BJU Press Blog

Search Results for: manipulatives

Decluttering Your Homeschool

by

Clutter stifles. It cuts off creativity, productivity, and efficiency. If you have to climb over math manipulatives and a life-sized cardboard Civil War cannon just to get to that microscope for today’s science lesson, you know it’s time to purge, cleanse, spring clean, and get some fresh air into your homeschool room.

In similar ways, spiritual clutter stifles spirituality. “Cleanse first that which is within the cup and platter, that the outside of them may be clean also” (Matthew 23:26). Thus, decluttering my homeschool room begins inside out. I need to be right with God, so that I can apply the principles I learn from Him to how I organize my life.

So, how do I declutter both inside and outside? Sweep. Stabilize. Shed.

Sweep

Sweep spiritually. The Word of God cleanses us from within. To be a “vessel unto honour, sanctified, and meet for the master’s use, and prepared unto every good work” (2 Timothy 2:20–21), I must have a teachable spirit. I set aside a daily quiet time to study God’s Word and draw closer to Him.

Sweep spatially. I start with an empty room. I clear out everything in the room, and then put back only what we need. Since I homeschool in multipurpose spaces, it’s necessary for our family room to be a functional room after we finish homeschooling for the day so that we can eat at our dining table without leaning over stacks of books.

Stabilize

Stabilize spiritually. Sanctification is a continual process (Romans 12:1). I surrender myself to the Lord so that He can sanctify me for service as wife, mother, teacher, and worker. I learn to abide in Christ.

Stabilize spatially. I keep only essentials in my homeschool room. Everything else goes behind doors or under lids. Yardsale bookcases and large containers are cost-effective storage solutions, as are the more expensive options of creating closets by closing off part of a room with louvered doors or installing shelves on empty walls above windows. Don’t be afraid to ask for suggestions from organized moms.

Shed

Shed spiritually. Encumbrances hinder us from running the race well (Hebrews 12:1). I must pay attention to what influences my family. The movies we watch, music we listen to, and library books we read can have a huge effect on my family. How are we pleasing or not pleasing the Lord? It’s not enough to have a Christian curriculum if we don’t live out our testimony before and after learning.

Shed spatially. Semiannually, my family fills up a box to give away. Inside the box are things that we don’t use that are still in good condition.

Yearly, I let go of children’s furniture we have outgrown. I have to be brutal about what not to keep, but at the same time I pray for wisdom lest I give away what I would use next year. Limited spaces can be a blessing, preventing me from accumulating things I don’t need.

I remind my family and myself to clean up as we go. Whatever can be picked up now, must be picked up now. Deferring tasks to a more convenient time means multiplying the mess. Children can be taught to put away toys before taking out the next set. Likewise, putting dishes incrementally in the dishwasher and doing laundry before it runneth over are practical ways to prevent clutter and distribute the workload.

On a spiritual level, whatever the Lord has called us to do now should not be postponed. We have a limited time to serve Him on earth. “Let all things be done decently and in order” (1 Corinthians 14:40).

In everything we do, let’s work efficiently for the Lord.

• • • • •

Written by Jan Thompson

Image Source: desk; books

Building Understanding with Negative Numbers

by

negative numbers activity
By the time I got to junior high, I was really confused about negative numbers. At first it was simple, but concepts like multiplying negatives and absolute value taxed my understanding. Of course, I joined in on the chorus sung by every math student who doesn’t understand what he or she is supposed to be learning: “When am I ever going to use this?” Once I reached high school, I realized that negative numbers play a significant role in science. Today, negative numbers play a major role in my problem solving in home budgeting and in business.

So how can we set up children for success when they start using negative numbers so they can solve ever more complex problems? The answer is exposure, development, and mastery. We need to expose children to significant concepts well before they need them to problem solve. Next we need to develop their understanding on the path to mastery. Then, children will be ready for success later on.

Exposing a New Concept

I’ve learned that with negative numbers you need to expose your child to the concept in the elementary grades. A good time to begin is in the second half of fourth grade. At this point in their math journey, children are ready to explore negative values but not quite ready to perform mathematical operations with those numbers.

If you live in a northern state, your child may have been exposed to negative numbers through real-life winter temperature. In the South, we’re never sure what to do when the mercury drops below 20 degrees Fahrenheit, so my daughters will need some other exposure to real-world negative numbers.

Interacting with Negative Numbers

So how do we introduce children to negative numbers? As with all math concepts, we need to make observations with our children as we do hands-on activities—but how? What makes negatives difficult for children initially is that you can’t look at or touch negative three apples.

The best way to interact with negative numbers is with a number line. Try the following questioning strategy for introducing your child to negative numbers.

negative numbers activity materialsMaterials

You can use this printable, which includes the following:

  1. Number line (from negative 9 to positive 9)
  2. Markers to cut out

(BJU Press has also created a fourth-sixth grade manipulative kit that helps children learn this and other math concepts.)

Activity

  1. Give your child the number line and the markers.
  2. Ask your child to place the blue marker above the number 5. This will be a point of reference.
  3. Ask your child to place the red marker above the number 7. Ask, “Which of the two numbers is larger?” and “Is it farther to the left or farther to the right?” Point out that the larger number is to the right and the smaller is to the left.negative numbers activity
  4. Direct your child to take the red marker from 7 and put it above the number 1.
  5.  Ask, “Now which number is the larger?” and “Is it farther to the left or to the right?”negative numbers activity
  6. Have your child move the red marker above number negative 1.
  7. Ask, “What do we call that first number to the left of zero?” Your child might say, “Minus 1.” Explain that it is called negative one and that any time that negative symbol appears before a stand-alone number, it shows the number is less than zero.

Seeing the Math

This is a critical point because your child is going to compare two negative numbers. In your child’s experience, 7 has always been more than 1. But when both are to the left of zero (negative), the 1 is larger. This may seem obvious to an adult, but to a child it is counterintuitive. Allow your child to be “wrong” without correcting. You can set up the manipulatives so your child can see the difference.

  1. Leaving the red marker on the negative 1, ask your child to move the blue marker to negative 7. Ask, “Which number do you think is larger, negative 1 or negative 7?  Remember when we compared 1 and 5, which number was larger?  Was it farther to the left or farther to the right?”negative numbers activity
  2. Now ask your child to compare negative 1 and negative 7 again. Say, “Remember if the number is the farther to the right, it’s the larger.” Then ask, “Which number is larger, negative 1 or negative 7.”
  3. If your child is struggling with how this can be true, ask, “What would you prefer, to owe me one dollar or seven dollars?”
  4. Explain that a negative number is like owing money when you don’t have any money at all. It is less than zero. So the bigger the numeral, the smaller or less the value.
  5. Try comparing several more numbers.

negative numbers activityDeveloping Understanding

This is a basic introduction to negative numbers. In the next few days, have your child try these exercises to develop his or her understanding:

  • Give your child a number line with negative 10, negative 5, 0, and 10 marked. Have your child fill in the rest of the numbers.
  • Create greater-than and less-than exercises for your child, using negative numbers.
  • Give your child a set of four or five numbers (including both negative and positive) to arrange from smallest to largest.
  • If your child is familiar with coordinate graphs, try extending the x to the left beyond the zero and the y down below the zero.

Try a variety of these activities over the next week or two. Never take more than twenty minutes or so, and make sure you are keeping the time engaging.  You will want to revisit negative numbers again in fifth grade. Once you review what you’ve already covered, you can begin to introduce adding with negative numbers.

If you introduce, review, and develop a mathematical concept in the elementary years, your child will be prepared to be successful in junior high and high school math.

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!