Why Manipulatives for Math?
1) FUN The easy answer is that they are FUN. Motivation is critical for learning. The more appealing the materials, the more likely the lesson will be successful. Motivation is the best way to help with math.
2) See the Wheels go Round: Manipulatives make your child’s thinking visible. This is great for teaching, as well as for diagnosing any little glitches that can happen.
3) Simulate the Real World: Some manipulatives replicate the real world. How better to learn time than using a teaching clock? Experience money through a play store and a teaching cash register to consolidate the value of our coins and bills.
4) Professionals use Them: Many professionals use manipulatives regularly. Where would architects be without their basic 3D shapes? When you visit your doctor or dentist, they may use a model (which is a manipulative) to explain a procedure for you or a technique you need to do to get better.
But I probably had you with FUN.
So, if you are working with kids from 5 to 8, what are the best manipulatives for math that you need to have, and how do you use these tools effectively?
Allow Free Exploration Time
Usually, manipulatives are very appealing to all individuals, even adults. It is important to give exploratory time with the manipulative before you decide to use them in any organized way. Make sure you have given ample free playtime for kids and adults to build or explore the possibilities with manipulative before using them in your lesson. Some kids will need a week or more of time to fully explore these 3D objects.
Also, you may not want to pack away the manipulative when you have finished the lesson as your child may want to continue exploring mathematical concepts during their free time. Many teachers keep these objects available all day to be used for play.
The Areas of Mathematics
Most primary math curriculum is divided into 5 sections, and the manipulatives are often very different for each type of mathematical concept: Numbers, Algebra (patterning), Data, Spatial Sense, and Financial Literacy. Woven through every activity are some social-emotional goals to maintain a positive outlook while working with mathematical concepts. The basis of the following summary comes from an article: New Math Curriculum 1 to 8.
Let’s take a look at what types of manipulates are essential for each area of mathematics. They will help with math lessons.
By far, when you introduce the word mathematics, most people conjure up numbers first. Young children need a multitude of experiences with numbers as numbers act as a foundational learning experience for mathematics. Numbers are to mathematics as what the ABCs are to reading and writing. Here are some of the milestones by grade levels in most districts. The following expectations are grossly simplified. To understand the details, you will need to refer to your area’s curriculum. They give parents a baseline for instruction but do not include any teaching strategies.
- can count to 50
- can skip count by 10s, 5s, and 2,s to 50
- can do addition and subtraction facts to 10, including problem-solving
- understand place value – tens and ones
- begin an understanding of fractions as part of a whole and in groups
- can make equal groups up to 10, can make half a group up to 10
- can count to 200
- can skip count by 3’s and 4’s to 100
- can do addition and subtraction facts to 20
- understand place value – hundreds, tens, ones
- continue working with fractions as a whole and in a group through the concept of sharing
- can count to 1000
- understand place value hundreds, tens, ones
- proficient in addition and subtraction facts to 20
- multiplication is introduced through work on area – X2, X5, X10
- continue with fractions – fractions have many names – 1/2 = 4/8
Linking Cubes: These cubes can be used for so many applications. For numbers, you needs small objects you can count to explore all of the basic number facts for adding, subtracting, multiplying and dividing. There are 100 blocks in a set. They come with activity cards to stimulate math activities. You can use any small objects such as teddy bears, too.
Number Line Activities: For adding and subtracting, some primary kids like using a number line to calculate the number facts. These activities start from the easiest to more difficult.
Ten Frame Set: This is another method for investigating facts. The ten frame format replicated our counting system that is based on grouping numbers in 10’s, but it can be used to investigate many different facts.
Fraction Circles: Once you have taught the basic idea of fractions, you can use these circles to explore the relationships such as 1/3 = 2/6.
Fraction Tiles and Circles: Fractions can be applied to many different circumstances. The tiles and circles gives you the opportunity to demonstrate that circles are not the only circumstance where mathematicians use fractions. The tiles leads to parts of a group concept.
LEGO: LEGO is the all time kick ass manipulative for mathematics. With it kids can internalize so much! Each piece relates perfectly to the other so a 2 block is one half of a 4 block etc. It is perfect for solidifying concepts about fractions. Best to let kids play with LEGO.
Hundreds Board: This set comes in a pack of 10 with a blank board on the back. You can use these boards very effectively for skip counting. Once you color all of the 3’s by skip counting you can easily see the pattern your highlighting makes.
Base Ten Set: You start with the yellow and green blocks in grade one to show place value for ones and tens. By grade 3 you will need the blue squares to show hundreds. This set is great as the place value is differentiated by color for young learners.
Although many parents think of algebra as part of an older child’s knowledge, many concepts can be taught at a younger grade by thinking of patterns in mathematics.
- from geometric patterns established in kindergarten, students advance to number patterns
- elementary steps of coding are introduced
- modeling is introduced such as seating for a large family dinner
- more complicate patterns are introduced, students need to extend them
- the concept of equality is explored through the manipulation of addition and subtraction statements on either sign of the equals sign
- coding on a grid is introduced
- mathematical modeling is applied to real-life situations
- students not only can extend patterns but they can describe what is happening: the number increase by 2 each time
- equality is extended to multiplication statements
- coding will include repeated number patterns.
- mathematical modeling will continue to more complicated situations
Linking Cubes: Use these linking cubes to make patterns that your child can extend. The cards provide you with some examples to get you started.
Stamps: Have your kids stamp out patterns using different numbers of stamps. For the simplest start with 2 stamps and then increase the number of stamps. Use mathematical concepts for artwork. Make a border for a picture that is a pattern for example.
Coding: This is a new area for the Ontario curriculum. To the left is an Angry Bird Maze Game. This is perfect for the beginner and so engaging for kids.
Here is an article with many ideas and electronic manipulatives. Do you want to challenge your kids? Try getting them involved with coding. Coding for Kids
- students ask questions such as what zoo animal is the favorite? First, they predict what might happen. Then they develop recording charts, take surveys of their classmates, and draw conclusions.
- they extend their understanding of collecting data by turning their attention to more complicated situations.
- start to understand the terminology such as likelihood, for certain, maybe and impossible.
- the students move from pictographs into graphs that include a scale to display the data they have collected or are interpreting
- experience the length, mass and capacity of different object
- become familiar with time through the use of daily calendars and seasonal activities
- take apart shapes to become familiar with their 2D parts
- increase their knowledge of complex shapes
- make maps of places they know
- use tools such as a ruler for measurement and a clock for time
- work with more 3D objects and their parts; they recognize the object when flipped around
- along with more work on length, they begin measuring the weight of an object and the capacity
- learn to tell time on digital and analog clocks
Folding Geometric Shapes: This kit of shapes has the advantage of also including the nets (or patterns) for the shape. Some people have found the pieces a little difficult to use. The clear shapes also allow you to investigate the capacity of the various shapes.
Early Pattern Blocks: This set of traditional shapes can grow with your kids’ abilities. The 10 large double sided cards make matching the shapes easy. However the smaller cards will give them a challenge. These shapes can also be used for fractions, too.
Mini Geometric Shapes: These shapes are perfect for investigating the characteristics of various 3D solids. Use plasticine or sticky tack to count the corners (verticies), sides, and edges. Trace the shapes to see the 2 D components. Many kids will enjoy playing with these blocks and in the meantime will internalize their characteristics.
Student Clock: This clock is geared so that by moving the minute hand the hour hand moves appropriately. Pair it with digital cards to show the relationship between the 2 methods of telling time.
Measuring Tape: You can use a standard ruler for measurement but these flexible tapes a great for measuring 3D objects. The scale is detailed but the numbers are clearly marked for young children. The tapes are double sided with inches on one side and centimetres on the other. This is a learning opportunity to understand different scales.
Calendar: Build a sense of time and seasons month by month as you complete the calendar on a daily basis. This large visual representation of time will help your kids understand the patterns involved and the changes taking place. Every primary classroom has a calendar.
This area is a new section of the Ontario curriculum, but some of its expectations were in the 2006 curriculum under a different section.
- recognize Canadian coins and dollar bills; they understand the value of each coin
- use various coins to make specific different values such as ways to make a dollar and ways to make $100.
- use coins to make change from whole dollar amounts.
Calculator Cash Register: This solar powered cash register will add authenticity to any money dealing activities you simulate, whether it is a lemonade stand, or grocery store. The calculator function allows kids to add several items for a total purchase.
Layered over what students will know and do, are some expectations that address how students feel about their mathematical skills. These expectations also expand on how students problem solve using a wide variety of manipulatives and techniques to enhance their thinking.
- develop a positive approach to mathematical problem solving by using positive self-talk when they approach challenges
- learn different methods for solving problems: sometimes they may draw a picture, make a list, use manipulatives, or think backward, etc.
- learn to manage their emotions as they work through a solution to a problem, the “I can do this” attitude, “I have the tools to finish this.”
It is time to LEVEL UP your teaching of Mathematics.
Manipulatives can do that for you.
One, two, three . . . . Six: The Dos and Don’ts of Teaching Numbers to Toddlers Find out how to start your toddler’s mathematical education.
Do you want to challenge your kids? Try getting them involved with coding. Coding for Kids
Mathematical Games: Here are some suggestions to make academic time FUN. Instead of mathematics assignments, try games.