Using Manipulatives

From KNILT

Using Manipulatives in the Elementary Classroom Introduction

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Even those in ancient times used physical objects to help solve everyday math problems. The first forms of manipulatives would have included a clay or wooden tray with sand that individuals could draw tally marks in to count. Another early manipulative would be the first abacus that was created by the Romans. In the early 1900’s Maria Montessori developed many various manipulatives for students to use as she felt this was crucial in their learning. Over the years, manipulatives have grown in popularity and have been recommended for use with students to teach mathematics in all grades, however they are primarily used with elementary age students.

While some may feel that the use of manipulatives is just for fun, however using manipulatives provides many learning benefits for students when learning mathematical concepts. The use of manipulatives helps children to learn by moving concepts from the concrete stage to the abstract stage where manipulatives would not be used.

At the end of this mini-course, you will be asked to create a mathematics lesson for the topic and grade-level of your choosing. In this lesson, you will be required to incorporate at least one manipulative that effectively enhances the learning. The manipulative used in the lesson can be one that we will focus on during this mini-course, or it can be something different we do not discuss, however you will want to ensure that it enhances the learning of the particular topic you decide on.

MODULE 1- TYPES OF MANIPULATIVES

Objective for this Module- Learners will be able to identify commonly used manipulatives leading them to create a lesson utilizing at least one commonly used manipulative.

Cuisenaire Rods

-Created in the 1920’s by a Belgian educator

- The first sets were wooden rods of varying lengths and colors where each length and color represented a different number from one to ten

-All Cuisenaire rods follow the same color/number (length) pattern:

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White =1

Red = 2

Light Green = 3

Crimson = 4

Yellow = 5

Dark Green = 6

Black = 7

Brown = 8

Blue = 9

Orange = 10

-Most students who are introduced to these manipulatives at a young age will be able to identify numbers with the corresponding color


Hundreds Number Board

-Number boards are often used to aid students in skip counting, learning and exploring number patterns and practicing factors for multiplication

-Using a hundreds board allows younger students to practice math equations, whether it is addition or subtraction with numbers that may normally be beyond what they normally can handle.

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Interlocking “Multilink” Cubes

-often referred to as Snap Cubes

-these one-cubic centimeter colored cubes are often used to teach patterns with young students

-the cubes can be linked together and are mutli-colored which is what is helpful when learning patterns

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Pattern Blocks

-various wooden or plastic shapes that are used to teach students the relationships among shapes and early geometry

-shapes that are usually found with pattern blocks are green trianlges, red trapezoids, yellow hexagons, orange squares, tan (long) rhombi, and blue (wide) rhombi.

-The shapes are sized so the learner can use the various shapes separately to see how they can be used together in varying patterns to create the other shapes.

For example- two red trapezoids make a yellow hexagon or a blue rhombus is made up of two green triangles

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Number Lines

-Helps to teach integer addition and subtraction-Usually a typical positive/negative number line spans from -20 to 20

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Now that you've learned about different types of manipulatives, you will move on to Module Two where we learn how to use some of these to learn mathematical concepts!

MODULE 2- WAYS OF INCORPORATING MANIPULATIVES EFFECTIVELY

Objective for this Module- Learners will be able to explain how manipulatives can be utilized to teach a mathematical concept leading them to be able to describe, in detail, how the manipulative they utilize in their lesson plan will be used to teach a mathematical idea.

In this module we will explore the many uses for manipulatives and the ways they can be incorporated into a lesson. Please read through the examples below and watch BOTH of the video examples. While reading and watching, start thinking of ways that you may be able to use manipulatives in a mathematics lesson as you will be creating a lesson at the end of the course.


Cuisenaire rods are often used to illustrate factors of ten and other numbers as the learners can use varying smaller rods to build the length they are looking for; For example, learners illustrating factors of ten can lay one orange (10) rod down and then underneath it use two yellow (5) rods to show that two yellow rods equal one orange. Leaners can also use five red (2) rods or ten white (1) rods.

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Hundreds number boards can be used by many different age groups to practice various relationships between numbers. Skip counting practice is one of the most common uses for a number board for young elementary students. Students can be asked to start at number one and count by two's, five's, or ten's up to one-hundred. To make the activity more complicated, students can be asked to count by five's starting with the number 18. Older students can be asked to color in the square for every fourth number or every five numbers so they can visually see the pattern. Older elementary students can use the chart to see how many numbers are between two given numbers, such as 28 and 42. They can be asked, what does it mean to count from one number to the next? Are you adding or subtracting?


Please watch the first half of this video below to see how fraction strips can be used in an upper elementary classroom. Teaching fractions with manipulatives.

This short video shows how something as simple as a colored tile can help learners see patterns and rules in relation to numbers. Number Patterns and Rules

MODULE 3- BENEFITS OF USING MANIPULATIVES

Objective for this Module- Learners will be able to describe the benefits of using manipulatives in an elementary mathematics lesson and how the manipulative they will utilize in their lesson will enhance student learning.

This module discusses the benefits of using manipulatives in the classroom. Please review the information and keep these ideas in mind as you will need to explain why the manipulatives you use in your lesson are beneficial to student learning.

There are various benefits for learners when manipulatives are used effectively in the classroom. As you heard in the first video in Module 2, manipulatives cannot just be thrown into a lesson for minutes and be expected to be effective for learning. Incorporating manipulatives needs to be well thought-out and when they are, the benefits can be great.

Learning takes place in three different forms; auditory, visually, and kinesthetically. In most cases, learners do best when all three of these learning styles are utilized, but some are stronger than others. The use of manipulatives focuses on the visual and kinesthetic learning styles to help learners take concepts from the concrete to abstract stage. Using these two styles together allows students to see relationships between ideas and concepts.

Using manipulatives exemplifies visual learning by bringing a mathematical concept right to a student’s desk. When students physically move manipulatives to show various relationships, their sense of touch is actively engaged. This enhances understanding and, in turn, promotes communication of ideas. Since the use of manipulatives is a multi-sensory activity, it ensures access to ideas and concepts, as well as reasoning so all students can be actively engaged in the lesson.

Please read the following article about the benefits of using manipulatives in the elementary classroom and particularly focus on the chart on page 3, which gives more detail on how manipulatives support learning theories. Research on the Benefits of Manipulatives

MODULE 4- VIRTUAL MANIPULATIVES IN THE CLASSROOM

Objective for this Module- Learners will be able to describe a virtual manipulative and determine what appropriate manipulative can be used with their lesson plan.

There may be various instances where a physical manipulative cannot be used in a classroom, this could be that they are not available for all students, the school does not have any, or the teacher may have decided to incorporate them at the last minute. A way to overcome these challenges is to use virtual manipulatives. Virtual manipulatives are used via computer or can even be used on a tablet if available. There are numerous types of manipulatives that can be used virtually and they can be utilized for any grade level. Instructors can use virtual manipulatives during a whole-class lesson, where the computer-manipulatives are shows on a screen for all students to see, or they can be used on individual computers.

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One of the most commonly used and publicized sources for virtual manipulatives is the National Library of Virtual Manipulatives where math manipulative are available for all grade levels and many mathematical concepts.

Please click HEREto visit the National Library of Virtual Manipulatives website and try out at least one type of manipulative for the grade level and concept of your choice. There are many options to pick from within the site without creating or paying for an account. After you have tested out one type of manipulative, please share your experience in the discussion forum for this module. Please include which grade level and concept you chose, if you feel this could be effectively used in the classroom, and your thoughts on using this type of manipulative in a lesson.

ASSESSMENT - USE WHAT YOU HAVE LEARNED

Now that you have been introduced to various types of manipulatives and how they can be used, as well as the benefits of using manipulatives, please create a lesson where you utilize one type of manipulative to either introduce or practice a mathematical skill. If you are able, try to also find a virtual manipulative that would be able to be used for your lesson in the event that manipulatives are not available.

Please post your lesson to the discussion board to share with your peers.