BJU Press Blog

math manipulatives

5 Ways to Use Leaves in Your Homeschool This Fall

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use leaves in your homeschool
One of the wonderful things about homeschooling is the freedom to adapt your lessons to the seasons or to your kids’ needs! This autumn, why not incorporate natural elements, fresh air, and movement to spice up those lessons? Check out these five ways to use leaves in your homeschool lessons.

1. Hone those identification skills.

One way to use those fall leaves is to have a classification session. Run outside with your kids and gather up some freshly fallen leaf specimens. Make sure your kids bring back several different kinds of leaves, of various shapes, sizes, and colors. With the help of the internet, some library books, or a BJU Press textbook, your kids can compare the leaves they have found to the pictures they see. Once they note the specific traits of each leaf, they’ll be able to identify which kind of tree it came from.

2. Have a homeschool microscope session.

There are a million fun and educational things you can do with a microscope; so if you don’t already have one, consider investing in a small, inexpensive model for starters. Maybe you can borrow one from a friend for this lesson.

After the initial “Wow!” moment when your kids see an autumn leaf under the microscope for the first time, ask them to describe what they see in a few sentences. Do leaves from various kinds of trees appear different under the lens?

Consider comparing a leaf that’s still green with one that is red or yellow. How do they look under the microscope when compared to a leaf that’s very brown and dry?

3. Create fall leaf art pieces for your homeschool.

For your homeschool art class, why not make leaf rubbings, leaf lanterns, leaf puppets, leaf masks, or leaf crowns? You can also create garlands, wreaths, prints, and collages with the leaves. Or just give your kids a bunch of art supplies (like glitter, glue, chalk, paper, yarn, and googly eyes) and see what they come up with! This post from HandsOnAsWeGrow.com includes links to dozens of fall leaf crafts.

4. Get down to the molecular level.

Older kids may be more interested in the actual process by which leaves change color. Talk with them about the cellular structure of the leaves and about the presence of carotenoids and other pigments. You’ll find excellent material in the BJU Press science textbooks as well as on the Harvard Forest website and at Environmental Education for Kids website.

5. Use leaves as math manipulatives in your homeschool lessons.

Almost anything can become part of a math lesson! To add seasonal flair, let your preschoolers or kindergartners count some fall leaves. For elementary-aged kids, teach fractions by snipping the leaves into sections and showing what three-fourths or two-fifths might look like.

Once you’ve used the leaves for your lessons, they’ll probably be crumbling and falling apart. That’s a great time to talk to your kids about properly disposing of yard waste and recycling it if possible. Fallen leaves can become mulch for your flowerbeds or an addition to your compost pile. In God’s world, nothing is wasted—even the death of the summer leaves enriches the earth and enables new life in the spring.

• • • • •

Rebecca is a work-at-home freelance writer, novelist, wife, and the mom of two bright-eyed little ones. She credits her success in writing and her love of books to her own mom, who homeschooled three kids from pre-K through high school.

A Third-Grade Probability Activity

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Probability activity with pom poms
Probability. It’s the reason my kids are required to wear a helmet when riding a bike and a seatbelt when riding in the car. It’s what determines the rate I pay for home and auto insurance and what helps me decide whether it’s worth purchasing an extended warranty for my vehicle. And it’s a challenging concept for an eight-year-old to grasp.

I know because my husband and I tried to explain it when we introduced our third grader to the board game Settlers of Catan. But she didn’t get it. Probability was a brand-new concept for her and, as with all new math concepts, she needed a hands-on activity to help her understand how it works.

Thankfully, Math 3 from BJU Press uses a simple hands-on activity to illustrate the concept of probability.

Materials Needed for This Probability Activity

  • Five different colors of pom-poms (blue, green, purple, red, and orange)
  • Small opaque bag
  • Printout

probability activity materialsGet Ready for Learning Success

Start by putting pom-poms in the bag (5 blue, 5 green, 2 purple, 2 red, and 1 orange). Explain to your child that the term probability refers to how likely or unlikely something is to happen. Ask him to predict what color pom-poms he will most likely get when he pulls out one. What color(s) is he least likely to pull out?

probability activity handoutDeepen Understanding Through Discovery

Now, it’s the child’s chance to test out his predictions. Instruct your child to reach into the bag and pull out a pom-pom without looking. Then he should make note of the color by placing a tally mark in the corresponding column on the probability handout before tossing the pom-pom back into the bag. Do this twenty times. (Hint: If you have preschoolers at your house, this is a great activity to get them involved in “school” too. Have them pull out the pom-poms one by one and see if they can name the color.)

doing the probability activityCommunicate Results

Now it’s time to do something with that data. Help your child turn the tally chart into a bar or line graph and report the findings. Did his predictions match the results? Why or why not?

My third grader was so fascinated by this activity that she wanted to do it again. So she did—several times in fact.  Each time she used a different mix of pom-pom colors and tried to predict the results. As her understanding grew, so did the accuracy of her predictions. And so did her excitement about learning. It was a great day.

Be sure to check out BJU Press’s Math 3 curriculum, which inspired this activity. You can get ideas for more math activities by clicking on the links below.
Dividing Fractions a Simpler Way
Activity for Simplifying Ratios

charting probability activity

Dividing Fractions a Simpler Way

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dividing fractions printable
The twelve-year-old’s T-shirt reminded me of my own homeschool experience with fractions and made me chuckle with delight. The shirt said, “Did you know that 5 out of 4 people struggle with fractions?”dividing fractions materials

When I was in the upper elementary grades, my mom switched us from a homeschool math program that used a hands-on approach to a program that was trendy among homeschool families at the time. It was during that phase of my math education that fractions became increasingly difficult. I had to multiply and divide with fractions, and it was all so confusing. Why is it that when I multiply, I get a smaller number, but when I divide, I get a larger number?

I think the hands-on approach would have helped me understand the basic arithmetic of fractions. If your child is struggling with dividing fractions, try the following hands-on approach to see if it helps. (I found this activity in BJU Press’s Math 6 textbook, which has lots more hands-on activities for teaching fractions and other challenging math concepts.)

dividing fractions circlesInstructions

  • Print out these circles and have your child cut along the outer solid lines. (Note: You can also use two apples instead.)
  • We’re going to work through the problem 2 ÷ ¾, but that’s rather abstract, so let’s use a real-world problem.

“We want to make apple tarts. Each tart requires ¾ of an apple. We have two apples. How many tarts can we make?”

dividing fractions cutting

  • Start with the two complete circles. These represent the number of apples we have.
  • Ask: “How do we need to cut the apples to make the tarts?” Since we’re going to need to separate out ¾ of an apple, the answer is “into quarters” or “into fourths.”
  • Now cut the whole circles into fourths.
  • Ask your child: “How many fourths are needed for each tart?”
  • Now have your child separate the fourths into piles of three.
  • Ask: “How many piles of three do you have?” Answer: 2
  • Ask: “How many quarters are left?” Answer: 2

Expressing the Answer

This might be tricky, but we want to express the exact number of tarts we can make. We could answer, “Two tarts,” but we would have two fourths or ½ an apple left over.” If we want to make a tart with the remaining apple fourths, how much of a tart could we make?  We would say, “Two and two-thirds tarts.” This confused me as a child. Why would I use thirds when I started with fourths? Walk your child through these questions to help with understanding:
dividing fractions coloring

  • Ask: “How many fourths do we need to make a whole tart?” Answer: 3
  • Ask: “How many fourths do we have left?” Answer: 2
  • Ask: “If it takes three to make a whole tart, and we have two of the three to make a whole one, how would we write that as a fraction?” Help your child see that the bottom number of the fraction tells us how many parts make a whole, and the top number tells us how many parts of that whole we have. So the whole tart has three parts (apple fourths), and we have two of those three parts or ⅔.
  • So we can make 2⅔  apple tarts with 2 apples.
  • Have your child color each group of three fourths and the two remaining fourths a different color so they can see which group of fourths will go into each tart.
  • Help your child write out how this would look as a math problem and solution: 2 ÷ ¾ = 2⅔.

dividing fractions completeWhy Hands-On Works

Working through this activity helped me understand some math that always challenged me as a child and into adulthood. Using hands-on activities helps many of us understand math. That’s because math is an expression of physical realities. When we see, touch, and talk about those physical objects that math is representing, the math makes more sense.

So if your child is struggling with fractions, try this and some other hands-on activities.

 

4 Steps for Teaching Math Comprehension

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comprehension with math manipulatives
When most of us think back to our experiences with math, we think of endless speed drills and a driving need to get the right answer. As a child, you may have wondered how memorizing formulas was going to help you understand math, and now it’s the same with your children.

You may feel like teaching your children to understand math is some kind of grand undertaking or incredible journey. Looking at it that way can be overwhelming. Where do you begin? How do you keep going? Maybe there’s a different way of achieving math comprehension?

As adults, we often remind ourselves to take everything one step at a time, and that’s probably some of the best advice, but what are the first steps of an approach that teaches your children to comprehend math rather than just memorizing meaningless facts?

1. Connecting numbers to tangible ideas

In and of themselves, numbers are abstract and nebulous. In order to ground number concepts in the real world for your children, you can use manipulatives. The manipulatives can be objects you use every day or the specially designed manipulatives found in the BJU Press elementary math curriculum. This physical understanding of numbers—or number sense—brings math comprehension into your children’s grasp.

2. Building a foundation for future learning

This step is two-fold. Once your children have made strong connections between the abstract concept of numbers and real objects, they’ll need to visualize the processes they’re using so that they remember that numbers mean something. In order to make sure that your children are visualizing math, try asking them questions that encourage them to think about their processes and how math works with real objects.

3. Expanding math comprehension

For math comprehension to grow deeper, it’s important that your children understand base ten math. You and I use base ten every time we break numbers into columns of thousands, hundreds, tens, ones, and so on. Making sure your children understand the concept of base ten math will make grasping the more difficult math processes easier for them.

4. Reaching real-world application

Learning comes full circle to the real purpose of math—a tool to assist us in wisely stewarding God’s creation to serve others—when it begins to reach real-world situations. The skills your children learned during carefully prepared lessons and activities will come into play naturally in real-world situations, such as grocery shopping. These life skills develop as a result of how well they understand math, not because of how well they do speed drills or what grade they make on a test.

Notice how each step after the first relies heavily on connecting numbers back to the real world in some way? As important as all the subsequent steps are, the first is still the key to really comprehending math.

As an ancient Chinese philosopher once wrote, “A journey of a thousand miles begins with a single step.” Once you make strong connections between abstract numbers and tangible objects, the other steps will begin to feel more natural.

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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