BJU Press Blog

Search Results for: manipulatives

Learning Place Value with a Hands-on Activity

by

place value cover
As a homeschool dad, I found it easy to fall into the trap of believing that my young child understood a number because she could say it and count to it. When my second daughter was in kindergarten, we enjoyed skip counting to a trillion by 100 billions. She felt like she grasped the number 1 trillion. But I was overlooking place value and the role it plays in deep understanding of foundational math concepts.

The concept of place value is crucial not only in gigantic numbers but also in more relatable numbers. It’s so easy for a six-year-old to recognize and count to a number such as 23 but not understand what the 2 and the 3 mean in practical, real-life experience.

One of the best ways to develop your child’s understanding of place value is through less-than and greater-than activities. Doing hands-on exercises develops number sense that will enable your child to solve real-world problems.

Preparing

  • Cut out twenty small squares of paper and ten strips of paper (ten squares each). [You can make strips and squares using the first page of the printable, or use the counting cubes from the Math 1 Student Manipulatives packet.]
  • Label three sheets of paper, the first as “Ones,” the second as “Tens,”  and the third as “Answers,” or use pages 2–4 of the printable.

place value activity materialsManeuvering

Give your child the following instructions orally, and guide him in carrying them out.

  1. Position the Tens paper and the Ones paper side by side with the Tens on the left. Make the number 32 on the top half of the Tens paper and the Ones paper.
  2. Skip count the tens aloud (i.e., count 10, 20, 30).
  3. Count the ones aloud (i.e., count 1, 2).
  4. Write the number on the answer sheet (i.e., 32).
  5. Now make the number 23 using the bottom half of the Tens paper and the Ones paper.
  6. Skip count the tens and count the ones.
  7. Write the number immediately below the 32 on the answer sheet (Example 1).

place value onesplace value more onesplace value answersObserving

This is the key point in the activity. You’re ready to ask your first-grade child to make some comparisons based on what he’s observing with the manipulatives.

  1. Ask, “Which group is bigger, the one on the top (32) or the one on the bottom (23)?”
  2. Follow up with, “Which one has more ones?” and “Which one has more tens?”
  3. Finally ask, “Which place should you look at to determine which number is bigger (greater), the ones place or the tens place?” Have your child respond by circling the correct digit on the answer sheet.

Repeating

  1. Remove the strips and squares from the Tens and Ones pages. Go through the process of building 19 and 45 but without the counting steps.
  2. Tell the child to write the numbers side by side with a box in between (Example 2).
  3. Ask which number is larger. The child should indicate his answer in the box by drawing the < symbol in the box.
  4. Now have your child pick two numbers (greater than 10 and less than 50) to repeat the activity.
  5. Have your child guess which number is larger before building the two numbers.
  6. Guide him in writing the numbers with a box in between and then drawing the correct symbol in the box (Example 3).

place value counting onesplace value more answersPracticing

Write out five or six less-than or greater-than problems for your child to practice what he just learned. Encourage him to make each number on the Tens and Ones pages before writing in the greater-than or less-than sign.

Try to spend about twenty-five minutes on this activity before moving on to something else.

Do the the activity again on another day with different numbers to continue developing your child’s number sense and understanding of the critical role that place value plays in determining how large a number is.place value finished answers

4 Steps for Teaching Math Comprehension

by

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.

Tips for Homeschooling with Little Ones

by

homeschooling little ones
Have you ever suspected that your children are in cahoots with each other to wreak havoc to your homeschool plans? How else can the house go from peace to chaos so quickly? Just yesterday, my house was blissfully quiet, but as soon as I sat down to teach a reading lesson to my third grader, the baby woke up from her nap. I rescued her from her crib, found her some toys to play with, and sat down again. Then my preschooler burst into the room with a soaked outfit. “Mommy! I spilled the water!” So I got up yet again and mopped up a river in the kitchen. Our reading lesson did eventually happen, but it was while I balanced both a preschooler and an infant on my lap and tried to keep them from losing my place in my teacher edition. Not exactly the ideal educational situation. What do you do when homeschooling with little ones?

Thankfully, not every day is as chaotic as that one was. But I’ve found that trying to homeschool little ones at home is anything but easy. And I’ve found that I’m not alone in my frustrations.

One of my homeschool heroes, who successfully homeschooled seven children, recently told me that her most difficult years of homeschooling were when she was homeschooling with infants, toddlers, and preschoolers in tow. I was grateful that she offered me a few suggestions that I’ve found helpful. I hope they will be useful to you as well.

One-on-One Time

Homeschooling takes a lot of our attention, and if we’re not careful, our little ones will feel neglected. I’ve found that giving them some special one-on-one attention goes a long way toward helping them be content during homeschooling time. BJU Press Distance Learning has helped me a lot because it has freed me up to spend time with my little ones. While my third grader watches her English, Bible, or science lessons, I try to use that time to read to my infant and preschooler or to play with them. Some days, if I’m really busy, I’ll ask my preschooler to help me with a kitchen project or a cleaning chore. She loves to help!

Special Toys

Several of my experienced homeschool friends suggested that I set aside some special toys just for homeschool time. This too has helped because it gives my little ones something to look forward to while I teach my third grader. The key is that these special toys or activities need to be something that little ones can do. I have found that simple puzzles and play dough work well.

Also, I have created some “busy bag” activities for our homeschool time. Here are some of my preschooler’s favorite busy bags that I’ve found on other blogs.

Learning Involvement

My preschooler also enjoys being involved in our homeschool lessons when possible. Sometimes when my third grader and I are reading a drama during our reading lesson, we’ll recruit my preschooler to “read” one of the parts (one of us will whisper her lines in her ear). During math, I sometimes give my preschooler manipulatives to play with. While I’m administering a spelling test, I will sometimes let my preschooler “take” it too. All of these activities have been valuable to get her excited about learning.

Homeschooling with little ones will probably always be challenging, but these suggestions have helped our family. I would love to hear about any ideas that have helped your family too. Please share them in the comments!

Building Long-Term Math Mastery

by

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.

 

How I’m Organizing My Homeschool Space (Video)

by


I’m about ready to dive into my second year of homeschooling. Last summer I spent a lot of time reading homeschooling books, poring over homeschool magazines, and listening to homeschool workshops in hopes of discovering the secret of homeschooling success. All of that “research” resulted in one very important lesson—homeschooling is an intensely personal experience.

During that time I also got all kinds of organizational tips from my homeschooling friends. Some of the ideas worked well, but some of them didn’t work at all for us. I recently made a video showing off some of our best organizational ideas. I hope it will give you some ideas for organizing your own space.

Here are some highlights from the video along with a few additional thoughts.

What Worked Well Last Year

• Our Distance Learning Notebooks

In the video, I showed off our Distance Learning notebooks. The idea is based on BJU Press’s Distance Learning Unpacking video. This method worked really well for us last year. I loved having all of my materials in one place, and it was so easy to find the information that I needed when doing my weekly lesson planning.

• My Lesson Planner

I didn’t take the time on the video to demonstrate how my favorite lesson planner works. I looked at a lot of lesson planners last year but settled on a God’s Word in Time Scripture planner sold by Rainbow Resources. It’s a fairly simple planner that includes a monthly and weekly view as well as a section to record weekly grades. I loved it so much that I bought another one for this coming homeschool year.

• My Bookshelf

My cube organizer bookshelf was perhaps my best organizational purchase last year. You can see it all set up in the video.

What We’re Doing Differently Now

• Our Math Manipulatives

I mentioned in the video that my storage method (a large plastic container) for our math manipulatives took up too much space last year. It also took a bit of time to find what we needed. So I’m using an accordion file system this year, and so far I’m loving it.

• Our School Supplies

Last year I separated like school supplies and stored them in mason jars and small plastic containers. That didn’t work well with my young children because they were continually putting things in the wrong containers. This year I plan to use more pictorial labels to help my nonreaders. But if you have any great ideas about how you organize school supplies, I would love to hear them!

We’ll be starting our homeschool year in just a couple weeks, and we’re all really excited! If you’re interested in seeing our third-grade curriculum, be sure to watch our unboxing video.