Place Value Cards and Holder

I am joining up with a great group of mathematics bloggers for a new series of blog hops–Fly on the Math Teacher’s Wall. ย Love that title, don’t you? ย Each blog hop will focus on a central math topic, and you’ll find blog posts across all grade levels discussing the same topic. ย You’ll also find some *freebies* along the way! ย The topic this first time around is place value.
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I’ve been working with my struggling 2nd graders on place value this week, and here are the three big ideas I would like to share:
1. Take it slowly
2. Use multiple representations

Let’s take a look at each idea individually.

Take it slowly

Bottom line, you’ve got to make sure students understand tens and ones before going on to hundreds or thousands. ย If students don’t have a strong understanding of tens and ones, they won’t get hundreds or thousands. ย If you are working with students, even in the upper grades, who are struggling with place value, you’ve got to go back to tens and one. ย Here is a great quote from Kathy Richardson’s book, How Children Learn Number Concepts:

“However, if place value concepts are to be meaningful, children need to know more than what digit is in the tens place and what digit is in the ones place. ย They need to know that the underlying structure of two-digit numbers is based on organizing numbers into groups of tens and ones. ย This understanding is critical and basic to successful future work with larger numbers and decimals.”

It is a major milestone for a child to transition from counting items one-by-one to understanding that we can count a group of ten as a single unit. ย This skill is call unitizing. ย Students should have ample experience working with numbers from 10 to 20 and seeing that numbers can be thought of as ten and some moreย before going on to greater 2-digit numbers. ย If a student can’t tell you immediately that a ten and 3 ones is 13, they probably need more practice with numbers less than twenty.

Use multiple representations

There are so many great materials for modeling place value concepts, and students benefit from being exposed to a variety of representations. ย Many primary teachers use bundles of straws to show tens and ones as they count the number of days in school, and that’s certainly a great representation. ย But Richardson shares a story in her book that shows how a rote routine can mask the fact that there is little to no understanding of the underlying concept. Think of turning that calendar process around. Picture this: the students enter the room on the 76th day of school only to find that their carefully bundled straws are now in a pile on the floor! ย Their task is to help you put the display back together by counting out groups of ten. :).

Another great way to count the days in school is to use ten-frames. ย I found this picture on Pinterest a while back, and I love it!

Van de Walleย tells us that traditional base-10 blocks are far too abstract for students at the beginning of their place value journey. Why? ย Because students can’t physically combine ones to make the ten and they can’t break it back into ones. ย Instead, students should use groupable materials, such as linking cubes, bundled straws, beans in small cups, etc., so they can build a ten and then break it back into ones.

Another great tool for exploring place value is the hundred chart. Because the structure of the chart groups numbers into rows of tens, it is a useful representation for exploring concepts such as ten more and ten less.As students are representing 2- and 3-digit numbers with concrete materials, be sure to connect their hands-on learning to the abstract symbols behind the models they are building. ย This handy little holder and set of place value cards helps students see the values behind (literally…ha ha) the digits. I made it to show numbers through the hundreds, but of course you would start with only tens and ones.

Let’s go back to how you might use this with the straw mess from the 76th day of school. ย As students count out bundles of tens, use the cards with the multiples of tens to keep count of how many straws they have. ย So when they count 10 straws and bundle them, put out the card that says 10. ย Don’t put it in the holder yet–just use the cards to keep track. ย As they bundle another ten, replace the 10 card with the 20 card. ย Keep doing this until they are showing the 70 card to represent the 70 straws that are now bundled. ย They count the final 6 straws and take out the 6 card. ย Now put the 70 card and the 6 card in the holder so they can see how the 70 bundled straws are shown as 7 tens.

Of course there are lots of other uses for the cards. ย You can grab your own set of cards and holder for free by clicking here!

Over the years, I think we’ve fallen into a routine when it comes to the questions we ask students to answer about place value. ย There are the old reliable questions like What digit is in the tens place?ย  or What is the value of the 7 in this number?ย  There’s nothing wrong with those questions, but they don’t really assess understanding. ย A correct answer to the first question only indicates that a student has memorized the place value names and positions; it does not tell you whether or not they understand that a 3 in the tens place means 3 groups of ten or that 3 tens is the same as 2 tens and 10 ones. ย One way to make your questioning more powerful is to simply add more to your question. ย For example, after asking a student to tell you the digit in the tens place, follow-up with one of these extensions:
• what does that mean?
• can you show me that with … (linking cubes, base-10 blocks, etc.)?
• can you draw that for me?
• how is that different from having the same digit in the ones place?
So just remember to dig a little deeper to make sure there is understanding below the surface.

Head on over to the next stop along the hop and see what The Recovering Traditionalist has to say about place value!

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1. Julia says:

Thanks so much for sharing! I always LOVE your ideas and use many of your materials. I am a 5th/6th grade math interventionist near San Antonio (SCUC ISD) and we are currently working on place value of bigger numbers. Would you be willing to share your schedule/how you organize your time with your kiddos? I only have about 40 minutes with each group so I’m definitely pinched for time. I’d be so grateful!!! juliapstephenson@gmail.com

1. Donna Boucher says:

Julia, I see each of my groups for 30 minutes a day, five days a week. It’s a pull-out program during what we call “extended learning” time, so the kiddos aren’t missing classroom instruction. My groups are from 3-5 students.

2. The Math Spot says:

I love your discussion of asking the “right” questions. I especially like “How is that different from having the same digit in the ones place?” This could be an especially powerful question for 4th and 5th grade students who are expected to understand patterns of ten on the place value chart and each place value being 10x more or 10x less than the place value to the left or right. Thanks for the thought provoking post! The Math Spot

1. Donna Boucher says:

Thanks so much! Questioning can definitely transform a good lesson into a great one.

3. TheElementary MathManiac says:

I love your point about base 10 blocks being to abstract for kids when they first start learning place value! The importance of multiple representations can not be emphasized enough!

Tara
The Math Maniac

1. Donna Boucher says:

Exactly, Tara! If we only use one type of manipulative, we run the risk of students beginning to think that “ten” has to look a certain way.

4. Sarah M says:

Love the points you make in this post! So important to use various tools depending on student readiness. Thanks so much for sharing!

Sarah

1. Donna Boucher says:

My pleasure, Sarah! I think multiple representations lead to deeper understanding.

5. Dianne Leoni says:

Hi Donna,

Just worked with a first grader and love the additional resources. I am heading to the copier right now to run off the place value holder and cards. I think to see the multiples of 10 and then 1s will help.

Your comments are spot on regarding assessment and manipulatives. It really bothers me that some publishers simply ask which digit is in the tens place, which digit is in the ones place? As if the response measures place value understanding. Add in the student has a 50-50 chance of getting it correct just with a guess.

Wish I could get PD or grad credits for reading your posts. I would have my PHD by now!!!