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Search Results for: manipulatives

One Thing Your Kids Need to Know to Excel at Math

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In this age of chip-card transactions and smartphone “tap and pay,” I don’t usually have a reason to carry much cash. When I do need some extra cash, I go to the ATM at my local bank. I usually have a specific item that I need cash for, so I know exactly how much I need down to the dollar. But the ATM lets me withdraw only in multiples of ten. It’s one of life’s minor frustrations.

Have you ever wondered why so many things are broken down by tens? Why is the number ten so important to our society? No one’s sure, but some historians theorize that it’s because humans have ten fingers.

Regardless of why, our number system based on ten is one of the most pervasive aspects of human society. Nearly all countries and cultures use the base-ten number system for everyday uses. As adults we take understanding it for granted, but base ten can be a difficult concept for kids to pick up, and learning it early is critical for math success.

What is base ten?

Base ten is the number system that we use every day that uses columns to show place value. When a number is written out, each digit is assigned a column to show its value. We can see from the graphic below, the value of the 5 is ten times greater than the 3, while the 6 is one-tenth its value. This pattern continues as you move left or right.

Why is base ten important?

Getting a firm grasp on base ten is key to understanding math. Once your child understands how base ten works, many new doors will be opened.

If children lack a good understanding of the base-ten number system, they’ll have a hard time counting or visualizing quantities. They may only be able to count by ones, instead of by tens or hundreds. Learning more advanced math concepts such as long division becomes nearly impossible.

If a child doesn’t understand that the 5 in 58 actually represents 50, then lots of calculation problems can begin to show up as you move into more complex concepts, leading to a lot of frustration for both parent and child.

How and when should I teach my kids base ten?

It’s important to start early. BJU Press Math introduces this concept in K5 and reinforces it throughout the early grades.

The key to mastering base ten is visualization. Separating groups of ten from groups of ones visually early on helps develop understanding. This can be accomplished using hands-on manipulatives such as Unifix cubes or pennies.

Take a look at page 81 of BJU Press Math K5 Worktext.

The worktext asks the child to circle the group of ten that is visually separate from the remaining items. It then asks the child to write the numeral below. The image groupings above correlate with the tens and ones columns below.

The important thing in teaching this concept is to stick with it. Don’t get frustrated if things don’t click at first.  Keep trying a variety of visualizations and hands-on manipulatives until you find something that your child relates to. Need some ideas? The BJU Press Math K5 Teacher’s Edition is packed full of teaching advice and strategies.

Learn more about BJU Press Math K5

Homeschool Outside with These Ideas (Printable)

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Lately, my homeschool has been plagued by spring fever. Warm air, bright sunshine, blooming trees and flowers, playful squirrels, and visiting birds have all conspired together to distract my children. And I can hardly blame them for being distracted. There are days when I, too, would much rather be outside soaking up the sun than inside teaching a math lesson.

One of the great things about homeschooling is that it can happen anywhere. We don’t have to do our lessons in our homeschool room. We can do them outside while sitting on the porch or on a picnic table at the park. In fact, we don’t even have to sit anywhere. We can learn a lot by just walking through our neighborhood and observing the world around us.  Download our walking activity sheets and use some of the ideas below (or come up with some of your own) to keep the learning going while you enjoy some fresh air and exercise.

1. Gather Math Manipulatives

Who said that you have to use paper to do addition and subtraction? Take a walk and gather twigs, small rocks, pinecones (or whatever else interests your child), and use those as your manipulatives for the day if possible.

2. Review Math Concepts

Are you learning about geometry? See if your child can identify some solid figures. Are you learning about measurement? Measure the distance in feet, yards, or even steps between two trees in your yard. Or measure the distance between your front door and the mailbox. Need to work on statistics? Grab a stopwatch and time how long it takes for each family member to walk around the block. Then figure out the average walking time. Your neighborhood is a great place to practice real-world math.

3. Identify Nouns or Verbs

After you finish walking, encourage your children to write down twenty nouns or verbs that they observed during your walk. Nothing can be on the list more than once.

4. Write a Description

What interesting things are going on in your neighborhood? Is someone building a house? Are there baby ducks in a nearby pond? Snap a picture if you can and have your child write a descriptive paragraph about it using the writing sheet in the activity packet.

5. Review Science Concepts

This week in Science 2, my daughter is learning about forces, so we’re going to take a ten-minute walk and list all the push-or-pull movements that we observe.  You could do something similar with other science concepts. Can your children find an example of a solid, liquid, and a gas? Can they list a dozen natural resources that they observed?

As homeschoolers, we know that learning is not confined to a specfic time or even to a designated space. So take advantage of the beautiful spring weather and move your learning outside. Everyone will be glad you did!

My Wife’s Teacher’s Aide

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My wife is doing a tremendous job in her first year of homeschooling. She is a fantastic planner and with some regularity is able to get our family ahead in covering the material. But homeschool is a family effort. So instead of just providing funds for the curriculum materials, I have decided to be my wife’s teacher’s aide.

My Wife's Teacher's Aide

In a traditional school setting, a teacher’s aide does menial tasks for the teacher. Lots of tasks—like stuffing papers into folders and grading worksheets—are things anyone can do and don’t require much evaluation. They just take time.

I’ve tried to support my wife by doing these types of tasks for her. When she had to organize manipulatives for the math program, I pitched in. Also, I usually do the daily grading of my daughter’s worksheets. It takes about ten to fifteen minutes of my time. Each of these tasks is small, but the reasons I do them are important.

Here are three motivations I have for choosing to serve as my wife’s teacher’s aide.

  • Loving my wife: The Lord commands me to love my wife as I love myself. Pitching in at the end of the day is one small way for me to show her I love her. I don’t want her to have to stay up fifteen minutes later or give up some personal time to grade these papers. When it comes down to it, I wish I could do more for her.
  • Seeing my child’s progress: It’s great to see how my daughter is progressing and what she’s learning. When she does great work, I have the opportunity to praise her. Sometimes, when she’s careless, I can challenge her to do better. I’ve seen her respond to praise and my challenges to do better. Her work keeps getting better.
  • Supporting our homeschool: Homeschooling allows our family to provide our children a Christian education, which is one of the most important gifts we can give them. I don’t want to stand on the sidelines of this journey of learning my children are on. Being my wife’s teacher’s aide allows me to actively support homeschooling on an everyday basis.

I enjoy being a teacher’s aide because of the ways it enables me to support my wife and children. I would encourage homeschool dads to consider similar ways they could get involved in the day-to-day homeschooling routine.

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What Does Math Look Like?

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Typically we don’t think about math as something to look at. It’s a field of study, not a physical object, but being able to see math is a skill that can be invaluable to children. Let me explain.

I regularly volunteer as a math tutor at a ministry that helps adults obtain a GED. Every student I work with learns at a different pace. Some of my students move through the material quickly, doing much of the math mentally. They see the patterns and are able to apply them to new material as they progress.

Other students are able to work though the math, but much more slowly. They stick to procedures, writing out each and every step of all the problems but never really understanding how the math works or how it could be used. It’s usually not a matter of difference in ability; it’s that the one group is able to visualize how math works while the other can’t. This difference probably has a lot to do with how the students were exposed to math when they were in the elementary grades.

JH_Math_2

Visualizing Not Just Repeating

Memorizing steps and formulas and then practicing them over and over might allow someone to pass a test, but it doesn’t promote retention. It also doesn’t train children to be good problem solvers. Teaching children to visualize how math works helps them build the problem-solving skills they will need as they move into advanced math.

Let’s look at an example page from our Math 5 that does a great job of showing this idea in action. (Example is from BJU Press Math 5 Student Worktext, page 129.)

math5student_p129-cropped

A student could solve these comparisons by changing the denominators to come up with the right answer. That’s a correct way of solving these math problems, and Math 5 teaches that approach. However, as the lesson shows, it’s also important to learn how to solve simple math problems mentally. By using strategies like thinking of ½ and seeing if each fraction is more or less or comparing the denominators, students are able to easily solve simple problems, check their answers, and learn new concepts more quickly.

Learning to See Math

When teaching math, parents should—in my opinion—approach each problem from various angles, even if the child gets the correct answer immediately. Use visuals such as money, cut-out shapes, and manipulatives to show how a problem looks both physically and on paper. Reinforce knowledge by asking questions whenever possible instead of just explaining how things work. As children learn to visualize math, they’ll begin to see math as a series of meaningful challenges to overcome as opposed to a boring list of problems to work though.

For more teaching tips like these, be sure to sign up for our homeschool email.

How to Make Sense of Math

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Growing up, I didn’t like math. The subject became slightly more enjoyable for me when I got to “play” with the math manipulatives. Shapes were for making art mosaics. Paper money facilitated a pretend shopping spree to the bookstore. And Unifix cubes were (and still are!) just plain awesome for making patterns or sculptures.

You see, I was the homeschooled child who was unwilling to memorize number facts or equations unless I knew the reason why. Using manipulatives gave me a better understanding of the concepts being introduced in BJU Press Math. Instead of trying to calculate abstract numbers in my head, I was able to associate the equation with a concrete object.

A good math curriculum links concepts with tangible elements that visually demonstrate the problem.

BJU Press Math manipulative place value mat

Place Value Mat

Take, for instance, the concept of renaming in subtraction. How can a child understand that adding ten to the next place value (such as the tens or ones place) allows her to accurately find the answer? Using a place value kit with ones, tens, and hundreds reinforces the mental calculation of an equation using the senses of sight, touch, and sound (if she counts aloud).

Watch the first five minutes of this Math 2 Distance Learning sample lesson video with Mrs. Walker to see how a place value mat aids learning.

Build Understanding over Memory

Building number sense through this hands-on learning experience allows your child to understand how a problem is solved and not just memorize a formula to get an answer. Teaching what math feels and looks like by using manipulatives builds a true understanding of the subject. This fun math “playing” helped to develop my number sense without my even knowing it, and other children can benefit from this same experience.

The BJU Press Elementary Math curriculum introduces new concepts using manipulatives. Beginning with a tangible demonstration of math concepts builds your child’s understanding so that she can solve problems when those concepts are presented on paper. The goal is to develop her thinking skills so that she can be a lifelong problem solver because knowing how math applies to everyday life prepares your child for success in the role God has planned for her.

Today, math isn’t my favorite subject, but I do credit my ability to understand and solve real-life math equations in the kitchen, at the office, or at the store to my hands-on learning experiences as a child. Yes, math manipulatives are that foundational.

Which math manipulatives do your kids enjoy the most?

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