In our base ten number system, each place value is ten times greater than the place value to its right. Ten frames can be used to model this abstract math concept.

For this activity, you will need a ten frame and place value tokens. If you don’t have place value tokens, you can easily have students make them. For the ones in the picture below, I used a dry erase marker to write on the ten frame dots that came with this set.

Begin by modeling a digit in the ones place. For example, to model the number 3, a ones place token would be placed in three of the boxes on the ten frame. 

To make a number ten times greater, exchange the ones place tokens for the tens place tokens. By making the place value ten times greater, the new number represented is 30. 

Continue by exchanging the tens place tokens with hundreds place tokens (creating 300), and so on. 

 

Designate each addend as a separate color. In this example, you see that 7 is green, while 5 is blue. Have the student model each addend in a separate ten frame. Then, use the ten frames to introduce new strategies for addition.

 

For example, if the student is still counting on to add, try a make ten strategy. Take three blue counters from 5 and use them to fill the frame that shows 7. Now, instead of adding 7 and 5, we are adding 10 and 2. 

Another strategy that can be modeled with ten frames is creating doubles. By moving one green counter to the second ten frame, the problem changes from 70 + 50 to 60 + 60. With repeated exposure to these manipulatives, students will internalize these flexible strategies. This will lead to more successful computation within their grade level problem-solving!

The post Three Ways to Use Ten Frames for Upper Elementary {Powerful!} appeared first on Shelley Gray.

Rounding numbers is a tricky concept for many kids. It can be somewhat abstract and a difficult concept to grasp. If there is one thing I’ve learned over the years, it’s that no one strategy works for every student. Concepts often need to be taught and reinforced in multiple ways to reach every student in the classroom.

When it comes to rounding numbers, I believe in a conceptual approach where students are taught to find the proximity of the number being rounded to the benchmark numbers and midpoints. This is one way to ensure that students truly understand what rounding means – rather than simply memorizing a rhyme or the steps to a procedure.

Related: Not Sure How to Teach Rounding Numbers? Make it Hands On! (Try This)

However, I also understand that students need to see concepts in different ways. In this post, my guest writer Katie has given a breakdown of how she uses Rounding Mountain in her classroom in order to help students visualize the rounding process. This is a visual that may give some students the “a-ha” moment with rounding, and we can use it to connect their new understanding to rounding on a number line.

Rounding mountain can be a helpful visual for students; however, remember to use this to support your students’ understanding of benchmark numbers and midpoints, not to replace it.

If you’ve taught elementary-level math, then you probably have taught some form of rounding. Rounding is important in elementary math because it helps our students build their sense of place value.  

When you round a number, you determine which benchmark number (ten, hundred, thousand, hundred thousand, million, etc.) a number is closest to. 

I like to teach my students different strategies when I review or introduce this topic to them. One of the most popular ways that my students have enjoyed learning and using has been the rounding mountain. 

What is the rounding mountain and why is it beneficial? 

The rounding mountain is a visualization tool that can help your students understand whether a number should round up or round down. As you can see in the example above, 41, 42, 43, and 44 would round down to 40. 45, 46, 47, 48, and 49 would round up to 50.

My students have always enjoyed this strategy because it allows them to “practice climbing up and down the mountain.” They enjoy making it a game or a competition. The more ways we can visualize and practice a concept, the better!

Related: Quick and Easy Place Value Activities (Try These to Boost Number Sense!)

How to Use the Rounding Mountain

1. Pass out a chart or allow your students to use an anchor chart on a stand or whiteboard. I like to laminate my anchor charts so they can be used year after year. 
2. Decide which place you are rounding to, for example, the nearest ten.
3. Give your students a number. In this example, we will use 43. Have them identify the benchmark numbers. These are the next lowest ten and the next greatest ten. In this case the benchmark numbers are 40 and 50. Students can use sticky notes to place these benchmarks on either side of the chart, or write with dry-erase markers. 
4. If we are rounding 43 to the nearest ten, we will underline the number in the tens place. Then we will circle the number to the right (in this case, the 3). 
5. The circled number will determine whether we round down or round up. In this case, we round down to 40.

This can easily be used as a partner activity to encourage collaboration and teamwork. Have students take turns and double-check each others’ rounding.

IMPORTANT: Make sure your students understand WHY they are underlining the number in the tens place, and circling the number to the right. We want to ensure that students understand rather than follow a series of steps with no real understanding. Ask questions like, “Why does the circled number determine if we round up or down?” or “What are some options the circled digit could be if we rounded up to 50?”

Helping Students Make Connections

One of the most important aspects of helping students develop a deep understanding in math is to help them make connections between concepts. If you decide to use the Rounding Mountain visual in your classroom, ensure that you are helping students make connections to a number line. Here are some ideas:

• Ask, “How is our Rounding Mountain the same as a number line? How is it different?”
• Discuss with students: “Look at our Rounding Mountain. Now look at this number line. What do you notice? What do you wonder?”
• Refer to the numbers at the base of the mountain (ex. 40, 50) as benchmark numbers, and the number at the peak of the mountain as the midpoint.
• If you are working with rounding to the nearest hundred, thousand, or ten thousand, ask: “Is there a way we could use the rounding mountain to round to these other place values?”

Free Rounding Mountain Printables

If you’re interested in using Rounding Mountain as an activity to supplement your students’ understanding of rounding numbers, here are some free printables that might be useful for you!

More Rounding Resources

The rounding mountain activity above can easily be connected to rounding on a number line. When students round on a number line, they use their knowledge of benchmark numbers and midpoints to find which ten (or hundred, thousand, etc.) a number is closest to.

Here are some other resources that will be helpful as you teach your students how to round on a number line:

• Rounding to the Nearest Ten (within 100) worksheets
• Rounding to the Nearest Ten and Hundred (within 1,000) worksheets
• Rounding to the Nearest Ten, Hundred, Thousand (within 10,000) worksheets
• Rounding: Digital Mystery Pictures

The post How to Round Numbers Using Rounding Mountain (Plus Free Printables!) appeared first on Shelley Gray.

Do you wish you had a way to easily spiral place value skills throughout the year – so your students continue to boost their understanding even after your place value unit is complete? Mystery Numbers place value activities are designed to do just that.

“My students look forward to mystery number each week. We are using it remotely as a way to start our Math thinking. I share the list of numbers with students and then we go through the clues together. I am proud to say my students have been beginning to predict what clue might come next based one the numbers left. It was been so very engaging for them. I look forward to continue using this even when we return in person.” – Karen

Mystery Numbers: Quick and Easy Place Value Activities

To complete a mystery number activity, students read a clue and use that clue to eliminate one or more of the numbers. This continues until there is just one number left. The clues involve essential skills like place value, odd/even, rounding, greater than/less than, and more. This is a great way for students to use their knowledge in a meaningful way.

“This was a great way to get my students to really think about numbers. They loved making their guesses and then being able to change their guess as they received new information. I used it as an informal assessment of their understanding of place value.” -Ruth

Mystery Numbers Make Differentiation Easy

Mystery Numbers are ideal for differentiation. Because you can choose from 2-digit, 3-digit, 4-digit, 5-digit, fractions, and decimals, there is something for every ability level…and students don’t need to know that their work is any different from someone else’s. This allows you to truly meet the needs of your students. For example, in your classroom you might have a few students working on 2-digit mystery numbers, while you work in a small group on some 4-digit mystery numbers. Students that are ready for something more challenging may even be working on fraction mystery number activities!

“LOVE these! They are really wonderful for boosting number sense, having students apply their thinking and making students read the questions/clues carefully!!” -Hayley

Because Mystery Numbers are available in both print and digital format, they can be used in the classroom or from home. If you choose to use the PDF versions in your classroom, you may also choose to put them inside plastic sheet protectors to save on paper.

Mystery Numbers are fantastic for many uses in the classroom. They’re a quick and easy way to reinforce place value skills all through the year. Here are how some teachers use them:

• as a 5-minute time filler or math warm-up
• to get kids excited about math at the beginning of math class
• as a pre or post assessment of place value skills
• as an early finisher activity
• to inspire students to try writing their own mystery number activities (fantastic for critical thinking!)

“I love these especially for getting my students’ minds ready for math.  They’re so engaged trying to figure out the mystery number not realizing that they’re using (and learning) key vocabulary terms and concepts.” -Patricia

If you’d like to try Mystery Number place value activities in your classroom, here are the links to get started:

2-Digit Mystery Numbers

3-Digit Mystery Numbers

4-Digit Mystery Numbers

5-Digit Mystery Numbers

Decimal Mystery Numbers

Fraction Mystery Numbers

Or see the entire Mystery Bundle (and make it easy to differentiate to all your students) HERE.

 

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The post Quick and Easy Place Value Activities (Try These to Boost Number Sense!) appeared first on Shelley Gray.

“Four or less, let it rest. Five or more, add one more.” Right? Wrong!! Do you find that rounding is confusing for your students? Do you find that many students don’t really seem to “get” what it means? It’s time to stop teaching the cute rounding rhymes and tricks and teach in a way that promotes real understanding.

If you are teaching rounding, this article is going to include everything you need to teach it in a way that promotes conceptual understanding. Let’s go deep with this concept so students are building number sense that will transfer to other concepts rather than simply memorizing a rhyme.

First, let’s take at how NOT to introduce rounding to your students. The whiteboard below shows a common way of teaching rounding. We look at the numbers, say a rhyme in our heads, and get a correct answer.

But let’s think about this approach.

• Is this meaningful to students? Do they actually understand what rounding is?
• Does this approach help them build deep understanding of the concept of rounding?
• Is the focus on understanding? Or is the focus on getting a correct answer?
• Does this rhyme transfer to other areas of mathematics and help students build their overall number sense?

Now let’s contrast this with a different approach. This time, let’s use a number line and let’s ask ourselves the same questions:

• Is this meaningful to students? Do they actually understand what rounding is?
• Does this approach help them build deep understanding of the concept of rounding?
• Is the focus on understanding? Or is the focus on getting a correct answer?
• Does this concept transfer to other areas of mathematics and help students build their overall number sense?

When we think about it in this way, it’s clear that we must stop teaching the cute rounding rhymes, and start teaching actual math. In the words of Nicki Newton, “Don’t teach tricks. Teach math. It’s easier!”

So how do we accomplish this? Where do we begin?

HANDS-ON ACTIVITIES

If you use the CRA Model in your math classroom (highly encouraged), you know how important it is to begin teaching any concept in a concrete way that students can visualize. In this concrete phase, students are using physical objects that they can manipulate. This stage is where students are rapidly building their understanding of a concept.

So often when we teach rounding, we begin with using the actual digits of a number, and introducing them to a rhyme or rule. But this does not help them understand what rounding really means. This does not enable them to build the connections that are so important for true understanding and number sense development.

When I am brainstorming concrete activities, I am asking myself a couple of questions.

• How can this concept be visualized without any digits involved?
• How can we eventually bridge this concrete representation to a more abstract representation?

Using Base Ten Blocks for Rounding Numbers

Base ten blocks are an excellent visual for rounding numbers because most students are already familiar with them. Here we are looking at the number 27. First, we can ask which tens 27 comes between. In this case, it comes between 20 and 30. Now we need to figure out which ten it is closer to: 20 or 30. When we can see what 27 looks like, it’s easy to see that 27 is closer to 30 than it is to 20.

Notice that we have not even used the term “rounding” yet – we are simply focusing on which ten each number is closest to.

Here’s another example with the number 32. We know that 32 comes between 30 and 40. When we can see it built with base ten blocks, it’s easy to see that 32 is closer to 30 than it is to 40.

Using A Rekenrek (Number Rack) for Rounding Numbers

Another common manipulative that we can use to visualize closeness to a number is a rekenrek. Again, we are focusing simply on building numbers and figuring out which ten they are closest to. In this example we have built 47. We know that 47 is between 40 and 50. This visual helps us see that 47 is closer to 50 than it is to 40.

In this example we can see that 63 is closer to 60 than it is to 70.

Using A Beaded Number Line (Bead String) for Rounding Numbers

A beaded number line is a fantastic tool to add to your manipulative collection. In this example we see the number 33, and can visualize it as being between 30 and 40. It’s easy to see that 33 is closer to 30 than it is to 40. I love beaded number lines because they are a wonderful transition to a drawing of a number line, which we will take a look at in the next section.

Incorporating Representational Models

The number line is a powerful representational model for rounding numbers. It helps students visualize which ten (or hundred or thousand) a number is closest to. In this example, we are making connections between the concrete representation of 27 and the representation of 27 on the number line.

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How to Use a Number Line To Teach Rounding

Number lines are powerful for so many concepts, and rounding numbers is no exception. The number line is a MUST-USE tool for teaching students how to round.

The first step in using a number line to round is to identify the benchmark numbers. But what are benchmark numbers? A benchmark number is a reference point. It is a “friendly” number that is easy to work with. Numbers like 10, 20, 25, 30, 50, 75 or 100 can be benchmark numbers. When we use benchmark numbers for rounding to the nearest ten, our benchmarks are the ten that is less than the number we are working with, and the ten that is greater than the number we are working with.

Once we know the benchmark numbers, we can find the midpoint. This is the halfway point between the two benchmark numbers. For example, 25 is the midpoint between 20 and 30. Or 95 is the midpoint between 90 and 100. (See the resource pictured here.)

Now that we have the benchmark numbers and midpoint, we can place the number on the number line. Let’s suppose we are rounding 84 to the nearest ten. Our benchmarks are 80 and 90. Our midpoint is 85. When we place 84 on the number line, we can easily see that it is closer to 80 than to 90. (See the resource pictured here.)

Number lines provide students with a visual. They make rounding easy to see, and not so abstract. When we round, instead of circling the digit, looking at the digit to the right, and then thinking of a rhyme like, “Four or less, let it rest. Five or more, add one more,” we can think about rounding in a conceptual way – a way that builds deep understanding and helps students understand what is actually happening when we round. (See the resource pictured here.)

Going Abstract

Once your students have built the conceptual understanding that is necessary, they will be able to move on to rounding in a more abstract way – without the tools and visuals. But this doesn’t mean that you stop using them! It’s a good idea to always come back to multiple representations of a concept. Even when students are comfortable with rounding, getting them to show their thinking on a number line can be valuable! The more connections we can make between concrete, representational, and abstract – the better!

Summary

To summarize, here are a few tips as you decide how to teach rounding in your classroom:

• Ditch the tricks! Teach math instead.
• Begin with concrete materials, and then help students make connections to more abstract models.
• Use number lines. These are a powerful tool for so many concepts – rounding included.
• Remember that number lines and concrete materials aren’t reserved for students who need intervention! These are powerful tools that all your students should be comfortable with.

Need Additional Support?

If you’d like additional support with teaching and reinforcing rounding to the nearest ten, try these engaging rounding activities:

• Rounding on a Number Line (nearest ten, within 100)
• Digital Rounding Practice (for rounding to the nearest ten)
• Rounding to the Nearest Ten Task Cards (for math stations or an “around the room” gallery walk activity)
• Rounding to the Nearest Ten Mystery Pictures

Here’s some additional support for rounding within 1,000:

• Rounding on a Number Line Within 1,000 (Nearest 100 and 10)
• Rounding Within 1,000: Digital Mystery Pictures

The post Not Sure How To Teach Rounding Numbers? Make it hands-on! (Try This!) appeared first on Shelley Gray.

VIDEO VERSION OF THIS BLOG POST:

BUILD A STRUCTURE/PICTURE/WORD AND CALCULATE THE VALUE

For this activity, give students a variety of base ten blocks and have them build something. This could be a structure, such as a tower or a picture as shown below. You can also have students use the blocks to spell their name. Then figure out the value of the picture. The picture below has a value of 254 because two hundreds, five tens, and four ones were used.

An alternative is to give students a target number, and have them build a structure with that value. For example, you might have your students build a structure with a value of 147. Each student’s structure will be different.

Add an extra challenge by having students build a structure with a specific value but a limit on the number of hundreds/tens blocks they can use. For example, “Build a structure with a value of 325, but you may only use TWO hundreds blocks!”

RACE TO 100

The second activity is called Race to 100. I’ve also seen this game called The Trading Game. The object of this two-player game is to be the first person to reach 100. Player 1 rolls a die and puts that many ones on the place value chart. Then Player 2 rolls and does the same. Play keeps alternating between players. Once a player has 10 ones, he can trade those for a ten. Players keep rolling, adding blocks, and trading until one person reaches 100.

To play this with place value to 1000, use two dice instead. Players can use the two dice to make a number, then add that many blocks. The object here is to be the first person to trade in 10 hundreds for a thousand block.

HOW MANY WAYS?

The third activity that we can use to introduce place value concepts with base ten blocks is “How many ways?” This works well as a carousel activity where groups of 2-3 students circulate the room, adding their answer to pieces of chart paper that are posted around the room. The idea here is to see what other groups have written and try to add an answer that has not already been added. Be sure that there are actual base 10 blocks available for students to work with before they write the answer on the chart paper.

Do you have other ideas for using base 10 blocks in your classroom with little to no prep? I’d love to hear them in the comments below!

The post Three Base Ten Activities to Introduce Place Value appeared first on Shelley Gray.

Do you struggle to find a way to teach place value that works for every student? Place Value Tent Cards are a great way to integrate hands-on learning into place value. All students love using these, and it helps make understanding more concrete.

I’d love to tell you a bit about how I’ve used these Place Value Tents in my classroom. At the end of this post, I’ll show you where you can download these for free!

Each place value group includes the numbers from 1-9. For example, the yellow “ones” cards include the numbers from 1-9. The pink “tens” tent cards include the numbers from 10-90. The blue “hundreds” tent cards include the numbers from 100-900. This continues for the “thousands” and “ten thousands” tent cards.

 

 

Now, a big teachable moment will come when one student inevitably does this:

In the above picture, the number 867 is made up of 3 yellow “ones” cards. If a student does this, it is the perfect time to reinforce the fact that the number 867 is not an 8, a 6 and a 7; rather, it is an 800, a 60 and a 7. Additionally, remind students that you can’t put a “one” in the tens or hundreds place.

I was given the templates for these tent cards at a professional development session by Manitoba Education when I first started teaching, but I searched online and found where you can download them from (for free)! Just click here, and then scroll down to where it says “Blackline Masters for the Classroom.” They are the “Place Value Tents.” You can choose to print off only the ones, tens and hundreds or all the way to hundred thousands. Just remember to copy each different place value on a different color of paper!

Hope these are helpful to your place value instruction!

Looking for more place value resources? Check out these fun ways to work with place value in your classroom!

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