rod each time.  Arramge the rods on the rug with the longest at the top and the shortest at the bottom. The left end of the rods should be flush with left side of the rug and even with each other.

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  • Draw attention to what you have done saying, “We have put these rods in order from shortest to longest.” You can show pride in work well done saying, “I like our work.” or “Our work is beautiful.” or “We worked really hard on this.” You can ask your child questions to check for understanding, “Show me the longest rod.” “Show me the shortest rod.”
  • When you put the work away start with the longest and continue to the shortest asking your child to carry the “next shortest” rod.
  • Make sure the material is accessible so your child can try it on their own later.

Second Presentation

  • Get out a large rug or towel.
  • Bring out the rods one at a time, but this time arrange them on the rug in mixed order. Make sure the left end of the rods are all flush with the left edge of the rug and even with each other. This will help your child visually to see the length of each rod and choose the appropriate one when rearranging them from longest to shortest.

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  • Ask your child to find the longest rod  and place it at the top of the rug, then search for the next longest and so on until the rods have been rearranged in the proper order from longest to shortest.

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  • You could also do this lesson with two rugs. Lay the rods in mixed order on one rug and arrange them from longest to shortest on the second rug.

* If your child is overwhelmed, simplify the work by limiting the number of rods to grade (maybe 3 or 5) and see if they can successfully grade them before grading all 10 rods. If your child becomes bored, frustrated, or confused just say, “This was fun. Thanks for doing this work with me. Let’s put it away and do it again later.” If your child cannot put the rods in the correct order on their own it means they visually cannot see it. Their ability will improve as they work with the material and this new skill will be gained.

Third Presentation: The Maze

  • Get out two large rugs or towels.
  • Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Move the longest rod to the top of the second rug.
  • Move the next longest rod to the second rug. Begin to create a square by placing the second rod vertically, extending from the end of the first rod down the right side of the rug.

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  • Move the third rod to the rug and form the bottom of the square.

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  • Continue adding rods in decreasing length until you have created a spiral, square maze. Your child can walk between the rods to the center of the maze and out again.

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The Introduction Lesson: Counting 1-10 (quantity only)
  • Get out a large rug or towel.
  • Have your child bring each rod to the rug. Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • You should sit next to your child on his/ her dominant side or you can sit across from your child. Wherever your child sits he/ she should see the longest rod at the top of the rug and the shortest at the bottom.

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  • Move the “one” rod down slightly away from the others and tell your child, “This is one”. With the rod laying on the rug, grasp the one section with your whole hand as you count, “one”. Give your child the opportunity to count the one rod.

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  • Next, move the two rod down slightly away from the others and say, “This is two.” With the rod laying on the rug, grasp each section with your whole hand as you count them from left to right, “One, two.” Give your child the opportunity to count the two rod.

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  • Next, move the three rod down and say, “This is three.” With the rod laying on the rug, grasp each section with your whole hand as you count them from left to right, “One, two, three.” Give your child the opportunity to count the three rod.

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  • Here you should stop and check for understanding. Starting with the most recent rod introduced, the three rod, say, “Can you show me three?” Your child should indicate the three rod. Next say, “Can you show me two?” Your child should indicate the correct rod. Finally say, “Can you show me one?” Your child should indicate the one rod.
  • Check for further understanding by asking your child to supply you with the information. Start with the rod you just finished checking, the one rod, pointing and saying, “What is this?” Your child should answer, “One.” Point at the two rod and say, “What is this?” Your child should answer, “Two.” Point at the three rod and say, “What is this?” Your child should answer, “Three.”
  • If your child answers incorrectly, for example indicates the two rod when you’ve asked them to indicate the three rod say, count it with them then say, “You’ve shown me two.” Or, “This is two.”
  • If your child seems frustrated and un-receptive you can end the lesson with a smile, thank them for working with you, and ask them to help you put the work away until next time. You can give the lesson another day when your child seems ready. If they can give you the correct answers, or seems receptive as you correct any mistakes continue on with the lesson.
  • Introduce rods 4-6 in the same manner as above, saying “This is…”.  Count each section with a whole hand grasp and always allow your child the opportunity to count each rod.
  • After six, stop and check for understanding. First ask the “Show me” question beginning with the most recently introduced, “Show me six…show me five…show me four.
  • Check for further understanding with the “What is this?” question beginning with the last rod checked, “What is this? 4…5…6.
  • Does your child seem frustrated, confused, unable to give the correct answers? You can end the lesson at any time and try again later. Does your child seem engaged, enthusiastic, quick to answer, doesn’t seem to need such direct instruction, they “get it”? Go along with your child, letting them “take the lead” counting and naming the rods. Treat this lesson as a game. Always keep checking for understanding as they explore the material.
  • Continue with 7-10 with, “This is…”, “Show me…”, and “What is this?”
  • Make sure this material is available for your child to do on their own or with you again. Practicing with this material leads to internalizing the concept of 1-10 quantity and rote counting.
The Fetching Lessons

First Presentation: Fetching in sequence from 1-10

  • Get out two large rugs or towels.
  • Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Ask your child to bring the one rod to the second rug. Say, “Let’s see what you’ve brought.” Count the rod with your child.
  • Next, ask your child to bring you the two rod. Say, “Let’s see what you’ve brought.” Count the rod with your child.
  • Continue asking for rods in sequence from three to ten always checking to see what rod has been brought by counting it together. If they bring the incorrect rod, count it together, simply state what they’ve brought, then ask them again for the rod you originally asked for. You can leave the incorrect rod on the rug with a space for the correct rod(s). You have corrected the mistake by counting what they have brought and giving them another opportunity to bring the correct rod without the frustration or confusion that may result from bringing a rod back to the original rug to find where it belongs and then searching for the correct rod.

Second Presentation: Fetching from sequence in mixed order.

  • Get out two large rugs or towels.
  • Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Ask your child to bring a rod out of sequence, for example, five.
  • Count the rod with your child. If it is correct leave the rod on the rug. If it is not correct you can simply state what they’ve brought, leave it on the rug, then repeat your original request. You correct the mistake by counting what they’ve brought and asking them to find the one you’ve asked for without undue attention to the mistake.
  • Continue asking for rods out of sequence. As they are brought to the second rug, count them and place them in their correct sequence.

Third Presentation: Fetching from mixed order in mixed order.

  • Get out two large rugs or towels.
  • Arrange the rods on the rug in mixed order, the left end of the rods should be flush with the left side of the rug and even with each other.

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  • Ask your child to bring you a rod out of sequence, for example, five.
  • Count the rod with your child. If it is correct leave the rod on the rug. If it is not correct you can simply state what they’ve brought, leave it on the rug, then repeat your original request. You correct the mistake by counting what they’ve brought and asking them to find the one you’ve asked for without undue attention to the mistake.
  • Continue asking for rods out of sequence. As they are brought to the second rug, count them and place them in their correct sequence.

Fourth Presentation: Larger or Smaller

  • Get out two large rugs or towels.
  • Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Ask your child to bring you a rod out of sequence, for example, five.
  • Next, ask them to bring you a rod larger than five. They can choose any rod to bring as long as it is larger than than the number you’ve asked for (in this example, 5). Compare the five rod with the rod your child has brought by placing them next to each other, the left ends even with each other. Visually they should see that the rod they brought is larger than the five rod.  Count the rod they have brought. Say, “____is larger than five.” Put the larger rod back in sequence on the first rug.
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“Eight is larger than five.”
  • Next, ask them to bring you a rod smaller than five. Go through the same process to check their number visually and by counting. Say, “____is smaller than five.” Put the smaller rod back in sequence on the first rug.
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“Two is smaller than five.”
  • Put the five rod back in sequence on the first rug. Ask your child to bring you a different rod out of sequence and have them bring rods larger and smaller as before checking visually, counting what they bring, and stating, “____is larger/smaller than ____.
  • VARIATION: You can switch roles with your child. They can ask you to bring a number rod of their choosing, then have your child ask you to choose and bring rods that are larger and smaller. They can visually check and count what you bring and state, “____is larger/smaller than____.
  • OPTIONAL: You can have your child find several rods larger than the chosen number rod before finding several rods smaller than the chosen number rod.

Fifth Presentation: One More or Less

  • Get out two large rugs or towels.
  • Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Ask your child to bring you a rod out of sequence, for example, five.
  • Next, ask your child to bring you one more than five. They should bring you the six rod. Compare it visually, then count it. Say, “Six is one more than five.”
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“Six is one more than five.”
  • Next, ask your child to bring you one less than five. They should bring you the four rod. Compare it visually, then count it. Say, “Four is one less than five.”
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“Four is one less than five.”
  • OPTIONAL: You can use the “one” rod to help your child visually see that six is one more than five by placing it at the end of the five rod so it is the same length as the six rod. Likewise, you can use the “one” rod to visually help your child see that four is one less than five by placing it at the end of the four rod so it is the same length as the five rod.
  • Put all the rods back in sequence on the first rug. Ask your child to bring you another rod of your choosing out of sequence. Continue as before asking for one more/one less than the number rod on the rug. Always compare visually, count, then state, “____is one more/less than____.”

*EXTENSION: You can extend this lesson by asking your child for 2 more than and 2 less than the number rod on the rug. How about 3 more and less than the number rod?

The Greater than, Less than Lesson
  • Get out two large rugs or towels.
  • Arrange the rods on one rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Ask your child to bring you a number rod out of sequence to the second rug, for example, five. Count it.
  • Ask your child to bring you one more than five. When your child brings you the six rod, compare it visually, count it, and say, “Six is bigger or greater than five.”
  • This time, explain that a hungry alligator likes to eat the bigger or greater number. On a card draw an alligator mouth : >. Ask, “Which is the bigger number six or five?” They should answer six.
  • Place the six rod on the left side of the rug. Place the five rod next to it on the right side of the rug. Say, “This alligator likes to eat the bigger or greater number. Which one will he eat, six or five? They should answer six. Place the open alligator mouth toward the six. Say, “This is the way we read it: Six is greater than five.”
  • Next, have your child bring you one less than five. When your child brings you the four rod, compare it, count it and say, “Four is less than five. The alligator likes to eat the bigger number, which is bigger four or five?” They should answer five.
  • Place the four rod on the left side of the rug. Place the five rod next to it on the right side of the rug.  Place the open alligator mouth toward the five. Say, “This is the way we read it: Four is less than five.”
  • Continue choosing rods of different lengths and comparing them using the greater than, less than symbol.
The Addition Lesson
  • Get out a large rug or towel.
  • Arrange the rods on the rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Move the ten rod down to the bottom of the rug.
  • Move the nine rod underneath the ten rod. Move the one rod down and place it next to the nine rod so that together the nine and one rods are as long as the ten rod. Say, “Nine plus one equals ten.”

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  • Continue making sums of ten with eight plus two, seven plus three, six plus four and five plus five. NOTE: Flip the five rod from left to right to show five plus five equals ten.

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When you finish finding all the sums for 10, this is what the material will look like on the rug.
  • EXTENSIONS: Next, try finding sums of nine, eight, seven, etc. Explore different combinations.
The Subtraction Lesson
  • Get out a large rug or towel.
  • Arrange the rods on the rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Repeat the lesson above for sums of ten. When you finish, move the ten rod back to the top of the rug. Move the nine and one rod underneath the ten rod. Say, ten take away one (take the one rod away from the nine and move it to the bottom of the rug) leaves nine.

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  • Move the ten rod below the nine rod. Move the eight and two rods underneath the ten rod and say, “Ten take away two leaves eight.” Take the two rod away and move it to the bottom of the rug.

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  • Move the ten rod below the eight rod and continue in the same manner with the seven and three rods.

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  • Continue with the rest of the rods.

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  • For the five rod you can flip it back from right to left.

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If your child is confused by flipping the five, you can combine the 4 and 1 rod so you can physically take 5 away and see five left.
The Counting Backwards Lesson
  • Get out a large rug or towel.
  • Arrange the rods on the rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Count the rods backwards.
The quantity and Symbol Lesson: Associating the written numeral with the quantity

*Prerequisite: Before this lesson children should be introduced to the symbols 1-10 (written numerals) in isolation. The Montessori lesson for introducing the written numerals is The Sandpaper Numerals. Children are shown the numeral and trace the rough sandpaper with their fingers. It is a very tactile lesson.

  • Get out a large rug or towel.
  • Arrange the rods on the rug from longest to shortest, the left end of the rods flush with left side of the rug and even with each other.
  • Lay out the numeral cards 1-10 at the bottom of the rug in sequential order.
  • Starting with the one rod, find the symbol that says “1”. Match it to the one rod.
  • Continue all the way to 10.

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  • EXTENSIONS:
  • You can put the rods in mixed order, the numerals in mixed order, or both.
  • You can put out two rugs. Lay the rods on one rug and the numeral cards on the other. The rods can be in sequential order or mixed order. The numeral cards can be face up or down, in sequence or mixed order. Have your child choose a numeral card, then take it to the rug with the rods and match it.

Have you ever given a lesson to your child using the Red and Blue Rods?

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