If you’re anything like many parents struggling with education at home, your day may look like this: your 3rd grade daughter is having problems with multiplication; your 5th grade son is wondering how ½ is bigger than ¼ when 4 is bigger than 2; and you’ve forgotten most of what you learned about those topics when you were their age.
As a parent who is striving to also be a teacher, you’ll start to see that sometimes the concepts being taught in elementary math are not necessarily meshing with what your child is actually understanding. It’s common. Lots of kids need extra boosts, and to see information presented in a different way, in order to grasp concepts in math.
This is where you can use manipulatives, visual posters, and math games to make learning math easier and, in most cases, more enjoyable for your at-home student.
What are manipulatives?
Since ancient times, people in civilizations across the globe have used physical objects to help them solve everyday math problems. In the late 1800s, the first true manipulatives – maneuverable objects that appeal to several different senses and are specifically designed for teaching mathematical concepts – were created.
Friedrich Froebel, a German kindergarten teacher, developed different types of objects to help his young students recognize patterns, count, and appreciate geometry found in nature. Maria Montessori further advanced the idea that these tools are important in the learning process. She herself designed many manipulatives to help developing students learn basic math concepts that are still used today.
Manipulatives are objects that are intended to give a student learning a math concept a hands-on experience. Manipulatives can come in many forms, and are utilized in endless ways.
Ways Manipulatives Are Used in the Classroom
Of course, every school district has its own set of guidelines and curricula, but commonly accepted ways that manipulatives are used to communicate ideas and processes in math in the classroom include:
- Sorting—a pre-math skill that aids in comprehension of patterns and functions
- Ordering—a pre-math skill that enhances number sense and other math-related abilities
- Distinguishing patterns—the foundation for making mathematical generalizations
- Recognizing geometric shapes and relationships
- Making measurements
- Understanding the base-ten system of numbers
- Comprehending mathematical operations— addition, subtraction, multiplication, division
- Recognizing relationships among mathematical operations
- Exploring and describing spatial relationships
- Developing and utilizing spatial memory
- Engaging in problem-solving
Why are manipulatives important?
No two children are fully alike in their learning. What’s more, math has a lot of different areas – patterns, geometry, measurement, probability, fractions…the list goes on. More often than not, they’re unfamiliar, abstract, and even confusing to kids. Giving a student the opportunity to learn math using actual items can be an engaging and fun experience – a plus for any student – and has been shown to aid in the absorption of new material, as well as increased understanding.
Though this list is not exhaustive, here are some reasons manipulatives are important when teaching math, in the classroom and at home:
Manipulatives make abstract ideas concrete
Students manipulate hands-on, concrete objects to model abstract math concepts/skill. Having students represent their concrete understandings via manipulatives supports a developing the needed skills to independently form solutions to problem solving situations. When students first develop a level of understanding for any math concept/skill, they can call upon this foundation to link their understanding to other abstract math topics in the future. Having students represent their concrete understandings via manipulatives supports a developing the needed skills to independently form solutions to problem solving situations.
Manipulatives provide tangible and interesting problem solving
This one is pretty simple. What’s more engaging for an elementary student: a sheet of paper, or a jar of jelly beans? Giving students physical objects takes math concepts off the page.
Manipulatives make math “more real”
Understanding and applying abstract concepts is not always easy, especially for younger students. Manipulatives mean that kids can feel a three-dimensional item in their hands, creating an understanding that pictures and videos just can’t provide. While using these tools, students form a step-by-step process that allows them to actually understand an abstract problem in stages, so the problem as a whole can more easily understand, then solved.
A student who can solve problems on their own using manipulatives is a more confident one, and that confidence helps them throughout their education. If children have physical evidence of how their mind is working when they tackle a math problem, their understanding is more robust.
Seeing your kids feel empowered that they were able to figure out that 2 + 2 = 4 by counting the correct amount of beans, or using a place value box, is also fulfilling for you, their at-home teacher. Kinesthetic learners especially benefit from such instruction in being able to touch and learn at the same time.
6 Easy Manipulative Exercises
Manipulatives give kids the opportunity to explain a math concept in an engaging manner. Instead of using words, they’re able to use objects. It grabs the attention of the listener but also keeps the child willing to explain in a clear and effective manner their thought process in solving a problem. The child becomes the teacher, and you are their student.
1. Base 10 blocks
Base 10 blocks are mainly used to teach place value. Units represent ones, rods represent tens, flats are hundreds and cubes are thousands.
However, base 10 blocks can also be used to explain decimals.
For example, take how a rod is split into 10 units. One unit equates to one hundredth, or 0.01 and that one rod equals 10 hundredths which ends up being one tenth, 10 x 0.01 = 0.1. Ten rods equals one whole, 10 x 10 x 0.01 = 1.
2. Dry erase boards
Dry erase boards with colorful markers can also be used as a manipulative. Children can draw the actual item being described in a word problem to help them answer a question.
For example, three cats and two dogs are outside. How many animals are outside? You cannot have your child literally go find cats and dogs to get the answer (unless you have that many pets), but they can have fun drawing the animals to see that the total will be five animals.
3. Fraction strips
Fraction strips are very useful in teaching equivalent fractions, adding and subtracting them, and comparing.
Sometimes fractions are a hard concept to tackle unless it is visually done. Children have been told that 4 is greater than 2 during their early years in school, so when they learn that ½ is greater than ¼, they question it! Showing how these fractions “look” as pieces of a whole, using strips, makes it easier to understand.
4. Interlocking cubes
Interlocking cubes can be used to create patterns as they come in various colors to help young students.
They also can be used to learn the basic operations in math – addition, subtraction, multiplication, division – as well as perimeter, area, and even volume (for older students).
For young students, give them eight cubes of different colors and ask them to create a pattern. To teach perimeter to a 4th grader, ask them to make a rectangle that has a length of 3 cubes and a width of 4 cubes, and then ask for both the perimeter and area.
5. One hundred chart/grid
This chart can be used in so many ways! Children can learn how to count up or down between numbers up to 100, how to skip count to teach multiplication and what multiples are, and number patterns.
You can also play Multiplication Bingo by stating a fact – let’s say 4 x 5. Your child should then place a small object on the product of 20.
6. Number lines
Number lines show positive and negative integers. Younger children can use number lines to learn how to count and add and subtract. Having a number line to write on can help do this.
Older children can number lines it to help with integer addition and subtraction. Seeing concepts visually and working out how to move forwards and backwards from an integer make it easier to grasp as a concept.
Here’s an example using -7 + 3 = -4.
These are not, of course, the only manipulatives that are useful in teaching math! Counting bears, scales, and dot grids are a few more manipulatives your child may have experience using in their math classroom. Whatever you use, find manipulatives that excite your at-home students, are interesting, and can be used for other math topics so that you can have the biggest bang for your buck.
Manipulatives in Homeschooling
Parents may not be able to buy the manipulatives that teachers and tutors use. That’s okay! You can use everyday household items. They still give your child the same hands-on experience that is desired from the manipulatives above to keep home learning engaging.
Some items include:
- Beans – various types of beans can be good for creating patterns; counting; basic operations; ratios
- Clothing – have your child create a bar graph/table showing how many shirts, jeans, dresses, shoes, etc.
- Coins – counting; teaching money and value
- M&M’s or Skittles – useful for counting, basic operations, ratios. You can also be your child’s best friend.
- Cereal – before eating, your child can learn about volume and filling up the bowl with a cup, pint or gallon of milk. fruit/vegetables – cut up an apple or celery into pieces into halves, thirds, etc.
- Toys – use your child’s cars or dolls to count but also can be used for grouping and ratios
How to be hands-on throughout the home
Parents may want to be creative and use regular household items as manipulatives but in an engaging, hands-on way. Here are some additional examples of things you can do at home that are secretly a chance to teach your kids math (shh, we won’t tell):
Baking and cooking – Children can learn perimeter and area by baking a pan of brownies. A child can also learn how to estimate the amount of chocolate chips go into a batch of cookies being baked.
Older children can figure out how many cups of strawberries and water are needed to serve 5 smoothies if you need ¼ cup of strawberries and ½ cup of water for 1 smoothie (Hint – Use multiplication).
Children can also learn about measurement and capacity. You can show how many cups it takes to fill a gallon. A child-friendly set of measuring cups and spoons can do the recipe on the side.
Gardening – Children can plant a certain amount of seeds of a certain type of flower, fruit or vegetable. They can work on estimation on how many of what they planted grew over a pre-determined amount of time. Younger children can then see how much off they were from the estimation by subtracting while older children can work on percentages.
You can also teach patterns if you have flowers arranged in such a way. This can also lead into ratios, proportions and fractions.
Be your kid’s biggest math cheerleader
Manipulatives can be utilized to a parent’s advantage to make math fun and as engaging as possible. Give your child tangible items to so that he/she can manipulate to get the right answer. As the parent and teacher, get comfortable and knowledgeable with the math topics and the manipulatives you want to use so that your child feels at ease in using it independently.
The more you can try to be a part of the experience of using manipulatives, the more your child will feel ready to use it independently when doing a math problem. Manipulatives are a great tool to keep your child’s attention. Use what you have and skills you use in everyday life to make math as much fun as possible. Children need to see adults enjoying math to enjoy it themselves!