Benefits of Math Manipulatives

The use of manipulatives in teaching math has a long tradition. Math manipulatives not only allow students to build their own cognitive models for abstract mathematical ideas and processes, but also provide them with a common language with which to communicate these models to the teacher and fellow students. Manipulatives are useful in many ways, and come with several benefits.


1) Math manipulatives engage students, and increase interest in and enjoyment of mathematics as a whole—Students who were given the opportunity to use manipulatives have reported that they were more interested in math.

2) Manipulatives build long-term interest in mathematics, which then translates to increased mathematical ability—They use concrete objects to observe, model, and internalize abstract concepts easily.

3)  Manipulatives are a powerful tool for classroom assessment and reduce the achievement gap while raising performance levels—Problem-solving, patience, critical thinking, creativity, concentration, and more are just some of the skills that can be achieved.  Students are more capable and competent when they regularly use manipulatives.  It’s a chance for them to become independent thinkers.


Dice are a great tool to have on hand for math games and activities. There are many types available today, such as these dice in many colors. There are also different sized dice available, such as these large foam dice. Jumbo dice are great for rolling during a class game or for “flashng” to kids to have them call out the number shown. We suggest putting pairs of dice into small clear containers that students can quickly grab and shake while playing games. My favorite type of dice for teaching addition andplaying games are the dice in dice.


Playing Cards

Playing cards make useful math tools because they have numbers on them. They can be used to teach addition and subtraction through games like addition “war” and subtraction “war”. Playing cardscome in traditional decks that you can find at most stores or dollar stores. Teachers would benefit from a set of jumbo playing cards to use for lessons and demonstrations as they provide a large visual for kids.


Unifix or Snap Cubes

Unifix cubes are the colored cubes that connect in one way and snap cubes are colored cubes that can connect in different ways. Both can be used in many ways to teach many math concepts, such as patterning, place value, and measurement. Snap cubes are one of the most used math manipulatives. They visually demonstrate many number concepts, such as counting, grouping, adding, and taking away. Children love snapping the cubes together to make number “trains”.


Hundreds Charts

Hundreds charts are important for teaching children to count to 100 in multiple ways. They are visual representations of numbers in order and are filled with patterns that children should be encouraged to find. Hundreds charts are important for whole-class lessons, independent practice, and games. My most used anchor chart on my wall is a hundreds chart, similar to this. We use these durable hundreds boards frequently. I also recommend having a mini hundreds chart visible on student work-spaces. These nameplates also have a ruler, number line, and addition table on them.


Place Value Blocks

Place value blocks are very helpful in teaching counting, number concepts, double-digit addition and subtraction. Place value concepts are more difficult to grasp and using these concrete manipulatives helps build understanding. We suggest have a large bin of of place value blocks similar to those below with enough for each student to represent the numbers you are learning. The magnetic set would be helpful for whole class demonstrations on a whiteboard. If you are teaching PreK or Kindergarten, consider introducing place value during calendar time with this counting pocket chart and straws.

Leonardo Da Vinci Math: Show Your Work!

leo drawingsWhen we type the word “Leonardo” in Google, the undisputed results are “Leonardo DiCaprio” and “Leonardo Da Vinci”. Leonardo DiCaprio is an A-lister in today’s generation, but Leonardo Da Vinci was a universal Renaissance Man, and believed nature is governed by math.

Even when Leonardo learned the language of mathematics, he preferred to express his thoughts through his art. His search for mathematical solutions is seen through his artwork and rough drawings.  Leonardo Da Vinci wasn’t the only person that used drawings to calculate math.  Drawing was how some ancient civilizations calculated mathematical precisions in their constructions, which is exhibited in the Egyptian pyramids.
Many things can be observed about Leonardo’s method of learning.  He showed his work.  He entertained his curiosity through writing and drawing. Students that lack confidence in math think that they are only good at mathematics if they can “do it their head”.  Not true!  Some of history’s greatest thinkers–Albert Einstein, Leonard Da Vinci, and Sir Issac Newton–made great discoveries by writing down their thoughts and theories–not by just computing numbers in their heads.

Why Should You Show Your Work?

Students should learn like Leo.  There is power in writing things down:

1)  Writing helps your memory
2)  Writing help you work through problems faster and easier
3)  Writing helps you create goals and find ways to reach them
4)  Writing encourages creative thinking

When math is part of the equation, writing things down is even more important: 

  • Showing your work in an organized way helps you organize your thoughts, which in turn makes you less likely to make a mistake.
  • On homework, usually you have answers available. If your answer doesn’t match the book’s answer, showing your work helps you figure out what you did wrong. It can also help a tutor figure out what you did wrong, if you go for help.
  • On tests, if you get a wrong answer your instructor can use your work to figure out what you didn’t understand, and point it out so that you avoid that mistake in the future.
  • If you get a wrong answer on a test, but your work shows you understood the core of the problem, most instructors will allow partial credit.  A bare answer that is wrong has to count as a zero.

Today’s students can reach success in mathematics through writing.  There is power in the pencil!!

Effective Study Skills for a Successful School Year

Developing effective study skills will naturally promote and enhance your learning experience, and can lead to a impressive grades.  Taking study breaks allows the brain time to order and organize the information you are learning in small manageable chunks that can then be located and recalled at a future date.
 The Study Break Process
Breaks should be taken before we begin feeling overwhelmed or fatigued.  Study breaks keep your body and brain fresh in ways that will improve long-term memory and help better categorize the information you are learning for more effective memory recall.
Study for 25 minutes
Studies have shown time and again that the human brain cannot fully concentrate on a specific topic for extended periods of time over 20 to 25 minutes. Even though throughout your study regime you may feel as though you are still within your learning zone – you may in fact be slowly moving out of your zone, becoming gradually less focused and productive as the minutes tick by.
 We naturally tend to remember and recall most of the information we learn at the beginning and at the very end of our study chunks. If you extend your study chunks to over 60 minutes, the information studied within the middle of that time period is likely to be misplaced or forgotten.
Take a Break for 5 minutes
Your breaks should be no longer than around 5 minutes. You don’t want to distract yourself from your studies. Your breaks should be utilized in ways that will settle your mind and effectively allow you to integrate the information you have learned.  Try to avoid television or other mind-consuming activities during your breaks.
Conduct a Review for 5 minutes
When you get back to your studies it is critical that you do a quick review of the material you studied during your most recent study chunk. This will further help to assimilate this subject into your long-term memory storage banks and assist you in creating strong associations to existing information within your brain.