Never Underestimate the Importance of the Fundamentals
Teachers, researchers, and Mathnasium of Parker agree that building a strong math foundation begins in the early years of childhood. Read Prepare Your Child for Calculus Starting in Second Grade and Math Takes Time to Conquer for more information on how early math instruction may impact a child’s attitude and ability in math through college.
If your child is already in middle school or high school it is not too late. Older children who missed a fundamental concept in school just need to revisit these fundamental concepts again. At Mathnasium of Parker we teach these concepts in an age appropriate way. Parents of older children may want to read the following articles for information about meeting the math needs of struggling older children.
As part of helping parents understand some of the fundamentals in mathematical concepts, we recently we published an article about counting. This article explains another fundamental skill, known as “wholes and parts”. Don’t let the simplicity of the term fool you. Some educators use the term “composing numbers” and “decomposing numbers" which could lead some parents to imagine numbers writing music or rotting. That’s why at Mathnasium we prefer the term “wholes and parts.”
Concepts of Wholes and Parts Helps with Numerical Fluency and Number Sense
Numerical fluency refers to a person’s ability to approach any mathematical problem in a variety of ways. Number sense refers to a person’s ability to understand and use numbers. Numerical fluency and number sense lay a strong foundation for success in math. For more info read “What is Numerical Fluency?” and Teaching Number Sense.
What are Wholes and Parts in Math?
The whole is the sum of the parts. Consider the number 6 as the whole number. It can be broken down into various parts, 1 and 5, 1 and 2 and 2 and 1, 2 and 4, 2 and 2 and 2, or 3 and 3. You may notice that these are essentially equations 1+2+2+1= 6 and 2 x 3 = 6. Trying to memorize all the equations equal to any given whole number would be ridiculous. The higher any number gets the more parts it has. A child who can break up any whole number into parts easily will have an easier time with adding, subtracting, multiplying, dividing, proportional thinking, fractions and many other math skills.
Combinations of 10
The number 10 deserves special consideration for teaching the concept of wholes and parts. Since our numbering system is based on the number 10, children need more than a basic understanding of the parts and whole of that number. They need to have the basic combinations of 10 memorized. These combinations of 10, or complements of 10, include 10 and 0, 9 and 1, 8 and 2, 7 and 3, 4 and 6, and 5 and 5. If a first grade teacher asks the class to solve 10-2, everybody should be able reply 8 without counting. The child will later realize they know 100-20=80, 1000- 800=200 without counting.
Furthermore, children who memorize 10-2= 8 in first grade and learn to use mathematical reasoning will be able to quickly mentally calculate 102- 88 in second grade. Read Is Your Child Dependent on Algorithms … and is That a Bad Thing? to learn about mathematical reasoning. You may also want to check your child’s current level of mathematical reasoning and numerical fluency with our quick tool.
Teaching Wholes and Parts to Young Children
Mathnasium of Parker and Common Core Math Standards emphasize teaching wholes and parts. Understanding that the whole is the sum of its parts, strong counting skills, and the ability to think proportionally are critical components to our curriculum.
There are many strategies to helping children experience the wholes and parts idea in math. Younger kids benefit from manipulating concrete tools such as Unifix cubes. Visual learners may remember wholes and parts concepts through the use of pictures. Some common tools for visual learners include dominos and ten frames. When children are ready for more abstract ideas with wholes and parts, fact families are introduced. The domino above shows the fact family of 5+4=9, 4+5=9, 9-5=4, 9-4=5.
Wholes and Parts Lessons Aren’t Just for Little Kids
Most of the examples given so far apply to kindergarten and first grade. But wholes and parts extends way beyond that. Fractions are one obvious example. Legos can be really helpful in teaching wholes and parts to second and third graders. Even geometry uses wholes and parts particularly with concepts such as the Pythagorean Theorem or finding the area of an irregular shape.
What You Can Do at Home
Wholes and parts in the younger grades are pretty easy to incorporate into everyday conversation. At dinner you might say, “We need 5 napkins total. Choose some red ones and some white ones. How many of each will you choose?” As they get older, incorporating wholes and parts into the conversation might sound more like this, “Your birthday party guests include 3 kids who are vegetarian and 2 who are gluten free and 10 who eat all types of pizza. Please order enough pizza of the right type to keep everyone happy.”
The Mathnasium Method of Teaching Wholes and Parts
When you ask your child what they learned at Mathnasium of Parker, don’t expect to hear “we learned about wholes and parts.” As foundational concept, wholes and parts lessons are woven throughout the curriculum. Your child might say instead, “I learned to add two digit numbers.” All you will notice is that your child keeps getting more and more confident in math the longer they are at Mathnasium of Parker. Their strength will come from their strong foundational skills, including concepts of wholes and parts.
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This article was written by and owned by Cuttlefish Copywriting. It is copyright protected. Mathnasium of Parker has permission to use it. Other Mathnasium locations should contact Heather at [email protected] or visit www.cuttlefishcopywriting.com before using it.
