Place Value Demands Sense Making
“Using strategies based on place value” is a phrase that can be found all over math standards, common core or otherwise, and with good reason!
First of all, learners who are not confident using tens as a unit will continue counting long after it is a reasonable strategy. I believe we lose far more students at the number 11 than we realize, and when we possess only a superficial grasp of units and value, all mathematics understanding is diminished.
Why? What topics in mathematics are not based on units? Measurement is based on units. Multiplication and division are units. All fractions are sums of unit fractions. Tens are basically the first unit
But are we doing all we can to truly develop this idea? Are we considering each piece of the place value puzzle?
Emerging Understanding of Tens & Ones
It is essential that first and second graders have many opportunities to make and break numbers and number units. In busy classrooms, we often find ourselves putting away the snap cubes once our students demonstrate understanding of tens and ones.
But these little parrots fool us into thinking the get it!! Repeat after me, “Saying it doesn’t make it true.”
And day after day, year after year, we fall for it. We fall harder than Charlie Brown kicking that football that gets pulled away every. single. time.
NOT THIS TIME, LUCY!
What IS IT about UNITS???
While these seem like first and second grade ideas, superficial understanding will hold a child back for years to come. So, how confident are you that your students are not faking you out? Every year I have fourth and fifth graders who need this quick but essential intervention!
Here is a quick check for young learners. Hold out a bag of snap cubes (or show a pile of virtual snap cubes or “ones”).
“I have 54 cubes in this bag. How many ten sticks do you think we could make with 54 cubes?”
Learners who think carefully about their answer, are still in the emerging stage. They need LOTS of opportunities to take that bag of snap cubes and build the ten sticks until they begin to answer immediately, “We can make 5 but we’ll have 4 leftover. ” Let’s build and build and build these towers until they can answer your questions as quickly and confidently as they can tell you their names! Then they are ready to really get flexible!
Of course, emerging learners can build numbers flexibly too! True understanding of place value means that we cannot lose the idea of 29 ones as just that; unless it looks like 2 tens and 9 ones; until it turns into 1 ten and 19 ones.
(Click here for the 2/3 Grade Tasks above)
Young learners need a lot more time predicting and building the “most tens possible” until they just know it, like they know they have five fingers. In second grade, they should be just as confident with numbers >120. Keep in mind, that many students are fuzzy with 111-119. Consider developing confidence identifying the “most tens you can make” with 124, 138, 145 and 199 and then going back to 108 and 115. Be sure to count up and back by tens from random numbers. This not only helps with adding and taking away tens, it develops an appreciation of UNITS. Students begin to look at a number like 159 and know that if give 30 more, they can simply combine the 5 tens and the 3 tens without using an algorithm.
How do we get there?
In addition to building group-able units of ten (with snap cubes, straws, popsicle sticks etc) we can give our small group of students a pile of tens and a pile of ones and begin playing. “Show me 25. Now add 10. Add another 10. Take away a 1. How many do we have now?” Repeat with variety and then begin changing numbers. Start small. “Show me 31. Change it to 33. Change it to 43. Change it back to 33.”
Many students will gain comfort with larger and larger differences. This is where we can level our groups if we haven’t already. Some first graders will jump from 23 to 93 or 123 rather quickly. Some second graders will struggle changing 35 to 25, even if they just added the last ten.
*Note: It is also helpful to write numbers down and ask them to “Make this number” without saying the number. Sometimes, we can point to numbers on a hundred chart. There are always learners who confuse 16 with 61 or 17 with 70. They need more experiences and explicit language support along with a 120 chart.
Next, give students different tools and repeat the game. For example, at one small group, one student may use place value blocks, another uses a Rekenrek, another uses ten dollar bills and one dollar bills, another uses mini ten frames, and one student stands at the white board with a marker and eraser and represents the changes to the number.
As students gain confidence, they love moving to “lightening rounds” where they build a little faster. I love when they get to the point that they can write 222 on their whiteboards (really big and spread out) and we play “Erase only one digit“.
“Add 1 hundred. Take away a ten. Add 3 ones. What is our new number?” When learners are confident with the units, they can erase and replace only the digit affected with a single command.
Finally, confident learners play games with greater numbers and combine place values, so we may begin with 222 and take away 21 tens. 😀 I mean we have to aim high, right?
Beat the Teacher Template!
Are your learners breaking down at the counting stage, or struggling to add or subtract 10?
Do you hear a lot of “seventy-niiiiiiiiiiiiine…..eighty!” when a learner is counting? Or do you have kids who cannot quickly add or subtract ten to any number?
Students who need to think about what number comes next (by ones or tens) needs more time here. Consider number chart games & activities, group counting circles and definitely check out 100 Number Dash!
- You can have some kids counting 1-100 by ones
- More kids counting 10-1,000 by tens
- Some kids counting from 100-200 by ones
- AND ALL PLAYING THE SAME FUN GAME!
Kids and teachers flip over this game. It is the most high energy game ever played in math class.
More Engaging Independent Tasks using Flexible Place Value
Learners also need experiences composing numbers in all the different ways by their place values. Don’t wait until they have “mastered” place value, but while they are learning it. This is how place value is mastered.
This is what is missing in place value!
Most textbooks do a terrible job with it, and many first and second grade teachers do not have access to effective resources. Textbooks typically offer a SINGLE LESSON using a place value table with such simple patterns that can be mimicked without any actual thinking. (heavy sigh) This is an idea that DEMANDS MORE TIME. More games. More tasks. More exploration. More discussion. More understanding.
(Click here for the Primary Place Value Tasks above)
Try Part-Whole Models!
I have had tremendous success using part whole models to break apart numbers by their place values. That is why I have created so many resources using this idea, that I have not seen elsewhere. It builds number sense at all levels and can be used from first or second grade through middle school.
(See what this looks like with decimal numbers here.)
I have also found that using a combination of words and numbers can be very powerful. This helps fifth graders learning decimal numbers, as much as it helps first graders learning about tens.
Consider infusing part whole model composition/decomposition into your lessons and more importantly, during independent time. I believe this is SO IMPORTANT that I worked early mornings and late nights on these Daily Number Reasoning Templates as soon as we shut down in March. The printable versions have been getting rave reviews for years, but now we were virtual overnight and we couldn’t let them go! (To read more about using a number of the day, read this post.)
I love them for all levels, and they are easy to differentiate by the number used each day. I have second graders who use 1,874 and fourth graders who use 139. If you do not currently use tasks and talks like these, try to incorporate them in some way or another.
(CLICK HERE for Daily Reasoning Number Templates)
I think the reason I always HATED teaching place value, was not just because it was hard, but because I never had any go-to resources to develop the big ideas. I am an inquiry based and game based teacher, and place value never came with anything engaging. I wanted it to end just as much as my students did.
Not anymore!
Want to teach place value with Mystery Number riddles? Knockout Games? Beat the Teacher? and interactive games? Join me as we continue to explore the most elusive understanding in primary mathematics.
Do you have any other go-to’s for building place value number sense?
(Click here for the Place Value Chart Board Topper above)
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