Subitizing

Subitizing is the ability to see small amounts without having to count. For example, many students can quickly recognize 3 objects sitting in a group, or the number of dots on a dice.

To support students who are developing their ability to subitize, play lots of games that use dice or dominoes. Quick flashing dot cards and doing number talks with dot patterns also reinforces this skill.

Magnitude

Students have a sense of which set has more in it, which shows their sense of magnitude.

Practice this skill by making piles of objects. Which has more? How can you tell? Young children can often tell you that one must be more because the pile looks “bigger” or “higher.” Count out the objects in the piles and line them up to further develop their concept of more and less.

Counting

Students may learn to count orally before their one-to-one correspondence is developed.

There are so many ways to practice oral counting with your students. Switch it up and keep it fun! Sing counting songs (YouTube is filled with them), play count around the circle (each student says the next number in the sequence until you get to the target number), count as you march around the classroom.

One-to-One Correspondence

When students say one number for each object, they are using one-to-one correspondence. Students who count faster than they point or point faster than they count do not yet have a fully developed one-to-one correspondence.

Students who do not yet have one-to-one correspondence may count faster than they point or point faster than they count. Or they may touch the same objects over and over again, counting them multiple times. Students who do not yet have one-to-one correspondence need lots of practice counting out objects! Playing simple board games is also a great way to practice one-to-one. When your child must “hop” the exact number of spaces rolled, they are working on that idea that each “thing” gets one number assigned to it.

Cardinality

When students know that the last number they said when counting tells how many there are in all, they have cardinality.

You can have them count out objects and put them in a line, then push the objects closer together to count them again. Then spread them out and count them yet again! This reinforces the idea that the quantity stays the same even though the arrangement looks different.

Hierarchical Inclusion

When students understand that smaller numbers are a part of bigger numbers and that numbers increase by 1 as you count up, and decrease by 1 as you count back, they have the idea of hierarchical inclusion. They understand that the number six contains all of the numbers before it.

To see if your student has this idea, ask him or her to count out a small number of counters (say, 8). Now tell them, give me 6 counters. If the student gives you counter number 6, but not six counters, they do not yet have this concept down. Keep practicing. The concept of one more/ one less also falls under this skill.

Part/Whole Relationships

Understanding that 8 is made of 4 and 4, and also 6 and 2, 7 and 1, etc.

Children can explore part-whole relationships when they count out a set and divide the into parts. Number bonds, rekenreks, and ten frames are great tools for exploring different ways to make numbers.

Compensation

When students know that if 6 plus 1 equals 7, then 5 plus 2 also equals 7 because the one from the six was given to the 1 in order to get the same amount.

Most kindergarten students will not be ready for compensation, but playing with numbers as you engage in number talks will give students beneficial exposure to this concept.

Unitizing

Unitizing develops as students begin to work with larger numbers and see them in groups. For example, 12 is made up of 10 and 2 extra ones, and 20 is made up of two tens. This is not a skill that we discuss formally in kindergarten (it comes later), but working with teen numbers and allowing the students to see that teen numbers are made of 10 plus some extra will support this understanding.

I hope this has given you a better understanding of young students’ number sense and some ways you can support their development. For more information on helping students build their number sense, I highly recommend you read Teaching Student-Centered Mathematics and Number Sense Routines. (Affiliate links provided below).

If this post was helpful to you, here is an image to pin it so you can come back! Thanks for reading!

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Number Books

Have students create their own number books. Creating a book of their own will give them ownership of something that they can “read” again and again to help them learn their numbers. Provide pages that include the numerals you are working on. Allow the students to create the set using bingo dabbers, stickers, or pictures. Click Here to download this free number book!

Number Bingo

Bingo is a classic, fun way to practice recognition of numbers. Students will enjoy playing this game, and they will learn their numbers quickly if you play it on a regular basis.  Here is a free Number Bingo to print.

Squishy Mats

In a gallon baggie, squeeze in some hand sanitizer or hair gel. Add a few drops of food coloring, and seal the bag at the top with tape. Allow students to practice forming the numbers in the goo using their fingers or a cotton swab.

Writing in Sand

Sand is a great place to practice forming numbers. Students can practice formation without worrying on mistakes the way they do while practicing on paper or even dry-erase boards. It’s hands-on, tactile, and fun!

Play Doh Mats

Students love to play with play doh any chance they get. Teach your students how to make “snakes” with their play doh. They can form the numbers and make sets with balls of play doh to match. Grab these free play doh number mats here.

Clip Cards

Clip cards are a fun way to assess your students’ knowledge of numbers. Students love counting out the pictures and clipping the clothespin on the correct numeral. Bonus points for working those fine motor skills!

Anchor Charts

Create an anchor chart for each number. Include the numeral and also other ways the same number might appear. This will help students relate the quantity to the numeral and also see that there are many different ways to make a number. Show the number with pictures, tally marks, ten frames, and more. My Learning Our Numbers Pack includes large numerals and different ways to make each number, plus practice sheets to work on number formation and showing the number in different ways.

Hop to It

This is a game to get students up and moving! Write numerals on note cards and place them on the floor around your classroom. You can also use die-cut shapes (lily pads are fun!). When you say “Hop to it!” the students hop to a new number. They then share out the number they landed on.

Songs with Movement

Sing songs that get students using their whole bodies to create the numbers. The Numeral Song by Dr. Jean and I Can Write my Numbers by Harry Kindergarten teach number formation. Students can listen to the song and practice writing the numbers in the air using big movements with their whole arm.

Count it Out

Write the numbers you are learning on note cards or on cups. Have the students count out manipulatives to match each numeral.

The key to teaching numbers is to keep it hands-on, engaging, and relevant to your students. They will learn those numbers in no time!

The post 10 Ways to Teach Children Numbers appeared first on KTeacherTiff.

Introducing Rekenreks

Like any other manipulative I introduce, I always allow my students to hold and play with the rekenreks for a while before we use them for instruction. After a few minutes of exploration I ask: What do you notice? What do you wonder?

I then explain that a rekenrek is a tool that will help us work with and understand numbers. I show the students what the rekenrek looks like when it’s in “rest position.” This is when all of the beads are pushed over to the right.

Next, I model how to make a number by sliding beads over to the left. I invite students to make the same number on their rekenreks. Once your students are comfortable with the procedures for using the rekenreks, you are ready to use them for number talks, games, and problem solving!

5 Favorite Activities for Rekenreks

1. What’s my Number?- Create a number on  your own rekenrek and show it to the students quickly (3-5 seconds). Ask the students to tell you what number they saw.
2. Show Me- Hold up a number card or call out a number. Have the students create the number on their own rekenreks and then hold them up to show you. Record different ways students made the number on chart paper.
3. Story Problems- Use rekenreks to model story problems. “5 ducks were swimming on a pond. 2 more ducks came to join them. How many ducks are swimming on the pond now?”
4. What’s My Way?- Invite the students to make a target number on their rekenreks. At the same time, you create the number on your own so the students can’t see. Have students share the way they made the number, in an attempt to guess “your way.” For example, say the target number is 6. You made 6 on your rekenrek with 4 on the top and 2 on the bottom. Sally shares out that she made 6 with 3 on the top and 3 on the bottom. You respond, “that’s a great way to make 6! 3 on the top and 3 on the bottom! But it’s not my way!” Continue calling on students until someone shares that they made 6 with 2 on the top and 2 on the bottom. “Congratulations! You guessed my way!”
5. How Many More?- Choose a target number. Push a portion of the number over on the top row. The students will push the remaining beads needed to make that number on the bottom row. For example, say the target number is 10. You push 6 beads over on the top row. Have students do the same. Then ask, “How many more do we need to make ten?” The students will then push 4 beads over on the bottom row.

I hope I gave you some ideas to help get you started with rekenreks in your classroom. They are a powerful learning tool!

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Teach with Problem Solving

It is critical that as teachers, we shift from the traditional practice of modeling “how to do math.” Mathematics instruction is much more effective when we use a problem-based approach (Van De Walle & Loven). Allowing students to struggle with any task is hard for teachers (so hard!) But it is so important that we allow this to occur in math. Instead of teaching a strategy and saying “now use this strategy to solve this problem,” try posing the problem first at the beginning of your lesson. This will allow students to engage in analytical thinking and reflective thought, which is crucial to a solid understanding.

For example: Let’s look at a lesson on decomposing the number five. I could begin the lesson giving students red and yellow counters and showing them how to put the counters in a cup, shake it up, and count the yellow and the red to “see” that the two sets shows a way to make five. Then the students could practice it, sharing out the ways they made five.

What was wrong with the lesson above? It was a great hands-on way to have students explore numbers. But what is the activity really focusing on? I would argue that the focus on the lesson above is the procedure of shaking the cup, dumping the counters, counting the colors. What if instead of starting with the activity, this problem was posed instead?

“Boys and girls, I just ordered my mom a flower arrangement for Mother’s Day. I know that it has five flowers, and some flowers are red and some are yellow. I’m trying to figure out what the flower arrangement might look like. How many could be red? How many could be yellow?” Allow the class to figure out ways you could solve this problem. Some students might draw. Some students might use fingers or manipulatives. Some students will get it wrong and that’s OK. Students share out their ideas and you record them on chart paper. This problem-based approach will help students “get” what you are doing when you decompose the number five using those counters.

Next time you plan a math lesson, think about how to can flip it to begin with a problem. My problem solving every day pack includes many different types of problems which support number sense.

Number Sense Routines

If you teach primary, then you probably already have some routines in place that support number sense. Your calendar routine, counting on the hundreds chart, and graphing the daily weather are all such routines. Adding in additional activities that support seeing and conceptualizing quantities can provide a huge boost in the number sense of your whole class. If your calendar time is separate from your math block, having a daily math warm-up prior to your main lesson is where you will do these activities.

Here are some number sense routines to try:

• Quick Images with dot cards
• Ten frame flash
• Rekenrek games
• Count around the circle

The book Number Sense Routines, by Jessica Shumway, is filled with these strategies and more which support number sense to add to your math block (affiliate link below).

Number Talks

A number talk is a short discussion between you and your students about a math problem that you have shown. Your students will solve the problem mentally and will then share out their thinking about the process. In kindergarten, I always start with dot cards. “What number did you see? How did you see it? What did you notice?” Open it up to allow other students to share out. Some students may have seen six right away because they saw 2 groups of 3 and know that 3 and 3 make six. Another student may have seen the first group of three and then counted on. Another student may have counted by ones. Hearing other students’ strategies (and misconceptions, which is often even more powerful) is an important component of an effective number talk. For more information about number talks, check out the book Number Talks (affiliate link).

Throughout all of these activities, the conversation is key. Having students explain their thinking, working through misconceptions together, and reflecting on what was learned will have a profound effect on your students’ number sense.

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In science, we made predictions about whether the apple would sink or float.

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I’m excited to be sharing an easy project with you today–one of my favorite math tools: rekenreks!

I don’t know about you, but I love to use rekenreks in my classroom. If you’ve never heard of rekenreks before, you will! These arithmetic racks consist of two strings, with a row of beads on each string. Each row is traditionally made up of five red beads and five white beads, but you can use any two colors you like. They are great for helping students to understand number concepts such as basic addition and subtraction, subitizing, and decomposing numbers. These have become an essential part of my math workshop, but they are an expensive purchase!

What I’m about to show you is a much better method of making rekenreks that will last a lifetime!

 Yeah, I know this was not the best setup. Don’t make fun. After drilling the holes, get some sandpaper and give the edges and the areas around the holes a quick sanding.

 Trim the excess string along the back. This is what the finished product will look like!

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