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Elementary Math Websites To Build Number Sense

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A list developed by Cindy Lawrence, 3rd grade teacher in Texas. This list accompanies Unit 1 of the Third Grade Everyday Math Curriculum.

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Grade: K-2

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This post contains affiliate links for your convenience. View disclosure policy HERE.

Are you someone that scours the internet looking for the perfect activities for building number sense? Do you want lessons and ideas that are engaging, fun, and effective at building fluency with numbers? But you don't have time to waste! Right?!

The math tips and strategies you need for building number sense to 20 are right here. You will have everything you need to easily implement and bring a wealth of number sense activities, games, and centers into your classroom or home.

The activities, books, resource suggestions (including a FREE one) cover a ton of number sense concepts and are perfect for Kindergarten and first grade. Plus, find valuable number sense materials and manipulative suggestions, as well as freebies you can access today! Warning: It's LONG but filled with so much you won't want to miss anything!

Children need opportunities to learn and experience numbers. Learning to count, identify numbers, and understand quantity are a few of the important concepts. Repeated experiences build understanding and fluency with numbers. These experiences help expand understanding and learn new concepts. A strong number sense is vital for future understanding of more complex math topics.

The activities below are ones that have been used successfully. Use them as they are described or adapt them for your own needs. Be flexible. Have conversations about numbers and encourage questions. When there is an opportunity to order, count, match, or describe with a child, go for it! They benefit from seeing numbers in natural, fluid ways.

Make time for fun and engaging number activities daily and watch fluency develop.

Counting

It is very important to count with children every day. Repeated oral counting helps them hear what numbers sound like and to learn their order. Using math manipulatives, like counting chips, can help build a connection to oral counting and counting objects. This one-to-one counting is an important skill that needs to be practiced often.

Activities

Count out loud as a class starting at 1 and building to higher and higher numbers.

Sit with a partner or in a circle and take turns counting by 1's.

As counting develops, teach number patterns and counting by 2's, 5's, and 10's.

Use a number chart to visually see what numbers look like. Point to each number as it is said.

Encourage kids to practice one-to-one counting with small objects. Have small groups of objects set up in a center for them to count.

Provide number cards (like those seen below) for kids to represent with counting chips.

Matching Numbers to Quantities

Provide materials for kids to count and connect with objects and numbers. This encourages children to see that numbers are more than words. Teach children that numbers have many representations, such as dots, fingers, counters, numerals, objects, ten frames, etc.

Activities

Match two different types of objects together, such as 5 counting bears and a domino that shows 5 dots.

Use links to create a number chain for a number.

Work up to showing quantity with more than 2 types of objects (as seen in the photo).

Have many different items available for activities, such as dice, dominoes, number magnets, bears, counting chips, cubes, and number cards.

Match number cards from a card deck or game of Uno with dots on dominoes. Find every number combination on the dominoes.

Complete number puzzles that have a different number representation on each piece. They helps kids see that numbers can be modeled in many ways. These number puzzles to 20 are available as a FREE download further on.

Encourage one-to-one counting with clip cards. Kids count groups of objects and clip the numeral that matches to the correct quantity.

Ten frames are great for organizing numbers so that they can be easily counted. Matching numeral cards with ten frame representations is simple, yet effective at connecting quantity with numbers.

Number of the Day

When kids see numbers in many ways at once in a repeatedly their number sense develops. Pick a number of the day starting at 1 and dissect it during your math block.

Activities

Learn about a specific number for each day that you have been at school. Teach and dissect that number during calendar time. Represent that number on a number line, count to that number, show that number with straws or cubes, etc.

Use a number of the day poster or anchor chart to break numbers down. Create your own number of the day poster with the FREE poster templates.

Encourage kids to participate and show their understanding on paper or mini white boards. Ask a question, such as "How do we show 5 with tally marks?" and allow them time to try on their own. This makes a great fluency building warm-up to math lessons.

Read more tips on starting a number of the day routine in your classroom.

Ordering Numbers

Provide opportunities for kids to put numbers in order. While they put numbers or objects with numbers on them into the correct order they are counting and building number sense.

Activities

Provide opportunities with using a number line and number chart that puts numbers in order for us.

Give sets of numbers to order correctly by finding them on the number line.

Cover different numbers on a number chart with sticky notes and ask kids for the missing numbers.

Build Lego stacks by putting the pieces together in an order written on the blocks.

Work together with a partner to order number cards from 0 to 20. Create a number caterpillar like the one seen below.

Number puzzles are a fun way to order numbers. Put the strips in the right order to reveal a picture.

Puzzles are simple and easy to create. Take an old puzzle and write numbers on the back of each piece.

Grab a piece of paper and write numbers in rows. Cut out pieces randomly and trade with a partner. Put the puzzle back together again for practice.

Complete a number order maze starting at 0. This activity can be reused when put into a pocket protector.

Place Value

Teaching kids about place value should begin with teaching them to see ten in many ways. Move on to illustrating numbers with base ten blocks.

Activities

Practice making groups of ten things. Group straws, beans, counters, or any small objects.

Teach counting by 10's to count groups. Extend to teaching groups first and then singles.

Make groups of ten to get to the 100th day.

Show and examine a tens block and ones block. Discuss that a tens block has ten ones put together.

Use base ten blocks to represent numbers. Do plenty of examples where kids must use and count blocks. Use a chart to help count the blocks.

Say "Show (or draw) me 14 with place value blocks!"

Represent the number of tens and ones on place value mats (seen below). Ask questions like "How many ones are there?" or "How many groups of ten?". Make sure they understand what each number within the number stands for (i.e., the 1 in 18 is a ten and not a one).

Represent a number in different ways: expanded form, standard form, word form, numeral, etc. Worksheets like the one below can help build this connection.

Reading and Writing Numerals

Kids are constantly surrounded by numbers in their environment. They quickly learn to recognize the individual numerals 0 to 9 through different experiences. Continue to encourage this familiarity by having numbers on the wall. Posters, number lines, and calendars are helpful tools.

Activities

Build numbers with playdough in a math center.

Print numbers from 0 to 9 daily in different ways - in booklets, on whiteboards during math lessons, etc.

Draw numbers on paper and give students do-a-dot markers or bingo dabbers to dot numbers.

Use a Boogie Board (seen below) or whiteboard to quickly practice numbers over and over.

Trace numbers frequently and repeatedly to build coordination and correct form. The mini-book below encourages this, as well as locating numbers.

Encourage the correct formation of numbers by teaching it explicitly. The posters (seen below) are helpful tools to use and post on the wall.

Catchy number poems help students visualize and remember number formation. Use your whole body to make actions or draw in the air.

Reading and Writing Number Words

Teach kids how to read number words as they learn to read. Teach each number word one at a time and how to spell them phonetically (when applicable).

Activities

Have number posters with both the numeral and number word on it.

Include number words on spelling lists so that kids learn to read and spell number words.

Use a number of the day routine to teach and focus on one word each day.

Match numbers word cards with numeral cards (seen below).

Play memory with a partner with number word and numeral cards. Look for pairs (twelve and 12).

Build recognizing and speed with mental math flash cards cards. Flash cards to kids and they race to call out what they see (tally, numerals, number words, etc.).

Counting On and Back

Teach the strategy of counting on and back from a number to prepare kids for addition and subtraction.

Activities

Give students a number and a group of small objects to count on. Ask "How many more do I have?" given 7 to start and a group of 9 counters to count on with.

Play games with small objects and decks of cards where counting on is needed.

Play a group counting game called 'Around the World'. Say a number and each person counts on and says the next number as you go around the circle.

Use small objects to count on or back from a number given (cubes, counters, dice, etc.).

Put numbers in backwards order. Take the ordering activities seem above and reverse them.

Estimating

Provide lots of opportunities for kids to guess how many things they see in their day to day lives. Ask prompting questions to encourage this thinking. Make sure kids know that they are estimating and that these are just guesses. Stress that estimates do not need to be exact but that they should be thoughtful. With more practice, estimations should become closer to the actual number of objects.

Activities

Fill clear or open containers with different sized objects for kids to guess. Keep them simple and work up in difficulty and size of objects. Smaller objects and bigger containers are usually harder.

Create an Estimation Station" where containers are set up with objects inside. Kids can take a close look and make estimates.

As a whole group activity, grab a pile of objects to show quickly. Cover them and have kids make guesses.

Play 'Show & Hide' with a partner. Use a cup and put some small counting bears inside. Quickly show a partner and them hide them. They make an estimate and then you count together to check.

Comparing Numbers

As familiarity with numbers grow, so does an ability to compare numbers with each other. Provide opportunities to compare numbers daily. Ask questions about which number is bigger, smaller, or the same.

Activities

Use a chart or number line to compare numbers.

Use small objects to make comparing easier. Say "Show 11 and 15 with cubes". Ask "Which number is smaller?".

Teach the symbols < > and = and what they each mean. Use the alligator strategy (The alligator likes to eat the bigger number) to remember the signs and what they mean.

Create number towers. Kids use cubes to form towers to represent numbers. Compare 2 towers to see which is the tallest and therefore the bigger number. The alligator eats the bigger tower.

Compare numbers with math tools and indicate the correct symbol on clip cards (seen below). As kids become fluent, they should recognize the correct symbol without support.

The activities seen in this post can be found in the following resources.

Free Number Puzzles to 20

Grab 20 FREE number puzzles with different representations on each piece by clicking the image below.

Number Sense Books

I Spy Numbers by Jean Marzollo
1,2,3 Peas by Keith Baker
Chicka Chicka 1,2,3 by Bill Martin Jr.
Splash! by Ann Jonas (counting)
The Very Hungry Caterpillar by Eric Carle (counting)
How Do Dinosaurs Count to 10? by Jane Yolen
Number Everywhere by Elliot Kaufman
10 Black Dots by Donald Crews
How Many Bugs in a Box? by David Carter
How Many Snails? by Paul Giganti, Jr.
Ten Sly Piranhas by William Wise
None the Number by Oliver Jeffers
Zero the Hero by Joan Holub
More or Less by Stuart Murphy
Tally O'Mally by Stuart Murphy
Place Value by David Adler
What's the Place Value by Shirley Duke
Quack and Count by Keith Baker
Betcha! by Stuart J. Murphy

Number Sense Materials

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Activities for Building Number Sense to 20

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This post contains affiliate links for your convenience. View disclosure policy HERE. Are you someone that scours the internet looking for the perfect activities for building number sense? Do you want lessons and ideas that are engaging, fun, and effective at building fluency with numbers? But you don't have time to waste!

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Upper elementary students beneﬁt from activities that help reinforce their understanding of factors, multiples, and prime numbers. In this two-person game, students take turns identifying factors of successive numbers, continuing until one of them can no longer contribute a new number.

Directions for Playing the Game

1. Player 1 writes down a number greater than one and less than 100.

2. Player 2 writes down a factor of the ﬁrst number underneath it.

3. Player 1 writes down a factor of this new number.

4. Each player, taking turns, writes down a factor of the preceding number.

5. If a player writes down a prime number (i.e., it is not divisible without a remainder by any other integers except one and itself), the next player adds seven to it and writes down the resulting sum as his or her turn.

6. The player who can no longer contribute a new number loses the game.

Additional Rules

1. Once a number has been written down, it can't be used again.

2. The number one can't be used at all.

Caren Introduces the Activity

"Today I have a game for you," I announced to the sixth graders in Lyndsey Lovelace and Shea Carrillo's class. "It's called One Time Only. To play the game you need a partner. One of the partners begins by picking a number greater than one and less than 100. So you can see how it works, the whole class will be my partner for this ﬁrst game. There are just a few rules, and I'll explain them while we play."

I wrote 36 on the overhead.

"Now it's your turn," I said. "You need to think of a factor of 36. Can anyone tell me a number that goes evenly into 36? Another way to think about it is by skip counting. Which numbers can you skip count by and get to 36?"

By introducing several ways to think about factors, I hoped to explain the game more quickly. If I'd just asked for a factor of 36, students who weren't sure what a factor was or who weren't sure about the difference between a factor and a multiple might not have been able to participate. As the students used the terminology in the context of the game, they'd become more comfortable with it.

"So, what do you think?" I asked. "Can anyone tell me a factor of 36?"

"How about six?" offered Fred.

"Is six a factor of 36?" I asked the class.

Several students nodded or vocalized their assent. I pushed for more of a commitment. "Who can explain why they think six is a factor of 36?" I asked.

Jessie raised her hand. "Because six times six is 36," she explained.

"Also," added José, "if you count by sixes you'll say 36. Like 6, 12, 18, 24, 30, 36."

"All right," I said, "I'm convinced that six is a factor of 36." I wrote 6 under 36 on a projected transparency. "Now I need to ﬁnd a factor of six to add to the chain of numbers we're making here. I think I'll say two." I wrote 2 under the 6. "Okay, now it's your turn to think of a factor of two," I said.

"Two," said Derek. "Two times one is two."

"Well, yes," I responded, "two is a factor of itself, but one rule is that you can't use the same number twice. That's why the game is called One Time Only. If a number is already written down you can't use it again. Can anyone think of a factor of two that's not already up here?" I asked, pointing to the overhead.

"One," said Ali.

"Well, that brings up another rule in One Time Only. You can't use one. You're correct, Ali, that one is a factor of two. But in this game you're not allowed to use one. So you can't use a number that's already up there and you can't use one. Those are the two main rules of this game. Can you think of any other factors of two?"

"How about four?" asked Chrissy.

"How do you know four is a factor of two?" I inquired.

"Because two times two equals four," Chrissy explained. Chrissy had confused factors and multiples. I was glad she had made the multiplication connection, but I needed to prompt her a bit to get her back on track.

"I know that two is a factor of four, because I can count to four by twos," I said to her. "But it doesn't work the other way around. Four isn't a factor of two, because you can't count to two by fours."

"Oh, yeah," Chrissy replied.

"Does anyone know what we call four in this situation?" I asked the class.

"A multiple!" exclaimed Neal. "If you can times a number to get the number it's a multiple. Like 36 is a multiple of six because six times six is 36."

"All right," I continued, "so are there any factors of two besides two and one?"

"Can we use fractions?" asked Howard.

"Sorry," I told him, "but factors need to be whole numbers, like the numbers you use to count. Take a minute and talk at your tables," I suggested. "See if you can think of any other factors of two."

I let the students talk brieﬂy and then I called them back to attention. "Did any tables ﬁnd any other factors of two?" I asked. The class consensus was no. "So, do you think there are any other factors of two?" I prodded, checking to see if the students were really convinced.

"Not if we can't use fractions," Ana qualiﬁed.

"Well," I told the class, "you're right. There are only two factors of two, two and one. Does

anyone know what you call a number that only has itself and one as factors?"

"Prime?" Greg ventured in a barely audible tone.

"Prime!" several students announced with authority after hearing Greg.

"Yes, those are prime numbers." I wrote prime next to 2 on the overhead. "In One Time Only when you hit a prime number you add seven to it. So what's two plus seven?"

"Nine," several students responded.

I wrote 9 on the overhead under the 2.

"Okay, now it's my turn, and I need to think of a factor of nine. I'll say three," I said, as I added 3 to the list on the overhead. "Now you need to ﬁnd a factor of three."

"It's prime," announced Natalie with authority.

"If it's prime, what happens?" I asked.

"Add seven," José reminded us. "So it's ten."

I wrote prime next to the 3 and put a 10 below it.

"How many times can you use plus seven?" Jessie asked.

"There's no limit," I explained. "Anytime you're playing and a prime number comes up, you just add seven to it. It's my turn again and I need to put a factor of ten that's not already listed. I'll say ﬁve."

"Oh no," exclaimed Alejandro, "another prime number for us."

I raised my eyebrows in feigned surprise as I looked at the numbers on the overhead. "Wow, it is a prime number." I agreed. "You keep getting prime numbers on your turn. I wonder if that always happens in this game. Maybe there's a pattern." While I knew that this particular pattern didn't always happen, I took the opportunity to spark a little curiosity. I hoped that in subsequent games students would pay more attention to patterns in general as they played. Looking for patterns is a powerful way to build number sense, particularly when students have opportunities to think about the patterns and their relationships to numbers and operations. I referred to the string of numbers on the overhead, which now looked like this:

"Okay," I said to the class, "it's your turn and since ﬁve is prime, what do you need to do?"

"Add seven," Jasper replied.

"Right," I agreed, "so now it's 12." I wrote 12 on the overhead. "Hmm," I said, "I need to ﬁnd a factor of 12 that's not already up here." I paused for a few seconds to give students a chance to review the numbers and think about factors of 12. I also wanted the students to see that math involves taking time to think.

"I know," I brightened, "I'll say four." I wrote 4 on the overhead beneath the 12. "Now you need to ﬁnd a factor of four that's not already up here. Talk at your tables for a minute or two and see what you can come up with."

"We're stuck," Ali soon announced.

"What do you mean?" I asked.

"Well," Fred explained, "we're not allowed to use one. Four and two are used already. There are no other factors, so we can't go."

"Does everyone agree with Fred and Ali?" I asked, looking around.

The nods and yeahs were unanimous.

"Then I guess the game is over," I said. "This time I won, because I was the last player to add a number to the list. You want to get your partner stuck so she or he is unable to add a number to the string. But winning isn't really the important part of this game. You're going to play a bunch of times, and sometimes you'll win and sometimes you'll lose. The important part of the game is the mathematical thinking that you do."

I played one more game with the whole class. This second game went more quickly, because I didn't need to stop to explain the rules and vocabulary. After two games, I was satisﬁed that the students understood the rules and knew how to determine a winner. The factor concept had been reinforced, the term multiple had been introduced in context, and the students knew how to identify prime numbers. The students were ready to play with their partners. In addition to having practice with multiplication facts, students who play One Time Only search for winning strategies by thinking about relationships among numbers and factors. In so doing, they build their number sense.

From Printed Newsletter Issue Number 26, Fall/Winter 1999-2000

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Upper elementary students beneﬁt from activities that help reinforce their understanding of factors, multiples, and prime numbers. In this two-person game, students take turns identifying factors of successive numbers, continuing until one of them can no longer contribute a new number. Player 1 writes down a number greater than one and less than 100.

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There's a summer online book study for the book

Number Talks being hosted by

I've had the pleasure of reading this book and got some wonderful activities to use with my Firsties...

Here's some of my thoughts, ideas, and finds about this wonderful resource...

Number Talks are great springboards in helping students develop a better understanding of the number concepts and skills.The better a student's number sense and cardinality, the more prepared they are to begin memorizing and becoming fluent with Math Facts

*Try to do every day for a small amount of time (10 minutes)...a few minutes often is much better than a lot of minutes every once in awhile.

*Establish a routine for showing you're ready or that you agree quiet thumb up

*Ask questions and let the kids do the talking!

*Use different mediums...whiteboard, chart paper, smartboard

*Name/label the strategies that your students talk about using...

*Create a safe environment during the number talks

Math Number Talk Resources Site:

 Each card has a numeral for the whole and a dot pattern for each part. Cover one of the dot patterns with a flap of paper or fold over the card so that only one part can be seen.

 Have the child say the missing part that is covered up and/or the number sentence, i.e. "Eight is five and three" for an 8 card showing five dots and hiding three.

 Make sure to have the child explain how they knew the missing part.

You show the child the missing part card, say the amount of the dot pattern that is not covered up, and say that you wish you had the numeral. For example with the 8 card that has five dots showing and hiding three, you would say "I have 5; I wish I had 8...how many more do I need?"

Choose a number in your head... then have the students guess what that number is by process of elimination.For example if your number is 10 and a student guesses the number 7....you would say "my number is more than seven". Then they have to tell which numbers need to be covered up and why they need to be covered. This is a great game to get the kids thinking in terms of more than and less than. Each guess helps them narrow their focus of a number choice and should eliminate the shouting out of random numbers.

Number Squeeze - this is not a link to my creation, but is available on the web

Similar to 'Guess My Number' but using objects to move on a number line to get closer to the number I'm thinking.

Using a linking cube stick of 10 cubes (5 red and 5 blue), I show the kids the stick of cubes and begin asking them to tell me what they notice...there's no fear in what you notice, because you can "notice" a lot of things...colors, shapes, amounts...etc...there's really no one right answer when you ask "What do you notice?"...

Then I put the stick behind my back and break off a piece...when I show the kids and ask "What do you notice now?"...we can begin to create number bonds and equations...Remember...it's the thought process I'm trying to get at...

tell me how you know you're right...

tell me if you agree with what so and so just said...

why do you agree with so and so ...why do you not agree

What number they do you think is on my board now?

...then I'll reveal the board and have someone tell how they knew the number I was hiding.

Add this to your calendar time:Show the number of the day (which is the number of days in school) using ten-frames.Each day have a student add another dot to the ten-frame. Put adhesive magnet squares on the back of the ten-frames and then you can move them around.Students can then show different ways to make the number of the day....think about when it gets to double digits like 25 or 56... they can use two addends.Record their equations on a white board or chart paper.Double digits mean they can slide the ten-frames into two columns to show the two addends.Then the class counts aloud each addend (practicing counting by tens) and confirms that the expression is correct.You could also do 3 addends.

Every week put a new "answer" on a class Think Math board.As soon as a new question goes up, students can write a question that matches the answer on a sticky note and place it on their class number.Think of the possibilities of the questions that could be written and then explained by your students.There are as many different correct answers as there are students. You'll need to take several weeks of modeling and going over correct answers before the majority of students are able to correctly write number stories that match the answers, but the learning will be well worth the effort!

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There's a summer online book study for the book Number Talks being hosted by I've had the pleasure of reading this book and got some wonderful activities to use with my Firsties... Here's some of my thoughts, ideas, and finds about this wonderful resource...

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Math Number Talks K 5 - Lessons - Tes Teach

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Video 1.Video 2.Video 3.Video 4.Video 5.Video 6.Video 7.Video 8.Video 9.Video 10.Video 11.Video 12.Anchor Chart.NT Printables.Hand Signals.Sherry Parrish: Number Talks: Building Numerical Reasoning

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Mathematical Games: Number Sense & Numerical Operations

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What is a Number Talk? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation:

keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics.

spend only 5 to 15 minutes on Number Talks

Talks are most effective when done everyday

Every Hall County school has six copies of Number Talks: Helping Children Build Mental Math and Computation Strategies by Sherry Parrish. This is probably housed in your school library under "teacher resources" or with your grade chair. Number Talk Resources: Pictures of Number Talk Spaces and Anchor Charts Subitizing Resources Making and Using Rekenreks

How to Make Rekenreks
(directions submitted by another Georgia educator, Chantelle Kirk) The Rekenreks are made with a cut 4′ x 8′ sheet of 1/8 inch Tempered Perforated Hardboard from Lowe's (make sure you do not pay for each cut). The ribbon is 3/8 inch grosgrain ribbon (I singe the ends of the ribbon in a candle flame). The pony beads are the 6 x 9 mm size. I do add a drop of a "fabric" glue to each end before I add the duct tape. I have made 100 bead Rekenreks with these materials as well. One Kindergarten class that I work with used a set of these Rekenreks for about a 2 months. They held up well and I loved seeing the kids build understanding with the Rekenreks! The yellow beads on the blue ribbon is the 1,000 display. I have bought bags of 1,000 pony beads. I put a whole bag of beads on the spool of ribbon. And then, I tie knots to separate the groups of ten and two knots with space between the hundreds. I singe both ends. I am making some with blue beads on yellow ribbon. The last picture shows the red and white hundred strand and tens. These are also on the 3/8 inch ribbon with knots and singed ends. I was hearing about frustration with "regrouping" in second grade. I thought about a way to be able to decompose a ten with these beads. Some of the tens have a clip on the end so that students can decompose the ten.
Also check out these easy to make, paint-stick rekenreks.

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What is a Number Talk? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation: keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics.