3 - 6, 6 - 12, Math and Geometry, Montessori Materials, Uncategorized

Long Live the Short Chains

The Montessori Short Chains and Arrows pack a big learning punch and are often under-utilized.IMG_4716  They’re great for a homeschool environment because they don’t take up any shelf space.  Their initial purpose is to help the child first count linearly and then skip-count.  But when your child is comfortable with these two concepts, you can use the chains for much more!  Here are four ideas…

IMG_4657Find the number: Ask the child to set out the hundred chain with the corresponding arrows, while you cut up a few blank paper arrows (cut little rectangles and trim the corners to make arrows).  Write a number on the arrow (any number between 1 and 99) and have the child place the arrow on the corresponding bead.  If you notice mistakes, you can either let it be for now (and encourage more practice) or invite the child to count from the nearest tens-arrow (e.g. if the paper arrow says “26” and it’s in the wrong spot, invite the child to count linearly from the “20” arrow).

When they get comfortable with this activity, you can place blank arrows on random beads along the chain and ask the child to write down the numbers on the arrows. Later the child can do the same activities but without the tens arrows as guides.  You can ask questions like, “What number would you reach if you added 10 beads to 26?” or “What number would you reach if you counted backwards 8 beads from 45?”  You can do all these activities from around the age of 5 if counting skills are solid.

Find the missing number in a sequence: When a child knows how to skip-count, youIMG_4500 can present a new challenge by having them find the missing number in a number sequence.  The first few times you do this, you can use the regular arrows for any chain and hide one behind your back.  Ask the child to lay out the arrows and tell you which one is missing. (e.g. The child lays out 5, 10, 20, 25 and tells you that 15 is missing.)

Later, with the ten-chain, you write sequence numbers on paper arrows and the child has to use addition and subtraction to figure out the sequence and which numbers are missing. (e.g. Make arrows for the numbers 2, 19, 36, and 70 and the child has to lay them out and then figure out the pattern in the sequence and what number arrows are missing).  Help the child verbalize the process he’s using in order to solidify the concept and extend it to any number sequence without the material.  The first part of this work is great from the age of five, and the sequence activity is great from six onwards, increasing in complexity.


Rounding to the nearest ten: The concept of rounding is not presented in isolation in the Montessori elementary, but is instead part of an ongoing conversation when working with money, estimating, etc.  However, if a child isn’t understanding the concept, you can use the hundred chain to support their comprehension.  Have the child match the tens arrows to the bead chain, and then talk about how the tens are numbers that we can work with easily. Give examples of when we might want to work with numbers rounded to ten instead of exact numbers.

Write the number 62 on a paper arrow and ask the child to place it on the corresponding bead on the chain.  Then ask him what “ten” the arrow is closest to, and explain that 62 can be rounded down to 60 (or is closest to 60).  Do the same with a couple of numbers with the units under 5.  Then make an arrow with a number that has the units higher than 5 (e.g. 68).  Ask the child what “ten” that number is closest to and point out that 68 rounds up to 70.  Then write a number with 5 in the units (e.g. 65) and tell the child that our rule is that if a number has a 5 or above in the units, you round UP to the nearest ten.  Give a couple of examples for the child and then encourage him to make his own examples.  The book “Sir Cumference and the Roundabout Battle” has a lovely story that fits well with this activity.

IMG_4719Polygons: The chains provide a fun exploration of shapes, from triangle to decagon.  Have the child carry all the chains on a tray to a large rug and ask her to make a closed shape with each chain imagining that the center was pressing out evenly on all sides.  Then ask her how many sides each shape has.  If you have a Geometry Cabinet, ask her to find the corresponding shape from the cabinet and put it inside or next to the bead shapes.  The child can write on a slip of paper the number of sides each shape has, and then you can give the names.  You can do a three-period lesson with a Primary child, and you can make an etymology chart with an Elementary child.  The child can also build the shapes around each other, with the square surrounding the triangle, the pentagon surrounding the square, etc.

I hope these fun chain activities bring new life to your bead cabinet!

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BOTW: The Story of Money

Is your child afraid of math?  I know many who are.  I also know that one of the most effective ways to help them overcome their fear of math is to give them an allowance.  In addition to teaching your child patience, opportunity cost, and the value of things, money is a hands-on way to work through many math skills!

My son got hooked on math through his allowance.  At the age of four, he wanted to save up for a LEGO kit. On a piece of graph paper, I marked one square for each dollar he would have to save.  Whenever he got his allowance, he would color in the associated squares and we would count how many more squares – or dollars – he needed to reach his goal.  By the age of five, he was using addition to calculate his goals, and by six he was multiplying.  Now that he’s seven, he has a money journal, where he writes down his debits, credits, and current balance.

His interest in money, and his age, led to the question: “Why do we use paper money?  Why don’t we use gold or computers?”

I’m glad we had The Story of Money in our home library!  This lovely book, written by an elementary teacher, traces the fascinating history of world currencies from the time of the very earliest humans. The engaging illustrations and clear text will take you and your child on a journey through ancient civilizations like Sumer and China.  You’ll then make your way to colonial America and discover how the dollar came to be. storymoney

The Story of Money is written in the style of Montessori’s Cosmic Stories, which helps children stay engaged from start to finish.  My son loved looking at all the different ancient coins, all carefully illustrated to actual size.  This book can inspire many avenues of research for elementary students, from timelines to coin collections.

So, the next time your child feels scared of math, connect math to money, and money to human history with The Story of Money, and watch their fear turn to enthusiasm!

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Montessori Materials, Montessori Theory

When Help Is A Hindrance

Few clean-ups seem as overwhelming as that of the Montessori fractions.  The halves through sevenths are easy enough for most children, but the 27 hard-to-distinguish red wedges that make up the eighths, ninths, and tenths can leave even Elementary children feeling stuck and discouraged. Screen Shot 2019-02-16 at 7.03.31 AMI’ve inherited Montessori fractions in several of my classrooms, and I’ve often found that a well-meaning predecessor had written the corresponding value on the underside of each fraction piece.  At first glance, this might seem helpful.  It sure makes cleaning up those pesky fractions a lot quicker!

So, why did Dr. Montessori design the fraction pieces without labels?  Did she harbor some evil desire to torment children and their over-worked adult guides?  Or did she observe that leaving the fractions unlabeled led to the development of problem-solving skills through creative use of the child’s knowledge?

The answer becomes clear when we consider Dr. Montessori’s advice: “Every unnecessary help is a hindrance to the child’s development.”

Is writing the values on the underside of the fraction pieces really necessary?  Or, by doing so, are we preventing the child from developing essential skills?  If we don’t want to be a hindrance to their development, but we need them to eventually clean up, what can we do to guide a child who’s feeling discouraged by this overwhelming task? IMG_0573

When a child is faced with sorting a pile of unlabeled slim red wedges, it’s enough to help him recall that two eighths are equivalent to – or take up the same space as – one fourth.  Depending on the child’s prior knowledge, you can ask, “What do you know about equivalences?” or “What do you know about the relationship between fourths and eighths?”

If the child is younger and doesn’t know this information, simply guide him in a sensorial exploration.  Invite the child to bring out the fourths inset, ask him to remove one fourth, and show how the space within the inset serves as an objective control of error.  When fractions other than two eighths are placed within the space vacated by the fourth, you will see a gap.  Only two eighths will fit perfectly within the space of the missing fourth.

The monumental clean-up now becomes a fun puzzle that satisfies the child’s love of precision and bolsters his self-confidence.  You can back away, returning only if he needs guidance to find the relationship between fifths and tenths, or thirds and ninths (children familiar with equivalences will likely make the connections on their own).IMG_0577Take a moment to observe the child’s concentration, enjoy his smile of accomplishment, and know that you helped him move one step closer towards reaching his full potential as a creative problem-solver.