How To Teach Place Value While Building Math Confidence

When my college students (remedial math students) finish the first chapter in Fractions, Decimals, and Percents, we focus on place value. Over the years, I have come to the realization of how vital it is to provide a careful development of the basic grouping and positional ideas involved in place value. An understanding of these ideas is important to the future success of gaining insight into the relative size of large numbers and in computing.  A firm grasp of this concept is needed before a student can be introduced to more than one digit addition, subtraction, multiplication, and division problems. It is important to stay with the concept until the students have mastered it. Often when students have difficulty with computation, the source of the problem can be traced back to a poor understanding of place value.

It was not surprising when I discovered that many of my students had never used base ten blocks to visually see the pattern of cube, tower, flat, cube, tower, flat.  When I built the thousands tower using ten one hundred cubes, they were amazed at how tall it was.  Comparing the tens tower to the thousands tower demonstrated how numbers grew exponentially.  Another pattern emerged when we moved to the left; each previous number was being multiplied by 10 to get to the next number.  We also discussed how the names of the places were also based on the pattern of:  name, tens, hundreds, name (thousands), ten thousands, hundred thousands, etc. 

I asked the question, "Why is our number system called base ten?"  I got the usual response, "Because we have ten fingers?"  Few were aware that our system uses only ten digits (0-9) to make every number in the base ten system.

We proceeded to look at decimals and discovered that as we moved to the right of the decimal point, each number was being divided by 10 to get to the next number. We looked at the ones cube and tried to imagine it being divided into ten pieces, then 100, then 1,000. The class decided we would need a powerful microscope to view the tiny pieces.  Again, we saw a pattern in the names of each place:  tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.

I then got out the Decimal Show Me Boards.  (See illustration on the left.)  These are very simple to make. Take a whole piece of cardstock (8.5" x 11") and cut off .5 inches. Now cut the cardstock into fourths (2.75 inches).  Fold each fourth from top to bottom. Measure and mark the cardstock every two inches to create four equal pieces. Label the sections from left to right - tenths, hundredths, thousandths, ten thousandths. You can type up the names of the places which then can be cut out and glued onto the place value board.

Here are some examples of how I use the boards.  I might write the decimal number in words.  Then the students make the decimal using their show me boards by putting the correct numbers into the right place.  Pairs of students may create two different decimals, and then compare them deciding which one is greater.  Several students may make unlike decimals, and then order the decimals from least to greatest.  What I really like is when I say, "Show me", I can readily see who is having difficulty which allows me to spend some one-on-one time with that student.

Show Me Boards can also be made for the ones, tens, hundreds and thousands place.  Include as many places as you are teaching. I've made them up to the hundred thousands place by using legal sized paper. As you can see in the photo above, my two granddaughters love using them, and it is a good way for them to work on place value.

$3.75

A good way to practice any math skill is by playing a game. Your students might enjoy the No Prep place value game entitled: Big Number.  Seven game boards are included in this eleven page resource packet. The game boards vary in difficulty beginning with only two places, the ones and the tens.  Game Board #5 goes to the hundred thousands place and requires the learner to decide where to place six different numbers.  All the games have been developed to practice place value using problem solving strategies, reasoning, and intelligent practice.

Is Your Data Analysis Missing Out on the Power of Glyphs?

What is a Glyph?

A glyph is a non-standard way of graphing a variety of information to tell a story. It is a flexible data representation tool that uses symbols to represent different data. Glyphs are an innovative instrument that shows several pieces of data at once and necessitates a legend/key to understand the glyph and require problem solving, communication, and data organization.

Remember coloring pages where you had to color in each of the numbers or letters using a key to color certain areas? Or how about coloring books that were filled with color-by-numbers? These color-by-number pages are a type of glyph. Some other activities we can call glyphs would be the paint-by-number kits, the water paints by color coded paint books, and in some cases, even model cars. Some of the model cars had numbers or letters attached to each piece that had to be glued together. These days, this could be considered a type of glyph.

What is the Purpose of a Glyph?

A glyph is a symbol that conveys information nonverbally. Glyphs may be used in many ways to get to know more about students and are extremely useful for students who do not possess the skill to write long, complex explanations. Reading a glyph and interpreting the information represented is a skill that requires deeper thinking. Students must be able to analyze the information presented in visual form. In other words, a glyph is a way to collect, display and analyze data. They are very appropriate to use in the CCSS data management strand (see standards below) of math. Glyphs are actually a type of graph as well as a getting-to- know-you type of activity.

CCSS.Math.Content.1.MD.C.4  Organize, represent, and interpret data with up to three categories;

ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 

CCSS.Math.Content.2.MD.D.10  Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. 

For example, if the number of buttons on a gingerbread man tells how many people are in a family, the student might be asked to “Count how many people are in your family. Draw that many buttons on the gingerbread man." Since each child is different, the glyphs won't all look the same which causes the students to really look at the data contained in them and decide what the glyphs are showing.

$3.00

Holiday glyphs can be a fun way to gather information about your students. You can find several in my Teachers Pay Teachers store.  My newest one is for Thanksgiving and involves reading and following directions while at the same time requiring problem solving, communication and data organization. The students color or put different items on a turkey based on information about themselves. Students finish the turkey glyph using the seven categories listed below. 

1) Draw a hat on the turkey (girl or a boy?)
2) Creating a color pattern for pets or no pets.
3) Coloring the wings based on whether or not they wear glasses.
4) Writing a Thanksgiving greeting based on how many live in their house.
5) Do you like reading or watching TV the best?
6) How do they get to school. (ride or walk?)
7) Pumpkins (number of letters in first name)

How to Make Fractions Fun: Identify Equivalents and Reduce to Lowest Terms

Here is a Halloween riddle: Which building does Dracula like to visit in New York City? Give up? It's the Vampire State Building!! (Ha! Ha!) Here is another riddle. What do ghosts eat for breakfast? Scream of Wheat and Ghost Toasties!

Okay, so what do these riddles have to do with teaching math? I have been attempting to come up with ways for my students to recognize fractional parts in lowest terms. As you know from this blog, I have used Pattern Sticks, the Divisibility Rules, and finding Digital Root. These are all strategies my students like and use, but to be a good mathematician requires practice - something most of my students dread doing. I can find many "drill and kill" activities, but they tend to do just that, drill those who don't need it and kill those who already know how to do it. So to drill and "thrill", I created fractional word puzzles for specific times of the year.

The one for October is Halloween Fraction Riddles. It contains ten riddles that the students must discover by correctly identifying fractional parts of words. For instance, my first clue might be:

The first 2/3's of WILLOW. The word WILLOW contains six letters. It takes two letters to make 1/3; therefore, the first 2/3's would be the word WILL. This causes the students to group the letters (in this case 4/6), and then to reduce the fraction to lowest terms. The letters are a visual aid for those students who are still having difficulty, and I observe many actually drawing lines between the letters to create groups of two. 

$3.00

Here is one from my Halloween resource.

Which part of a road do Ghosts love to travel the most?

1) The first ¾ of THEY. ____________

2) The first 1/3 of DETOUR, the last ½ of GLAD. __________

3) The last 1/3 of USE, the middle 1/3 of AND, and the 

     first 1/5 of DOUBT.    ____________

At first, I thought my students would breeze through the activities, but to my surprise, they proved to be challenging as well as somewhat tricky - just perfect for a Trick or Treat holiday. Maybe this is an activity you would like to try with your intermediate or middle school students. Just click on this link: Halloween Fraction Riddles.

The Absolute Best Ice Cube Science Investigation

As a budget-conscious educator, you know the value of resourcefulness. That's why I'm excited to share some simple yet effective science investigation activities that use everyday objects like ice cubes. These ideas are perfect for teachers like you who are looking to maximize learning potential without breaking the bank. So, let's get started!

Ice experiments are always fun, easy to set up, and often mess-free! Whether you're trying to beat the heat during summer or embrace the chill of winter, ice experiments are the perfect way to engage students and discover the fundamentals of scientific principles. These activities are a great addition to any STEM curriculum that can do in the classroom or at home. Every ice cube holds surprises waiting to be discovered. Supplementing these activities to your STEM curriculum will not only make learning fun but will also help students understand fundamental concepts in a hands-on way.

Hands-on ice cube units invite kids to:

• Ask questions
• Make predictions
• Test ideas
• Observe changes
• Try again when results surprise them

Hands-on ice cube units guide and direct the student through the six steps of the scientific method:

1. Investigating Properties
2. Interactions
3. Making a plan
4. Determining the Investigative Question
5. Prediction and Data Collection
6. Writing a conclusion based on the data.

Why not join this ice cube exploration and uncover the mysteries of ice with engaging hands-on activities that will fascinate, educate and interest your students? Let's turn ordinary ice cubes into unexpected tools for learning; then watch as your students become the ultimate scientists.

-----------------------------------------------------------------------------

$5.75

The science unit consists of a three-page student investigation organizer, a property word list, an optional student checklist, and a four-point grading rubric for the teacher. Materials needed for the whole unit, things to do prior to the investigation, and initial instructions are included. Besides simple and clear step-by-step directions for each of the six lessons, specific supplies needed and visual examples of the charts used in the investigation are shown in detail. Each lesson is 30-45 minutes long and the complete investigation will take 6-8 days to carry out depending on the length of your science class. It is appropriate for grade 3-4.