Additional Math Pages & Resources

Wednesday, November 7, 2012

Teaching Students Place Value and Regrouping

In Excel Math, we begin teaching children about place value in kindergarten by having them arrange and sort objects. By first grade, students start to group objects into tens, ones and eventually hundreds. You can give your students hands-on learning experiences with these activities to help them understand place value. Make an Exchange Board for each student as shown. This is a hundreds exchange board. If your students are still using tens, simply divide the paper in half with columns labeled "tens" and "ones":

Give students tiles or paper squares and bars similar to those shown below. Have them color the tiles, using different colors for the tens and ones. To start, have everyone use the same colors so you can refer to the red ones or the blue tens bars, etc. Let the students cut apart the ones squares but leave the tens bars intact, cutting apart the blue bars but not the individual squares:

Keep the tens grouped as shown. Write a two-digit number (20 or below) on the board. Have each student count out a group of ones pieces that match the number and place those pieces in the ones column. Now have the students exchange ten of their ones pieces for one tens bar and place the tens bar in the tens box. Have them exchange the tens back into ones and count the ones. Do this a few times, having one student demonstrate to the whole class. Alternate students to demonstrate.

Now let the students work in pairs. Ask one student in each pair to put his/her head down on the desk. Write a number on the board. The students with their heads up with silently count that many ones counters onto their exchange board in the ones box.

When done, erase the number from the board. Have the remaining students raise their heads and look at the counters. Let them take the ones counters and do any exchanging for tens. They should silently write the answer for you or their partner to check. Have them exchange the tens back into ones and count the ones. Do this several times, alternating students to put down their heads.

Write a new number on the board. Ask the class what number is shown. Point to the ten counter and explain that they can count up from there. For example, if the  number is 13 you could say, "11, 12, 13" as you touch each of the three ones counters.

Some students will not get the concept the first day or week it is introduced. They will still need time manually setting up the numbers and then checking by counting. Do not be discouraged if it takes them some time to begin to understand. That's the beauty of the Excel Math spiraling process—we don't expect mastery when a concept is first introduced.

This unique spiraling  process is a basic feature (and a major advantage) of Excel Math. Students continue to review and practice regrouping on a regular basis throughout the year (and the next)—long after the concept is first introduced. In subsequent lessons, students are given many ways to review the concept of place value. They use manipulatives, charts, paper and pencil, and even Projectable Lesson slides such as this one:

Projectable Lessons can be projected from a computer or document camera onto a whiteboard, screen, wall or interactive electronic board, giving the entire class a visual reminder of the concept. Keeping the slide projected as the students work on Guided Practice problems can be a huge help to students who may lose their focus or become easily distracted while working independently.

The Learning Box website has a fun, interactive way for students to practice regrouping hundreds, ten, and ones. (You can mute the sound if the repetitive drumbeat becomes nerve-wracking.) Students can choose whether to play with tens and ones or include hundreds. They drag individual blocks and groups of ten or hundreds onto a blank page. As they do this, a finger points to a ruler showing the number they've created. The crowd cheers when they get the correct answer. Try it out for your yourself:

Students can more easily recognize place value when the blocks or tiles are different colors for the ones, tens, and hundreds places. Once they can identify place value by color, they can make a fairly natural transition to recognizing place value by columns. Richard Garlikov, philosopher, educator and photographer, has written an interesting series of papers about place value, teaching techniques, and how children can be taught progress from color value to place value. As he concludes, "Place-value is a very difficult concept for children to comprehend, but for some reason children have no problem with using color tiles whose values depend on their colors, when you simply tell them what the exchange values of white, blue, and red tiles are." Read more at

Another way to give students a visual picture of place value (before you ever begin using exchange boards) is with base ten cards. Here are some star Base Ten Star Cards you can use all year round. These are also wonderful incentives for your star students. Those who show kind, considerate behavior traits can use the star cards for the week. You can bring these back into play whenever you need an incentive to help keep students behaving appropriately in the classroom.
Base Ten Cards
Click on this link to download the PDf file.
Read our previous blog post for some activities your students can do with Base Ten Cards. Then download the PDF file for these cards and copy a set for each student. Let your students cut them apart. Follow the instructions in the file to help your students use the cards to recognize place value, identify numerals, add, subtract, and multiply.

Now that you've had a refresher course on place value, can you identify the place value for each digit in the following number?
1 2 3, 4 5 6, 7 8 9, 0 1 2, 3 4 5. 6 1 2
Don't let the decimal point throw you off. See how many places you can identify. Then scroll down to see the answer and check your knowledge.

New to Excel Math? Visit our website at for elementary math lessons that really work!

How do you teach place value to your students? If you have tips to share with others, post them in the comments box below.

Here's the answer to the place value question above:

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