# … it’s IMPERATIVE!

Did you know that when you practice counting with your kids you are building their future understanding of math?

* Counting with visual and tactile aids is important for a child’s foundation and counting practice doesn’t (or SHOULDN’T) stop in the lower grades.* Counting skills progress as children grow and should include visual aids to count with (5 Frame, 10 Frame, Place Value Chart) as well as tactile things to count with (sort & organize connecting cubes, cars, buttons,etc.), K-2 kids spend a great deal of time on counting activities but it’s important not to leave our 3-5th graders out to dry when the numbers get more complex and processing them can become even trickier, so keep practicing!

*A regular Counting Routine teaches:*

- Sequencing
- 1:1 (matching one-to-one or 1:1 correspondence)
- Counting on
- Counting by or in groups (multiplication)
- Sorting by groups or attribute (division)
- Recognizing the last number counted is the total of that group of objects that you have (cardinality)
- Grouping larger numbers & regrouping (place value)
- Adding and subtracting
- Perseverance
- Self confidence
- Cooperative learning (when you choral count or count in partners or groups)

## Best counting routine idea:

### Sing Songs

What songs did you sing as a kid? I remember *1, 2 Buckle My Shoe*. Singing is a great way to practice counting.

*Numbers to 5*

**5 Green and Speckled Frogs by Mother Goose Club**

*Numbers to 20*

My favorite song is** The Number Rock by Greg and Steve**! You can download it on Amazon, buy the CD or watch them on You Tube.

### More Counting routines you can start today (if you haven’t already):

#### Sorting Bags

*Materials:*

- bags of toys (in multiples, sortable by one or more attributes ex: size, shape, color
- sorting organizers (10 frames, 100’s chart, large cups or small cups)
- recording sheet and pencils with erasers (Kinder & up)

This activity is fabulous! Counting and sorting toys makes this a super engaging activity, kids can’t wait to get their hands on the toys.

Kids need YEARS of counting and sorting objects . This is easy to set up and free if you print out my 10 frame and use your own toys from home.

**Here’s how to set it up:**

**GATHER TOYS TO SORT**few different sets of toys for sorting and counting; in the photo is Cars vehicles, Matchbox style cars, Construction vehicles monster trucks and dinosaurs.**SORT**them into bags & or box**SORT**(beginners… just line them up) and**COUNT**away

*Sort by color and type of toy*

*Sort by Movie Theme*

Use this 5 frame for preschoolers learning to count and identify numbers to 5 and use the 10 frame to sort and count to 10, and to help you keep track you can have one set of 5 and 10 frames with the numerals inside as you count.

PRINT the 5 Frame 10 FRAMES

### Counting Dots

*Subitize Cards PRINT and cut out squares.*

### Draw or write

### Counting, the first years:

*There are 3 things to look for when children are counting:*

*1. sequencing **2. 1:1 correspondence**3. cardinality (do they recognize that the last number counted is the sum)*

A child with a solid understanding of numbers (also known as Number Sense: the child’s fluidity and flexibility with numbers) and how they work will understand all three principles, simultaneously.

* Children working on number sense will know any combination of the three.* As you build confidence in the beginning of number activities if a child counts and touches each object 1,2,3,5,6,7 no corrections need to be made during “their turn”. Simply say “lets count together” and then both of you touch and count them together. Do they notice the mistake (& or correct it)? If yes, then they are at an intermediate level of this understanding, but have not quite mastered it yet. If no they are still at the beginning level of understanding numbers.

**Where do I start?**

**Toddlers & Preschoolers**

- Sing counting Songs & other number sense activities
- Rote counting (memorization and choral counting of numbers in sequence)
- Start with toddlers to the number 3

- Matching the number you count to a specific object or set of objects you are choral counting together
- move on to counting and matching items to three
- once kids are able to independently count and match items to 3 move on to choral counting and matching to 5, then to 10 then to 20, 50 and 100

- Begin subitizing (instantly identifying numbers)
- use a 5-frame
- use subitize cards (dot cards) to instantly identify numbers to 5

Glue to card stock or construction paper and laminate. Practice identifying the numbers. (Use like flash cards. I tell them it’s a game called tell me fast or tell me… now, then I flip over the card. Kids tell what number they think it is & we count it to check and make sure it’s correct. When there are no more mistakes move on to the next set of cards.

**Kindergarten & 1st Grade**

- Continue rote (choral) counting to 100
- skip counting by 10’s
- ” ” 5’s
- Learn doubles facts to 10

- draw and talk about collections
- Subitize (instantly recognize numbers to 10)
- use a 10 frame or multiple 10 frames to count larger numbers

While you are in the process of learning it is important to provide the child enough time to make connections on their own and constructive feedback, which for younger children it’s guided practice.

**Sample Dialogue**

“Great work, I like how you stayed focused and counted and touched every single block.” “Let’s count together, ready? 1,2,3,4,5,6! There are 6!” Counting with the child afterward you can see if they notice the numbers you count are different . You may offer a Choral Counting session as follow up and reinforcement. This child is working on sequencing.

After they count it incorrectly ask how many are there? If they have the concept of cardinality they’ll say out the last number they counted “7!” it won’t be correct until they understand sequencing but they are more than half way to fully understanding counting

If there are signs of frustration support your child as best as you can with regular choral counting (counting together until they are able to fully participate), activities where they are counting and matching 1:1 with items that are of interest to them (matchbox cars, princesses, toy animals, etc.)

*NOTE: There appears to be no particular order in how children learn these concepts with the exception of life experience and which one(s) they are able to make sense of first. This may change or “re-calibrate” as children get progress to more complex thinking and learning. (Numbers get larger and organizing and processing them becomes more complex.)*

**Second Grade**

- Review rote (choral) counting to 100, then rote count (in sections NOT starting from 1 every time) into the hundreds (maybe even 1,00 by the end of the year)
- skip counting by 10’s
- ” ” 5’s
- ” ” 2’s
- learn doubles facts to 20

- draw and talk about collections (mixed bags of items numbers 10’s to 100’s)
- Subitize (instantly recognize numbers to 10)

Second graders can sort and count items independently. Use a skip counting routine and provide organizational supplies like, large and small sorting cups, a hundred’s chart, multiple 10 frames, laminated (FAUX Laminate tip: Use packing tape on both sizes to make reference sheets more durable when you can’t get to a laminator!

These supplies help make it more practical for kids to count larger collections faster.

** Third Grade**

- Review rote (choral) counting to 100, then rote count from the hundreds to 1,000 (skip counting)
- skip counting by 10’s
- ” ” 5’s
- ” ” 2’s

- Count in the 1,000’s
- Learn to skip count by remaining numerals to 10
- skip count by 3’s & relate it to multiplication (by counting real objects in groups of 3
*NOTE: it helps to create a personal multiplication reference sheet as you go along* - ” ” 4’s
- ” ” 6’s
- ” ” 7’s
- ” ” 8’s
- ” ” 9’s

- skip count by 3’s & relate it to multiplication (by counting real objects in groups of 3
- Draw and talk about collections (mixed bags of items numbers 100’s to 1000’s, use whole boxes of colored pencils, markers, or crayons for the 1,000s use multi packs of paper clips or other household items)
- Subitize (instantly recognize ALL numbers to 10 & doubles)

As they re-calibrate or expand their understanding they may have a shift in self-confidence, interest or ability to focus. “It’s too hard” is a really common response as children begin to realize that numbers are infinite (groups of numbers continue to get larger and larger and for some this is very overwhelming.)

**Fourth Grade**

- Review of 3rd Grade counting skills to continue exploring relationship between factors and multiples (use 2’s, 4’s & 8’s side by side factors chart & discuss the patterns they observe see sample above)
- Skip count forward and backward (fluently add and subtract, multiply and divide multi-digit whole numbers, in the thousands)
- Count forwards and backwards using fractions, understanding equivalent fractions using 2, 3, 4, 5, 6, 8, 10, 12, and 100 as denominators
- understand decimal notation as fractions and compare 2 decimals to hundredths
- Notice, discuss and record observations of patterns

**Fifth Grade**

- Review of 4th grade counting skills
- Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left
- Skip count forward and backward (fluently add and subtract, multiply and divide multi-digit numbers, whole & mixed)
- Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors
- Count forwards and backwards using fractions, understanding equivalent fractions & mixed numbers
- Interpret multiplication as scaling (resizing)
- Understand decimal notation as fractions and compare 2 decimals to thousandths, add & subtract decimals to the hundredths
- Notice, discuss and record observations of patterns

BookUnitsTeacher.com has a really great place value activity printable that kids make themselves to use as a reference. https://bookunitsteacher.com/math/PlaceValue/PlaceValue.pdf This is really handy as the depth and complexity of place value increases in 5th grade and some kids really struggle.

## This is why a regular counting routine is imperative?

It helps kids make connections about concepts they have previously learned and expand on them. Place value is where most kids struggle, as numbers become larger kids can get confused about what to put where.

The closest related example is the process of learning how to read. For some it seems SO easy and for others its such a huge challenge.

If you break it down the process of learning to read is the same no matter who you are, it’s the experiences that make the difference.

### Related Example:

Kindergarteners learning to read first learn the sounds each letter makes. Then they learn how letters combine together to make words (equations). They learn how paired letters can make new sounds like sh and th (regrouping). Taking what you’ve learned, applying it and expanding it is a HUGE conceptual shift and some kids have a hard time transitioning.

Kids learn to count first and what small numbers (1-10) represent. One means one of something and counting 2 means two of something. Numbers get larger and larger and larger and you’ll notice kids who will need help with regrouping when you hear them count. “47,48,49… 60!” They do not recognize that 49 and one more makes 5 tens or 50. Those same kids are the kids that need help when counting larger numbers “997, 998, 999, ____”. This takes time.

Kids count by 1’s, and 5’s and 10’s usually starting from 1 and when they get in the higher grades kids who have not had enough practice counting get mixed up as numbers get higher. They get stuck when regrouping is needed and

## Your counting routine should include:

- Manipulatives (items kids can sort, group & count)
- 5 Frame or 10 Frame
- an anchor chart (an overview of what you’ll be counting or pre-planned opportunity to notice and talk about patterns)
- Paper for processing what they just counted (children should be encouraged to draw what they counted
- follow up play based counting practice

They only thing you actually have control over is consistency and patience. Know that you regularly practice counting, it doesn’t matter how often, they WILL make connections. Consistency is the key. If you practice it once a week then stick to that. Another key element I have found useful for all children is having “math talks”. A math talk is carving out a few minutes to talk about what you’re learning & what you notice(with math and reading it’s usually patterns).

**Other Counting Routines and Activities to try:**

Teacher tip: Use the above criteria & teach children to count by ability not by actual grade level. EX: if your child can count to 100 but cannot match 1:1 start with Pre K- 5 frame & work your way up.

**Pre-K**

- Read counting books

Playdough numbers - Choral Count by 1’s (to 10, 20, 50 or even 100)
- Use 5 frames (enlarged) & later 10 Frames (enlarged) to practice counting to 3, then to 5 then to 10 (move on only when they have mastered counting to the highest number in the set). First model then use count together to match your number words to each object you are counting as you count it.

**Kindergarten**

- Read Counting Books

10 frames (enlarged)

Counting bags or pencil boxes collections of 10-30, 30- 50 & 50- 100

How do you organize the larger numbers to make it easier to count? (ask this as you’re holding 10 small cups for sorting) - Paper for drawing your collections
- Choral Count by 10s, 5’s, 2’s
- Charted sequences of numbers (not starting from 1)

**First grade**

- Read Counting Books

10 frames (enlarged)

counting bags or pencil boxes collections of 10- 100. How do you organize the larger numbers to make it easier to count? (ask this as you’re holding 10 small sorting cups) - Paper for drawing your collections
- Charted sequences of numbers (not starting from 1) that follow the pattern you will be skip counting. Provide the opportunity for children to talk about what they notice about the chart “it starts at 5”, “it’s counting by 5”, etc.
- Choral Count by 10s, 5s & 2’s not starting from 1

**Second Grade**

- Read Counting Books
- 10 frames (enlarged)

counting bags or pencil boxes collections of 10- 100. How do you organize the larger numbers to make it easier to count? (ask this as you’re holding 10 small sorting cups) - Paper for drawing your collections
- Charted sequences of numbers (not starting from 1) that follow the pattern you will be skip counting
- 100’s chart

**Third Grade**

- Read more complex Counting Books (see the second grade sections)
- 10 frames, 100’s chart, 1,000’s chart

counting bags or pencil boxes collections of multiples 100- 1,000. - How do you organize the larger numbers to make it easier to count? (ask this as you’re holding 10 small sorting cups)
- Paper for drawing your collections
- Charted sequences of numbers (not starting from 1) that follow the pattern you will be skip counting

**Fourth Grade**

- 10 frames, 100’s chart, 1,000’s chart

counting bags or pencil boxes collections of 10- 100. How do you organize the larger numbers to make it easier to count? (ask this as you’re holding 10 small sorting cups) - Paper for drawing your collections
- Charted sequences of numbers (not starting from 1) that follow the pattern you will be skip counting including fractions.

**Fifth Grade**

- 10 frames, 100’s chart, 1,000’s chart

counting bags or pencil boxes collections of 10- 100. How do you organize the larger numbers to make it easier to count? (ask this as you’re holding 10 small sorting cups) - Paper for drawing your collections
- Charted sequences of numbers (not starting from 1) that follow the pattern you will be skip counting including fractions and decimals.

## When is counting no longer appropriate for my child?

When your child can count, sort, add, subtract, multiply and divide starting at any whole number, decimal, or fraction they no longer need regular counting practice.