Check out the other posts in this series! Emergent Part 1, Figurative Part 3, Initial Number Sequence Part 4, Intermediate Number Sequence Part 5, Facile Number Sequence Part 6.

Get the full overview in one place! Presented at the Making Math Moments Summit, you can get the full presentation here!

## Counting is Tricky

Counting is a lot trickier than people think. Because it has been so long since most adults have learned to count, they don't realize how long it takes and the nuances of becoming an efficient and accurate counter.

To become a good counter, students need to:

Know the forward number sequence (verbal)

have a one-to-one correspondence, and have the concept of cardinality- or knowing that the number they said is how many are in the collection

Know the symbolic representation or numeral and know that the symbol indicates the number of objects

Use that information to solve problems

To help students become amazing counters, each of these areas needs to be practiced together to develop a well-rounded idea of numbers and number sense. This becomes even more important as they get older and if they need number sense everything in math becomes more difficult for students to access and use that knowledge to solve problems.

## Perceptual Counters

### What is a Perceptual Counter?

A perceptual counter is a student needs to perceive the object they are counting or “bring it to life.” Whether it be touching, taping, seeing, or hearing (like counting claps) what they are counting they need to perceive an object in order to count it, and when counting always start counting from 1 vs. counting on.

This is different from the next type of counter, the figurative counter because they can solve a problem only when all of the counters are visible. If you show two collections of counters 5 in one and 3 in the other, they will count 1,2,3,4,5 (collection A) then 6,7,8 (collection B).

### They may be able to:

Count objects a small number of objects (one-to-one, correct number sequence, cardinality)

Count arrangements to 10

Write numbers up to 10 to represent a collection of objects they counted

May be able to tell you the number before and after by counting but need a “running start”

If asked what comes after 6, they would have to count from 1 but can tell you 7, they may not know it is 7 without counting

Working on counting 20

## What do I look out for?

There are some things you might see students do to let you know that this is where your students are:

They can count a small collection of 15 or fewer and tell you how many

If given a large number of objects (50) and asked to get 7 they can count out 7 from the larger collection

When given two different types of objects and asked how many, the student will count one and then the other

## How can I help students in this stage of counting?

Students at this stage have solidified the idea of one-to-one correspondence they would benefit from opportunities to count objects to 20.

This includes

Working on the number sequence and rote counting.

One-to-one correspondence

Cardinality (understanding that the last number said tells you how many have been counted)

Subitizing- Quickly recognizing the number of objects in a small group without counting

## Subitizing and Spatial Recognition

Subitizing, also sometimes spelled “subitising,” is the ability to instantly recognize a number of objects without counting them. Some students may already be subitizing small numbers if they are familiar with dice, or play dice games at home, and know finger patterns to 5. If students can say the number of items quickly they are subitizing vs. counting the objects and then saying the number.

There are two types of subitizing, perceptual and conceptual. We can only really subitize numbers to around 5 easily which is perceptual subitizing. Conceptual subitizing is when we start to see the small numbers inside of bigger ones and relate them to each other. For example, if you are looking at six on a die, you may see three and three, or 2 groups of two.

## Activities for Spatial Recognition

### Quick Images Number Sense Routines

Quick Images in a number sense routine where you show students an image (like a dice face or 10 frames) quickly so they don’t have time to count and have to begin to subitize and go beyond counting by ones. You can learn more about it in this 4 Ways to Use Quick Images Blog

### Dice Games

Dice games are a great way to have students learn dice faces in a fun way since dice are so versatile! You can see some dice games in this 5 Dice Games post! One of my favorite games is Roll, Count, and Cover with pattern blocks. It comes with 3 levels of differentiation to support learners at various levels of counting development. To play you roll one die or two depending on the mat, and students have to find the numeral that goes with the value they rolled and cover it with a pattern block outline that has the matching number.

You can listen to this subitizing episode or read this subitizing post to learn more about some routines and activities you can do to support rote counting with your students.

## Activities for Decomposing Numbers

Decomposing numbers is knowing that numbers are made up of other numbers. You might hear people talk about "friends of 10" or "making 10" but that also includes other numbers. Like knowing 6 is 1 and 5, 2 and 4, 3 and 3 etc.

Kids need opportunities to practice those combinations and some of my students' favorites are listed below!

### Snap It, Hide It

In this partner game, you start with a target number of cubes in a tower. Let's say 5, and partner one hides the tower behind their back, breaks it, and shows their partner one half of the tower. Their partner would then have to figure out how many they are hiding behind their back and both partners would write the answer down on their recording sheet if they are using them. Take a closer look and Snap It, Hide It!

### Drop the Cubes

Your students will love Drop the Cubes getting to toss things without getting in trouble! Your students will be working with the same number the whole time. To play, students gently shake and drop the cubes, figure out how many fell inside the circle and outside the circle and continue until they finish their recording sheet. For example, if they were playing with 5 and they have 5 cubes they drop, 3 fall outside and 2 fall inside. They would draw or write 3 outside the circle and 2 inside the circle and repeat. Once they have learned how to play, this station can become independent for them as they work their way though the numbers!

### Snap 5 or 10

This game is a fun fast-paced way for students to practice subitizing, number combinations and fluency of adding numbers to make 5 and 10. This game is best played when students have some familiarity with decomposing numbers to five and ten to be able to find number combinations quickly.

How to Play

Distribute cards evenly between the players

Take turns flipping over the cards, if a player sees two cards that when added together make 5 or 10, they must quickly cover the two cards and say “SNAP” and they take the pair. Ex. 2 and 8, 5 and 5 etc.

Continue taking turns flipping cards until there are no more cards or combinations.

The person with the most pairs wins!

Alternatively, players can have all cards face up and find pairs that way.

Note: cards that have been flipped stay facing up and you can use them to also make pairs with any future cards that are flipped, or by themselves.

## Activities for Counting to 20

### Rekenreks or Number Racks

Rekenreks are a great way to work on counting objects to 20 and relate objects to each other since the provide anchors to 5, and 10. You can learn more about Rekenreks in this All About Rekenreks post and try some free Number Rack activities here!

In Pick, Build, and Cover your students pick a numeral or rekenrek card, create that number on their rekenrek, and cover the number they made on their mat.

A favorite of mine is Spin and Slide. Students spin the spinner and slide their rekenrek beads to match. This game is great to help get students to move from counting by ones to starting to move items as a unit.

### 20 Frames

20 Frames like Rekenreks help students relate numbers to 20 to each other. Some of my favorites are Pick, Build, and Cover 10 Frames or Spin and Build.

In Pick, Build, and Cover your students pick a numeral or 20-frame card, create that number on their 10 or 20 frame or rekenrek, and cover the number they made on their mat.

Spin and Build is similar, instead of picking, you spin a number and create the matching number on your mat. This game has an optional recording sheet so students can sneak in some number writing practice in this game!

You can always add some fun counters to any game to increase student engagement.

Save on the bundle of differentiated teen number math centers!

## Don’t Rush to Addition and Subtraction

The goal of developing number sense is for students to understand numbers, and how they relate to each other. While we want students to be successful with addition and subtraction, if you move on before they are ready, they may be stuck counting each object one by one instead of relating numbers to each other.

If you say there are 5 apples and you got 2 more, they will count 5 objects, then 2 then count them together being able to see all of the objects they are counting. If their understanding of number relationships is deeper, they might be able to count from five instead of one or use their knowledge of number bonds or number pairs (composing and decomposing numbers) to get the answer of 7.

## Keeping Track of Counting Progress

It can be easy for students to get frustrated with counting as it is a combination of skills that need to be developed together in order for them to become proficient and efficient counters.

One way I found a lot of success in tracking students'' counting progress is with a visual goal-setting and counting sheet. Since I taught Spanish Immersion it is available in English and Spanish. It has a quick progress tracker so I can quickly check the numbers they know and the numbers they are still working on.

It goes beyond just counting and includes goals for:

✅Identifying numbers to 20

✅Counting to 100

✅Writing numbers to 20

✅Counting objects to 20

✅Subitizing numbers

✅Decomposing number to 10

✅Number before and after

The best part is that these big goals are broken down into smaller bite-sized goals so your students can build their confidence and momentum throughout the year!

You can take a closer look at this visual goal-setting and counting sheet in this post!

## Yorumlar