BJU Press Blog

number sense

Learning Place Value with a Hands-on Activity

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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

Building Long-Term Math Mastery

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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.

 

Shopping for Math Number Sense at the Grocery Store

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Shopping for Math Number Sense at the Grocery Store
My wife Megan is a terrific teacher who effectvely uses real-life situations to teach our grade-school children number sense. When we recently celebrated our youngest daughter’s third birthday, our two oldest children wanted to buy something for her. So my wife gave them some extra chores and paid them enough money to buy one of those fancy helium birthday balloons—on sale for ninety-nine cents! My five-year-old stored her coins in a tin container made for holding tea.

Once they made it to the checkout line, Megan had the cashier ring up the balloon as a single order so my daughters could pay for their gift individually. When the cashier announced the cost, our kindergartener took her tin can and dumped all the coins out. Coins clanged on the floor and rolled to a stop. Then she started counting out the change for her purchase.

Megan said she was a little embarrassed, but our daughter counted out the needed change for her contribution to the gift, and our girls bought the balloon.

While the shopping excursion took extra time, it was a powerful homeschooling moment in my daughters’ understanding of math.

Starting with Creation

Children understand math when they begin their exploration of mathematical principles in God’s created order. When we teach counting, our family starts with counting grapes. Then we help our daughters learn place value by connecting blocks into groups of ten. We want our children to know that all those mathematical symbols represent something real. We call connecting mathematical symbols with the physical world number sense. It’s something they can touch and move. Starting with objects in God’s creation when learning math ignites a child’s understanding.

With the light of understanding, children are ready to practice so that math becomes automatic for them.

Practicing with Creation

We teach our children math so they can exercise good and wise dominion over God’s creation. This means that accurate computation is a means to an end. If we can show children that the math skills they’re learning will enable them to do more in the world around them, that gives math a purpose, and math mastery becomes more satisfying than getting a perfect score on a worksheet. They’re learning to solve real-life math problems by practicing with creation.

Bringing it together at the grocery story

Grocery shopping provides an ideal situation for developing number sense. Touching and moving physical coins and dollar bills allows them to manipulate objects as  they do the calculations. Then they can see how the money they have in hand corresponds to price tags in the store. This is the essence of number sense—knowing how those numerical symbols relate to the real world.

Now children are ready to use computation. “Do I have enough money to make this purchase? How much money will I have left over?” When they get older, they can calculate how much sales tax will add to their purchase. All of these activities demonstrate to children that their math skills are critical for everyday activities, such as buying groceries.

Math is a powerful tool for wisely stewarding the little part of creation that God has assigned to each of us. When we start teaching math to our children, it should have meaning that goes beyond plus and minus signs.

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