math

A Third-Grade Probability Activity

March 22, 2018 by Megan

$Probability activity with pom poms$
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

Get 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?

Deepen 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.)

Communicate 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

Activity for Simplifying Ratios

February 22, 2018 by Ben

Ratios compare two quantities that are related. It’s a concept that can be challenging for kids to understand. As a child, I could solve problems related to ratios, but I never quite “got it” . . . that is, until my mother was teaching me how to half a recipe. For the recipe to work, the relationship of all the ingredients needed to remain the same. So, we divided all of the parts by two.

My mom wasn’t trying to teach me a math lesson that day, but she pointed out how important ratios are in the kitchen to solve a basic problem. I received understanding that day by getting my hands involved in learning as we solved an actual problem.

We can help children begin with understanding if we start teaching math with a hands-on activity that solves a real-world problem. So here’s a simple activity to help children master the concept of ratios and use them to solve a problem. I found the inspiration for this activity in BJU Press’s Math 5 Teacher’s Edition, where you can find scores of other hands-on activities that can help your children understand math concepts.

Making a snack

We want to make a simple trail mix for a hike. Each member of our family needs a miniature snack bag of raisins and peanuts.

We want to have a consistent snack bag, so each bag needs to have 5 raisins for every 7 peanuts. Ratios can help us get the right amount of ingredients for every family member to have the same snack.

Sketching out the ratios

Let’s start with paper and pencil, but without diving into abstract equations. To help children grasp the idea of ratios, we can represent each raisin with the letter r and each peanut with the letter p. We use a colon instead of the word to. Let’s start with just one bag.

1 bag

rrrrr:ppppppp

Your child probably won’t need to count, but let’s write out the ratio for one bag.

5 raisins: 7 peanuts

So counting the r’s and p’s will be more helpful when determining the number of raisins and peanuts needed for the three children on the hike.

3 bags (3 children on the hike)

rrrrr:ppppppp
rrrrr:ppppppp
rrrrr:ppppppp

15 raisins: 21 peanuts

How many r’s are there? How many p’s?

Does the number of raisins or peanuts change for each bag? This question helps your child see that a ratio is expressing a consistent relationship, in this case raisins and peanuts in the miniature snack bag.

Now let’s suggest we make bags for Mom and Dad too.

5 bags (total family members)

rrrrr:ppppppp
rrrrr:ppppppp
rrrrr:ppppppp
rrrrr:ppppppp
rrrrr:ppppppp

25 raisins: 35 peanuts

Now your child can count the r’s and p’s or multiply each number in the ratio by 5 to determine the total number of raisins and peanuts needed for the hike. You might also want to mention to your fifth grader that writing out r’s and p’s is useful for seeing how ratios work, but it’s not a fast way to solve the problem. Multiplying is the quickest way to solve with ratios.

So for the whole family, we need 25 raisins and 35 peanuts.

Now have your fifth grader count out the total number of raisins and peanuts into distinct piles of 5 raisins and 7 peanuts each. Then put the piles into sandwich bags. Of course, you could adjust the snack portions according to your family’s needs. Now you’re ready for a hike!

Using Ratios

Ratios are useful in helping us determine the total needed before we begin the project. That way we can check our supplies before we get started and make a run to the grocery store if needed. Once we’re ready to begin a project, the ratios help us create consistent snacks.

Consistency is critical in baking at home. But ratios also help construction workers, restaurant owners, manufacturers, and a host of other professionals as they order the appropriate amounts of supplies before they begin a large-scale project. And they will use ratios to consistently use those supplies. When children see how they can use ratios like professionals do in planning and executing projects, they will have a concrete understanding of the concept.

Dividing Fractions a Simpler Way

January 25, 2018 by Ben

$dividing fractions printable$
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.)

$dividing fractions circles$ Instructions

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.

$dividing fractions complete$ Why 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.

What Is STEM and How Do I Teach It?

October 19, 2017 by Justin

If you’re like me, you have a hard time keeping up with all the new buzzwords in education. When you hear about STEM, it’s usually being talked about as if it’s a subject all its own—one more thing you need to worry about teaching your kids. The reality is that you’re probably already teaching it, especially if you are using BJU Press textbooks for science and math. We were doing STEM long before it was called STEM.

What STEM Is

STEM is an acronym for

Science
Technology
Engineering
Math

Technically, any lesson that falls into one of these subject areas is a “STEM lesson.” But the term is typically used when describing activities that seek to teach kids how to apply those subjects to real-world applications. If hearing about STEM brings to mind pictures of kids building robots, that’s because robotics and programming are examples of real-world applications. They are definitely STEM, but STEM isn’t limited to electronics. Exercises can also include chemistry experiments, math equations used to design buildings or vehicles, weather analysis, and more.

Why It’s Hot

The acronym actually dates back to 1998 but has recently gained a lot of popularity. Experts in the United States determined that we were behind other countries in these areas in terms of test scores and the number of college graduates holding degrees in those fields. The majority of high-paying new jobs fall into the STEM category, and there aren’t enough graduates to meet that demand.

Why It Matters

Homeschoolers usually aren’t big on educational fads, focusing instead on time-tested approaches that we know work. The acronym STEM might be trendy but the idea isn’t new. The fundamental processes used in math and science never change, but the way we apply them to the real world has to because the demands of the job market change. If we’re going to bring up our children to be good stewards of God’s creation and to love their neighbors, we have to equip them with the tools they need to accomplish those things in a modern world. That’s why BJU Press has been including these real-world applications in our science and math textbook lines from the beginning.

What to Do

One of the best things about homeschooling is that you can do what’s right for your family. I believe STEM is very important, so here are two things I plan to do with my own son:

I’m going to make sure that the curriculum I’m using has plenty of up-to-date STEM exercises that will help him learn.
I’m going to personally come at the activities with a learner’s attitude. A lot of the lessons, especially ones involving technology and programing might be foreign to parents who aren’t actively involved in fields that use them, but I’m excited about learning along with my son and certainly won’t skip over lessons that may seem unfamiliar or difficult. We’ll get through them together.

Did you find this post helpful? Would you like to share a STEM activity that has worked in your homeschool? Be sure to comment below! Also, to get you started, here are six free STEM activities from BJU Press science textbooks.

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Building Long-Term Math Mastery

September 28, 2017 by Jenna

$BJU Press Math$
Have you ever stopped and asked yourself, “Why does one plus one equal two?” Most people who find themselves faced with this math question will probably say something along the lines of “it just does.” But if you thought about it, you could probably come up with a more articulate answer. For example, if you have one marker, then buy another one, and count how many markers you have, you will have two. That’s why one plus one equals two.

What did I have to do in order to answer the question? For most adults, connecting number problems to familiar objects is automatic. That’s because, as children, we learned number sense by working with objects that we could count and move around. You know that manipulatives are key to developing math comprehension. But are there other keys to math comprehension that are essential for long-term mastery?

Yes. Our Math 2 student worktext constantly asks your child questions about the processes he used and how he found his answer.

Students must learn to think about and explain the processes and formulas they use in order for math to have any lasting purpose for them.

For example, in high school, I was at the top of my class in math, but not because I had any idea of what all those numbers meant. It was simply because I could put numbers in the right places in a formula. In fact, I always loved the quadratic equation, and I still remember x equals negative b plus or minus the square root of b-squared minus 4ac all over 2a. But when I got to geometric proofs, I was hopelessly lost. My high school math textbooks never reminded me that the formulas and numbers I loved playing with actually meant something. It was like putting together a puzzle with edge pieces but no middle.

A child’s ability to solve equations doesn’t mean he gets it.

So how do you ensure that your child will be able to make sense of math as he moves into more and more complex ideas?

Ask him to explain his process. What would the equation he’s solving look like in real life?
Ask him for observations about the concepts he’s learning. Does he see any new patterns? Do other math concepts apply to the new one? Does the new math concept apply to old ones?
Incorporate common objects as manipulatives. As he begins learning about area and surface area, can he find the surface area of a tissue box? How would that information be useful to the person designing the box or putting it together?

Look through the thought bubbles in Math 2 student worktext for more ideas of questions to ask your child.

When math has meaning, it also has purpose. If you can create a strong connection between your child and the meanings of the numbers and formulas, you might also connect him to a future career.