How My Son Taught Himself to Learn Place Value.

I'm no math teacher, we include mathmatetics as part of our everyday homeschool routine. Sometimes, even when we think we're prepared, our children throw us for a loop.

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 flabbergasted. We have spent SO much time working on place value. He knew it before our winter break and then- poof- it seemed to be gone.

It can be incredibly frustrating when we feel like our children have mastered something only to come back to it and find out they are in need of a refresher or they’ve forgotten it all together. It’s also totally normal. “Use it or lose it” exists for a while in these early years. They’ll get there. I took a calm breath, pulled out our number cards and built the number.

- “It’s not quite that number, let’s look at it together. How many units are there?”

- “Eight” he responded.

- “Yes, how many tens do you see?” - I asked

- “One.”

- “Yep, how many hundreds?”

- “Two,” he then got an incredibly confused look on his face. The ‘learning moment’ was happening and he was realizing that it was NOT 2,118.

- “Great, how many thousands do you see?”

- “None?” he responded slowly and cautiously.

- “I don’t see any either, what number do you see here?”

- “Two hundred eighteen!!!” He responded enthusiastically.

Yes!! Isn’t it a sweet moment when you’ve worked through it with your child and seen them generate their answer??

Place value will be something you’ll keep coming back to through the years. As you get into 3 & 4-digit numbers, decimals, and beyond; you’ll need to revisit this concept to make sure it’s cemented. It is a truly foundational math skill and something most children don’t pick up in one 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 number (0-9) 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 a lot of practice. In our curriculum, you’ll use place value materials throughout your student’s math education in numerous ways. Incorporating place value identification as part of your daily routine can also be helpful. Ask your student about place value for numbers you see on street signs, price tags, in books, etc. to help reinforce the concept.

Decimal Materials?

Montessori decimal materials are 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 to a ten rod when they get to ten units.

This is an excellent way for them to start grasping the concept of place value. As your student progresses, they can “trade” in for hundreds and thousands as well. Many children enjoy playing this like a 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’ll begin using number cards. These helps 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. They then move into matching unit cubes to the proper number card. This helps create the foundation for place value by giving the child a visual and a number at the same time. The number cards will be incorporated with the decimal materials we discussed above as well. Eventually children will use number cards to build large numbers and will be able to tell the place value for each number, as well as build a number with verbal directions for which number card goes in each place value location.

Number Tiles.

Not 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 the number cards with some differences. Number tiles are multiple tiles of 1, 10, 100, and 1000. They are used as an alternative way to help children build numbers, solve math problems and move their understanding of place value to the next level.   For the number 218, in number cards the child would select 200, 10, and 8. With our number tiles, the child would obtain 2 “100” cards, 1 “10” card and 8 “1” cards. These are an excellent way to make the connection between decimal materials to building numbers, as well as to practice “exchanging” tiles from one place value for other place value tiles when completing math problems. Children take the solid foundation of number awareness they learned with the other two resources and use them throughout book 3.

Moving Beyond Book 3.

While these materials are not included in our Math Kit 2, children can certainly still benefit from using these materials throughout elementary school. (Plus, the decimal materials make great building blocks for free time!). If your older child seems to struggle to grasp 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. Make sure to check out our upcoming webinar on Teaching Place Value with Montessori Materials for more tips and tricks to help incorporate multisensory place value learning into your homeschool day.

Make Division Easy for Kids with Montessori Decimal Materials

Division With Montessori Base 10 Decimal Materials

When most of us think about learning division, we remember sitting in our lesson looking at a funny looking symbol and talking about ways to split apart pizza. Typically division isn’t introduced until the middle of Elementary school. In a Montessori school, or Montessori homeschool, division concepts are presented as early as five-years-old.   These concepts can be grasped from a young age with the help of Montessori golden beads, or the ShillerLearning decimal materials.

Montessori Makes Math Concepts Easy to Grasp With Hands-On Learning

Math doesn’t have to be hard or intimidating for the homeschool parent to teach. Division especially seems to be something that parents worry about introducing. With the Montessori method, a division can be presented in a non-threatening fun way which allows the child to thrive. By utilizing manipulatives and hands-on multisensory learning, we engage the child in many ways which help reinforce the concepts in a kid-friendly way.

The decimal materials are our starting point for addition, subtraction, multiplication, and division. They are utilized in counting, sorting, balancing, and much more throughout preschool and elementary education. By utilizing something children are already familiar with, new concepts are less scary to learn. Decimal materials provide a visual, tactile, and kinesthetic way to learn division. By engaging the auditory system through songs and listening to directions, division becomes a whole-body experience that sticks.

What are the Montessori Decimal Materials?

Traditionally in a Montessori school, you will find a golden bead set utilized for decimal materials. While these sets are beautiful, they’re also large and quite costly. The ShillerLearning decimal materials serve as a more cost effective option which take up less space as well.

These materials are kept in a wooden tray out on the shelf. There is 1 plastic 1,000 cube, as well as 16 cardboard 1,000 cubes. 27 hundred flats, 27 ten rods, and 100 unit cubes. These materials form the basis for grasping number size as well as serving as manipulatives for solving equations.  

Check out what these materials look like on a homeschool shelf in this video:

Beginning Division With Young Students.
 

The decimal materials are introduced very early on. First, the unit cubes are introduced as children learn numbers 0-9, then 10 rods are introduced and children work on numbers up through 99. Children also learn how to exchange 10 units for a tens rod. Next, hundreds flats and thousands of cubes are incorporated for making larger numbers and addition and subtraction. When we get to multiplication and division, these materials are familiar to the student.

A student’s first introduction to division comes in building numbers with unit cubes.  

Here is an example of how that first lesson might look:

• The teacher or parent asks the student to make a number with unit cubes (let’s use eight as our example)

• The student takes out eight unit cubes and places them in a row at the top of the work area

• Next, the teacher, or parent, shows the student how to break the group of eight into two even groups of four

• Groups of two are made next

• Then, the eight cubes are separated into eight groups of one

• Last we take out 32 unit cubes and demonstrate all the different groupings of eight that are possible

As you can see, this is a basic division made easy. This can be repeated with any number so long as it divides evenly.

Another great early division lesson begins in a similar way to building numbers. A 3 or 4 digit number can be created with the number cards. Typically, a number that can easily be divided by two is best to start with. The student will then build that number out of the decimal materials. Next, the parent or teacher says “now we will divide this number by two” and will demonstrate how to divide the materials into two even piles. Together the number representing each group will be determined and made out of number cards. If desired, the materials can be combined again and broken apart further as above.

Moving Away From The Decimal Materials

Once a student feels comfortable and confident using the decimal materials for basic division as above, we move into more advanced skills. Students will use the decimal materials to work on division with remainders, division with exchange, and will work through many division problems with the materials.  

The ultimate goal in Montessori is for a student to move onto being able to solve equations without the materials at all.

The first transition away from decimal materials is division using number tiles only. The process is similar to the process of learning division with the decimal materials.   Typically around third or fourth grade, we begin to move away from using decimal materials, but students may use them as long as they need.

The decimal materials are used in over 60 lessons in our Math Kit I. Check it out today and get your student on the path to learning division.

How to Choose the Correct Math Level for Your Child

When starting with a new curriculum, or transitioning from a traditional school to homeschooling, choosing the proper math level can be intimidating. Does “level 1” equate to 1st grade? Is the curriculum a rotating curriculum and you always start on level 1 no matter what age your child is? Do the numbers even mean anything at all? Placing a child in the proper level is one of the most intimidating and overwhelming part for new homeschoolers. Heck, even seasoned homeschoolers get scared by new curriculum sometimes!

Easy Level Placement With ShillerLearning

We feel your pain. Placing your child doesn’t have to be confusing. Many kids don’t like to feel like they’re being tested any more than you want to wade through a bunch of resources trying to figure out what to do. Our system is easy, quick, and effective.

Step 1 - Start with the first book in your kit.

Step 2 - Open to the front cover where you’ll see “Quick start guide.”

Step 3 - Read through the guide and get ready to work through the Review Tests.

Step 4 - Begin at review test 1 in the book. The introduction will tell you what materials you need. Grab the needed materials and get ready.

Step 5 - Prepare your child for the review. Each test reminds your child that the review exists to help them get the most out of their math time. The child-friendly language and step-by-step instructions will make this a relaxed time for both of you.

Step 6 - Administer the test and make sure to take notes. All you have to do is follow our script and work your way through the test. Each question lists the corresponding lessons in which the concepts were introduced. You’ll want to take notes to write down any lessons that your child needs to cover.

Step 7 - If your child has lessons that need to be introduced, begin with those lessons before moving on. Once you’ve finished all the lessons in a section, you can move on to the review test for the next section.

• If you find your child mastered the first two tests in a book, you may want to jump ahead to the last test in the book to see if they master it as well. Or, if you do a brief flip-through of the section and you’re sure your child has a good knowledge of all the concepts in the test, you may choose to only ask questions you suspect your child might not know.
   
• Most review tests don’t take more than 10-15 minutes. Your child might become fatigued from this process, it is advised to do one test a day until you’ve properly placed your child.

Step 8 - Once you have placed your child, will complete the review test again at the end of the section so that you can make sure to cover the lessons your child needs to be repeated.

This process is easy, fun and quick for you and your child. It requires no prep work for you and very little follow-up work. Then you can open and go with the curriculum at the right lesson and be on your way!

Need some more guidance on placing your child, or determining which Kit is best for your needs? Shoot us an email or give us a call and we’re happy to help!

How Getting Kids to Read Improves Math.

Children today are the first generation to grow up without reading as a primary free-time activity. This is concerning for homeschooling families, as well as teachers. In previous generations, before the advent of technology, kids spent many a lazy afternoon pouring over a good book. We are seeing reading ability, comprehension and the time spent reading are lower than ever before. A decrease in reading ability pours over to the obvious fields such as vocabulary as well as, surprisingly enough, math skills.

The link between reading ability and math has been a hot topic of study lately. Numerous research projects have been completed and the results continue to show the same things. Getting kids reading fluently and with good comprehension translates to an increase in math abilities. This is especially true with word problems, but overall skill in all the maths increase as children’s reading levels increase.

Dywayne Nicely from Ohio University Chillicothe recently studied this effect on 63 high school juniors. He enrolled them online test preparation programs focused on building reading comprehension for one year. At the end of the study, he found that they increased their algebra II scores by 14.8% and pre-calculus improved by 5.4% percent. This is a profound increase for students who were focused on reading comprehension and not math!

Word problems are an important component of reading and math. They require reading comprehension skills to be strong or the child won’t be capable of solving the problem. We use word problems to help children gain a better grasp of how math works in the real world. These problems help them start thinking about everyday scenarios in a different way.

Children who read for pleasure, and have solid reading skills, are typically found to be better problem solvers overall. This leads to kids who are better able to solve arithmetic problems, as well as handle problems they face in real life. By focusing on reading skills, especially comprehension, teachers and homeschoolers alike see spillover benefits in all of the subjects, including math!

Reading is a fundamental skill, and one that kids are not engaging in nearly as often these days. The ShillerLearning Language Arts curriculum include an emphasis on reading comprehension.  

You can get more time-tested tips on improving math skills on our blog.  

The U.S Math Crisis

We have a math crisis in the U.S.

Maybe that's the least of our problems. But maybe not. Consider this:

• 80% of US 8th graders cannot calculate fractions, decimals and percentages.

• 40% of US 4th graders cannot tell NE from SW on a map.

•  

It's really just us. The world does better:

• In Germany 35% of teens take and pass advanced placement exams; in the US it's 4%

• In Japan kids start algebra two years ahead of those in the US.

What are the repercussions?

• In the California State University system 60% of Freshman are required to take remedial math and science classes

• One in five adult Americans cannot:

  • Calculate the total of a purchase w/tax & tip

  • Locate an intersection on a road map

  • Enter background information correctly on a form

• MIT economist Lester Thurow says that only 20% of Americans have the work skills and education to be competitive in the global marketplace

And no one believes it! In a recent study 71% of high school parents say that they are satisfied with the math education their children are getting. Ouch.

The US has a math crisis. And the repercussions are serious. Join ShillerMath in creating better outcomes for our children and country.