Welcome to all things number sense. From recognizing numbers to ordering and comparing. Essential math information for teaching preschool math and beyond!
Number sense is a broad term that refers to a group or set of skills that are needed to perform basic math operations.
You might think that number sense is just simple counting and that young children will master number sense quickly. However, number sense refers to deep understanding of HOW numbers work. It will take some time for young children to master these skills!
Number sense is the critical foundation that ensures that students will be successful in mathematics for years down the road. It lines them up for success in addition and subtraction and understanding how these operations are related. In a nutshell, it is a critical part of preschool and kindergarten math development.
Number Sense Skills Include:
- Rote Counting (naming numbers in order)
- Number Recognition (recognizing numbers in print)
- Counting with One to One Correspondence (each number has a constant value)
- Comparing Quantities (understanding the concept of more/less/same)
- Cardinality of Number (recognizing that the last number said when counting is the number of total objects)
- Conservation of Number (understanding that the number of objects is always the same even when rearranged)
- Subitizing (the ability to recognize “how many” in a set without counting individually)
Let’s dive in! We’ll tell you a little more about each number sense skill, and give activities to practice it.
Plus, grab our free counting mats to get started on these skills right away!
Number Sense Skill: Rote Counting
Rote counting is like dipping the toe into the number sense pool. Young children begin rote-counting (with mistakes) at an early age, often around 2 years old.
To rote count is to count verbally in sequential order. Children mimic the pattern of numbers that they have heard, without understanding number value or quantity. Once children have mastered rote counting skills, they are able to progress to tagging – which is the prerequisite for one to one correspondence.
Rote Counting Activities
Rote counting is a breeze to practice – the important part is to make it fun and exciting! There are many fun, simple rote counting activities that can be added to your preschool math plans.
- Invite young children to count along with you using different voices (soft, loud, silly, grumbly, etc.).
- Sing along with counting songs like 5 Little Speckled Frogs and One, Two, Buckle My Shoe. You’ll find plenty of counting songs in our list of songs that teach.
- Move and count! Incorporate counting as you clap, dance, jump, and hop.
- Use a puppet or stuffed animal to practice rote counting. Play a game that when the puppet gets to 10 it has to dance and start all over again!
Number Sense Skill: Number Recognition
Number identification is the ability to recognize a number in print and verbalize or write it. “At its most basic level, numeral identification is a form of shape recognition, which can result in a simple association of the word “two” with the symbol ‘2’ without a cardinal meaning” (Mix, Sandhofer, & Baroody, 2005). This means number recognition can develop at a different time than number value.
Number Recognition Activities
- Number bingo and number scavenger hunts are all creative and fun ways for young children to practice identifying the numeral.
- Textured numbers – sandpaper numbers and/or glitter/salt numbers are a great way to invite children to trace the number’s formation with their index finger.
- Using playdough snakes to form numbers is a great way to practice learning and making numbers!
- Stamping numbers is a kid favorite for practicing number recognition
- Give numbers a purpose – teach your students their phone number!
Number Sense Skill: One to One Correspondence
During the tagging stage, children will begin assigning numbers to objects. The numbers will be often out of order or random during this phase. For example, a student who has 6 apples placed in front of him may say, “1, 2, 4, 7, 8. There are 8 apples!” This student is making the connection that we use numbers to count objects, but his number sense is still too immature to understand that each number has a value. Tagging precedes one to one correspondence and children may not physically touch or attempt to manipulate the items, rather they just “count” by observation, which often results in incorrect counting or accidental re-counting.
During the one to one correspondence stage, children begin to understand the rule of counting. It’s the rule that each number translates to a specific quantity AND recognizes that numbers are a symbol to show a quantity. The student in the tagging example above has now begun to use correct number order to count the 6 apples placed in front of him.
Check out our post about one to one correspondence for even more great information around this critical number sense skill.
One to One Correspondence Activities
- Use ten frame mats to help children count accurately. Show the child how to count to the desired number by slowly touching each object. Then, have the child do it after you so that you can assess any areas that they might need help with, whether it’s counting or following their finger. Check out our free dinosaur ten frame mats!
- Use counting at every natural opportunity. Count the grapes on your plate, count the butterflies in the book, and count the school buses in the parking lot.
- Use dice to help count out coins, pasta, stuffed animals, or books. Incorporate dice into an easy scavenger hunt at home or school. The options are endless!
We’ve got a set of counting cards in our store specifically to help with one to one correspondence! Each theme has a card with numbers 1-24. Switch out the seasonal counting cards to keep children’s interests and to follow along with your theme. These make a wonderful addition to your preschool and kindergarten math centers!
Number Sense Skill: Comparing Quantities
Learning to compare quantities helps preschoolers make sense of the relationships between numbers: three is one more than two, but it is one less than four. Most preschoolers naturally understand the concept of more or less, as they can quickly tell you if someone got more cookies than them!
Since many preschoolers understand more and less in a general sense, learning to compare with small numbers is a great place to start.
Comparing Quantities Activities
- Use a foam number puzzle as a creative way to count gems using one to one correspondence, and then compare the amounts in each number.
- Line up a small number of objects, perhaps 4 cars. Then line up 5 cars directly below each of the 4 cars. Ask children which row has more cars. Encourage them to share how they know. Use this same activity for less and same quantities.
- With connecting cubes, Legos, or building blocks invite the child to build two towers. Invite the children to make one tower more/less/or the same as another.
- Use real-life examples of more/less/same as they arise. Call attention to the two students who are wearing red and the four students who are wearing green. Invite the students to notice other ways to compare.
Number Sense Skill: Cardinality
Cardinality is recognizing that the last number said when counting is the number of total objects in the group. It’s the ability to count each object individually and correctly declare the total number of items in a set. This is the final and BIG step in one to one correspondence! During this stage, students may also begin to see patterns, such as five-frames and begin to know the total number of objects without counting (also known as subitizing).
- Encourage children to be helpful! Invite them to count out items (snack, blocks, crayons, etc.) to share with other children.
- Invite children to count everything! Count the pencils on the table, the windows in the house, or the trucks in the sand box. Reinforce the total number of objects by confirming the child’s count. For example, “Yes, Maya! There are 5 trucks in the sandbox today. The total number is 5 trucks.”
Number Sense Skill: Conservation of Number
This important component of number sense is one that takes time for young children to master. Conservation of number shows that the child is able to understand that a number of objects remains the same even when rearranged, therefore there is no need to recount.
For example, Billy counted out 7 red fire trucks and declared the total proudly. You then moved the fire trucks all around and rearranged them and asked Billy, “How many fire trucks are there now?” If Billy recounts them each time the question is asked, he is still working on conservation of number and needs more time to conceptualize the value of numbers. Repeated practice with this concept is crucial in preschool math.
Conservation of Number Activities
- Invite a child to join you in a counting game. Place six items on the table and ask the student to count how many total items there are. Once it is counted correctly (if not, work on one to one correspondence), mix up the items and ask the student to share how many there are now.
- If the child needs to recount, tell the student that you did not add any more items and you did not take any items away. If the child continues to recount, model counting the group of items in lots of configurations and stating that it’s always 6 because I didn’t add any items or take any away.
- Invite one child to count 5 objects into a box. After counting the 5 objects, ask the child to tell you how many are inside the box. If needed, remind them that the number they put inside is still 5 because they did not add or take away any objects. Repeat with other numbers.
- Show multiple children a numeral, perhaps 4. Invite them to hunt the room and find 4 of the same items (crayons, books, blocks, counters, etc.). Invite the children to bring back the 4 items they found and share and count the items with their peers. Encourage them to discuss why some sets of the same number of objects look different.
Number Sense Skill: Subitizing
Subitizing is the ability to recognize “how many” in a set without counting individually. It’s the ability to know the number by “sight”. It’s also an ideal way to introduce simple addition and subtraction. Use dot cards, tally marks, fingers, and ten frames to help your littles becoming subitizing masters! Subitizing practice is a vital part of your preschool and kindergarten math curriculums.
For even more subitizing tips, tricks, and insight, check out our Subitizing 101 post!
- Use music, movement, and Jack Hartmann to teach subitizing! These engaging videos, Subitize to 5 and Subitize to 10 are a great way to get some quick and fun subitizing practice.
- Subitize with dot cards, dice, or dominoes. Hold one up to the class for a few seconds and then ask the students to share how many they saw. Help students see the pattern inside the dots. For example, a 4 on a dice shows 2 rows of 2 which equals 4.
- Subitize with fingers! Hold up 3 fingers and ask students to share how many without counting. Then ask the children to model showing three fingers on their hand.
We hope this introduction to all things number sense has given you loads of ideas for your students and helped you feel more confident when teaching preschool and kindergarten math! Incorporate a variety of these activities into your lessons and watch the light bulbs illuminate in your little ones’ brains. Keep it fun, hands-on, and engaging and their number sense is sure to flourish.
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You are not only a caring mother but also a wonderful educator.
Katie T. Christiansen says
Thank you for your kind words!