# data[].attributes.attachment_link.readable_text
This article is a summary of a report that was first published in the Association of Teachers of Mathematics journal 'Mathematics Teaching' in February 2021
Early counting

Families recognise how important it is for children to be able to count but we know that learning to count is complex and takes time. Children need to count regularly and in a range of contexts. There are frequent opportunities for children to count during their day, using verbal counting (saying or singing the counting sequence) and object counting (counting to find how many) as they go about their everyday activities. These are hugely valuable and meaningful counting experiences but, alongside these, moments where children deliberately focus on counting and attend to how to count are important too. They allow children to spend time playing with counting, experimenting with ways to count and to wallow in counting as an enjoyable activity. In this article we explore one such approach, counting collections, detailing how practitioners might develop this approach for use with 2 to 5 year old children (see also the NRICH activity Counting Collections). The examples are drawn from our project work with twenty-one early years settings.

The counting collections approach

The collaborative counting of sets of objects is currently promoted in classrooms in the United States and New Zealand with older children. These counting collections sessions follow a teacher-led, carefully sequenced structure. Children work in pairs to plan, count and record their shared counting of collections of objects (Schwerdtfeger & Chan 2007). The teacher observes and interacts with the children as they engage in paired discussion, counting and representing the structure of their count on paper. The teacher then draws the class together, choosing selected examples of children's counting strategies to share with the class, perhaps modelling a specific approach.

Resources for counting collections in the early years

Counting collections are containers (boxes, jars or bags) with differing numbers of items within them, depending on the children. Some settings organise the collections into number ranges so the pink collections are 0-5, blue are 6-10, green are 10-20, and so on. It is important to have at least one zero collection and some larger collections too, even if these are fewer when working with the youngest children. The objects should be varied with many collections containing non-identical items to support development of the abstraction principle (as described by Gelman & Gallistel, 1978) so children realise they can count like and unlike items as one set. Some items, such as toy cars or balls, work less well because they can distract children from counting.

Alongside the collections, there are tools which the children may select to help them with their count. Bowls, dishes, pots, bags, mats, five and ten frames can be used to move objects into or out of when counting or opportunities to create groups for counting (e.g. 'in 3s' or '10 and 5 more'). Wooden and tactile numerals or writing equipment help children label counted collections.

Counting collections can also be used outdoors using buckets as containers. With these larger outdoor collections, children are able to use features of the outdoor environment such as walls or grass verges to line up their items to count or as a space to count their items into. They can transport collections around the outdoor area by carrying the buckets or taking them for journeys on their ride-on vehicles.
List of possible counting collections and tools
An important aspect is the everyday availability of the collections and tools so that children freely access them throughout the day as part of the continuous provision. They can choose to play, pattern and count with the collections during their child-initiated play, expressing and expanding their mathematical interests.

It works well for children to create their own collections in addition to those provided by adults. They can then choose to count each other's collections and can change the number of items in their collection over time. Families can be provided with bags, jars or boxes to create collections at home. Counting collections is also a lovely activity to do with parents invited into the setting where children engage in paired counting with their parent.

Counting collections sessions in early years

Counting collections sessions follow a general structure where children work in pairs to:

1. Choose a collection

2. Plan how they will count

3. Count the collection

4. Record the count

The structure needs to be appropriate to the children. A session can be very fluid with a practitioner working with two children to count and draw. Equally, a session might be more structured with the practitioner leading four clear sections with a whole class. The important thing is that children talk and communicate as they count. Working in pairs helps with this. The children often count the collection more than once as there is often some recounting to check the total, providing additional counting practice as well as supporting accuracy.
Roman and Maya's Reception class are engaged in a counting collections session. They choose the box of corks from the shelf of counting collections. Maya gets a bowl and Roman places one cork into it at a time. He counts each cork as it is moved into the bowl but miscounts. He empties the bowl and starts again. Maya counts with him this time and they count 10 corks. Roman looks up and states "There's 10 in the bowl", Maya nods "ten". They agree to count them again and this time Maya puts them in a line on the floor. They count to 8 but then the next cork rolls away and Roman has to retrieve it. Maya continues from 8, where she still has her finger poised, and they count together "9, 10".
Counting the collection

Counting collections support young children to develop one-to-one correspondence, giving one number word to one object when counting. Having pots, tray and bags to count into can help children to move one item at a time, knowing that all the objects counted so far are in the container. Small containers, such as muffin cases, can be used to hold just one item each helping younger children to match one object to one container before counting.
Abbie, choosing to count with her toy dog, used upturned clear plastic shot glasses to cover the wooden cubes in her collection. She then lifted each glass one by one high in the air, shouting the numbers as she counted each cube. This deliberate physical activity clearly separated the counting words and attributed one number word to each item.

One-to-one correspondence can also be developed through drawing around the items in a collection when recording the count. As children's counting develops, they might use containers or perhaps 5 or 10 frames for counting. They can count out 5 or 10 and then the remaining objects, emphasising the '5 and some more' and 'ten and some more' relationships.

Older children enjoy counting in unitised groups. They might create groups of 2, 3, 5 or 10, containers or frames. In some of the Reception classes that we worked with, pairs of children continued to fill ten frames until all of their objects were placed, using multiple frames. Others used one frame as a way of creating units of ten, collecting up the ten and settling them in another container safe in the knowledge that the container held ten items. Some practitioners noticed children predicting how many units there would be in their collection. For example, Sarah noted:
"One child estimated how many ten frames they would need before they started counting 34 buttons. They got three and were delighted when they were all filled up and they had to go and get another one!"
Recording the count

It is important that children's recording is their own and that how they represent the collection graphically is left open-ended. This ensures that the children feel ownership of the mathematics, making their own decisions over how to record (further developing mathematical thinking), and making their thinking visible to practitioners. Children's own recording is rich and varied and can include (as described by Carruthers & Worthington, 2005):

Pictographic representations which capture something of the appearance of what is in front of the child

Iconic representations which record one mark (of the child's own devising) for one object

Dynamic representations which are suggestive of action

Symbolic representations which begin to incorporate standard forms of numerals

Children need to see adults using these different forms of representations to know that these are valued and are ways to be mathematical. In the settings we worked with, the practitioners made a conscious effort to use more iconic representations, in particular.

Working in pairs, children make shared decisions about how to record their count. The process of recording provides additional counting and organisation opportunities. Some children prefer to record as they count (for example by drawing around items). Some children (particularly if they have seen an adult modelling this) might use an iconic style of recording, using circles or lines to represent plastic fish, spoons or toy cars, for example.
Macey, a three-year old, recorded her count in an increasingly efficient iconic style, along with her partner, four-year old Eva. They had counted their collection of ten objects in groups of three, using dishes. Having created three groups of three, they discussed what to do with the remaining one item. Macey and Eva initially made one group a group of four, but then moved that final item to create an additional group of one. They recorded this change on a large sheet of paper with two groups of three (left), a group of four (bottom right) then a long line to show the dynamic movement of one object (middle) into the group of one (top right). The practitioner prompted Macey to record the groups they were counting in and Macey frowned for a moment before writing 'M' (top right). When the practitioner looked quizzically at her, Macey exclaimed "I'm three!". She had apparently used her name as her symbol for '3'. Eva looked and exclaimed, "I can't, I'm four!"
Through storing counting objects as collections (sets), children seemed more confident with attributing a number to a collection (typically using numerals), focussing attention on the cardinality (how many-ness) of the set. Children can collect numerals or number cards to label collections or can use dry-wipe pens (on a plastic lid) or sticky notes to write the number for themselves.

The impact of using counting collections

Using counting collections increases the frequency of counting, range of strategies for counting and the amount of communication of counting (oral and recorded). As Rachel, a Reception class teacher, explained:
"My class now really enjoy counting and have the confidence to talk to others about it".
The paired activity seems to slow down the act of counting. It makes counting actions more deliberate and overt, supporting accuracy. Cooperative counting provides young children with 'a heightened awareness of the need to keep track of one's counting acts' (Wiegel 1998: 222). Keeping track is more explicit as a shared endeavour. There are greater opportunities for error spotting and self-checking with mathematical thinking communicated through both manipulation of the objects, and articulation of strategy and reasoning. It also enables children to learn how to count from each other.

Slowing down the counting process and exposing children's thinking through collaborative activity helps us, as practitioners, to assess children's counting. It provides the opportunity for us to pinpoint the specific aspects of counting or counting principles that each child seems secure with and which are emerging. We can observe and listen in on children's counting as well as initiate purposeful conversations about counting. This is evident in Leah and Alfie's counting in 3s. The recording enables us to assess the accuracy of their counting and also to recognise that the counting has been in ones, despite the grouping in threes (because they would have put the group of two last or miscounted it as a group of three when skip counting). The physical organisation of the count, the dialogue between the two, and the recording, together support the practitioner in identifying appropriate next steps in learning.

In counting collections, children express preferences about the collections, identifying their favourite ones to count. Having a range of different types of objects in the collections is important as some children like to count long objects which they enjoy lining up, some prefer round objects, and some enjoyed larger objects to cover a space. Fuson, Clements and Sarama (2015) explained that repeatedly counting collections of objects is interesting to young children in the same way that they enjoy repeatedly reading a familiar story. Children have favourite stories and favourite counting collections which are comforting and enjoyable to return to again and again, each time rehearsing the familiar alongside attending to previously unnoticed features.

One of the most important things that practitioners and children say about the counting collections approach relates to the pure joy of counting. Clara explained the effect in her Reception classroom:
"Children are excited about counting and show enthusiasm. They are engaged and asking to count!"
The collections gave children something to talk with, something to talk about and someone to talk to...
"Are we doing counting today? I love it" (Jacob, age 4). Dr Catherine Gripton is an Assistant Professor in primary education at the University of Nottingham. Deliah Pawluch is a Senior lecturer in primary education at Nottingham Trent University. This project was funded by East Midlands West maths hub. The work was part of a larger research project into children's mathematical agency in early years.
References

Carruthers, E. & Worthington, M. (2005) Making Sense of Mathematical Graphics: The Development of Understanding Abstract Symbolism. European Early Childhood Educational Research Journal, Vol. 13(1), 57-79.

Fuson, K.C., Clements, D.H. and Sarama, J. (2015). Making early math education work for all children. Phi Delta Kappan, 97 (3), 63-68.

Gelman, R. & Gallistel, C. (1978) The Child's Understanding of Number. Cambridge, MA. Harvard University Press

Schwerdtfeger, J.K. & Chan, A. (2007). Counting Collections. Teaching Children Mathematics, 13 (7), 356-361.

Wiegel, H.G. (1998). Kindergarten students' organization of counting in joint counting tasks and the emergence of cooperation. Journal for Research in Mathematics Education, 202-224.

Further information about counting collections:

DREME TE (2020) Supporting the development of representation. https://prek-math-te.stanford.edu/counting/classroom-videos-counting

Franke, M.L., Kazemi, E., & Turrou, A.C. (Eds.). (2018). Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. New Hampshire: Stenhouse Publishers.

Teacher Education by Design (TEDD) (2014) Counting Collections. https://tedd.org/counting-collections/

# data[].attributes.attachment_link.description
In this article for practitioners, Cath Gripton and Deliah Pawluch explore the 'counting collections' approach, which encourages children to spend time playing and experimenting with counting.

# data[].attributes.attachment_link.description
Free, Research-Based Materials for Supporting Family Math.

# data[].attributes.attachment_link.readable_text
StoryWalk® is an innovative and delightful way for children - and adults! - to enjoy reading and the outdoors at the same time. Laminated pages from a children's book are attached to wooden stakes, which are installed along an outdoor path. As you stroll down the trail, you're directed to the next page in the story.

StoryWalks® have been installed in 50 states and 13 countries including, Germany, Canada, England, Bermuda, Russia, Malaysia, Pakistan and South Korea! They are always received with appreciation.

​

StoryWalk® was created by Anne Ferguson of Montpelier, VT

and has developed with the help of Rachel Senechal, formerly of the

Kellogg-Hubbard Library. If you are interested in having a StoryWalk®

in your community, see our FAQs at the bottom of the page.

If you are interested in borrowing a StoryWalk® book, download

the list of books that are available.

Falmouth Public Library in Massachusetts featured StoryWalk®

and Anne Ferguson in their Fall 2012 Early Childhood Resource

Center Newsletter.

A young reader enjoying a StoryWalk®...

There are several StoryWalk® projects in Massachusetts!

The Gunn Memorial Junior Library of Washington, CT hosted a woodworking project to create a StoryWalk®.

Click on the text below for more information:

​

Interested in offering a storywalk at your Library? Email Anne!

# data[].attributes.attachment_link.description
StoryWalk® is an innovative and delightful way for children - and adults! - to enjoy reading and the outdoors at the same time. Laminated pages from a children's book are attached to wooden stakes, which are installed along an outdoor path. As you stroll down the trail, you're directed to the next page in the story.

# data[].attributes.attachment_link.description
Each year's winners and honor books join a selective and ever-growing list of new and previously published fiction and non-fiction titles for youth. These titles are as varied as the intersection between literature and mathematics.

# data[].attributes.attachment_link.readable_text
Storytelling Math books show that all children can be mathematical thinkers. Stories feature children of color using math as they play, build, and discover the world around them. Includes activities for families to do together. Storytelling Math goes beyond counting and shapes to explore concepts that all young children need for later school success.

Learn more, get extras, and watch author interviews here!

# data[].attributes.attachment_link.description
Storytelling Math books show that all children can be mathematical thinkers. Stories feature children of color using math as they play, build, and discover the world around them. Includes activities for families to do together. Storytelling Math goes beyond counting and shapes to explore concepts that all young childre

# data[].attributes.attachment_link.description
Bedtime Math fan Sophia Y. asked us how many ants would it take to pick you up and carry you? Read on to see how

# data[].attributes.attachment_link.readable_text
​Whether you are an experienced teacher, a teacher trainee, a teacher educator, a parent, a researcher or a policy maker, we hope you will find this website interesting and useful. Specifically, we want to share with you the benefits of te﻿aching and learning mathematics through stories and creative writing, as well as to offer practical ideas for teachers and parents on how to embrace this approach.

This website has been designed and continuously developed based on the feedback we receive from the key stakeholders as noted above. There are plenty for you to do on this website, including, but not limited to:
Please take your time to explore the website using either the menu bar at the top of the page or from the menu below.

Finally, consider s ubscribing to our free quarterly newsletters, and please help spread the word about our project and its website :-)

Best wishes,

Dr. Natthapoj Vincent Trakulphadetkrai B.A. (Hons), M.Sc. (Oxford), M.Sc. (London, UCL), Ph.D. (Cambridge), QTS

@NatthapojVinceT Natthapoj.org

Associate Professor of Mathematics Education
​University of Reading (UK)

Founder & Principal Investigator
​MathsThroughStories.org
​

# data[].attributes.attachment_link.readable_text
What is a StoryWalk?

A StoryWalk is a movement and literacy boosting project that places an illustrated children's book, taken apart and displayed page by page, along a walking route in your community. Anne Ferguson, the genius behind the StoryWalk concept, sums it up nicely with these sentences, which she asks to be posted when creating your own StoryWalk: "The StoryWalk® Project was created by Anne Ferguson of Montpelier, VT and developed in collaboration with the Kellogg-Hubbard Library. Storywalk® is a registered service mark owned by Ms. Ferguson."

When Anne Ferguson was working with the Vermont Department of Health, she created The StoryWalk® Project as a way to convince families to get outside and be active while engaging with literacy. She was on the hunt to create something that required the adults to be active alongside children, with no financial limitations that would leave some families out. StoryWalk was born.

What does this actually look like? The creator literally takes a book apart and displays it outside, one page at a time, in the correct order. Ms. Ferguson shares tips for her preferred supplies in the StoryWalk FAQ, but I have seen StoryWalks displayed in a variety of ways. From pages attached to fences to fancy podium-style boxes with plexiglass lids, the possibilities are vast, but the outcome is the same: people are encouraged to continue walking to find the next page of the book. There is literacy, there is nature, there is movement. Win, win, win.

By signing up you agree to our terms of use

Where do you put a StoryWalk?

The original goal for The StoryWalk Project was to have stories placed outside in nature. Public walking trails are a natural and obvious place to start, but the project has expanded to include city settings such as main street businesses and school playgrounds. If you consider that the aim is to have families moving outside, any safe route that lets you space out pages can be used. In my city, I've spotted books spaced along the walking trail that circles a local pond, and around the circumference of our city-owned working apple orchard.

There are, of course, practical considerations that need to be addressed. Spaces that take a hard hit from the elements (super high winds, for example) are not ideal. Anne Ferguson hilariously shares these tips for avoiding damage caused by humans in her StoryWalk History: " Vandals are a recurring challenge. They seem to be threatened by a story about Gossie, a small duck who has misplaced his red rubber boots. A range of approaches has been used to address this issue, some with greater success than others. The Velcro® makes it easy to take down the pages before dark and post them again in the morning. Vandals prefer the cover of darkness. "

How do you make a StoryWalk?

The creation of a StoryWalk is deceptively easy, but there are some particulars that make all the difference in success rates. Copyright laws allow you to use existing books you have purchased, but you cannot enlarge or alter the text in any way, so the move is to carefully dismantle the book itself. After you have your pages, they need to be backed on something stiff (card stock is a favorite) and, most importantly, laminated. Anne Ferguson, in her StoryWalk FAQ page, gives amazing detail into how she prepares books to be displayed. A wide margin of laminate and extremely strong velcro seem to be key components.

What books are good for a StoryWalk?

There is a lot to consider when choosing a title. It's important to have engaging illustrations and pages that don't include too much text. A plot-driven story that will motivate the families to find the next page is extremely helpful. Different communities and even areas within your community might have different literacy needs, including languages spoken and messages conveyed.

There are a few instances in the Northeastern U.S. of StoryWalk libraries, where community organizations can borrow titles already prepared for StoryWalk. The Massachusetts Department of Early Education and Care has five resource centers with StoryWalk books available. Anne Ferguson herself has a collection of books available to borrow for up to two weeks, which are let through the Kellogg-Hubbard Library in Montpelier, Vermont.

Looking to install a StoryWalk in your community?

Start with your basics. Who will be paying for this? Who will be in charge of routine upkeep? Once you have these details, it'll be easier to get others onboard. Great places to look for partners include your public library or your local recreation department. Boston Children's Museum has an amazing, in-depth brochure that includes extensive how-tos on sponsoring a StoryWalk, as well research into early literacy and the benefits of StoryWalks, which could be helpful in making your pitch. Check out the brochure, titled Take A Hike! Building Literacy Skills Through StoryWalk, here.

1. Next, choose the venue. This is where conversations with local officials and stakeholders can really help. Will this be deep in nature or along a well-traveled sidewalk? Target audience, time of year, and community support will all play into this decision.

2. Now, decide on your method of display. If you're on a walking trail, you might go with stakes and Velcro. If you're in a city space, store windows might be the move. Your budget, venue, and ability to commit to routine upkeep will help you decide which display method will work best.

3. Finally, you choose a title! Keep in mind things such as the languages spoken by the people who travel this route, manageable text length, and engaging illustrations. You might decide to outsource and borrow a title already prepared from one of the libraries of StoryWalk books, or create your own using a book specially chosen for your community.

Hopefully you've found some tips to help you better understand StoryWalks, and maybe even been inspired to sponsor one of your own!

# data[].attributes.attachment_link.title
Literacy Among The Leaves: Everything You Want To Know About StoryWalks

# data[].attributes.attachment_link.description
StoryWalks are an excellent family activity that combine movement with reading. Here's how to start one for your community.

# data[].attributes.attachment_link.readable_text
Secure a Fully Designed StoryWalk®

Curious City's beautifully designed StoryWalk® panels (see slideshows below) feature each spread of a picture book with a companion reader engagement prompt. Each StoryWalk is customized to thank your sponsors and deliver community messages.

Curious City StoryWalks are now managed by our longtime collaborators at Banacom Sign in South Portland, Maine. Nicole and Jeff at Banacom Sign (contact form below) will work with you to:

* Select a StoryWalk from our collection of picture books (slideshows below)
* Create a community profile to secure publisher permission
* Secure publisher permission for you to print and display the StoryWalk in your community for at least 5 years
* Select a StoryWalk size that fits your sign holders and/or advise on ideas for display
* Customize the opening and closing signs of StoryWalk to thank your sponsors and offer community messaging
* Prepare your files for printing

For the above project, Banacom Sign charges $600 post-project.
Discounts available for multiple stories purchased at once.
Print Version: Curious City StoryWalks with Banacom Signs (PDF)

The StoryWalk® Project was developed by Anne Ferguson in cooperation with the Kellogg Hubbard Library and the Vermont Bicycle & Pedestrian Coalition.

Print StoryWalk Signage

Banacom Sign has been printing local and national StoryWalk signage for over a decade. With the new partnership, you can now have your signs design, printed, and shipped by the same vendor. Nicole and Jeff at Banacom Sign (contact form below) will work with you to print signage to:

* Insert into Barking Dog Exhibit fixtures
* Affix or insert into to other StoryWalk fixtures
* Work as portable signage for "pop-up" StoryWalks

Contact them below for pricing.
Need to print locally? No problem. Banacom Sign will supply print files to your regional printer.

Available Curious City StoryWalk Signage

The Summer Nick Taught His Cats to Read
By Curtis Manley & illustrated by Kate Berube (Simon & Schuster)
Number of Signs: 17
Available Sizes: 24″w x 18″l
VIEW a slideshow of the StoryWalk

Mouse House Tales
By Susan Pearson & Illustrated by Amanda Shepard (Blue Apple Books)
Number of Signs: 13
Available Sizes: 24″w x 18″l | 24″w x 20″l
VIEW a slideshow of the StoryWalk
NOTE: The "action prompts" for this StoryWalk are STEM-aligned questions and observation prompts designed by educator Dana Allen of the Birth to Three Family Center in Ipswich, MA.

Nest, Nook, & Cranny
By Susan Blackaby & Illustrated by Jamie Hogan (Charlesbridge Publishing)
Number of Signs: 12
Available Sizes: 24″w x 18″l
VIEW a slideshow of the StoryWalk (TBD)
NOTE: Because of the wide age-range of this StoryWalk (Age 7-Adult), it does not include physical activity prompts. Many communities have used this StoryWalk on nature trails. Because each sign is an individual poem, the signs do not have to be sequential. They can be placed by the habitat that each sign represents. The poems in Nest, Nook, & Cranny represent habitats nationwide. This StoryWalk only represents the habitats of the Northern climate, but we can develop the pages/signs for other climates.

Rainbow Stew
By Cathryn Falwell (Lee & Low)
Number of Signs: 15
Available Sizes: 24″w x 20″l and 24″w x 18″l
VIEW a slideshow of the StoryWalk
NOTE:This title's publisher requires a $500 license fee in addition to Curious City's fees.

Looking to develop a different book into a StoryWalk? Due to the current pandemic demands for StoryWalks, Curious City StoryWalks and Banacom Signs are not developing new books into StoryWalks at this time, but hope to in the future.

Tell Us About Your StoryWalk Project

# data[].attributes.attachment_link.description
Secure a Fully Designed StoryWalk® Curious City's beautifully designed StoryWalk® panels (see slideshows below) feature each spread of a picture book with a companion reader engagement promp...

# data[].attributes.attachment_link.readable_text
This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

# data[].attributes.attachment_link.description
This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

# data[].attributes.body
Includes a handout

# data[].attributes.attachment_link.title
Dog's Colorful Day Storywalk Prompts.pdf

# data[].attributes.attachment_link.title
Grandma’s Purse Storywalk Prompts (1).pdf

# data[].attributes.attachment_link.description
Counting Collections Overview is a resource that provides a set of activities designed for teacher educators to begin to engage participants in the activity of Counting Collections. They have been developed to provide support for connecting the content of counting, children's thinking in counting, and pedagogy in classroom practice.

# data[].attributes.headline
Why are patterns and structure important in early math?

# data[].attributes.subject
Why are patterns and structure important in early math?

# data[].attributes.attachment_link.readable_text
In mathematics, patterns are more than a beautiful design (though they are often that too), patterns follow a predictable rule and that rule allows us to predict what will come next. Mathematicians say that mathematics is the study of pattern-of patterns and structure in numbers, and patterns and structure in geometry. Seeing pattern and structure in the world around us is a key mathematical habit of mind and one that children are developing from the first days of life. Children are naturally attuned to patterns because it allows them to predict what will come next and make sense of their world. When we see patterns we are able to predict-to count on things happening-and feel more secure and confident. Noticing these routines and patterns in everyday life helps prepare children to notice other patterns. Many stories, dances, and chants follow a predictable pattern. "Five Little Monkeys" follow a pattern where the words repeat but the number of monkeys decreases by one each time. "Head, Shoulders, Knees, and Toes" follows a pattern that speeds up as you go. Dancing or movement patterns such as clap, clap, stomp, clap, clap, stomp also help children build an understanding of pattern that includes the kinesthetic. As you engage children in these everyday activities, help them notice the pattern and describe it in words.

View All Patterns and Structure Games

Why are patterns and structure important in early math? Sub-Topics

Explore More About Patterns and Structure

# data[].attributes.attachment_link.title
Patterns and Structure - Young Mathematicians

# data[].attributes.attachment_link.description
In mathematics, patterns are more than a beautiful design (though they are often that too), patterns follow a predictable rule and that rule allows us to predict what will come next. Mathematicians say that mathematics is the study of pattern-of patterns and structure in numbers, and patterns and structure in geometry.

# data[].attributes.attachment_link.readable_text
Welcome! Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

# data[].attributes.attachment_link.description
Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

# data[].attributes.attachment_link.description
Eddie Gray & David Tall are two British researchers who worked with students, aged 7 to 13, who had been nominated by their teachers as being low, middle or high achieving students. All of the students were given number problems, such as adding or subtracting two numbers. The researchers found an im…

# data[].attributes.attachment_link.readable_text
Math tips and strategies for building number sense to 20 in Kindergarten and first grade: An extensive list of number sense activities and resources are included: books, materials, math manipulatives, and FREE activities!
By Proud to be Primary

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

Building Number Sense to 20

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!

Why is Building Number Sense Important?

Children need opportunities to learn and experience numbers. Learning to count, identify numbers, and understand quantity are a few of the essential concepts. Repeated experiences build understanding and fluency with numbers. These experiences help expand knowledge and learn new ideas. 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 to 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.

Number Sense Concepts & Activities

Build Number Sense Through Counting

It is crucial 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 verbal 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 one 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 see what numbers look like visually. 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.

Build Number Sense by 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 five counting bears and a domino that shows five dots.

Use links to create a number chain for a number.

Work up to showing quantity with more than two 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 help 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.

Build Number Sense with 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 one 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 number of the day poster with the FREE poster templates.

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

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

Build Number Sense by 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.

Build Number Sense with Place Value Activities

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

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

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 words and numeral cards. Look for pairs (twelve and 12).

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

Build Number Sense by 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 backward order. Take the ordering activities seen above and reverse them.

Build Number Sense through 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 then hide them. They make an estimate, and then you count together to check.

Build Number Sense by 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 two 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 found on Teachers Pay Teachers.

Free Number Sense Puzzles to 20

Prep this fun set of number puzzles for your classroom centers and help kids build their number sense!
Numbers to 5 for Kindergarten
Grab 20 FREE number puzzles with different representations on each piece by clicking the image below.
Numbers to 10 for Kindergarten

Numbers 11-20 for Kindergarten
Number Sense Books
Mindful Math Kindergarten Curriculum Numbers to 10 for First Grade Numbers to 20 for First Grade

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
Mindful Math First Grade Curriculum
Number Sense Materials

Try the Mindful Math Comprehensive Program

Read about the Mindful Math program and how it can change your math block in positive ways! This comprehensive math curriculum is available for Kindergarten, first grade, and second grade.

Learn More about Teaching Number Sense

PIN
Building Number Sense free email series Number of the Day Activities 5 Tips for Building Math Fluency

# data[].attributes.attachment_link.title
Building Number Sense to 20: Lessons and Activities for Kids

# data[].attributes.attachment_link.description
Math activities for building number sense to 20 in Kindergarten and first grade. A list of resources, books, manipulatives, and freebies are included!

# data[].attributes.attachment_link.title
Conversations with Children! Questions that Spark Conversations and Deepen Understanding

# data[].attributes.attachment_link.description
This is the first article in a series about asking questions that foster rich conversations. Visiting a variety of preschool settings, we'll consider the different types of questions teachers ask and listen to children's responses.

# data[].attributes.attachment_link.description
Learning to see mathematics as living in our world is a central mathematical practice, one that has been historically neglected. Mathematics is not a purely abstract, procedural pursuit, but, rather, a way of understanding our world. Children will more deeply understand other big ideas if they see t…

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
The Mathical Book Prize is an annual award organized by the Mathematical Sciences Research Institute (MSRI). With an aim to "inspire a love of mathematics in the everyday world in children of all ages," the winners are selected by a nationwide committee of mathematicians, librarians, teachers, and early childhood experts.

Looking through the winners, there are some fantastic choices. Among them are three innovative counting books for children in the early years that offer mathematical opportunities beyond the typical counting book. Read how they introduce young children to the principals that underlie the process of counting while having loads of fun.

This book provides an appealing context for acting out market stories, counting and putting groups of foods into a basket. And, not only does this book have a counting down structure, it introduces the number relationship of one less. With every gift of food, Baby puts one less in the basket. He starts with 6 bananas, but only 5 bananas go into Mama's basket, and so on. What if Baby is given 7 yams, how many go in the basket? What about 8 beans?

Delightfully silly, this book provides interactive counting opportunities that naturally reinforce one-to-one correspondence. The narrator instructs us, "Say 'thank you' six times, very politely" to 6 sweet, old beekeepers who shoo away a swarm of bees. Later, we are told to give 8 lumberjacks each a high five for taking care of a pack of wolves. Alas, the narrator runs out of pages before getting to count any monkeys. A perfect time to talk about what 0 monkeys means.

8: An Animal Alphabet by Elisha Cooper (2016 winner)

This book works as an alphabet book, a counting book, and a compendium of weird-but-true animal facts. An alphabet book because over 150 animals are organized from A to Z. A counting book because one animal on each page is pictured 8 times. A "Did you know?" section at the end provides fun facts and helps readers identify the less familiar animals.

The most unique quality of this counting book, however, is the opportunity to find a group of 8 animals on each page. Cooper makes the hunt a fun challenge since the animal that is pictured eight times is not necessarily in the same pose or depicted at the same age or with the same coloring. Discussions of attributes and sorting are bound to happen as readers seek and find sets of 8 on each page. Counting, yes, but which ones are we counting? This book reinforces the importance of naming the unit when labeling the quantity of a set.

# data[].attributes.attachment_link.title
3 "Mathical" Counting Books with Winning Appeal

# data[].attributes.attachment_link.description
The Mathical Book Prize is an annual award organized by the Mathematical Sciences Research Institute (MSRI). With an aim to "inspire More →

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
Series: Book Ideas

This series of book ideas encourage using stories to infuse the early years with mathematical learning. From the infant years until they are putting together more advanced numeracy concepts in elementary school, books can be a gateway for early math discussions.

Below find all the resources we have placed in our series titled BOOK IDEAS.

September 28, 2022

Counting books that offer children opportunities to participate bring play into math learning. These books engage children physically, cognitively, and emotionally-making them favorites that children will ask to read again and again.

Free videos.

Free newsletter packed with ideas.

Free professional learning modules.

# data[].attributes.attachment_link.title
Book Ideas | Early Math Collaborative at Erikson Institute

# data[].attributes.attachment_link.description
Book ideas for using stories to infuse the early years with mathematical learning and exploring. From birth to age eight.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
Counting books that offer children opportunities to participate bring play into math learning. These books about numbers and counting engage children physically, cognitively, and emotionally -- making them favorites that children will ask to read again and again.

Whether at home or in a classroom, children can create their own artwork in the style of these books. Read on for ideas how to play around with numbers!

1 Smile, 10 Toes by Nelleke Verhoeff

This mix-and-match counting book is clever and won the Mathical Book Prize in 2022! Children can flip the split pages around in any order to make creatures with different tops and bottoms. The silly creatures have 4 ears, 5 feet, and so on. With so many combinations, children will have ample counting practice in a non-routine way.

The book practically begs children to draw their own wacky creatures and talk about how many different body parts they drew. One way to do this is to fold a sheet of paper in half. At the fold line, mark where the creature's torso will meet from the top and the bottom. Have one child draw the top of the creature and a second child (without looking) draw the bottom. Then open the page to reveal the silly creature! Have children label their creature with the number of different body parts like the book does.

The illustrations are uncluttered and clearly show the growing set of children playing at the playground. Yet, look closer and there are other representations of the given number on each page. As the number of children increases, readers will have to look more closely to find all the children. This brings the opportunity to discuss number composition and the number relationship of "one more."

Ask children to draw their own playground pictures and talk about the number of friends they like to play with. Contextualizing numbers within a child's social-emotional life provides a natural and meaningful reason to count!

Two Dogs on a Trike by Gabi Snyder, illustrated by Robin Rosenthal

What a zany and fun counting book! The narrative is told chiefly through the illustrations, which show a growing group of dogs traveling by wacky modes of transportation. As the number of dogs grows, the jumbled and sometime overlapping arrangement of the dogs might be challenging for young children to count. But, for more proficient counters, finding all the dogs could be part of the fun.

The text is simple. Each page clearly states the number of dogs. But when it comes to books about numbers and counting, there is much to bring children back for repeated readings. The subplot of a cat's pursuit of the dogs provides humor and adds to the variety of vehicles in the story. This would be a fun book to physically reenact, building both transportation vocabulary and a sense of numbers in a playful way.

# data[].attributes.attachment_link.title
4 Playful Counting Books That Bring Numbers to Life

# data[].attributes.attachment_link.description
These books about numbers and counting engage children physically, cognitively, and emotionally -- making them favorites for children.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
At-Home Activity Cards: Shapes

This is a Download - for grade levels Pre-K, Kindergarten
Tagged Roseanne Thong, download, Cubes Cones Cylinders & Spheres, Color Zoo, Color Farm, Round as a Tortilla, Shapes Shapes Shapes, Tana Hoban, Lois Ehlert

Books can illustrate kindergarten and preschool shape concepts while introducing foundational Big Ideas of math. These activity cards can help take the learning to the home environment where parents and caregivers can spark such discussion.

Want free printable activities and card sets? Join our website (or log in if already joined) to unlock much more.

Join or Log in

# data[].attributes.attachment_link.title
In Preschool Shape Can Start at Home with These Take Home Activities

# data[].attributes.attachment_link.description
Books can illustrate kinder and preschool shape concepts while introducing core Big Ideas. When talking shapes preschool activities like these can help.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.title
5 of the Best Kids’ Books that Involve Sets and Sorting

# data[].attributes.attachment_link.description
Sorting items by attributes affords children the opportunity to make sense by organizing. Here are some of the best kids books for exploring sorting.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
At-Home Activity Cards: Sets and Sorting

This is a Download - for grade levels Pre-K, Kindergarten
Tagged Stuart J Murphy, download, Is it Red? Is it Yellow? Is it Blue?, Five Creatures, Opuestos/Opposites, Exactly the Opposite, A Pair of Socks, Emily Jenkins, Cynthia Weill, Tana Hoban

Five Creatures

This book by Emily Jenkins includes three humans and two cats in one house. That allows a lot of opportunities for sorting! This printable activity card in both English and Spanish invites home explorations with sets and sorting using the book. You can watch and read further about an example activity here in our Ideas at Work series: All Sorts of Families: Connecting School and Home with Math.
Download

Download All

Here you can download a PDF that includes all of the SETS activity cards.
Download

Want free printable activities and card sets? Join our website (or log in if already joined) to unlock much more.

Join or Log in

# data[].attributes.attachment_link.title
Sets and Sorting Take Home Activity Cards | Early Math Collaborative

# data[].attributes.attachment_link.description
These printable activity cards in both English and Spanish provide fun activities at home with sets and sorting using books and stories.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
5 Books and Songs for Exploring Growing Patterns

by Cody Meirick and Jeanine Brownell This is an Article - for grade levels Pre-K, Kindergarten, 1st Grade
Tagged Animals, Lily Toy Hong, One Grain of Rice, Two of Everything, The Waterhole, We Had a Picnic This Sunday Past, Demi, Graeme Base, Jacqueline Woodson, Culture

Cumulative tales and rhymes such as The Napping House illustrate growing patterns, typically an increase or decrease by one on each page. As the growing pattern is revealed through the story, children get excited because they can figure out "what comes next." Suddenly a nice pattern book for kindergarten or preschool becomes an adventure. As we point out in our book Big Ideas of Early Mathematics, children are naturally "tuned in" to patterns, which can deepen their understanding of them.

Like all patterns, growing patterns feature repetition and regularity. In this case, it's not a sequence of elements that repeats such as in the AB pattern of a checkerboard, but a quantitative change that repeats. Our counting system is a basic growing pattern because each number is one more that the number that precedes it. The plus-one rule is what brings predictability to our count sequence.

Because children will be so engaged by these stories and songs, you can guide them to notice the growing pattern, using geometric models such as stacking blocks or pictographs to show how each repetition has a constant change in quantity. For example, if you stack block towers in order of size, children will see the resulting stair-step structure of a plus-one growing pattern. Acting outing out the stories and songs is another way to make the pattern structure come to life!

Here are a few of our favorite mathy books and songs that illustrate all the math going on in growing patterns.

1. We Had a Picnic This Sunday Past by Jacqueline Woodson

This tale vibrantly captures an annual family picnic. As guests arrive with food-and Teeka and Grandma dread the arrival of Cousin Martha's dried out apple pie-a growing story emerges! There are two sets: people at the party and food on the table.

With preschool children, a reader can pause and comment on how there are more people and more food! They may also be interested in sorting the different types of food into binary sorts by attributes such as "food I like" vs. "food I don't like" or "dessert" vs. "not dessert."

Kindergarten and first grade children may wish to keep track of the quantity of each set and discover that the change does not always follow a growing pattern - especially when Cousin Trevor comes empty handed, and Teeka complains, "you can't eat air!" The delicious surprises in this book are a result of disrupting the pattern and are what make it such a rewarding read. After enjoying this fun read-aloud many times, children can write their own growing stories about their families' traditional gatherings.

2. The Waterhole by Graeme Base

In this gorgeously illustrated tale of animals convening to drink from a watering hole, author and illustrator Graeme Base takes a counting book and does something magical with it. As each animal comes to drink from the watering hole one by one, the water in it diminishes each time. It is a demonstration of a growing pattern as well as an example of cause and effect, a decreasing or shrinking pattern paired with the growing pattern, and an exploration of volume all in one unique story. What a great way to spark a conversation with children.

3. Two of Everything by Lilly Hong

Not all growing patterns use the same plus-one rule for growing. For children ages 6-8, introducing more advanced growing patterns through books can help provide a context for understanding multiplicative change. Two of Everything is a great Chinese folktale that introduces a doubling pattern with wit and wisdom. You can pair this book with activities that involve input and output such as function machines or in/out boxes. Whatever goes in comes out double!

4. One Grain of Rice by Demi

Another doubling pattern can be found in this Indian folktale, in which a clever girl, Rani, outsmarts a greedy ruler who is hoarding the people's rice harvest for himself. Despite her hunger, Rani returns some spilled rice to the raja instead of keeping it and is rewarded for her honesty. What payment does she ask for? One grain of rice, but with the condition that the grains of rice will double each day for 30 days. Thinking this a meager amount, the raja agrees and is surprised to see that the reward doubles to more than a billion grains of rice in 30 days! The beautiful illustrations capture the growing pattern in a powerful way as the volume of rice given to Rani takes up more and more of the page, eventually taking a fold-out, 4-page spread to show it all.

A chart at the back of the book shows the number of grains of rice given to Rani on each of the 30 days. First and second graders learning about the units of our base-10 system can practice reading these large numbers. Make a photocopy of the chart, cut it apart, and have children put the 30 days back in order according to the doubling pattern.

5. Songs for Growing or Decreasing Patterns

The classic song Over in the Meadow uses fun animal sounds and a catchy tune to make its growing pattern. It creates a great opportunity to allow children to illustrate what they hear happening in the song and the change that happens with each new verse.

Ten in the Bed is another song that has a decreasing pattern that children love to sing and act out. Imagine an activity that gets kids moving while visually demonstrating how there is one less in the bed while also creating an increasing set of people on the floor along the way. It's a familiar and fun song that can spark great dialogue around the concepts of constant change.

# data[].attributes.attachment_link.title
5 Books and Songs for Exploring Growing Patterns

# data[].attributes.attachment_link.description
Cumulative tales and songs illustrate growing patterns. As the pattern is revealed, children get excited because they can figure out "what comes next."

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
Children explore the everyday shapes in their environment from birth. They informally learn about the properties of 3D shapes as they mouth, touch, and play with blocks, balls, and other objects in daily life. Long before children have language to name or describe these different types of shapes, they develop intuition about which shapes roll, how a flat surface feels, and that "corners" are pointy.

Though we live in a 3D world, common language and materials used to teach children about shapes focus on 2D shapes. In fact, the majority of emphasis gets put on just four shapes: circles, triangles, rectangles, and squares. And these shapes are usually presented in only one typical way so that children often develop rigid and fixed notions of what shapes must look like.

So it's up to us to find, share, and talk about a variety of shapes with children in ways that expand their understanding and build connections between shapes (think, how is a square a special case of a rectangle?) and connections between the shapes drawn on paper and the concrete objects in our world.

Take triangles for example. Most children's books present triangles as equilateral (3 equal sides) and oriented to sit on a horizontal base. As a result, children may not recognize isosceles and scalene triangles as triangles because they look "stretched out." Children may say that a triangle with a vertex pointing down is "upside down." Watch a small group discussion about "upside down" triangles during a preschool activity called Feel for Shapes.

Talking about diverse shape examples along with nonexamples can go a long way to help children understand what defines a shape-what makes a triangle a triangle, for example. Nonexamples are highly visually similar to a type of shape but lack at least one defining attribute.

Luckily, it's easy to find nonexamples to discuss in everyday life. How often might we point to a piece of pizza and call it a "triangle?" As adults, it's not our main concern to correct children's language, but to listen to what shape knowledge children reveal by what they say and to build on it. So, if a child says a pizza slice is a triangle, you might ask them why they think that. Likely, the child will have noticed that the slice has three sides. This is a great opportunity to focus on the defining attributes of a triangle. For example, you might say, "Yes, I see three sides, but the crust side is curved so it's not exactly a triangle. Triangles have three straight sides."

Going on a "Shape Hunt" in real life or through picture books such as Shapes, Shapes, Shapes by Tana Hoban is bound to turn up many common 3D objects that get labeled with 2D shape names. This is a great opportunity to help children see the relationship between different types of shapes, particularly 2D and 3D shapes. For example, many children will say that a ball is a "circle" because it is round. You can acknowledge what the child knows while pushing for greater precision-"Yes, the ball is round like a circle, but it's not flat. A ball is round in every direction so we call its shape a sphere." The book Now What? A Math Tale by Robie H. Harris tells the story of Puppy putting together blocks to build a bed that's just the right size for a nap. As Puppy solves problems, readers get to explore how 2D shapes are the flat faces of 3D prisms and share in the delight of discovering "a rectangle block-that's a square block, too!"

Most of the world around us is not made of regular 2D shapes the way they are drawn in simple shape books and posters. And that's okay. What a wonderful opportunity to start a conversation with children about different types of shapes and the attributes of shapes!

# data[].attributes.attachment_link.title
Different Types of Shapes and Nonexamples to Spark Learning

# data[].attributes.attachment_link.description
It's up to us to find, share, and talk about a variety of shapes with children in ways that build connections between different types of shapes.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
4 Fun Books that Explore Math, Patterns, and Sequences

by Cody Meirick This is an Article - for grade levels Pre-K, Kindergarten, 1st Grade
Tagged Bill Martin Jr., Sue Williams, The Napping House, I Went Walking, Brown Bear Brown Bear What Do You See?, Pattern Bugs, Audrey Wood, Trudy Harris, Eric Carle, Animals

From an early age, children notice and appreciate patterns in the world around them. Patterns and sequences of different kinds begin to pop up all over the place, especially in the books that children love. Pattern books for kindergarten and preschool ages can mean a lot of things, since pattern itself is a complex topic.

Many children's books contain patterns because that supports literacy development. Children use language and picture patterns to "read" predictable books. Patterns in stories allow children to predict what will happen next. Here are some of our favorite read alouds that invite children to make use of patterns to "read" along with you.

1. Pattern Bugs by Trudy Harris

This colorful and fun picture book is full of visual and verbal patterns. Not only do you see worms crawling with every other one arching its back, creating a pattern, you will also find that same pattern in the words of the poem, such as"flutter-float, flutter-float," and in the decorative border on the page. Have children help to find all the illustrations that share the same pattern structure (AB, ABBA, etc.) on any given page. A pattern hunt like this highlights the Big Idea that the same pattern structure can be found in different forms.

2. Brown Bear Brown Bear What Do You See? by Bill Martin Jr.

This classic book illustrated by Eric Carle is on virtually any list of great books to have in the classroom. And it has a clear pattern that young children can quickly notice, and also repeat. Teachers and parents can ask children to identify the words that repeat to help them see the regularity and rhythm in the story.

3. I Went Walking by Sue Williams

This vibrant storybook is similar to Brown Bear Brown Bear What Do You See? in some ways, but it adds some interesting complexity to a pattern story. As the red-haired boy comes across different animals on his stroll, the menagerie of creatures trail him on his walking journey. The illustrations reveal a growing pattern. Each page adds one more animal to the long line of followers.

4. The Napping House by Don and Audrey Wood

Here is one of the pattern books for kindergarten and preschool ages that we recommend often. The illustrations in The Napping House are fun and humorous and provide a great opportunity for children to identify a plus-one growing pattern. As the characters pile one by one onto the bed for a nap, each page clearly shows the growing, linear sequence and foreshadows what comes next. You can find an example of two teachers exploring this book in our Focus on the Lesson video Who is Napping?

# data[].attributes.attachment_link.title
4 Fun Books that Explore Math Patterns and Sequences

# data[].attributes.attachment_link.description
Children notice and appreciate math patterns in the world around them. Pattern books for kindergarten and preschool ages can help.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
The Mathical Book Prize is an annual award organized by the Mathematical Sciences Research Institute (MSRI) with an aim to "inspire a love of mathematics in the everyday world in children of all ages." We previously highlighted some of their selected titles that introduced children to the principals behind counting.
In another look at books awarded the Mathical Book Prize, we focus on three books that go beyond one-to-one counting. These books provide compelling contexts that help primary grade children understand why more advanced counting is useful and that it isn't always efficient to count by ones.

1. Sheep Won't Sleep by Judy Cox

Sheep Won't Sleep (2018 Winner) brings a colorful and creative twist to the dilemma of what to do when counting by ones doesn't work. When she tries counting sheep, Clarissa's eyes pop open to discover 10 wooly sheep crowding into her bedroom. So she tries counting alpacas by 2's only to have 20 of them join the sheep. When she switches to counting llamas by 5's, 20 more wooly critters show up; counting yaks by 10's brings another 50 creatures. When she counts them all back down, rolling all their wooly threads into a ball, Clarissa finally gets to sleep.
Besides the pictures of ever-increasing groups of wooly animals, this book invites questions about how to select the most efficient "friendly" number for skip counting. Create a large classroom chart (that might be fun to share on a classroom bulletin board) about what collections might be best counted by 2's, 5's or 10's. An easy place to start is to figure out how many body parts in total there are in the classroom. It's easy to count eyes and ears, hands, and feet by 2's, for example. In the same way, counting how many fingers or toes calls for counting by 5's and might also be done by 10's. It might be fun to have groups of children work on illustrating the chart as well as writing out the counts.

2. Max's Math by Kate Banks

The idea of counting sheep to get to sleep comes up again as a way to end a busy night described in Max's Math (2016 Winner). Max and his brothers travel though Shapeville and Count Town, passing many sets of things to count such as five clouds, two buses, four triangles, and one square. They find numbers everywhere they look! Have your students look for everyday collections of things that come in equal sets (i.e. pairs of shoes, boxes of crayons, packs of trading cards) to make their own counting stories.

3. One Big Pair of Underwear by Laura Gehl

One Big Pair of Underwear (2015 Winner) is bound to appeal to 5- to 8-year olds who think just the word underwear is hilarious. However, they are virtually sure to be willing to continue through the book, playing with the idea that when you have an even number of objects and an odd number of critters who want them, it just isn't fair! For example, if you have 4 large jars of candy bars and 5 greedy goats in red cars, there's nothing left for the 1 goat who drives up to find 4 empty jars and no candy bars. It isn't until 20 pigs decide to go piggybacking and take rides on 10 slides that everyone else decides that sharing might be the way to go. The final pictures show all kinds of sharing and swapping going on that kids can have a grand time putting into number sentences. Once they have done that, many might love to pair up with a classmate and think up some fair share tales of their own that push mathematical thinking into more advanced counting and beyond one-to-one counting.

# data[].attributes.attachment_link.title
3 "Mathical" Books for More Advanced Counting

# data[].attributes.attachment_link.description
Along with being "mathical" award winners, these books provide compelling contexts that help primary grade children understand why more advanced counting is useful and that it isn't always efficient to count by ones.

# data[].attributes.attachment_link.provider_name
Erikson Institute Early Math Collaborative

# data[].attributes.attachment_link.readable_text
4 Books That Can Expand Children's Spatial Sense

by Cody Meirick This is an Article - for grade levels Pre-K, Kindergarten, 1st Grade, 2nd Grade, 3rd Grade
Tagged Mapping, Over Under and Through, Me on the Map, We're Going on a Ghost Hunt, The Secret Birthday Message, Marcia Vaughan, Joan Sweeney, Tana Hoban, Eric Carle, Books, Seasonal

A great way to have children explore spatial relationships is to read books that call for children to think and talk about where objects and people are in relation to something else. Young children show their understanding of these relationships by acting out the stories and moving their own bodies through space. They also use language to describe positions and locations and can make their own maps.

Here are a few of our favorite children's books that can be great opportunities to start an activity or conversation.

1. We're Going on a Ghost Hunt by Marcia Vaughan

This Halloween favorite is a variation of the old "We're going on a bear hunt" story. Children set off on a ghost hunt, which takes them through all sorts of scary places like an ooky spooky swamp and a creepy cave. It's a fun read, but it's even more fun to act out the ghost hunt and the helter skelter dash back to the safety of home. Just like the bear hunt tale, children come to obstacles and have to decide whether they go over, under, through or any number of other ways to get to their destination. The more children can immerse themselves with these positional words and act out what they really mean, the better.

2. Over, Under, and Through by Tana Hoban

Another great photographic book by Tana Hoban, this simple yet powerful book lets young children explore those important positional words. Not just those three words, but a host of others words like beside, below, on, and in and many others allow children to hear and examine the many different ways objects can be in relation to others. Pair this with an activity and have children discuss! For one example, watch our Focus on the Lesson video involving an obstacle course in a preschool classroom. Here are related lesson plan ideas from website MathatHome.org.

3. Me on the Map by Joan Sweeney

Having fun with spatial and positional words often leads to fun with maps. Me on the Map is a great entry point for discussing what maps are. And it can become the beginning of children's experiences in making their own maps!

4. The Secret Birthday Message by Eric Carle

This classic uses shapes and spatial relationships to tell the story of Tim and his quest to find his birthday surprise. The treasure hunt that ensues allows for all kinds of opportunities to work with mapping to represent the world (and a birthday expedition) in the form of a map. Here are more related ideas from the Eric Carle website.

# data[].attributes.attachment_link.title
Four Books That Can Expand Children's Spatial Sense

# data[].attributes.attachment_link.description
Here are a few of our favorite books that can be great opportunities to improve childrens spatial sense.