I am not a math teacher, but we include mathematics as part of our everyday homeschool routine. Sometimes, even when we think we are prepared, our children surprise us in the best possible way.
I had 218 written out on a piece of paper. "You may tell me this number," I said to my seven-year-old.
"Two thousand, one hundred and eighteen," he responded.
I was taken aback. We had spent so much time working on place value. He knew it before our winter break and then it seemed to be gone.
It can be incredibly frustrating when we feel our children have mastered something, only to return to it and find they need a refresher. This is also completely normal. "Use it or lose it" is very real in these early years. They will get there. I took a calm breath, pulled out our number cards, and built the number.
"That is not quite the right number. Let us look at it together. How many units are there?"
"Eight," he responded.
"Yes. How many tens do you see?"
"One."
"Good. How many hundreds?"
"Two." He then got an incredibly thoughtful look on his face. The learning moment was happening. He was realizing it was not 2,118.
"Great. How many thousands do you see?"
"None?" he responded slowly and cautiously.
"I do not see any either. What number do you see here?"
"Two hundred eighteen!!!" he responded enthusiastically.
Yes! Is there anything sweeter than watching a child work through a problem and arrive at the answer on their own?
Place value is a concept you will keep returning to through the years. As you move into three and four-digit numbers, decimals, and beyond, you will need to revisit it regularly to make sure it is cemented. It is a truly foundational math skill and one that most children do not master in a single lesson.
What Is Place Value?
Place value is how we determine the value of a number. Our number system is based on groups. A single digit (0 to 9) is referred to as a "unit" in Montessori teaching. Tens come next as two-digit numbers, hundreds help us make three-digit numbers, and so on.
Teaching Place Value
The best way for a child to learn place value is through a great deal of practice. In our curriculum, you will use place value materials throughout your student's math education in numerous ways. Incorporating place value identification into your daily routine is also helpful. Ask your student about place value for numbers you see on street signs, price tags, and in books to help reinforce the concept.
Decimal Material
Montessori decimal material is a foundation for teaching place value. Providing children with something tactile for a concept that can be quite abstract is essential. Children begin by building numbers with unit cubes, ten rods, hundred flats, and thousand cubes. They can use these materials to trade up to the proper materials. For example, provide your student with 12 unit cubes and encourage them to trade for a ten rod when they reach ten units.
This is an excellent way for children to begin grasping the concept of place value. As your student progresses, they can trade in for hundreds and thousands as well. Many children enjoy this as a kind of shopping game, where they buy the next decimal material for the proper amount of trade.
Number Cards
Once a child is familiar with the unit cubes, they will begin using number cards. These provide a visual for creating numbers, the tactile experience of building numbers, and the auditory experience of hearing numbers. Children begin by matching the correct number card to the corresponding number of units, then move into matching unit cubes to the proper number card. This creates the foundation for place value by giving the child a visual and a number at the same time.
The number cards are incorporated with the decimal materials as well. Eventually children will use number cards to build large numbers, identify the place value of each digit, and build a number from verbal directions specifying which card goes in each place value position.
Number Tiles
Not to be confused with number cards, number tiles are introduced after the student has a firmer grasp on place value. In our curriculum, number tiles are not introduced until Book 3.
These materials are used similarly to number cards, with some differences. Number tiles are multiple tiles of 1, 10, 100, and 1000. As in the Montessori Stamp Game, they are used as an alternative way to help children build numbers, solve math problems, and deepen their understanding of place value. For the number 218, with number cards the child would select 200, 10, and 8 cards. With number tiles, the child would obtain two "100" tiles, one "10" tile, and eight "1" tiles. This is an excellent way to connect decimal materials to building numbers and to practice exchanging tiles between place values when completing math problems. Children bring the solid foundation of number awareness they built with the earlier materials and apply it throughout Book 3.
Moving Beyond Book 3
These materials are included in our ShillerLearning Math Kit I, and children can certainly continue to benefit from them into middle school. The decimal materials also make wonderful building blocks for free play. If your older child has dyscalculia or struggles with number sense and place value, incorporating these materials can be extremely beneficial.
Feel free to reach out if you need additional guidance for teaching regrouping, place value, or anything else with your child.
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